**Operation of Plug-In Electric Vehicles for Voltage Balancing in Unbalanced Microgrids**

Guido Carpinelli, Fabio Mottola, Daniela Proto and Angela Russo

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.68894

#### Abstract

The widespread use of distributed energy resources in the future electric distribution systems represents both a challenge and an opportunity for all the Smart Grid operators. Among these resources, plug-in electric vehicles are expected to play a significant role not only for the economic and environmental benefits they involve but also for the ancillary services they can provide to the supplying grid. This chapter deals with realtime operation of unbalanced microgrids including plug-in electric vehicles. The operation is achieved by means of an optimal control strategy aimed at minimizing the costs sustained for the energy provision while meeting various technical constraints. Among the technical constraints, the optimal control allows guaranteeing the satisfaction of power quality requirements such as the containment of slow voltage variations and the unbalance factors. Case studies are investigated in order to show the feasibility and the effectiveness of the proposed approach.

Keywords: microgrids, slow voltage variations, unbalances, optimal control strategy, plug-in vehicles

### 1. Introduction

Smart grids (SGs) are playing a vital role in the future of power systems mainly due to their potential to minimize costs and environmental impacts while maximizing reliability, power quality (PQ), resilience, and stability. These goals can be attained by means of a proper exploitation of the SG's distributed energy resources (DERs). However, the integration of DERs (i.e., generation units, controllable loads, and energy storage-based devices) is a challenging task in the view of the optimal planning and operation of the SGs. Thus, new research contributions aimed to guarantee the DER correct behavior are of high interest for all the

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

involved operators (from System Operators to Electric Utilities and Energy Traders, Independent Power Producers and Consumers). Among the energy storage-based devices, plug-in electric vehicles (PEVs) are achieving particular attention in the relevant literature. PEVs, in fact, are expected to have a wide diffusion in the next future especially due to the current attention paid worldwide to the reduction of greenhouse gas emissions mainly caused by the use of internal combustion engines. However, PEVs require to charge from the power grid, then their massive spread could pose critical issues. The charge of a large number of PEVs is a huge load demand that the grid is called to face and a number of problems can occur in terms of PQ degradation, instability of electrical networks, and degradation of operation efficiency [1]. On the other hand, PEVs connection to the grid could represent also an opportunity due to the presence of on-board batteries that could have an important role in grid operation. The electrical energy storage devices, in fact, are a particular typology of loads that are expected to be key components in modern power systems. When opportunely coordinated, these devices can become distributed resources for the grid so providing benefits rather than criticisms to it. The benefits achievable by their use are mainly related to voltage support, price arbitrage, PQ, reliability improvement, reduction of the cost for energy provision, and renewable energy fostering. In order to gain these benefits, the storage systems need specific charge/ discharge control strategies able to account for the requirements of the storage itself and of the grid they are connected to, in addition to adequate communication infrastructures. In particular, when the storage systems are included in a microgrid (µG), the control strategies should guarantee the correct operation of the whole µG taking into account also the presence of other controllable sources, such as DG units and dispatchable loads. In these cases, the adopted control tasks should take into account also the possibility of load shedding or generation curtailment in case of increased demand or generation, respectively.

A proper PEV control strategy would take into account targets such as cost minimization and PQ improvement.

Regarding the first target, in the frame of demand response paradigms, PEVs have a great potential. More specifically, in the case of dynamic pricing schemes, an appropriate control of PEVs charging would allow reducing costs by shifting the peak load in response to changes in the price of electricity over time. Different time-based rate programs are available: time-of-use (TOU) pricing refers to different prices applying to determined periods of the day (block of hours of the day). In these periods, the tariff is constant. Real-time pricing (RTP) is characterized by pricing rates typically applying on an hourly basis. Variable peak pricing (VPP) is a hybrid of time-of-use and real-time pricing not only with different periods of the day for pricing but also with a price for the on-peak period that depends on market conditions. With the critical peak pricing (CPP), utilities identify critical events during a specified time period when the price for electricity may substantially increase (e.g., very hot hours in a summer afternoon). Finally, critical peak rebate (CPR) is a pricing structure similar to the CPP that allows customers to be paid for cutting back on electricity during critical events relative to the amount they normally use [2]. In this variegated pricing scenario, the optimal operation of PEVs allows substantial reduction of the operation costs for the µG that could optimize the expense for the energy provision. Of course, an optimized control should be performed by taking into account the preferences and the comfort levels required by the vehicle owners.

Regarding the PQ improvement target, several benefits can be achieved by a proper control of the PEV charging. In the case of low voltage (LV) µGs, typically characterized by the presence of unbalances, the benefits PEVs can provide are even more significant. LV µGs, in fact, are characterized by significant unbalances due to their structure, to the presence of single-phase loads and renewable generation units (i.e., single-phase photovoltaic systems). For this reason, voltage unbalances can be excessive and represent a burdensome PQ issue [3]. Consequences of unbalances in LV µGs can be the increase of losses and heating effects affecting power electronic converters and induction motors [4], overloading of distribution feeders and transformers [5], excessive mechanical stress and noise due to a double system frequency in the synchronous generators equipping microgeneration units [6].

This chapter is framed in this multifaceted scenario of µG real-time operation and deals with advanced strategies for the control of µG's distributed energy sources (DERs) aimed at minimizing operation costs and at ensuring an optimal grid and storage systems operation with reference to various technical constraints. More specifically, the DERs to be optimally controlled in the considered µG are: the batteries on board the electric PEVs connected to the grid for charging and the DG units connected to the grid through power converters. The optimal operation of µG refers to the cost minimization under real-time pricing while grid constraints on bus voltages and line currents are satisfied. Among the voltage constraints, a maximum allowed voltage unbalance factor is imposed on the basis of the current standards [7]. Specific requirements for the storages (e.g., a vehicle's battery has to be fully charged at a specified departure time) are also guaranteed.

The proposed control strategy refers to real-time operation and helps the µG's operator better control the operational processes and plan appropriate energy market bidding, due to the most proficient use of electrical storage systems. It is formulated as a multi-period non-linear constrained optimization problem (OP) which aims at minimizing the energy costs for the whole µG while satisfying technical constraints related to the correct operation of the components and of the grid as well as to the needs of the vehicle owners.

The technical strength of the proposed operation strategy is related to the proper control of DERs which allows

• minimizing the costs for energy provision;

involved operators (from System Operators to Electric Utilities and Energy Traders, Independent Power Producers and Consumers). Among the energy storage-based devices, plug-in electric vehicles (PEVs) are achieving particular attention in the relevant literature. PEVs, in fact, are expected to have a wide diffusion in the next future especially due to the current attention paid worldwide to the reduction of greenhouse gas emissions mainly caused by the use of internal combustion engines. However, PEVs require to charge from the power grid, then their massive spread could pose critical issues. The charge of a large number of PEVs is a huge load demand that the grid is called to face and a number of problems can occur in terms of PQ degradation, instability of electrical networks, and degradation of operation efficiency [1]. On the other hand, PEVs connection to the grid could represent also an opportunity due to the presence of on-board batteries that could have an important role in grid operation. The electrical energy storage devices, in fact, are a particular typology of loads that are expected to be key components in modern power systems. When opportunely coordinated, these devices can become distributed resources for the grid so providing benefits rather than criticisms to it. The benefits achievable by their use are mainly related to voltage support, price arbitrage, PQ, reliability improvement, reduction of the cost for energy provision, and renewable energy fostering. In order to gain these benefits, the storage systems need specific charge/ discharge control strategies able to account for the requirements of the storage itself and of the grid they are connected to, in addition to adequate communication infrastructures. In particular, when the storage systems are included in a microgrid (µG), the control strategies should guarantee the correct operation of the whole µG taking into account also the presence of other controllable sources, such as DG units and dispatchable loads. In these cases, the adopted control tasks should take into account also the possibility of load shedding or generation

curtailment in case of increased demand or generation, respectively.

PQ improvement.

234 Development and Integration of Microgrids

A proper PEV control strategy would take into account targets such as cost minimization and

Regarding the first target, in the frame of demand response paradigms, PEVs have a great potential. More specifically, in the case of dynamic pricing schemes, an appropriate control of PEVs charging would allow reducing costs by shifting the peak load in response to changes in the price of electricity over time. Different time-based rate programs are available: time-of-use (TOU) pricing refers to different prices applying to determined periods of the day (block of hours of the day). In these periods, the tariff is constant. Real-time pricing (RTP) is characterized by pricing rates typically applying on an hourly basis. Variable peak pricing (VPP) is a hybrid of time-of-use and real-time pricing not only with different periods of the day for pricing but also with a price for the on-peak period that depends on market conditions. With the critical peak pricing (CPP), utilities identify critical events during a specified time period when the price for electricity may substantially increase (e.g., very hot hours in a summer afternoon). Finally, critical peak rebate (CPR) is a pricing structure similar to the CPP that allows customers to be paid for cutting back on electricity during critical events relative to the amount they normally use [2]. In this variegated pricing scenario, the optimal operation of PEVs allows substantial reduction of the operation costs for the µG that could optimize the expense for the energy provision. Of course, an optimized control should be performed by taking into account the preferences and the comfort levels required by the vehicle owners.


This chapter is structured as follows. The state of the art of the PEV charging devices and the challenges and benefits related to their inclusion in µGs are described in Section 2. Section 3 shows the analytical formulation of the proposed control strategy. The results of numerical applications are reported in Section 4. Finally, Section 5 draws conclusions and opens problems for future research.

### 2. Plug-in vehicles in the frame of low voltage microgrids: State of the art

The relevant literature on plug-in electric vehicles is very wide and rich. In this section, review papers are mentioned to a large extent and, in some cases, research papers are shown on particular topics.

### 2.1. Classification of charging systems

One of the key elements of a successful electric vehicle diffusion is the charging equipment. Some common features are required for the electric vehicle charger (EVC), for example, battery performance, high reliability of the charger, high power efficiency, and minimum impact on the PQ [8]. In addition, since a large-scale diffusion of PEVs can also pose new challenges for the power system operators (e.g., congestions, voltage profiles, etc.), the "smart" charging solutions may transform PEVs in a resource for the system [9–11].

With specific reference to PEVs, in Ref. [1], the battery charging schemes are classified as follows: uncontrolled, indirectly controlled, smart, and bidirectional. In the uncontrolled charging, the vehicle immediately begins recharging as soon as it is connected to the grid. Indirectly controlled, smart, and bidirectional charging schemes are used to control energy prices; in the smart charging schemes, the battery charging is subject to some measure of intelligent control by the utility or system operator.

Regarding the charger device, an AC/DC converter is required since the batteries charge by absorbing DC power. The main function of this converter is to rectify the AC power from the electrical grid. Chargers can be installed on board and off board of the vehicles. Onboard charger is often designed in small size to reduce the weight burden for PEV. Offboard chargers are particularly convenient in fast charging service [12].

Different charging methods can be implemented. Ref. [12] classifies the charging methods as constant current, constant voltage, constant power, taper charging, trickle charging, advanced charging that involves combination of the above methods, pulse-charging and negative pulsecharging.

### 2.2. Adverse effects and services provided by plug-in electric vehicles

PEVs can be operated in two configurations when connected to the electric grid:


In the first configuration, the flow of the electric power is uni-directional, that is, the electric power flows from the grid to the PEVs. In the second configuration, the flow of the electric power is bi-directional, that is, the PEV can absorb electric power from the grid and inject electric power to the grid. In this case, PEVs can be assimilated to a distributed energy resource (distributed generator or storage system).

A large number of studies indicates some adverse effects of PEVs on electric distribution systems (for instance, see the review Ref. [13]). Among them, we can mention voltage instability, increased peak demand, PQ problems (e.g., voltage profile, voltage unbalance, harmonics, etc.), increased system energy losses, transformer heating, and overloading [12–14]. It should be noted that most of them occur when the charging of vehicles is uncoordinated.

In spite of the impact on the distribution systems, PEVs are considered valuable resources for the electric power grids because they can provide a large number of services to the local distribution system and also to the power system. When V1G configuration is adopted, the charging method assumes an important role. For instance, shifting the charging to off-peak periods can be exploited to better integrate a large diffusion of PEVs into the electricity grid. Another contribution [15] proposes an integration of PEVs able to improve the PQ levels of the distribution system. An autonomous control of PEVs charging systems (in V1G configuration) is proposed in order to reduce voltage unbalances in a distribution network, in which local voltage measurements drive the modulation of the charging current.

However, the most promising configuration is the V2G.1 V2G power is an interesting concept that was first proposed in Ref. [16]. Operating in V2G mode, a PEV can provide services to the grid when it is parked. Considering that PEVs are parked much of the time (e.g., Ref. [17] estimates a parking time equal to 96% of the time), the contribution can be important. Typical services that PEVs are able to provide in the V2G operating mode are [12, 18]:

• baseload power and peak power provision; and

2. Plug-in vehicles in the frame of low voltage microgrids: State of the art

The relevant literature on plug-in electric vehicles is very wide and rich. In this section, review papers are mentioned to a large extent and, in some cases, research papers are shown on particular

One of the key elements of a successful electric vehicle diffusion is the charging equipment. Some common features are required for the electric vehicle charger (EVC), for example, battery performance, high reliability of the charger, high power efficiency, and minimum impact on the PQ [8]. In addition, since a large-scale diffusion of PEVs can also pose new challenges for the power system operators (e.g., congestions, voltage profiles, etc.), the "smart" charging

With specific reference to PEVs, in Ref. [1], the battery charging schemes are classified as follows: uncontrolled, indirectly controlled, smart, and bidirectional. In the uncontrolled charging, the vehicle immediately begins recharging as soon as it is connected to the grid. Indirectly controlled, smart, and bidirectional charging schemes are used to control energy prices; in the smart charging schemes, the battery charging is subject to some measure of

Regarding the charger device, an AC/DC converter is required since the batteries charge by absorbing DC power. The main function of this converter is to rectify the AC power from the electrical grid. Chargers can be installed on board and off board of the vehicles. Onboard charger is often designed in small size to reduce the weight burden for PEV. Off-

Different charging methods can be implemented. Ref. [12] classifies the charging methods as constant current, constant voltage, constant power, taper charging, trickle charging, advanced charging that involves combination of the above methods, pulse-charging and negative pulse-

In the first configuration, the flow of the electric power is uni-directional, that is, the electric power flows from the grid to the PEVs. In the second configuration, the flow of the electric power is bi-directional, that is, the PEV can absorb electric power from the grid and inject electric power to the grid. In this case, PEVs can be assimilated to a distributed energy resource

A large number of studies indicates some adverse effects of PEVs on electric distribution systems (for instance, see the review Ref. [13]). Among them, we can mention voltage instability, increased

solutions may transform PEVs in a resource for the system [9–11].

board chargers are particularly convenient in fast charging service [12].

2.2. Adverse effects and services provided by plug-in electric vehicles

• Grid-to-vehicle, usually referred to as V1G (also G2V); and

• Vehicle-to-grid, usually referred to as V2G.

(distributed generator or storage system).

PEVs can be operated in two configurations when connected to the electric grid:

intelligent control by the utility or system operator.

topics.

charging.

2.1. Classification of charging systems

236 Development and Integration of Microgrids

• ancillary services (frequency control, load balance, and spinning reserve services).

Other services provided in V2G mode [18, 13, 9] are reactive power support (for instance, Ref. [19] proposes a coupled energy and reactive power market considering the contribution of PEVs), power leveling (i.e., valley filling and peak shaving), and PQ improvement (for instance, harmonic filtering). In addition, in the presence of high penetration of intermittent renewable power generation, the V2G mode can be exploited to use PEVs as storage systems, backup systems, and to balance power fluctuations.

As a consequence of V2G diffusion, an increase of stability and reliability of the distribution system and a reduction of distribution costs are expected [20].

### 2.3. Plug-in electric vehicles modeling in µGs

µG operation is significantly affected by the wide diffusion of PEVs, in both configuration V1G and V2G. In the relevant literature, a lot of scientific contributions inquire into the possible exploitation of PEVs to provide numerous services at µG level and to strengthen the operation of a µG.

An early contribution [21] analyzes a large exploitation of PEV batteries in islanded operated µGs and proposes several control strategies to improve µG islanding.

One issue considered in the relevant literature is the day-ahead scheduling when PEVs are present in the µGs. Many contributions are available [22–29]. The proposed models may take

<sup>1</sup> A thorough comparison between V1G and V2G configurations is provided in Ref. [13].

into account the uncertainties of the problem variables, characteristics of different intermittent energy resources, and different optimization objectives. The integration of intermittent generation and PEVs into scheduling problems is taken into account in [23, 24, 26–29].

A two-stage energy scheduling for a µG with renewable generation is proposed in Ref. [23] and the impact of PEVs on the energy scheduling is evaluated considering different charging schemes. A two-stage framework for a µG, including PEVs and solar energy generation, is proposed also in Ref. [26]; at the first stage, a stochastic energy schedule problem is formulated for the next 24-h operation; then at the second stage, a predictive online charging control method is implemented to account for uncertainties. Also in Ref. [28], the uncertainty of the load demand and of PEVs along with the intermittency of the renewable energy resources are taken into account in the µG energy scheduling. In particular, peculiarities of wind generation and coordination among wind power plants and PEVs are considered in Refs. [22, 30, 31]. In Ref. [22], a solution of the coordinated wind and PEV (in V2G configuration) energy dispatch problem in a stochastic framework is proposed; uncertainties of wind power and of PEV driving patterns are taken into consideration. In Ref. [30], the problem of power balance in a µG including PEVs and wind turbines is addressed and a hierarchical stochastic control scheme for the coordination of PEV charging and wind power is proposed.

The presence of responsive loads together with PEVs and intermittent generation is considered in Ref. [27], where the PEVs are used to reduce peak power and modify load curves.

In Ref. [25], a regional energy management strategy based on the use of PEVs and battery swapping stations whose charging is coordinated by a price-incentive model is proposed.

The optimization models formulated for the µG energy scheduling take into account several objectives, such as the minimization of the expected total operation costs [28], the minimization of the total cost of PEVs and maximization of the profit of battery swapping stations [25], the minimization of the total cost of the network including the cost of power supply for loads and PEVs as well as the cost of energy not supplied [29].

Particular case studies are presented in Refs. [32–34]. Ref. [32] proposes to jointly control the electricity consumption of home appliances and PEVs in a µG context; in Ref. [33], an office building µG, and in Ref. [34], a commercial µG are considered.

Further topics related to the presence of PEVs in µGs are considered in the relevant literature. Refs. [35, 36] address the problem of the unit commitment for µGs including also PEVs. In particular, Ref. [36] proposes a probabilistic model able to account for the uncertainties on wind power generation, loads, and PEVs operation.

V2G strategies are developed to allow PEVs to contribute to congestion management to help maintain a secure state of the grid supporting the system in critical conditions [37]. The presence of PEVs can also be used to actively participate in µG service restoration, as shown in Ref. [38]. In addition, PEVs have been demonstrated to be able to support the system also in smoothing frequency fluctuations due to insufficient load frequency control capacity. In Ref. [39], the power control of PEVs in V2G configuration is applied to compensate for the inadequate load frequency control capacity and to improve the frequency stability of µGs, especially in island operation mode. Ref. [40] proposes a new controller able to take instantaneous power available from the fleet of PEVs in order to provide a frequency support service.

into account the uncertainties of the problem variables, characteristics of different intermittent energy resources, and different optimization objectives. The integration of intermittent gener-

A two-stage energy scheduling for a µG with renewable generation is proposed in Ref. [23] and the impact of PEVs on the energy scheduling is evaluated considering different charging schemes. A two-stage framework for a µG, including PEVs and solar energy generation, is proposed also in Ref. [26]; at the first stage, a stochastic energy schedule problem is formulated for the next 24-h operation; then at the second stage, a predictive online charging control method is implemented to account for uncertainties. Also in Ref. [28], the uncertainty of the load demand and of PEVs along with the intermittency of the renewable energy resources are taken into account in the µG energy scheduling. In particular, peculiarities of wind generation and coordination among wind power plants and PEVs are considered in Refs. [22, 30, 31]. In Ref. [22], a solution of the coordinated wind and PEV (in V2G configuration) energy dispatch problem in a stochastic framework is proposed; uncertainties of wind power and of PEV driving patterns are taken into consideration. In Ref. [30], the problem of power balance in a µG including PEVs and wind turbines is addressed and a hierarchical stochastic control

The presence of responsive loads together with PEVs and intermittent generation is considered

In Ref. [25], a regional energy management strategy based on the use of PEVs and battery swapping stations whose charging is coordinated by a price-incentive model is proposed.

The optimization models formulated for the µG energy scheduling take into account several objectives, such as the minimization of the expected total operation costs [28], the minimization of the total cost of PEVs and maximization of the profit of battery swapping stations [25], the minimization of the total cost of the network including the cost of power supply for loads

Particular case studies are presented in Refs. [32–34]. Ref. [32] proposes to jointly control the electricity consumption of home appliances and PEVs in a µG context; in Ref. [33], an office

Further topics related to the presence of PEVs in µGs are considered in the relevant literature. Refs. [35, 36] address the problem of the unit commitment for µGs including also PEVs. In particular, Ref. [36] proposes a probabilistic model able to account for the uncertainties on

V2G strategies are developed to allow PEVs to contribute to congestion management to help maintain a secure state of the grid supporting the system in critical conditions [37]. The presence of PEVs can also be used to actively participate in µG service restoration, as shown in Ref. [38]. In addition, PEVs have been demonstrated to be able to support the system also in smoothing frequency fluctuations due to insufficient load frequency control capacity. In Ref. [39], the power control of PEVs in V2G configuration is applied to compensate for the inadequate load frequency control capacity and to improve the frequency stability of µGs, especially

in Ref. [27], where the PEVs are used to reduce peak power and modify load curves.

ation and PEVs into scheduling problems is taken into account in [23, 24, 26–29].

238 Development and Integration of Microgrids

scheme for the coordination of PEV charging and wind power is proposed.

and PEVs as well as the cost of energy not supplied [29].

wind power generation, loads, and PEVs operation.

building µG, and in Ref. [34], a commercial µG are considered.

Finally, a day-ahead scheduling strategy is proposed in Ref. [3] which refers to unbalanced µGs including in addition to PEVs, other distributed resources. The operation strategy is based on a multi-objective approach, whose objective functions refer to cost minimization, PQ improvements, and energy savings.

### 3. Plug-in vehicles in the frame of low voltage microgrids: The proposed optimal operation strategy

SGs need to optimally operate its DERs. PEVs are particular types of DERs whose benefits can be achieved by adopting appropriate charge/discharge control strategies able to account for the requirements of the on-board storage units and of the grid they are connected to. These control strategies should take into account also the presence of other DERs and should guarantee the correct operation of the whole µG during its operation.

In this section, we formulate a control strategy based on the solution of a multi-period, nonlinear, constrained OP which aims at minimizing the energy costs for the whole µG while satisfying technical constraints related to the correct operation of the components and of the grid as well as to the needs of the vehicle owners. In particular, the technical constraints include limits on some power quality disturbances such as slow voltage variations and unbalances.

The strategy is applied to a three-phase LV µG that includes loads and distributed resources, such as DG units and batteries on board PEVs, and is connected to the MV distribution grid through an MV/LV transformer.

The loads of the µG are supposed to be non-responsive, single-phase and three-phase loads.

The DG units are assumed non-dispatchable, single-phase PV systems which are the most extensively used type of DG units in LV systems. The connection to the distribution network of the PV units through power converters allows the control of their reactive power.

The PEVs' batteries are connected to the µG using EVCs which consist of single-phase devices connected to the grid through power converters that allow the control of active power and reactive power in both charging and discharging stages.

The proposed control strategy is used to evaluate the reference signals for the converters which connect the DERs to the grid. To obtain the above signals for the kth control interval, the nonlinear, constrained OP: (i) is formulated over a time horizon Ωk, composed of elementary time intervals, each of duration Δt, and (ii) is solved within one elementary time interval ahead the considered control interval (e.g., the control signals for the kth elementary time interval are obtained within the (k-1)th elementary time interval).

More specifically, the dispatching of the DERs must guarantee the desired energy level to be stored in all of the connected PEVs at their departure time; thus, the procedure for the kth control interval takes into account all of the time intervals included within the longest among the plug-in times of the connected vehicles (time horizon Ωk). Based on this consideration, the time horizon Ω<sup>k</sup> to be considered will change along with the arrivals of PEVs, and, at each new arrival, it has to be properly defined once more. To explain how to select the adequate time horizon Ω<sup>k</sup> for the kth control interval, let us refer to the example shown in Figure 1, in which the time is discretized in time intervals of duration Δt, as mentioned above. In Figure 1, NEV is the total number of EVCs in the μG.

In the figure, for each EVC, the time intervals between the arrival and the departure of the vehicle are highlighted. For instance, the vehicle charged at the ith bus is already connected at the kth time interval and its departure is scheduled at the end of the (k+nk,i)th time interval. The set of time intervals {k,…, k+nk,i } is referred to as ωk,i. The time horizon of the optimization has to account for all the vehicles connected at the kth control interval. Generally speaking, since the control procedure would account for the desired energy stored into the batteries of all of the plugged vehicles, the time horizon of the optimization at the kth control interval is:

$$
\Omega\_k = \langle k, \dots, k+n\_k \rangle \tag{1}
$$

being

$$\mathfrak{m}\_{k} = \max\{\mathfrak{n}\_{k,1}, \dots, \mathfrak{n}\_{k,N\_{EV}}\} \tag{2}$$

that is the last interval of the time horizon Ω<sup>k</sup> that has to be considered when the procedure is applied to the kth time control interval.

Due to the presence of constraints referring to different time intervals, the OP involved in the desired control strategy is multi-period and solved for all the time intervals of Ω<sup>k</sup> at the same time.

Figure 1. Time horizon of the procedure at the kth control interval.

The OP is a single-objective (SO) OP that uses as inputs the values, for all of the time intervals included in Ωk, of (i) forecasted load demand, (ii) forecasted DG production, and for all of the vehicles that are plugged in at the time interval k, (iii) initial state of charge (SOC) of the on-board batteries, (iv) departure time, and (v) desired value of SOC at the departure time.

Regarding the outputs of the solution of the OP, they are control actions and/or data useful for the monitoring of µG operation. More in detail, in the case of control action, the outputs of the procedure are reference signals that the CCS sends to the interfacing converters of the distributed resources that are the active and reactive phase powers that the EVC exchange with the grid when the vehicles are plugged in, and the reactive phase power requested to the DG units. Outputs useful for the monitoring are (i) the voltage profile at each bus, (ii) the unbalance factor at each bus, and (iii) the currents flowing in the lines. The active power exchanged with the upstream grid at the Point of Common Coupling (PCC) is another output of the procedure that is useful for the knowledge of the µG's energy request and the corresponding cost. Figure 2 shows a schematic of the proposed control strategy evidencing its inputs and outputs.

Figure 2. Schematic of the proposed control strategy.

control interval takes into account all of the time intervals included within the longest among the plug-in times of the connected vehicles (time horizon Ωk). Based on this consideration, the time horizon Ω<sup>k</sup> to be considered will change along with the arrivals of PEVs, and, at each new arrival, it has to be properly defined once more. To explain how to select the adequate time horizon Ω<sup>k</sup> for the kth control interval, let us refer to the example shown in Figure 1, in which the time is discretized in time intervals of duration Δt, as mentioned above. In Figure 1, NEV is

In the figure, for each EVC, the time intervals between the arrival and the departure of the vehicle are highlighted. For instance, the vehicle charged at the ith bus is already connected at the kth time interval and its departure is scheduled at the end of the (k+nk,i)th time interval. The set of time intervals {k,…, k+nk,i } is referred to as ωk,i. The time horizon of the optimization has to account for all the vehicles connected at the kth control interval. Generally speaking, since the control procedure would account for the desired energy stored into the batteries of all of the plugged vehicles, the time horizon of the optimization at the kth control

that is the last interval of the time horizon Ω<sup>k</sup> that has to be considered when the procedure is

Due to the presence of constraints referring to different time intervals, the OP involved in the desired control strategy is multi-period and solved for all the time intervals of Ω<sup>k</sup> at the same

Ω<sup>k</sup> ¼ {k, …, k þ nk}, ð1Þ

nk ¼ max{nk,1,…, nk,NEV } ð2Þ

the total number of EVCs in the μG.

240 Development and Integration of Microgrids

applied to the kth time control interval.

Figure 1. Time horizon of the procedure at the kth control interval.

interval is:

being

time.

The OP to be solved is formulated as:

$$\min F(\mathbf{x})\tag{3}$$

subject to:

$$\Psi\_h(\mathbf{x}) = \mathbf{0}, \quad h = 1, \dots, n\_{\text{eq}} \tag{4}$$

$$
\eta\_m(\mathbf{x}) \le 0, \quad m = 1, \dots, n\_{\text{int}} \tag{5}
$$

where Ψ<sup>h</sup> is the hth equality constraint, η<sup>m</sup> is the mth inequality constraint, x is the vector of the optimization variables, F(x) is the objective function.

The objective function refers to the cost of the energy purchased from the upstream grid, that is:

$$\text{CE}\_{k} = \sum\_{\tau \in \Omega\_{k}} \sigma\_{\tau} (P\_{1,\tau}^{1} + P\_{1,\tau}^{2} + P\_{1,\tau}^{3}) \Delta t \tag{6}$$

where P<sup>1</sup> <sup>1</sup>;<sup>τ</sup>, P<sup>2</sup> <sup>1</sup>;<sup>τ</sup>, and P<sup>3</sup> <sup>1</sup>;<sup>τ</sup> are the phase active powers imported from the upstream grid at the τth time interval and στ is the price of energy during the τth time interval. Regarding this last, a real-time tariff is considered whose variation is on an hourly basis. It has to be noted that, in this formulation, it is assumed that the µG is not allowed to sell energy to the upstream grid.

The equality and inequality constraints can be classified on the basis of the part of the system they refer to. Thus, they are grouped into constraints imposed on:


For the sake of clarity, in what follows, busses are supposed to be pure load or pure generation or EVC busses; it is trivial to derive the case of mixed typologies.

#### 3.1. Constraints on the whole µG

Since we deal with unbalanced µGs, the three-phase grid, loads, and generations systems were modeled in phase coordinates [41, 42], and then the three-phase load flow equations are included in the optimization model:

$$P\_{i, \tau}^p = V\_{i, \tau}^p \sum\_{j=1}^{ng} \sum\_{q=1}^3 V\_{j, \tau}^q \left[ G\_{ij}^{pq} \cos(\mathfrak{S}\_{i, \tau}^p - \mathfrak{S}\_{j, \tau}^q) + B\_{ij}^{pq} \sin(\mathfrak{S}\_{i, \tau}^p - \mathfrak{S}\_{j, \tau}^q) \right] \tag{7}$$

$$\begin{aligned} Q\_{i,\tau}^p &= V\_{i,\tau}^p \sum\_{j=1}^{ng} \sum\_{q=1}^3 V\_{j,\tau}^q [G\_{i\bar{j}}^{pq} \sin(\mathcal{S}\_{i,\tau}^p - \mathcal{S}\_{j,\tau}^q) - B\_{i\bar{j}}^{pq} \cos(\mathcal{S}\_{i,\tau}^p - \mathcal{S}\_{j,\tau}^q)], \\ &\quad \tau \in \Omega\_k, i \in \Omega\_G, p = 1, 2, 3 \end{aligned} \tag{8}$$

where ng is the number of μG busses, Bpq ij and <sup>G</sup>pq ij are the terms of the susceptance matrix and of the conductance matrix, respectively, corresponding to the bus i with phase p and the bus j with phase q; V<sup>p</sup> i, <sup>τ</sup> <sup>ð</sup>V<sup>q</sup> j,τÞ is the magnitude of the ith (jth) bus voltage with phase p (q) during the τth time interval; ϑ<sup>p</sup> i, <sup>τ</sup> (ϑ<sup>q</sup> j,τ) is the phase-voltage argument of the ith (jth) bus voltage with phase p (q) during the τth time interval; P<sup>p</sup> i,<sup>τ</sup> and <sup>Q</sup><sup>p</sup> i,<sup>τ</sup> are the active and reactive powers injected at the phase p of the ith bus during the τth time interval; Ω<sup>G</sup> is the set of µG busses.

Inequality constraints are imposed on the phase-voltage magnitudes that must be within admissible ranges and on the unbalance factor at all busbars that cannot exceed a maximum value:

$$V\_{\min} \le V\_{i,\tau}^{\mathcal{V}} \le V\_{\max}, \quad \tau \in \Omega\_k, \ i \in \Omega\_{\mathcal{G}}, \ p = 1, 2, 3 \tag{9}$$

$$kd\_{i, \mathbf{r}} \le kd\_{\max} \qquad \pi \in \Omega\_k \text{ } i \in \Omega\_G \tag{10}$$

where Vmin and Vmax are minimum and maximum values for voltage magnitudes, kdi,<sup>τ</sup> is the unbalance factor at the ith bus during the τth time interval and kdmax is the maximum value imposed to the unbalance factor. The unbalance factor is given by the ratio of the positive and negative components of voltages that are expressed as functions of the bus phase voltages.

The line phase currents cannot exceed the lines' ampacities:

$$I\_{l,\tau} \subseteq I\_{l'}^{\tau} \quad \quad \tau \in \Omega\_k, l \in \Omega\_l \tag{11}$$

where Il,<sup>τ</sup> is the phase current flowing through line l during the τth time interval expressed as function of bus voltages, I r <sup>l</sup> is the ampacity of the line l, and Ω<sup>l</sup> is the set of the μG lines.

#### 3.2. Constraints on the slack bus

The OP to be solved is formulated as:

242 Development and Integration of Microgrids

optimization variables, F(x) is the objective function.

CEk <sup>¼</sup> <sup>X</sup> τ∈ Ω<sup>k</sup>

they refer to. Thus, they are grouped into constraints imposed on:

or EVC busses; it is trivial to derive the case of mixed typologies.

j¼1

j¼1

X 3

q¼1 Vq j, <sup>τ</sup>½Gpq

X 3

q¼1 Vq j, <sup>τ</sup>½Gpq

τ∈ Ωk, i∈ ΩG, p ¼ 1; 2; 3

subject to:

where P<sup>1</sup>

<sup>1</sup>;<sup>τ</sup>, P<sup>2</sup>

i. the whole µG; ii. the slack bus;

<sup>1</sup>;<sup>τ</sup>, and P<sup>3</sup>

iii. the busses where loads are connected;

3.1. Constraints on the whole µG

included in the optimization model:

Pp i,<sup>τ</sup> <sup>¼</sup> <sup>V</sup><sup>p</sup> i,τ X ng

Qp i, <sup>τ</sup> <sup>¼</sup> <sup>V</sup><sup>p</sup> i,τ X ng

iv. the busses where DG units are connected, and

v. the busses where plug-in vehicles are connected.

min FðxÞ ð3Þ

<sup>1</sup>;<sup>τ</sup>ÞΔt ð6Þ

ΨhðxÞ ¼ 0, h ¼ 1;…, neq ð4Þ

ηmðxÞ ≤ 0; m ¼ 1;…, nin ð5Þ

where Ψ<sup>h</sup> is the hth equality constraint, η<sup>m</sup> is the mth inequality constraint, x is the vector of the

The objective function refers to the cost of the energy purchased from the upstream grid, that is:

τth time interval and στ is the price of energy during the τth time interval. Regarding this last, a real-time tariff is considered whose variation is on an hourly basis. It has to be noted that, in this formulation, it is assumed that the µG is not allowed to sell energy to the upstream grid. The equality and inequality constraints can be classified on the basis of the part of the system

For the sake of clarity, in what follows, busses are supposed to be pure load or pure generation

Since we deal with unbalanced µGs, the three-phase grid, loads, and generations systems were modeled in phase coordinates [41, 42], and then the three-phase load flow equations are

i, <sup>τ</sup> � <sup>ϑ</sup><sup>q</sup>

i,<sup>τ</sup> � <sup>ϑ</sup><sup>q</sup>

j, <sup>τ</sup>Þ þ <sup>B</sup>pq

j,τÞ � Bpq

ij sinðϑ<sup>p</sup>

ij cosðϑ<sup>p</sup>

i,<sup>τ</sup> � <sup>ϑ</sup><sup>q</sup>

i, <sup>τ</sup> � <sup>ϑ</sup><sup>q</sup> j, <sup>τ</sup>Þ�,

j, <sup>τ</sup>Þ� ð7Þ

ð8Þ

ij cosðϑ<sup>p</sup>

ij sinðϑ<sup>p</sup>

<sup>1</sup>;<sup>τ</sup> <sup>þ</sup> <sup>P</sup><sup>2</sup>

<sup>1</sup>;<sup>τ</sup> <sup>þ</sup> <sup>P</sup><sup>3</sup>

<sup>1</sup>;<sup>τ</sup> are the phase active powers imported from the upstream grid at the

στðP<sup>1</sup>

Constraints (ii) refer to the magnitude and phase of the voltage at the slack bus (V<sup>p</sup> 1;τ), (ϑ<sup>p</sup> <sup>1</sup>;<sup>τ</sup>) and on the apparent three-phase power ðP<sup>1</sup>;<sup>τ</sup> <sup>2</sup> <sup>þ</sup> <sup>Q</sup><sup>1</sup>;<sup>τ</sup> 2Þ <sup>1</sup>=<sup>2</sup> that can be exchanged with the upstream grid and that must be within the size of the interconnecting transformer (Str):

$$V\_{1,\tau}^{p} = V^{\text{slack}}, \quad \tau \in \Omega\_{k} \text{ } p = 1, 2, 3 \tag{12}$$

$$\mathcal{S}\_{1,\tau}^p = \frac{2}{3}\pi(1-p), \quad \tau \in \Omega\_{k\prime} \ p = 1,2,3\tag{13}$$

$$(\left(P\_{1,\tau}\,^2 + Q\_{1,\tau}\right)^2)^{1/2} \le \mathcal{S}\_{tr\prime} \quad \tau \in \Omega\_k \tag{14}$$

with Vslack the specified value of the voltage magnitude at slack bus, P1,<sup>τ</sup> and Q1,<sup>τ</sup> are the threephase active and reactive powers at the slack bus expressed as functions of the active and reactive phase powers.

#### 3.3. Constraints on the load busses

They refer to the load busses (whose set is ΩL) where active and reactive powers are equal to specified values (Pp,sp i,<sup>τ</sup> and <sup>Q</sup>p,sp i,<sup>τ</sup> ):

$$P\_{i,\tau}^p = P\_{i,\tau}^{p,sp}, \qquad \tau \in \Omega\_k \quad i \in \Omega\_{L\prime} \quad p = 1,2,3 \tag{15}$$

$$\mathbf{Q}\_{i,\tau}^{p} = \mathbf{Q}\_{i,\tau}^{p,sp}, \qquad \tau \in \Omega\_k \quad i \in \Omega\_L \quad p = 1,2,3 \tag{16}$$

#### 3.4. Constraints on DG busses

They refer to the active power (P<sup>ξ</sup><sup>i</sup> i, <sup>τ</sup>) at the ith bus DG busses (whose set is ΩDG) with phase ξ<sup>i</sup> that must be equal to a specified value (P<sup>ξ</sup>,sp i,<sup>τ</sup> ) and to the maximum DG unit's apparent power that is constrained by the rating of the interfacing converter at the ith bus with phase ξ<sup>i</sup> (S<sup>ξ</sup><sup>i</sup> DG,i ):

$$P\_{i,\tau}^{\xi\_i} = P\_{i,\tau}^{\xi\_i, sp}, \qquad \tau \in \Omega\_{k\prime} \quad i \in \Omega\_{\mathrm{DG}\prime} \tag{17}$$

$$(P\_{i,\tau}^{\xi\_i, sp^2} + Q\_{i,\tau}^{\xi\_i^2})^\frac{1}{2} \le S\_{\text{DG}, i'}^{\xi\_i} \qquad \tau \in \Omega\_k \qquad i \in \Omega\_{\text{DG}} \tag{18}$$

Since we deal with single-phase DG units, the active and reactive powers at the other phases are imposed equal to zero.

#### 3.5. Constraints on EVC busses

Finally, constraints on the EVC bus refer to the limits on the active power at ith bus with the specified phase ξ<sup>i</sup> during the τth time interval (P<sup>ξ</sup><sup>i</sup> i,τ) that is limited by the maximum power that the EVC can absorb from (P<sup>ξ</sup>i, ch EVCi, <sup>τ</sup> ) or supply to (P<sup>ξ</sup>i,dch EVCi, <sup>τ</sup> ):

$$-P\_{EV\_{i\_{\tau}}}^{\xi\_{i,ch}} \le P\_{i\_{\tau}\tau}^{\xi\_{i}} \le P\_{EV\_{i\_{\tau}\tau}}^{\xi\_{i,ch}} \qquad \tau \in \omega\_{k,i\nu} \qquad i \in \Omega\_{EVk} \tag{19}$$

with ΩEVk the set of nodes where the vehicles are plugged in at the time interval k and ωk, i the set of time intervals within Ω<sup>k</sup> in which the vehicle at the ith bus is connected (see Figure 1). Obviously, when the ith vehicle is not connected to the grid, its active power (P<sup>ξ</sup><sup>i</sup> i, <sup>τ</sup>) and reactive powers (Q<sup>ξ</sup><sup>i</sup> i,τ) must be equal to zero:

$$P\_{i,\tau}^{\mathcal{E}\_i} = 0, \qquad \tau \mathfrak{g} \omega\_{k,i\nu} \quad i \in \Omega\_{EVk} \tag{20}$$

$$Q\_{i,\tau}^{\varepsilon\_i} = 0, \qquad \tau \notin \omega\_{k,i\nu} \quad i \in \Omega\_{EVk} \tag{21}$$

Again, the apparent power at the ith bus, phase ξi, must be limited by rating of the charging equipment (SE<sup>ξ</sup><sup>i</sup> EVC,i ):

$$(P\_{i,\tau}^{\mathbb{X}\_i} + Q\_{i,\tau}^{\mathbb{X}\_i})^\dagger \le \mathcal{S} E\_{\text{EVC},i'}^{\mathbb{X}\_i} \qquad \tau \in \omega\_{k,i\nu} \quad i \in \Omega\_{EVk} \tag{22}$$

Finally, constraints on the SOC of the on-board batteries impose that it is limited by the size of the battery (SE<sup>ξ</sup>i,max <sup>i</sup> ) and by a minimum value corresponding to the admissible depth of discharge (SE<sup>ξ</sup>i,min <sup>i</sup> ):

Operation of Plug-In Electric Vehicles for Voltage Balancing in Unbalanced Microgrids http://dx.doi.org/10.5772/intechopen.68894 245

$$SE\_{i,k}^{\xi\_i,0} - \sum\_{m=k}^{\tau} (\delta\_{i,m}^{\xi\_i} P\_{i,m}^{\xi\_i} \Delta t) \le SE\_i^{\xi\_i, \max} \qquad \tau \in \omega\_{k,i\nu} \quad i \in \Omega\_{EVk} \tag{23}$$

$$\left( SE\_{i,k}^{\xi\_i,0} - \sum\_{m=k}^{\tau} (\delta\_{i,m}^{\xi\_i} P\_{i,m}^{\xi\_i} \Delta t) \ge SE\_i^{\xi\_i, \min} \right) \qquad \tau \in \omega\_{k,i} \quad i \in \Omega\_{EVk} \tag{24}$$

where SE<sup>ξ</sup>i,<sup>0</sup> i, <sup>k</sup> is the initial value of the energy stored in the battery on board the PEV plugged into the EVC connected to the ith bus with phase ξi, and where

$$\delta\_{i,m}^{\mathbb{X}\_i} = \begin{cases} \frac{1}{\eta\_{EVC}} & \text{if } P\_{i,m}^{\mathbb{X}\_i} > 0 \\ \eta\_{EVC} & \text{if } P\_{i,m}^{\mathbb{X}\_i} \le 0 \end{cases} \tag{25}$$

with ηEVC the charging efficiency related to the EVC. A specified SOC value is also imposed to the vehicle's battery at the time of departure:

$$\text{SE}\_{i,k}^{\xi\_i,0} - \sum\_{m=k}^{k+n\_k} (\delta\_{i,m}^{\xi\_i} P\_{i,m}^{\xi\_i} \Delta t) = \text{SE}\_i^{\xi\_i, \text{exp}}, \qquad \tau \in \omega\_{k,i} \quad i \in \Omega\_{\text{EVk}} \tag{26}$$

where, SE<sup>ξ</sup>i, exp <sup>i</sup> is the specified value of the energy stored in the battery of the PEV plugged-into the EVC connected to the ith bus with phase ξi, at the departure time.

#### 4. Numerical applications

Pp

Qp

3.4. Constraints on DG busses

244 Development and Integration of Microgrids

are imposed equal to zero.

3.5. Constraints on EVC busses

the EVC can absorb from (P<sup>ξ</sup>i, ch

powers (Q<sup>ξ</sup><sup>i</sup>

equipment (SE<sup>ξ</sup><sup>i</sup>

the battery (SE<sup>ξ</sup>i,max

discharge (SE<sup>ξ</sup>i,min

EVC,i ):

<sup>i</sup> ):

They refer to the active power (P<sup>ξ</sup><sup>i</sup>

that must be equal to a specified value (P<sup>ξ</sup>,sp

i, <sup>τ</sup> <sup>¼</sup> Pp,sp

i, <sup>τ</sup> <sup>¼</sup> <sup>Q</sup>p,sp

Pξi

ðP<sup>ξ</sup>i,sp<sup>2</sup> i,<sup>τ</sup> <sup>þ</sup> <sup>Q</sup><sup>ξ</sup><sup>i</sup>

specified phase ξ<sup>i</sup> during the τth time interval (P<sup>ξ</sup><sup>i</sup>

�P<sup>ξ</sup>i, ch EVCi, <sup>τ</sup> <sup>≤</sup> <sup>P</sup><sup>ξ</sup><sup>i</sup>

i,τ) must be equal to zero:

ðPξi i, τ <sup>2</sup> <sup>þ</sup> <sup>Q</sup><sup>ξ</sup><sup>i</sup> i, τ 2 Þ 1 <sup>2</sup> ≤ SE<sup>ξ</sup><sup>i</sup> EVC,i

EVCi, <sup>τ</sup>

Pξi

Q<sup>ξ</sup><sup>i</sup>

i, <sup>τ</sup> <sup>¼</sup> <sup>P</sup><sup>ξ</sup>i,sp

2 i,<sup>τ</sup> Þ 1 <sup>2</sup> ≤ S<sup>ξ</sup><sup>i</sup> DG,i

that is constrained by the rating of the interfacing converter at the ith bus with phase ξ<sup>i</sup> (S<sup>ξ</sup><sup>i</sup>

Since we deal with single-phase DG units, the active and reactive powers at the other phases

Finally, constraints on the EVC bus refer to the limits on the active power at ith bus with the

with ΩEVk the set of nodes where the vehicles are plugged in at the time interval k and ωk, i the set of time intervals within Ω<sup>k</sup> in which the vehicle at the ith bus is connected (see Figure 1).

Again, the apparent power at the ith bus, phase ξi, must be limited by rating of the charging

Finally, constraints on the SOC of the on-board batteries impose that it is limited by the size of

<sup>i</sup> ) and by a minimum value corresponding to the admissible depth of

EVCi, <sup>τ</sup> ):

) or supply to (P<sup>ξ</sup>i,dch

i,<sup>τ</sup> <sup>≤</sup> <sup>P</sup><sup>ξ</sup>i, dch EVCi,<sup>τ</sup>

Obviously, when the ith vehicle is not connected to the grid, its active power (P<sup>ξ</sup><sup>i</sup>

i, <sup>τ</sup> , τ∈ Ωk, i∈ ΩL, p ¼ 1; 2; 3 ð15Þ

i,<sup>τ</sup> , τ∈ Ωk, i ∈ ΩL, p ¼ 1; 2; 3 ð16Þ

i, <sup>τ</sup>) at the ith bus DG busses (whose set is ΩDG) with phase ξ<sup>i</sup>

i,<sup>τ</sup> ) and to the maximum DG unit's apparent power

i, <sup>τ</sup> , τ∈ Ωk, i∈ ΩDG, ð17Þ

, τ∈ Ωk, i∈ ΩDG ð18Þ

i,τ) that is limited by the maximum power that

, τ∈ ωk,i, i∈ ΩEVk ð19Þ

i,<sup>τ</sup> ¼ 0, τ∉ωk,i, i∈ ΩEVk ð20Þ

i,<sup>τ</sup> ¼ 0, τ∉ωk,i, i ∈ ΩEVk ð21Þ

, τ∈ ωk,i, i∈ ΩEVk ð22Þ

DG,i ):

i, <sup>τ</sup>) and reactive

In this section, some results of numerical applications of the proposed control strategy are reported. The test µG considered in this application is the three-phase unbalanced µG reported in Figure 3, whose lines' parameters are reported in Tables 1 and 2.

The µG is connected to the upstream medium voltage (MV) distribution network through a 250 kVA, 20/0.4 kV transformer. Both single-phase and three-phase loads are connected to the

Figure 3. Test network.


Table 1. Network data.


Table 2. Line type.

µG: their nominal active values are reported in Table 3 (cos φ= 0.9 is assumed for all of the loads).

In Table 3, bus locations and rated active powers of the photovoltaic systems connected to the µG and of the EVCs are also reported. In this application, it is assumed that all the considered DG units are able to control their reactive power according to the control signals that are outputs of the proposed strategy performed by the µG operator. The rated power values of the converters interfacing DG units correspond to the rated powers of the DG units.

PEVs can be connected to different busses of the µG through EVCs. As an example, the numerical application was performed with reference to the case of two PEVs connected to the µG according to the locations and time schedule of Figure 4. The batteries on board the PEVs are assumed to have capacities of 24 kWh; it is assumed that the full SOC is requested at their departure time. The charging (discharging) efficiency is 90% (93%).

With reference to the case of Figure 4, the control strategy was applied at each elementary time interval (Δt = 10 min) of the following two time horizons:



Table 3. Allocation nodes and rated power of loads and DG.

µG: their nominal active values are reported in Table 3 (cos φ= 0.9 is assumed for all of the

Type Material <sup>n</sup>�mm2 Diam. [mm] Ampacity [A]

T1 Copper 3�150+95N 53 311 T2 Copper 4�25 28.3 112 T3 Aluminium 3�70+54.6N 37 180 T4 Copper 4�16 24 85

Bus Type Length [m] Bus Type Length [m]

 3 T1 100 9 10 T2 81 4 T2 137 10 11 T2 70 5 T2 168 11 12 T2 93 6 T2 10 12 13 T4 174 7 T4 107 12 14 T4 66 8 T4 102 14 15 T4 86 9 T3 162 15 16 T4 173

From To From To

In Table 3, bus locations and rated active powers of the photovoltaic systems connected to the µG and of the EVCs are also reported. In this application, it is assumed that all the considered DG units are able to control their reactive power according to the control signals that are outputs of the proposed strategy performed by the µG operator. The rated power values of

PEVs can be connected to different busses of the µG through EVCs. As an example, the numerical application was performed with reference to the case of two PEVs connected to the µG according to the locations and time schedule of Figure 4. The batteries on board the PEVs are assumed to have capacities of 24 kWh; it is assumed that the full SOC is requested at their

With reference to the case of Figure 4, the control strategy was applied at each elementary time

• T1: one PEV is connected to bus i = 13 with phase p = 1: it corresponds to the plugged-in

• T2: two PEVs are connected to the µG; the first is connected to bus i = 13 with phase p = 1 (from 8:00 to 8:40 a.m.) and the second is connected to bus i = 8, phase p = 2 (from 8:00 to 11:00 a.m.): it corresponds to the plugged-in time of the PEV connected at 8:00 a.m.

the converters interfacing DG units correspond to the rated powers of the DG units.

departure time. The charging (discharging) efficiency is 90% (93%).

interval (Δt = 10 min) of the following two time horizons:

time of the first PEV (from 6:20 to 8:40 a.m.);

loads).

Table 2. Line type.

Table 1. Network data.

246 Development and Integration of Microgrids

The energy tariff used in this application is an actual real-time tariff [43] whose values in the two considered time horizons are reported in Figure 5. This price is assumed to be known 24 h ahead. Loads and DG units' active powers are derived by short-term forecasting procedures. Figure 6 shows the active power injected at bus i = 6 (phase p = 1) where both the load and the PV unit are connected. In the figure, two forecasted profiles are shown: the first forecast (Figure 6a) refers to all of the intervals of T1 and is known one time interval ahead the first interval of T1; the second forecast (Figure 6b) refers to all of the intervals of T2 and is known one time interval ahead the first interval of ahead the first interval of T2.

Figures 7 and 8 show the active and reactive power profiles of the PEVs connected in the two considered time frames. They are outputs of the procedure and correspond to control signals for the EVCs. Figure 9 shows the energy stored by the PEVs during the two time horizons.

Figure 4. Case study: plug-in time of two plug-in electric vehicles (PEVs).

Figure 5. Price of energy.

Figure 6. Forecasted value of the injected active power at bus i = 6 (phase p = 1).

Figure 7. Active power of the PEVs.

Figure 8. Reactive power of the PEVs during T<sup>1</sup> (a) and T<sup>2</sup> (b).

Figure 5. Price of energy.

248 Development and Integration of Microgrids

Figure 7. Active power of the PEVs.

Figure 6. Forecasted value of the injected active power at bus i = 6 (phase p = 1).

By the analysis of Figure 7a, it clearly appears that in T<sup>1</sup> the EVC reduces its charging in the time interval from 7:00 to 8:00 a.m., that is, the time interval characterized by a higher value of the energy price. In this time interval, the EVC's reactive power increases, in order to reduce both losses and the power requested at the PCC, thus reducing the overall cost for the energy supply sustained by the µG. The same consideration applies to the case of Figure 7b. Due to the shortness of the PEV connection time, it can also be noted that the EVCs never discharge.

Figure 10 shows the active power imported at the PCC during T<sup>1</sup> and T<sup>2</sup> in both the uncontrolled and controlled cases. The uncontrolled case corresponds to PEVs charged at the maximum EVC's rated power until the full charge is reached and neither the DG units nor the EVCs provide reactive power support. The figure shows that in the time interval characterized

Figure 9. Stored energy of the PEVs during T<sup>1</sup> (a) and T<sup>2</sup> (b).

Figure 10. Active power imported at the PCC during T<sup>1</sup> (a) and T<sup>2</sup> (b).

by higher energy price (i.e., 7:00–8:00 a.m.), the energy imported at the PCC in the uncontrolled case is higher than that imported in the controlled case.

Finally, Figures 11 and 12 show the voltage profile and the voltage unbalance factor, both at the first time interval of T1.

Figure 11 demonstrates that the bus voltages are always within the limits imposed by regulations (i.e., 0.9–1.1 p.u.). Figure 12 shows that, in the controlled case, the unbalance factor is

Figure 11. Voltage profile at the first time interval of T<sup>1</sup> in the uncontrolled case (a) and in the controlled case (b).

Figure 12. Voltage unbalance factor at the first time interval of T1.

always lower than the limit of 2%. The proposed control strategy is able to satisfy the requirements in terms of unbalance limits even in particularly critical cases such as the case of bus i = 13, when in the uncontrolled case, the unbalance factor limit is exceeded. In this case, the use of reactive power provided by the DG units (here not reported for the sake of conciseness) and the PEVs is able to reduce the unbalances.

### 5. Conclusions

by higher energy price (i.e., 7:00–8:00 a.m.), the energy imported at the PCC in the uncontrolled

Finally, Figures 11 and 12 show the voltage profile and the voltage unbalance factor, both at

Figure 11 demonstrates that the bus voltages are always within the limits imposed by regulations (i.e., 0.9–1.1 p.u.). Figure 12 shows that, in the controlled case, the unbalance factor is

Figure 11. Voltage profile at the first time interval of T<sup>1</sup> in the uncontrolled case (a) and in the controlled case (b).

case is higher than that imported in the controlled case.

Figure 10. Active power imported at the PCC during T<sup>1</sup> (a) and T<sup>2</sup> (b).

the first time interval of T1.

250 Development and Integration of Microgrids

In this chapter, an optimal operation strategy was proposed that allowed managing the charging/discharging patterns of the plug-in vehicles connected to an unbalanced LV µG. Aim of the proposed procedure was the minimization of the costs sustained by the µG for the energy provision. The operating strategy allowed complying also with the standard limits for voltage unbalances and slow voltage variations.

### Author details

Guido Carpinelli<sup>1</sup> \*, Fabio Mottola<sup>1</sup> , Daniela Proto<sup>1</sup> and Angela Russo<sup>2</sup>

\*Address all correspondence to: guido.carpinelli@unina.it


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The lack of inertial response at microgrids is usually compensated by configuring primary controllers of converter‐interfaced devices to contribute in the transient response under power disturbances. The main purpose of this chapter is to study the modes of opera‐ tion of primary level techniques of generation, storage, loads, and other devices attached to hybrid ac/dc microgrids. Although the chapter includes an analysis of the modes of operation of lower‐level regulators, the focus is on upper‐level or primary controllers. In this context, we analyze mode‐adaptive controls based on voltage and frequency lev‐ els and we evaluate their behavior by simulation in the Matlab/Simulink® environment. The results demonstrate that mode‐adaptive techniques are adequate for maximizing the energy extracted by distributed generation (DG) systems and limit demand side man‐ agement actuations while ensuring an adequate regulation of the microgrid.

**Keywords:** demand‐response, demand side management, distributed generation, energy storage systems, inertia emulation, microgrids, mode‐adaptive control, primary control

### **1. Introduction**

The electric grid is undergoing various changes in its structure, among other reasons, caused by a high dependence on fossil fuels, a constant increment in the power consumption, and the associated environmental problems. The classical top‐down structure of the grid is shifting to a more decentralized topology where generation systems are located near consumption points—also known as distributed generation (DG) systems. This shift brings about several challenges, as the electric grid was not originally designed to handle the distributed and inter‐ mittent generating systems. In this context, microgrids are arising as one of the most suitable alternatives [1, 2], as they can efficiently integrate different types of DG systems thanks to the energy storage systems (ESSs) and advanced control strategies they include.

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Microgrids are used at a wide variety of applications—distribution grids, electric transpor‐ tation such as vessels or aircraft, isolated grids, etc.—and therefore can have very different features. However, one of the most common approaches is to classify them depending on the nature of their current [3]: ac, dc, or hybrid ac/dc.

Typically, researchers have focused most part of the research activity related to microgrids on ac systems, as they are the most straightforward solution based on the current infrastructure. The knowledge gained over the years with the electric grid can be directly applied for the development of ac microgrids. Therefore, these systems are characterized by efficient modi‐ fication of voltage levels with transformers and by advanced fault management capabilities with optimally designed devices.

However, during the last two decades, dc microgrids are arising as an interesting alternative due to the inherent advantages they provide over ac ones. The increment of dc‐based systems or devices that require a dc stage to operate, the lack of reactive power circulation or the fact that there is no need for synchronization, among other features, is clearing the path toward dc operated distribution networks. The main drawback resides in the fact that a complete substitution of the ac infrastructure would be unfeasible.

In this context, hybrid ac/dc microgrids are an interesting alternative, as they would enable the integration of dc‐based systems through a dc network while maintaining the ac infrastruc‐ ture [4]. This way the advantages of ac as well as dc grids can be combined, facilitating the shift to a more distributed electric grid composed by DG and ESSs.

As shown in **Figure 1**, hybrid microgrids are composed of ac and dc subgrids, which are linked by one or more interface converter. The integration of these converters not only

**Figure 1.** Hybrid ac/dc microgrid.

enables the power exchange between the ac and dc subgrids but they also increase the degrees of freedom regarding the management of the grid, as they can provide other ancillary ser‐ vices [5].

Microgrids are used at a wide variety of applications—distribution grids, electric transpor‐ tation such as vessels or aircraft, isolated grids, etc.—and therefore can have very different features. However, one of the most common approaches is to classify them depending on the

Typically, researchers have focused most part of the research activity related to microgrids on ac systems, as they are the most straightforward solution based on the current infrastructure. The knowledge gained over the years with the electric grid can be directly applied for the development of ac microgrids. Therefore, these systems are characterized by efficient modi‐ fication of voltage levels with transformers and by advanced fault management capabilities

However, during the last two decades, dc microgrids are arising as an interesting alternative due to the inherent advantages they provide over ac ones. The increment of dc‐based systems or devices that require a dc stage to operate, the lack of reactive power circulation or the fact that there is no need for synchronization, among other features, is clearing the path toward dc operated distribution networks. The main drawback resides in the fact that a complete

In this context, hybrid ac/dc microgrids are an interesting alternative, as they would enable the integration of dc‐based systems through a dc network while maintaining the ac infrastruc‐ ture [4]. This way the advantages of ac as well as dc grids can be combined, facilitating the

As shown in **Figure 1**, hybrid microgrids are composed of ac and dc subgrids, which are linked by one or more interface converter. The integration of these converters not only

nature of their current [3]: ac, dc, or hybrid ac/dc.

substitution of the ac infrastructure would be unfeasible.

shift to a more distributed electric grid composed by DG and ESSs.

with optimally designed devices.

256 Development and Integration of Microgrids

**Figure 1.** Hybrid ac/dc microgrid.

Although these microgrids are gaining a lot of interest especially during the last decades, most of the challenges still reside in their control and management, especially when they operate islanded from the main grid. Even if the control techniques employed at ac, dc, and hybrid ac/dc microgrids can be considerably different, their concept of operation is usually very similar. Inspired by the classical ac grid (**Figure 2**), the management of microgrids is most of the times carried out by employing a hierarchical structure. Each control layer is responsible for certain functions, such as the voltage/frequency control or the management of the islanding/reconnection process.

The main difference is that, at microgrids, conventional synchronous generators are replaced by converter‐interfaced generation and storage systems, and therefore, the inertia of the grid is drastically reduced. This is one of the main challenging tasks in the management of microgrids, as lower inertia in the grid means that their voltage and/or frequency is signifi‐ cantly deteriorated under power variations. Consequently, microgrids become more suscep‐ tible to failures—especially when operating in the islanded mode—and hence more advanced control strategies need to be adopted to replace the lack of inertial behavior and ensure a stable operation.

**Figure 2.** Main ac grid hierarchical control layer functions [6].

One of the most common solutions is to configure the converters associated to DG, ESSs, and even loads to contribute in the voltage and frequency regulation of microgrids. This is usually carried out by primary controllers, which are most of the times integrated locally in each device. **Figure 3** shows the dynamics of each control layer in a microgrid after a power variation.

As shown in the figure, the lack of inertial response is partially replaced by the primary control of converter‐interfaced devices connected to the microgrid. In the literature, there is a wide col‐ lection of this type of primary techniques that can be integrated at ac, dc, and hybrid microgrids. A review of some of the most relevant strategies can be seen for instance in Refs. [3, 7].

Primary control techniques employed at microgrids are usually composed of two main stages (**Figure 4**): the lower‐level stage usually contains the faster regulation loops, which are responsible for the current and/or voltage regulation of converters; similarly, the upper level of the primary control, which is slower than the previous one, determines the reference value where the converter should be controlled, e.g., the active or reactive power.

When there is a variation in the grid, the lower‐level control stage primarily defines the tran‐ sient response of the converter. In addition, the upper‐level stage determines the steady‐state operation point of the converter. However, depending on how are these stages designed, their effect in the transient as well as steady state response is coupled.

The aim of this chapter is to analyze the operation modes of primary control strategies employed at hybrid ac/dc microgrids, focusing on their lower‐ and upper‐level (primary)

**Figure 3.** Microgrid hierarchical control layer functions.

**Figure 4.** Primary controller configuration.

One of the most common solutions is to configure the converters associated to DG, ESSs, and even loads to contribute in the voltage and frequency regulation of microgrids. This is usually carried out by primary controllers, which are most of the times integrated locally in each device. **Figure 3** shows the dynamics of each control layer in a microgrid after a power variation.

As shown in the figure, the lack of inertial response is partially replaced by the primary control of converter‐interfaced devices connected to the microgrid. In the literature, there is a wide col‐ lection of this type of primary techniques that can be integrated at ac, dc, and hybrid microgrids.

Primary control techniques employed at microgrids are usually composed of two main stages (**Figure 4**): the lower‐level stage usually contains the faster regulation loops, which are responsible for the current and/or voltage regulation of converters; similarly, the upper level of the primary control, which is slower than the previous one, determines the reference value

When there is a variation in the grid, the lower‐level control stage primarily defines the tran‐ sient response of the converter. In addition, the upper‐level stage determines the steady‐state operation point of the converter. However, depending on how are these stages designed, their

The aim of this chapter is to analyze the operation modes of primary control strategies employed at hybrid ac/dc microgrids, focusing on their lower‐ and upper‐level (primary)

A review of some of the most relevant strategies can be seen for instance in Refs. [3, 7].

where the converter should be controlled, e.g., the active or reactive power.

effect in the transient as well as steady state response is coupled.

258 Development and Integration of Microgrids

**Figure 3.** Microgrid hierarchical control layer functions.

control stages. Taking into account that ac and dc microgrids are a particular case of hybrid microgrids, the study carried out in this chapter is also appropriate for these systems.

### **2. Lower‐level control operation modes**

When designing the lower‐level control stages of primary regulators, we can usually follow two main approaches.

In the classical approach, this control stage is composed by one or more cascaded PI regulators that are tuned to follow the reference value provided by upper‐level controllers, e.g., a voltage or a power reference. In this case, the regulators do not provide any inherent response over variations in the grid and are mainly designed to control the system so that it reaches the refer‐ ence value as fast as possible.

On the other hand, in the last decades, a different approach has been proposed where the lower‐level regulators are designed to participate in the transient regulation of the voltage and frequency of the network. These regulators are designed to emulate the behavior of classical synchronous generators with power converters associated to DG, ESSs, and loads connected to microgrids. In the literature, these techniques have been widely employed for different applications and are also known as virtual synchronous machines (VSMs) or synchronverters [8–15]. Following the main ac grid configuration—where synchronous generators are directly connected—most of these techniques are usually employed for devices connected to ac microgrids. However, recently, similar approaches have been developed to reproduce an analogous behavior at dc systems. For instance, the study carried out in Ref. [16] shows that a similar response can be emulated at dc systems by employing virtual‐impedances in the control strategy, for example, as virtual‐capacitors. In this case, instead of controlling the frequency as in VSMs, the variable controlled is the bus voltage.

### **3. Upper‐level (primary) control operation modes**

Due to the dispersed nature of microgrids, primary controllers are usually autonomous and operate based on local measurements of the device they are controlling. Whether the device contributes in the frequency/voltage regulation or not, their upper‐level regulator is responsible for defining the steady‐state point of operation of the converter.

Similar to lower‐level regulators, upper‐level ones are mainly classified into two different types.

On the one hand, there are certain devices that do not contribute in the frequency/voltage regulation of the microgrid and operate based on the reference provided by another control level (e.g., the secondary) or based on a reference internally calculated to, for example, extract as much energy as possible from the energy source they are connected to—a maximum power point tracking (MPPT) technique. These units are also named grid‐following devices, as they do not regulate the bus but rather they "follow" their frequency and/or voltage [5, 7].

On the other hand, systems that contribute in the regulation of the bus are known as grid‐ forming or grid‐supporting systems. These devices share the power variations occurring in the microgrid to decrease the variations of the bus frequency/voltage [5, 7].

We can design generation, storage systems, and loads connected via a power converter to operate differently for example depending on the bus voltage or frequency level. These sys‐ tems usually include both types of upper‐level controllers, and change their mode of opera‐ tion based on some external condition. This approach is also known as mode‐adaptive control, and one of the most interesting methods is to adapt the behavior of each controller based on the level of the bus frequency or voltage.

The authors in Refs. [17–22], for example, propose different types of mode adaptive con‐ trol strategies for microgrids inspired by this concept, where the devices connected to the microgrid adapt their characteristics based on the frequency or voltage of the grid.

**Figure 5** shows a possible configuration for the primary upper‐level control of genera‐ tion, storage systems, and loads connected to a hybrid microgrid. In addition, we have also depicted the connection to the mains grid, in case the microgrid is attached to it.

As we can observe, the primary control of each type of device is configured to behave differently depending on the value of the voltage or frequency. The solid thick lines illustrate an example of these and the shades show that the curves can be modified depending on the requirements. In a

**Figure 5.** Example of adaptive primary controllers for systems connected to a microgrid.

real application, the ideal approach would be to configure all converter‐interfaced devices to con‐ tribute in the power regulation. Each system could be designed to participate more or less for cer‐ tain conditions, but the system would become more robust and stable because power variations would be handled by a higher number of devices with different characteristics and dynamics.

In the following sections, we describe more details of the modes of each type of system.

### **3.1. Energy storage systems**

**3. Upper‐level (primary) control operation modes**

260 Development and Integration of Microgrids

for defining the steady‐state point of operation of the converter.

Due to the dispersed nature of microgrids, primary controllers are usually autonomous and operate based on local measurements of the device they are controlling. Whether the device contributes in the frequency/voltage regulation or not, their upper‐level regulator is responsible

Similar to lower‐level regulators, upper‐level ones are mainly classified into two different types. On the one hand, there are certain devices that do not contribute in the frequency/voltage regulation of the microgrid and operate based on the reference provided by another control level (e.g., the secondary) or based on a reference internally calculated to, for example, extract as much energy as possible from the energy source they are connected to—a maximum power point tracking (MPPT) technique. These units are also named grid‐following devices, as they

do not regulate the bus but rather they "follow" their frequency and/or voltage [5, 7].

the microgrid to decrease the variations of the bus frequency/voltage [5, 7].

the level of the bus frequency or voltage.

On the other hand, systems that contribute in the regulation of the bus are known as grid‐ forming or grid‐supporting systems. These devices share the power variations occurring in

We can design generation, storage systems, and loads connected via a power converter to operate differently for example depending on the bus voltage or frequency level. These sys‐ tems usually include both types of upper‐level controllers, and change their mode of opera‐ tion based on some external condition. This approach is also known as mode‐adaptive control, and one of the most interesting methods is to adapt the behavior of each controller based on

The authors in Refs. [17–22], for example, propose different types of mode adaptive con‐ trol strategies for microgrids inspired by this concept, where the devices connected to the

**Figure 5** shows a possible configuration for the primary upper‐level control of genera‐ tion, storage systems, and loads connected to a hybrid microgrid. In addition, we have also

As we can observe, the primary control of each type of device is configured to behave differently depending on the value of the voltage or frequency. The solid thick lines illustrate an example of these and the shades show that the curves can be modified depending on the requirements. In a

microgrid adapt their characteristics based on the frequency or voltage of the grid.

depicted the connection to the mains grid, in case the microgrid is attached to it.

**Figure 5.** Example of adaptive primary controllers for systems connected to a microgrid.

ESSs are one of the most important agents in the microgrid regulation because they serve as an energy "buffer" to compensate generation and demand deviations during normal operation. We must design and size these systems in order to cope with the most severe conditions of the system; otherwise, a poor regulation would cause the malfunction or disconnection of devices.

**Figure 6** shows the most important modes of operation of energy storage systems connected to a microgrid. Under a balanced operation (mode 1), the ESS does not exchange any power with the microgrid. This hysteresis range must be carefully determined in order to avoid an excessive cycling and therefore ageing of the ESS but also to prevent the system from entering into an unstable point of operation.

When the generated power is higher than the demanded one the voltage or frequency of the microgrid increases over the hysteresis upper value and therefore the ESS absorbs power according to the charging droop slope (mode 2). This slope depends not only on the charging capabilities of the ESS but also on the sizing of its power converter.

When the voltage/frequency of the microgrid increases above the preestablished value or the state of charge (SOC) of the ESS is too high, the device turns to mode 3, where the power absorbed from the microgrid is kept constant although the *v/f* deviation keeps increasing. As shown in **Figure 6**, if the SOC of the ESS continues to increase while in mode 3, the maximum power level value is decreased. The limit of this saturation would be when the SOC is on its upper limit and hence the ESS would not absorb power anymore.

**Figure 6.** ESS primary controller operation modes.

A similar behavior is reproduced when there is an excessive demand in the microgrid and the voltage or frequency decrease below the hysteresis lower value (mode 4). At this point, the ESS supplies power to the microgrid according to its discharging droop slope. We must note that we could design the droop slopes differently for the ESS charging or discharging process, which means they do not have to be symmetric.

The ESS remains in mode 4 until the voltage or frequency reach their minimum value or the SOC of the ESS is too low. When any of these conditions takes place, the ESS jumps to mode 5 and supplies a constant power regardless of the *v/f* negative deviation. As in mode 3, the maximum power provided by the ESS will be decreased if the SOC decreases below the pre‐ defined levels. At some point, when the minimum SOC is reached, the ESS will not supply more power to the microgrid.

### **3.2. Generation systems**

Generation systems mainly operate in two different modes (**Figure 7**): maximum energy extraction/constant power operation and droop regulation. During normal operation in mode 1, as most DG systems are based on renewable energy sources (RESs), the converters attached to generation systems are controlled to absorb as much energy as possible from energy sources. In the case of other types of DG systems such as diesel generators, secondary level controllers determine their constant power reference.

When the voltage or frequency of the microgrid increases above the preestablished level, DG systems shift out of their MPP to reduce the power amount they supply to the system. In this mode 2, DG systems contribute in the *v/f* regulation of the microgrid through a droop slope (**Figure 7**). As we can see in **Figure 7b**, the droop slope and saturation point depend not only on the value of the voltage or frequency, but also on the maximum power point (MPP) of the DG system. This means that depending on the available power that can be absorbed from the RES, the controllers will have to adapt their operation characteristics to meet the grid codes predefined by the system operator.

**Figure 7.** DG primary controller operation modes.

Classically, most converters associated to DG systems have been configured to exclusively operate on the MPP. However, the transition toward a more decentralized electrical system requires the participation of these generators in the regulation of the grid [13].

### **3.3. Demand‐response**

A similar behavior is reproduced when there is an excessive demand in the microgrid and the voltage or frequency decrease below the hysteresis lower value (mode 4). At this point, the ESS supplies power to the microgrid according to its discharging droop slope. We must note that we could design the droop slopes differently for the ESS charging or discharging process,

The ESS remains in mode 4 until the voltage or frequency reach their minimum value or the SOC of the ESS is too low. When any of these conditions takes place, the ESS jumps to mode 5 and supplies a constant power regardless of the *v/f* negative deviation. As in mode 3, the maximum power provided by the ESS will be decreased if the SOC decreases below the pre‐ defined levels. At some point, when the minimum SOC is reached, the ESS will not supply

Generation systems mainly operate in two different modes (**Figure 7**): maximum energy extraction/constant power operation and droop regulation. During normal operation in mode 1, as most DG systems are based on renewable energy sources (RESs), the converters attached to generation systems are controlled to absorb as much energy as possible from energy sources. In the case of other types of DG systems such as diesel generators, secondary

When the voltage or frequency of the microgrid increases above the preestablished level, DG systems shift out of their MPP to reduce the power amount they supply to the system. In this mode 2, DG systems contribute in the *v/f* regulation of the microgrid through a droop slope (**Figure 7**). As we can see in **Figure 7b**, the droop slope and saturation point depend not only on the value of the voltage or frequency, but also on the maximum power point (MPP) of the DG system. This means that depending on the available power that can be absorbed from the RES, the controllers will have to adapt their operation characteristics to meet the grid codes

which means they do not have to be symmetric.

level controllers determine their constant power reference.

more power to the microgrid.

262 Development and Integration of Microgrids

predefined by the system operator.

**Figure 7.** DG primary controller operation modes.

**3.2. Generation systems**

Similar to DG systems, loads operate normally in mode 1, absorbing the power required by the attached device. When generation systems are producing all the power they can, no power can be absorbed from the main grid, and energy storage systems are not able to provide more power, the voltage or frequency decreases below the predefined level and the power consumed by loads is consequently decreased (mode 2). In this case, as with DG systems, the droop slopes as well as saturation values are dependent on the instantaneous load (**Figure 8b**).

In the literature, this type of operation is a part of the so‐called demand side management, as the loads actively participate in the regulation of the microgrid by reducing their consumed power when required. A high research activity has been carried out in the last years high‐ lighting the importance of the participation of loads in the management of different types of electric systems [23].

### **3.4. Connection to the main grid**

Depending on the topology and type of microgrid, we can follow different approaches with respect to the connection to the main grid. On a classical approach, the connection to the main grid can be employed to contribute in the regulation of the microgrid for the entire voltage range [3]. Another solution would be to use the link to the main grid at specific cases where the voltage or frequency levels are above the maximum or below minimum levels, avoiding the malfunction or disconnection of other devices.

**Figure 9** shows the three main operation states of this last approach; as it can be seen, this link only operates when the *v/f* levels are out of some predefined levels. If the voltage or frequency goes above or below boundaries, we employ the link to the main grid to support the regulation

**Figure 8.** Load primary controller operation modes.

**Figure 9.** Grid connection primary controller operation modes.

of the system. An example of this situation is an excess of generated energy that causes an incre‐ ment in the voltage or frequency; as our purpose is to extract as much energy as possible from RESs, we could employ the connection to the mains grid to send this extra power to the grid.

#### **3.5. Interface converters**

Interface ac‐dc converters located along the microgrid provide an extra degree of freedom in the management of microgrids, as we can control them to perform diverse operations. The most typi‐ cal approach would be to employ these converters to compensate the *v/f* deviations in the ac and dc subgrid of the hybrid microgrid [5, 22, 24]. The converters would transfer power from one sub‐ grid to the other in order to equalize the excess of generated or demanded power at both systems.

As shown in **Figure 10**, interface converters carry out the power transfer between different subgrids with a droop controller. Unlike classical approaches, this droop is based on the differ‐ ence between the frequency deviation in the ac subgrid and the voltage deviation in the dc part.

**Figure 10.** Interface converter primary controller operation modes.

Whenever there is a mismatch between these deviations, ac‐dc converters located in the microgrid will transfer power to balance them. Modes 2 and 3 correspond to the maximum power that ac‐ dc systems can transfer in both directions.

According to Ref. [5], other techniques can be employed in the control of interface converters integrated at hybrid ac/dc microgrids such as the state of charge balancing of ESSs located in the ac and dc subgrid of the system.

### **4. Simulation results**

We have carried out different simulations in the Matlab/Simulink® environment in order to observe the operation modes of primary controllers of a hybrid ac/dc microgrid.

### **4.1. Simulation scenario**

of the system. An example of this situation is an excess of generated energy that causes an incre‐ ment in the voltage or frequency; as our purpose is to extract as much energy as possible from RESs, we could employ the connection to the mains grid to send this extra power to the grid.

Interface ac‐dc converters located along the microgrid provide an extra degree of freedom in the management of microgrids, as we can control them to perform diverse operations. The most typi‐ cal approach would be to employ these converters to compensate the *v/f* deviations in the ac and dc subgrid of the hybrid microgrid [5, 22, 24]. The converters would transfer power from one sub‐ grid to the other in order to equalize the excess of generated or demanded power at both systems. As shown in **Figure 10**, interface converters carry out the power transfer between different subgrids with a droop controller. Unlike classical approaches, this droop is based on the differ‐ ence between the frequency deviation in the ac subgrid and the voltage deviation in the dc part.

**3.5. Interface converters**

264 Development and Integration of Microgrids

**Figure 9.** Grid connection primary controller operation modes.

**Figure 10.** Interface converter primary controller operation modes.

A generation system, a storage system, and a load in the ac as well as dc subgrid of the microgrid compose the simulation scenario, and an interface ac/dc converter links these subgrids (**Figure 11**). We must mention that in this case, the hybrid microgrid also includes a connection point to the main ac grid in order to observe its behavior. As shown in the fol‐ lowing sections, the islanded operation is a particular case of microgrids connected to the main grid; the difference is that islanded microgrids do not exchange any power with this grid.

In order to evaluate the behavior of the different agents connected to the hybrid ac/dc microgrid, we introduce a power disturbance in the ac subgrid of the microgrid. The results would be equivalent if we introduce the disturbance in the dc part, so for the sake of simplicity we do not contemplate this case in this chapter.

**Figure 12** shows the primary curves employed for ESSs, DG systems, loads, and the connec‐ tion to the main grid. The purpose is to validate the operation modes of the different agents participating in the regulation of the microgrid, so we have made no distinction in the con‐ figuration of DG, ESSs, and loads of the ac and dc part.

In the proposed scenario, if the demanded and generated power is balanced, all systems remain in an equilibrium state and ac and dc buses remain at their rated values (**State 0**). When the voltage or frequency are out of their rated values, ESSs carry out the regulation of the bus based on a predefined droop curve as shown in **Figure 12** (**State I**).

When storage systems reach their boundary operation, the microgrid exchanges power with the main ac grid to carry out the regulation (**State II**). For instance, when the voltage or fre‐ quency reaches a certain upper boundary, instead of taking DG systems out of their maxi‐ mum power point, the exceeding power is supplied to the main ac grid. This is a key aspect of systems connected to the main grid because energy from RESs is not wasted and could be beneficial from the point of view of the electric market.

A similar situation occurs when the voltage or frequency fall below the limit; instead of reduc‐ ing the power consumed by loads—that could lead to a malfunction of the load—this lack of power is covered by absorbing power from the main grid (**State II**).

**Figure 11.** Simulated hybrid ac/dc microgrid scenario.

Usually the exchange of power with the main grid is limited—either by technical or by eco‐ nomical limitations—so when the voltage or frequency reaches the next upper or lower limit, generation systems, and loads are employed to contribute in the power regulation. Therefore, **State III** occurs when DG systems are out of their MPP and are controlled by a droop curve to regulate the power they generate. **State IV**, on the other hand, relates to the situation where loads reduce their consumed power, also known as demand‐response.

On an islanded system, where no power can be exchanged with the main grid, if storage sys‐ tems reach their upper or lower boundaries of operation, DG systems and loads directly carry out the regulation. This means there would not be any State II, and the system would directly enter into the State III or IV.

### **4.2. Modes of operation under disturbances**

In order to reproduce the states mentioned in Section 4.1, we have simulated two different power disturbances, a positive and a negative step‐shaped profile. We must mention that all

**Figure 12.** Primary controllers of the simulated scenario.

the variables of the following simulations are normalized and shown in per unit (p.u.) values to facilitate the analysis.

### *4.2.1. Positive power disturbance*

Usually the exchange of power with the main grid is limited—either by technical or by eco‐ nomical limitations—so when the voltage or frequency reaches the next upper or lower limit, generation systems, and loads are employed to contribute in the power regulation. Therefore, **State III** occurs when DG systems are out of their MPP and are controlled by a droop curve to regulate the power they generate. **State IV**, on the other hand, relates to the situation where

On an islanded system, where no power can be exchanged with the main grid, if storage sys‐ tems reach their upper or lower boundaries of operation, DG systems and loads directly carry out the regulation. This means there would not be any State II, and the system would directly

In order to reproduce the states mentioned in Section 4.1, we have simulated two different power disturbances, a positive and a negative step‐shaped profile. We must mention that all

loads reduce their consumed power, also known as demand‐response.

enter into the State III or IV.

**4.2. Modes of operation under disturbances**

**Figure 11.** Simulated hybrid ac/dc microgrid scenario.

266 Development and Integration of Microgrids

**Figure 12.** Primary controllers of the simulated scenario.

The aim of this simulation is to observe the modes of operation of ESS, DG systems, and the grid connection for positive power disturbances or deviations occurring in the microgrid.

**Figure 13** shows the most relevant variables of the hybrid ac/dc microgrid during the simula‐ tion. We resume these parameters below:


As we can observe, in the figure we can distinguish different stages during the simulation, based on the values of the frequency and voltage of the hybrid ac/dc microgrid.

The system begins at an equilibrium state with no power disturbance, which in this case is named State 0. At this stage, the demanded and generated power are balanced so the ac and dc buses remain at their rated values.

At the instant *t* = 1 s, a positive power step is introduced and therefore ESSs start regulating the bus by absorbing power, entering into State I. The interface converter transfers the power from the ESS located in the dc subgrid to the ac one in order to compensate *v/f* deviations in the system, as previously explained in Section 3.5.

At *t* = 2 s, a higher power disturbance is introduced in the system and ESSs continue regulat‐ ing the bus in State I until they reach their maximum power value. When this boundary is exceeded (*v/f* = 1.03 p.u.), the system enters State II and the extra power is supplied to the main ac grid.

Similarly, at *t* = 3 s, the power disturbance is increased and the microgrid continues supplying power to the main grid in State II until the maximum exchangeable power is reached. After exceeding this limit (*v/f* = 1.06 p.u.), the power supplied to the main grid is fixed and DG sys‐ tems begin regulating the system.

After the instant *t* = 4 s, the disturbance is reverted and the system recovers its original equi‐ librium state.

**Figure 13.** Microgrid response under positive power disturbances: (a) ac bus frequency, (b) ac subgrid power values, (c) disturbance power, (d) interface converter power, (e) dc bus voltage, and (f) dc subgrid power values.

In this simulation, we can see that the interface converter transfers power from the dc subgrid to the ac one in order to compensate the power deviations in both systems. However, it can be also noticed that the frequency in the ac grid and the voltage in the dc one do not reach their upper values at the same time, making the grids to change of state at different instants.

#### *4.2.2. Negative power disturbance*

In the following simulation, the main purpose is to observe the mode of operation of not only ESSs and the connection to the main grid but also the behavior of loads when lower limits of *v/f* are reached. Therefore, in this case, the power disturbance of Section 4.2.1 has been inversed, emulating different values of demanded power.

We show the most relevant parameters of the hybrid ac/dc microgrid for this simulation in **Figure 14**. As we can observe, the system goes through a very similar process as in the previ‐ ous case. The difference is that the voltage as well as frequency decrease instead of increasing due to the negative power disturbance.

In this context, the system begins in State 0 at an equilibrium point and enters into State I when the first negative power step is introduced. Afterwards, with the second power step the

**Figure 14.** Microgrid response under negative power disturbances: (a) ac bus frequency, (b) ac subgrid power values, (c) disturbance power, (d) interface converter power, (e) dc bus voltage, and (f) dc subgrid power values.

In this simulation, we can see that the interface converter transfers power from the dc subgrid to the ac one in order to compensate the power deviations in both systems. However, it can be also noticed that the frequency in the ac grid and the voltage in the dc one do not reach their upper values at the same time, making the grids to change of state at different instants.

**Figure 13.** Microgrid response under positive power disturbances: (a) ac bus frequency, (b) ac subgrid power values, (c)

disturbance power, (d) interface converter power, (e) dc bus voltage, and (f) dc subgrid power values.

In the following simulation, the main purpose is to observe the mode of operation of not only ESSs and the connection to the main grid but also the behavior of loads when lower limits

*4.2.2. Negative power disturbance*

268 Development and Integration of Microgrids

microgrid reaches the *v/f =* 0.97 p.u. limit and enters into State II, where the lack of power is handled by absorbing power from the main grid. Finally, with the third negative power step the system reaches the *v/f* = 0.94 p.u. limit and, as no more power can be absorbed from the grid, loads begin reducing their demanded power (State IV).

In the proposed configuration, all the systems attached to the hybrid microgrid participate in the regulation of the system at different conditions. This structure facilitates the analysis of the mode‐adaptive control techniques, but in a more realistic environment the most optimal approach would be to take advantage of the disperse characteristics of ESSs, DG systems, loads, and converters to design a bus regulating strategy composed by a mix of these systems for the entire *v/f* range.

### **5. Conclusions**

In this chapter, the hierarchical control of microgrids has been initially revised, showing that this operation concept is very similar to the one employed in the conventional ac grid. One of the main differences is that, at microgrids, classical synchronous generators are replaced by converter‐interfaced DG and ESSs, drastically reducing the inertial response of the sys‐ tem. In order to cope with this problem, the controllers of converter‐interfaced devices are equipped with more advanced primary level techniques that contribute in the regulation of the microgrid.

Throughout the chapter, we have studied the different modes of operation of primary tech‐ niques and lower‐level controllers of converter‐interfaced generation, storage, loads, and other devices. Regarding lower‐level techniques, we have shown that we can configure regulators to respond differently under power disturbances, providing more or less "inertial behavior." In the case of upper‐level/primary controllers, we have carried out a thorough analysis of their most relevant modes of operation. We can design these controllers to behave differently—by contributing in the bus regulation or not—depending on certain conditions such as the voltage or frequency level in the microgrid. This strategy is also known as a mode‐adaptive control, as generation, storage systems or loads adapt their mode of operation depending on some external condition.

The simulations carried out in this chapter demonstrate that a mode‐adaptive control is very useful to take advantage of DG systems and loads. In the proposed case, DG systems—which are usually based on RES—are only taken out of their MPP when the voltage or frequency of the bus reach a very high boundary, maximizing the energy produced. Similarly, loads only contribute in the regulation of the system when the voltage or frequency reaches a very low level, which avoids any possible malfunction of these devices. Although the proposed configuration is adequate to observe the mode‐adaptive control operation of each device attached to the microgrid, through‐ out the chapter we highlight that the most optimal approach would be to design a bus‐regulating strategy for the entire operation range composed by a combination of ESSs, DG systems, loads, and converters, taking advantage of their different dynamic characteristics.

### **Acknowledgements**

microgrid reaches the *v/f =* 0.97 p.u. limit and enters into State II, where the lack of power is handled by absorbing power from the main grid. Finally, with the third negative power step the system reaches the *v/f* = 0.94 p.u. limit and, as no more power can be absorbed from the

In the proposed configuration, all the systems attached to the hybrid microgrid participate in the regulation of the system at different conditions. This structure facilitates the analysis of the mode‐adaptive control techniques, but in a more realistic environment the most optimal approach would be to take advantage of the disperse characteristics of ESSs, DG systems, loads, and converters to design a bus regulating strategy composed by a mix of these systems

In this chapter, the hierarchical control of microgrids has been initially revised, showing that this operation concept is very similar to the one employed in the conventional ac grid. One of the main differences is that, at microgrids, classical synchronous generators are replaced by converter‐interfaced DG and ESSs, drastically reducing the inertial response of the sys‐ tem. In order to cope with this problem, the controllers of converter‐interfaced devices are equipped with more advanced primary level techniques that contribute in the regulation of

Throughout the chapter, we have studied the different modes of operation of primary tech‐ niques and lower‐level controllers of converter‐interfaced generation, storage, loads, and other devices. Regarding lower‐level techniques, we have shown that we can configure regulators to respond differently under power disturbances, providing more or less "inertial behavior." In the case of upper‐level/primary controllers, we have carried out a thorough analysis of their most relevant modes of operation. We can design these controllers to behave differently—by contributing in the bus regulation or not—depending on certain conditions such as the voltage or frequency level in the microgrid. This strategy is also known as a mode‐adaptive control, as generation, storage systems or loads adapt their mode of operation depending on some external

The simulations carried out in this chapter demonstrate that a mode‐adaptive control is very useful to take advantage of DG systems and loads. In the proposed case, DG systems—which are usually based on RES—are only taken out of their MPP when the voltage or frequency of the bus reach a very high boundary, maximizing the energy produced. Similarly, loads only contribute in the regulation of the system when the voltage or frequency reaches a very low level, which avoids any possible malfunction of these devices. Although the proposed configuration is adequate to observe the mode‐adaptive control operation of each device attached to the microgrid, through‐ out the chapter we highlight that the most optimal approach would be to design a bus‐regulating strategy for the entire operation range composed by a combination of ESSs, DG systems, loads,

and converters, taking advantage of their different dynamic characteristics.

grid, loads begin reducing their demanded power (State IV).

for the entire *v/f* range.

270 Development and Integration of Microgrids

**5. Conclusions**

the microgrid.

condition.

This work has been partially funded by a predoctoral grant of the Basque Government (PRE\_2016\_2\_0241).

### **Author details**

Eneko Unamuno\* and Jon Andoni Barrena

\*Address all correspondence to: eunamuno@mondragon.edu

Electronics and Computing Department, Mondragon Unibertsitatea, Arrasate‐Mondragón, Spain

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272 Development and Integration of Microgrids

TIE.2017.267462


## *Edited by Wen-Ping Cao and Jin Yang*

The utilization of AC or DC microgrids across the world has increased dramatically over the years and has led to development opportunities as well as technical challenges when they are connected to the main grids or used as stand-alone systems. This book overviews the development of AC/DC microgrids; explains the microgrid concepts, design and control considerations, discusses operational and technical issues, as well as interconnection and integration of these systems. This book is served as a reference for a general audience of researchers, academics, PhD students and practitioners in the field of power engineering.

Photo by Vladimir\_Timofeev / iStock

Development and Integration of Microgrids

Development and Integration

of Microgrids

*Edited by Wen-Ping Cao and Jin Yang*