**2. Renewable generation units in stand alone mode**

When it is necessary to supply electrical loads in stand-alone configuration there is no particular standard that define the power quality requirements. Anyway, the mains concepts of power quality regulation in grid connected systems can be used also for standalone systems and as general guidelines, a power quality level close to the one guaranteed for loads fed by the grid can be choose.

On the following sections, a list of the main power quality concepts is presented, focusing on how this concepts, originally dedicated to grid connected systems, can be adapted to stand-alone configurations, in order to obtain some guidelines to improve the performance of these systems.

For general purpose and to simplify the analysis, a stand-alone system, including some loads and one renewable hybrid generation unit equipped with a battery bank is considered.

These considerations can be generalised and adapted to a system of several renewable generation units parallel connected in order to supply the loads in stand-alone configuration. The main considerations regarding the battery bank can be adapted also to other energy storage systems, such as flyback wheels, hydraulic reservoirs, fuel cells, etc.

#### **3. Hybrid renewable generation units in stand-alone mode**

#### **3.1 Requirements on voltage waveform (voltage amplitude in normal operating conditions)**

In the considered renewable power units, the interface between power generators and loads is made by one ore more static converters. It is important that one of this static converter is a voltage controlled inverter (interface converter) that generates a voltage waveform corresponding to a certain reference given to its control system. By regulating the voltage reference signal, it's possible to obtain a sinusoidal voltage waveform with desired frequency and amplitude, within the limits of the power converter.

In order to maintain the nominal voltage level on the loads, it is important to include in the voltage regulator of the interface converter a compensation term that takes into account the voltage drops on the line impedance, by measuring the current drawn by the loads as it is shown in Fig.2.

Some consideration can be made about the Fig.2:

• The line connecting the power plants and the loads, in small application is a low voltage line, thus characterised by a mainly resistive impedance. The compensation term in the regulator should take into account the line impedance value and typology (reactive or resistive).

Integration of Hybrid Distributed Generation Units in Power Grid 7

As the system voltage waveform is generated by the interface converter, its frequency can be set by acting on the frequency of the reference voltage (and current) in the voltage regulator

As for the voltage regulation, in stand-alone microgrids several control techniques can be adopted to maintain the frequency of the supply in the range required for the power quality, with or without communication between paralleled generation units. The only difference from voltage regulation is that the control system of each generation units measure the same electrical frequency in every node of the system. To maintain the nominal frequency of the supply, the control actions of each interface converter must be coordinated through a signal coming from a higher level control system, if a communication system is present, or through a correct setting of the regulation parameters of each converter, if no communication is available.

The electrical system of a micro hybrid plants is composed by three elements: the hybrid power plant, the loads, and the low voltage grid converter. Usually the loads are concentrated in a small area, not bigger than a medium rural village, and the hybrid power plant is located as near as possible to the loads, so the low voltage grid has usually a reduced extension and presents a very simple radial structure. If the interface converter and its regulator working correctly, overvoltage on the low voltage grid can only be generated by faults or environmental phenomena (lightening) on the grid. Due to the reduced extension of the grid, these events are very rare and can be reduced by carefully designing

The considerations about the overvoltages can be extended also for voltage dips (sags). The main cause of voltage dips on grid connected loads is the fast reclosing action of switches in order to eliminate transient faults. In stand alone systems no fast reclosing procedure is necessary due to the low extension of the grid, so, voltage dips are not a problem to solve in

Flickers are fast variations of the voltage supplied to the loads. These voltage oscillations are generated by repetitive load connection and disconnection or by their discontinuous current absorption. Usually, the loads that origins flickers are big industrial loads, such as welders and arching furnaces. Stand alone hybrid power systems do not usually fed loads of this kind, anyway, if that may occur, the component who might prevent the flicker is, once

Depending on its regulator speed and performances, the interface converter can be compensate the fast variations in the current absorbed by the loads and prevent flickers.

High frequency harmonic components in the electric system can affect the grid current and the grid voltage too. Due to the impedances of the system, current harmonic components can produce voltage harmonics, and vice versa. Anyway, the primary causes of voltage and

The harmonic components in grid current are produced by the loads equipped with electronic devices that absorb high frequency current components. These harmonic

**3.2 Requirements on voltage frequency** 

(and, if present, in the current regulator).

**3.3 Overvoltages and voltage dips** 

and installing the grid components.

again, the interface converter and its regulator.

components can be reduced only by acting directly on the loads.

current harmonics are quite different.

this systems.

**3.4 Flickers** 

**3.5 Harmonics** 


Fig. 2. Stand-alone voltage regulation schema

In case of more than one generation unit connected in parallel in an stand-alone configuration (islanded microgrid) a different control algorithm is needed for the interface converters. Several techniques have been studied to manage the parallel operation of standalone inverters and to assure a correct power sharing between the generation units. The more complex control techniques relay on a communication system between generation units. Other techniques can be implemented if no communication system is installed.

The accomplishment, in every node of the islanded microgrid, of the power quality requirements on the voltage value is a problem concerning the coordination between the regulation actions of each interface converter.

#### **3.2 Requirements on voltage frequency**

6 Electrical Generation and Distribution Systems and Power Quality Disturbances

• Depending on the interface converter configuration and on the grid number of phases, the actuator that defines the switching command can be chosen according to different

• The dynamic of the interface converter regulator defines the ability of the converter to maintain a constant voltage on the loads even in case of sudden changes in the load power demand. To prevent the voltage amplitude to move from its nominal value, even in case of sudden changes in the loads, the interface converter regulator should be as fast as possible. On the other hand an excessive speed of the regulator can produce an instability behaviour of the system, for the presence of high frequency harmonic components in the measured voltage and currents, caused both by the loads and by the converter itself. To prevent this instability, that causes the generation of a highly distorted voltage waveform, the interface converter regulator should be slow enough to be immune from high frequency harmonics in the grid, but fast enough to control the voltage variation on the loads. The regulator indicated in the scheme can be different regulator type (P, PID, hysteresis, fuzzy,etc), but its parameters should be set in order to place the cut off frequency of the regulator at least one decade higher that the voltage

In case of more than one generation unit connected in parallel in an stand-alone configuration (islanded microgrid) a different control algorithm is needed for the interface converters. Several techniques have been studied to manage the parallel operation of standalone inverters and to assure a correct power sharing between the generation units. The more complex control techniques relay on a communication system between generation

The accomplishment, in every node of the islanded microgrid, of the power quality requirements on the voltage value is a problem concerning the coordination between the

units. Other techniques can be implemented if no communication system is installed.

techniques: space vector, PWM, hysteresis, ecc…

frequency.

Fig. 2. Stand-alone voltage regulation schema

regulation actions of each interface converter.

As the system voltage waveform is generated by the interface converter, its frequency can be set by acting on the frequency of the reference voltage (and current) in the voltage regulator (and, if present, in the current regulator).

As for the voltage regulation, in stand-alone microgrids several control techniques can be adopted to maintain the frequency of the supply in the range required for the power quality, with or without communication between paralleled generation units. The only difference from voltage regulation is that the control system of each generation units measure the same electrical frequency in every node of the system. To maintain the nominal frequency of the supply, the control actions of each interface converter must be coordinated through a signal coming from a higher level control system, if a communication system is present, or through a correct setting of the regulation parameters of each converter, if no communication is available.

#### **3.3 Overvoltages and voltage dips**

The electrical system of a micro hybrid plants is composed by three elements: the hybrid power plant, the loads, and the low voltage grid converter. Usually the loads are concentrated in a small area, not bigger than a medium rural village, and the hybrid power plant is located as near as possible to the loads, so the low voltage grid has usually a reduced extension and presents a very simple radial structure. If the interface converter and its regulator working correctly, overvoltage on the low voltage grid can only be generated by faults or environmental phenomena (lightening) on the grid. Due to the reduced extension of the grid, these events are very rare and can be reduced by carefully designing and installing the grid components.

The considerations about the overvoltages can be extended also for voltage dips (sags). The main cause of voltage dips on grid connected loads is the fast reclosing action of switches in order to eliminate transient faults. In stand alone systems no fast reclosing procedure is necessary due to the low extension of the grid, so, voltage dips are not a problem to solve in this systems.

#### **3.4 Flickers**

Flickers are fast variations of the voltage supplied to the loads. These voltage oscillations are generated by repetitive load connection and disconnection or by their discontinuous current absorption. Usually, the loads that origins flickers are big industrial loads, such as welders and arching furnaces. Stand alone hybrid power systems do not usually fed loads of this kind, anyway, if that may occur, the component who might prevent the flicker is, once again, the interface converter and its regulator.

Depending on its regulator speed and performances, the interface converter can be compensate the fast variations in the current absorbed by the loads and prevent flickers.

#### **3.5 Harmonics**

High frequency harmonic components in the electric system can affect the grid current and the grid voltage too. Due to the impedances of the system, current harmonic components can produce voltage harmonics, and vice versa. Anyway, the primary causes of voltage and current harmonics are quite different.

The harmonic components in grid current are produced by the loads equipped with electronic devices that absorb high frequency current components. These harmonic components can be reduced only by acting directly on the loads.

Integration of Hybrid Distributed Generation Units in Power Grid 9

interruptions occurred in a year, divided by the total energy required by the loads during

where *N* is the number of supply interruptions during one year, E*l\_NS,i* is the total energy required by the toad and not supplied during the interruption *I* and *El\_tot* is the total energy required by the loads during the year. The LPSP can also be expressed in function of the power demand of the loads during the supply interruption and the duration of the supply

l \_ NS,i l \_ tot

( )

l \_ NS,i l \_ tot

<sup>=</sup> (1)

= ⋅ (2)

N

i 1 LPSP E /E =

SI ,i

LPSP P t dt /E <sup>Δ</sup> <sup>=</sup>

where *Pl\_NS,i* is the load power demand during the supply interruption *I* and ∆*SI,i* is the

The expression (2) of the LPSP is more precise and it allows to take into account also the partial losses of supply. The partial losses of supply are produced by the intentional separation of the loads in case of lack of energy from the renewable power plants, or due to others critical conditions such as a low state of charge of the energy storage system. The separation of a part of the total loads is possible if, during the designing of the stand alone system, loads have been separated at least in two groups: privileged loads (PL) and non privileged loads (NPL). NPL loads are connected to the renewable generation unit through a

The separation of NPL is used to prevent the excessive discharging of the storage system and to extend as far as possible the supply of the PL. During partial LPS, the power not supplied to the loads is equal to the power demand of the non privileged loads. The LPSP

( ) ( ) T P

E

l \_ tot

P t dt P t dt

⋅ + ⋅

(3)

l \_ NS,i NPL \_ NS, j PSI, j i 1 j 1

This separation between global LPSs, that affects all the loads, and partial LPSs, that affects only the NPL, is useful if an economical evaluation of the LPSP must be carried out, e.g. to

A specific value of LPSP can be one of the requirements to be achieved through a proper design of the stand alone system, as a quality requirement of the supply service to the loads. The design value of LPSP can be calculated from the curve of the load demand during the year, the weather data (wind speed, solar radiation, temperature) in the system location, the size of the storage system and of the renewable generators of the hybrid power plant and the power management control strategies implemented in the renewable power plant. From the size of the renewable generators and the weather data of the location it is possible to calculate the power available form the renewable energies, *Pgen(t).*. The power demand curve of the two groups of loads (*PPL(t)* and *PNPL(t))* during the year can be known form enquiry on the territory or, more often, must be assumed by the designer knowing the type

globalLPS partialLPS

N

i 1

SI ,i

N N

perform a tecno-economical optimum sizing of the renewable power plant.

Δ Δ = =

the year as indicated in (1)

interruptions as indicated in (2)

duration of each supply interruption.

can be expressed as indicated in (3).

LPSP

=

controlled switch.

The voltage harmonic components are introduced in the system by the interface converter and are produced mainly by the switching of electronic components. Voltage harmonics can also be presents due to regulator malfunctioning or due to harmonic components at frequency lower than the cut off frequency of the power bus regulator. Generally, the power bus presents a parallel connection of the converters dedicated to the renewable generators, that inject power into the power bus, and of the converter dedicated to the storage system, that exchange power in both directions between the power bus and the storage system. To eliminate the grid voltage harmonics produced by the voltage harmonics on the power bus, it is necessary to guarantee the stability of the voltage level of the power bus. This can be achieved with a proper power flow control algorithm and by adding filters at the output of the other static converters connected to the power bus. Moreover, the dynamic behaviour of the storage system and its converter, can affect the harmonic content of the power bus voltage and, consequently, also of the grid voltage. The storage system converter regulator should maintain the energy balance between loads and sources on the common power bus. Any energy imbalance on the common bus causes fluctuations on the power bus voltage. More fast is the storage converter regulator and the more stable is the voltage on the power bus. A rapid compensation of energy unbalance on the power bus can be achieved imposing to the storage system fast and sharp charging and discharging operations, but these operations can lead to its premature ageing.

If some voltage harmonics still remain on the power bus and are transferred to the grid voltage, a solution to eliminate these can be the reducing of the cut off frequency of the inverter regulator, in order to make it able to compensate this lower harmonic components, too. Anyway, the cut off frequency of the interface inverter regulator should not be less at least one decade of the grid frequency.

#### **3.6 Supply interruptions**

In stand alone systems, the main issue regarding electric Power Quality is to guarantee the supply continuity. The main causes of power supply interruption in stand alone systems are due to fault in the renewable power plants. The electric grids that connect the renewable power plant to the loads is usually very short and simple so a fault event on the grid is very rare.

In stand alone systems, the supply interruptions caused by a lack of energy of the renewable power plants can be analysed using the concept of Loss of Power Supply or Loss of Load (LPS or LOL) and Loss of Power Supply Probability or Loss of Load Probability (LPSP or LOLP). The LPS and LPSP concepts are more or less equivalent to the LOL and the LOLP concepts, so only the LPS and LPSP indexes will be considered.

The LPS is the total energy required by the load that is not supplied during an interruption. The LPSP index depends on the duration of the interruptions and on the load power demand during interruptions. If a supply interruption occurs when no power is requested by the loads, it has no effect on the LPSP value.

The LPSP is a global index that defines the hybrid system availability during a particular period of time, usually one year; it takes into account the sum of the LPS and the energy demand during the year. As the renewable sources have a seasonally behaviour, the one year period is a good choice to evaluate the performances of hybrid systems.

The LPSP index expresses the probability to have a supply interruption on the stand alone loads, due to a lack of power of the renewable power plant. In an existing system, the LPSP can be defined as the sum of the energy not supplied to the loads during the supply

The voltage harmonic components are introduced in the system by the interface converter and are produced mainly by the switching of electronic components. Voltage harmonics can also be presents due to regulator malfunctioning or due to harmonic components at frequency lower than the cut off frequency of the power bus regulator. Generally, the power bus presents a parallel connection of the converters dedicated to the renewable generators, that inject power into the power bus, and of the converter dedicated to the storage system, that exchange power in both directions between the power bus and the storage system. To eliminate the grid voltage harmonics produced by the voltage harmonics on the power bus, it is necessary to guarantee the stability of the voltage level of the power bus. This can be achieved with a proper power flow control algorithm and by adding filters at the output of the other static converters connected to the power bus. Moreover, the dynamic behaviour of the storage system and its converter, can affect the harmonic content of the power bus voltage and, consequently, also of the grid voltage. The storage system converter regulator should maintain the energy balance between loads and sources on the common power bus. Any energy imbalance on the common bus causes fluctuations on the power bus voltage. More fast is the storage converter regulator and the more stable is the voltage on the power bus. A rapid compensation of energy unbalance on the power bus can be achieved imposing to the storage system fast and sharp charging and discharging operations, but these

If some voltage harmonics still remain on the power bus and are transferred to the grid voltage, a solution to eliminate these can be the reducing of the cut off frequency of the inverter regulator, in order to make it able to compensate this lower harmonic components, too. Anyway, the cut off frequency of the interface inverter regulator should not be less at

In stand alone systems, the main issue regarding electric Power Quality is to guarantee the supply continuity. The main causes of power supply interruption in stand alone systems are due to fault in the renewable power plants. The electric grids that connect the renewable power plant to the loads is usually very short and simple so a fault event on the grid is very

In stand alone systems, the supply interruptions caused by a lack of energy of the renewable power plants can be analysed using the concept of Loss of Power Supply or Loss of Load (LPS or LOL) and Loss of Power Supply Probability or Loss of Load Probability (LPSP or LOLP). The LPS and LPSP concepts are more or less equivalent to the LOL and the LOLP

The LPS is the total energy required by the load that is not supplied during an interruption. The LPSP index depends on the duration of the interruptions and on the load power demand during interruptions. If a supply interruption occurs when no power is requested

The LPSP is a global index that defines the hybrid system availability during a particular period of time, usually one year; it takes into account the sum of the LPS and the energy demand during the year. As the renewable sources have a seasonally behaviour, the one

The LPSP index expresses the probability to have a supply interruption on the stand alone loads, due to a lack of power of the renewable power plant. In an existing system, the LPSP can be defined as the sum of the energy not supplied to the loads during the supply

year period is a good choice to evaluate the performances of hybrid systems.

concepts, so only the LPS and LPSP indexes will be considered.

by the loads, it has no effect on the LPSP value.

operations can lead to its premature ageing.

least one decade of the grid frequency.

**3.6 Supply interruptions** 

rare.

interruptions occurred in a year, divided by the total energy required by the loads during the year as indicated in (1)

$$\text{LPSP} = \sum\_{\text{l}=1}^{N} \mathbb{E}\_{\text{l\\_NS}, \text{l}} \mid \mathbb{E}\_{\text{l\\_tot}} \tag{1}$$

where *N* is the number of supply interruptions during one year, E*l\_NS,i* is the total energy required by the toad and not supplied during the interruption *I* and *El\_tot* is the total energy required by the loads during the year. The LPSP can also be expressed in function of the power demand of the loads during the supply interruption and the duration of the supply interruptions as indicated in (2)

$$\text{LPSP} = \left(\sum\_{l=1}^{N} \int\_{\Delta\_{\text{SI},i}} \mathbf{P}\_{l\\_{\text{NS},l}} \left(\mathbf{t}\right) \cdot \mathbf{dt}\right) / \left|\mathbf{E}\_{l\\_{\text{tot}}}\right.\tag{2}$$

where *Pl\_NS,i* is the load power demand during the supply interruption *I* and ∆*SI,i* is the duration of each supply interruption.

The expression (2) of the LPSP is more precise and it allows to take into account also the partial losses of supply. The partial losses of supply are produced by the intentional separation of the loads in case of lack of energy from the renewable power plants, or due to others critical conditions such as a low state of charge of the energy storage system. The separation of a part of the total loads is possible if, during the designing of the stand alone system, loads have been separated at least in two groups: privileged loads (PL) and non privileged loads (NPL). NPL loads are connected to the renewable generation unit through a controlled switch.

The separation of NPL is used to prevent the excessive discharging of the storage system and to extend as far as possible the supply of the PL. During partial LPS, the power not supplied to the loads is equal to the power demand of the non privileged loads. The LPSP can be expressed as indicated in (3).

$$\overbrace{\text{LPSP}}^{\text{globalLPS}} = \overbrace{\text{LPSP}\_{\text{l}\sim\text{N}\_{\text{l}},\text{l}}^{\text{globalLPS}} \left(\mathbf{t}\right) \cdot \mathbf{dt}}^{\text{parallelLPS}} + \overbrace{\sum\limits\_{\text{l}=1}^{\text{partall PSF}} P\_{\text{NPL}\_{\text{l}},\text{NS}\_{\text{l}}\mid\text{l}} \left(\mathbf{t}\right) \cdot \mathbf{dt}}^{\text{parallelLPS}}$$

This separation between global LPSs, that affects all the loads, and partial LPSs, that affects only the NPL, is useful if an economical evaluation of the LPSP must be carried out, e.g. to perform a tecno-economical optimum sizing of the renewable power plant.

A specific value of LPSP can be one of the requirements to be achieved through a proper design of the stand alone system, as a quality requirement of the supply service to the loads. The design value of LPSP can be calculated from the curve of the load demand during the year, the weather data (wind speed, solar radiation, temperature) in the system location, the size of the storage system and of the renewable generators of the hybrid power plant and the power management control strategies implemented in the renewable power plant.

From the size of the renewable generators and the weather data of the location it is possible to calculate the power available form the renewable energies, *Pgen(t).*. The power demand curve of the two groups of loads (*PPL(t)* and *PNPL(t))* during the year can be known form enquiry on the territory or, more often, must be assumed by the designer knowing the type

Integration of Hybrid Distributed Generation Units in Power Grid 11

Analysing the (6), it can be seen that the LPSP, in stand alone systems supplied by a generically hybrid renewable power plants with a storage systems, depends mainly on two design aspects: sizing of the renewable generators and of the storage system and to the

A compromise between the power quality of the electrical supply and the costs of the system should be reached in the designing of renewable power plants in particular the use of a fuel generation unit to supply the load in case of a lack of energy from the renewable energy sources and the storage system can decrease the LPSP of the system up to zero.

As highlighted previously, the Power Quality in stand alone system supplied by a renewable hybrid generation unit depends mainly on the design of the generation units. Three main aspects of the design of renewable hybrid power plants for stand alone operation will be analysed, trying to point which are the possible choices that leads to a

The sizing of renewable generation units is the aspect that mostly affects the continuity of supply in stand alone systems. As it has been highlighted previously, the LPSP of a stand alone system depends on the energy available from the renewable generators and on the energy stored in the battery bank. This two variables are closely related to the sizing both of the renewable generators and of the storage systems, and depends on the control strategy

The optimal sizing of renewable hybrid power plants is a quite complex problem, because it

In this section, some considerations about the optimum sizing methods are presented, in order to underline the main constraints affecting the sizing of the hybrid power plant and to

To design a hybrid renewable power plant equipped with storage system, the typology and

The choice of the renewable generators type (photovoltaic, wind turbine, hydroelectric, geothermal,…) depends on the renewable sources availability in the location where the system will be installed. The most widespread and easily exploitable renewable source is solar radiation, followed by the wind. Many studies shows that wind and solar radiation distributions have often a complementary behaviour, thus making convenient in many cases to combine wind and solar renewable generators in the hybrid power plants. In the following, this two main renewable sources will be considered, but the analysis can be

The choice of the storage system should take into account, first of all, that storage systems can be classified into two groups: energy storage systems (batteries, hybrid compressed air systems,…) and power storage systems (super capacitors, flywheels,…). In stand alone systems the first need is to store exceeding energy produced by the renewable sources in order to deliver it to the loads when necessary. For this reason, the more suitable storage

highlight the drawbacks of a sizing choice in the continuity of the loads supply.

the size of the renewable generators and of the storage system should be fixed.

control strategies adopted for the energy management.

**4. Design aspects of HGDU in stand alone mode** 

used to manage the power flux in the renewable power plant also.

concerns the optimisations of several variables.

**4.1.1 Renewable generators and storage system** 

easily extended also to other renewable generators.

higher power quality of supply.

**4.1 Sizing** 

and number of loads that will be connected to the system. To define the working operations of the battery bank, its rated capacity, *Cnbat*, and its minimum admitted State Of Charge, *SOCm,* should be defined. The value of *SOCm* is usually indicated by the battery manufacturers, as the minimum rate of discharge of each discharging cycle that guarantees the required lifetime of the battery bank. In normal operation the battery maintains the energy balance between the sources and the loads, until its discharging rate doesn't exceed the minimum thresholds. When SOCm is reached, the loads are disconnected and the renewable energy is used only to charge the storage system.

To evaluate the design LPSP, it is possible to divide the reference period T (one year) in time steps Δt usually equivalent to one hour: If the energy demand from the loads is higher than the sum of the energy available from the sources and the energy still cumulated in the storage system, there is a of loss of supply and the LPS(t) can be calculated as indicate in (4).

$$\begin{array}{llll} \text{if} & \text{Ryn} & \text{found, from } \text{lau} \\ \text{if} & \left( \text{P}\_{\text{fl}} (\text{t}) + \text{P}\_{\text{NL}} (\text{t}) \right) \cdot \text{At} > \text{P}\_{\text{gn}} (\text{t}) \cdot \text{At} & + \left( \text{SCC(t) - \text{SCC}\_{\text{m}}} \right) \cdot \text{C}\_{\text{flat}} / 100 \\\\ \text{T} \cdot \text{LIS(t)} = \left( \text{P}\_{\text{fl}} (\text{t}) + \text{P}\_{\text{NL}} (\text{t}) \right) \cdot \text{At} - \text{P}\_{\text{gn}} (\text{t}) \cdot \text{At} - \left( \text{SCC(t) - \text{SCC}\_{\text{m}}} \right) \cdot \text{C}\_{\text{flat}} / 100 \\\\ \text{if} & \left( \text{P}\_{\text{fl}} (\text{t}) + \text{P}\_{\text{NL}} (\text{t}) \right) \cdot \text{At} \leq \text{P}\_{\text{gn}} (\text{t}) \cdot \text{At} + \left( \text{SCC(t) - \text{SCC}\_{\text{m}}} \right) \cdot \text{C}\_{\text{flat}} / 100 \\\\ \end{array} \text{ for } \text{ 100\% > \text{SCC(t)} > \text{SCC}\_{\text{m}} \text{ (4)} \\\\ \text{'I} & \left( \text{00\% > \text{SCC}\_{\text{m}} \text{ (7)} \right) \cdot \text{At} - \text{R} \cdot \text{I} \cdot \text{C}$$

When the battery SOC (t) reaches the threshold SOCm the loads are disconnected, the battery is charged with the energy coming from the renewable sources and the loads are not supplied. The global supply interruption goes on until the battery is recharged at a certain level of charge, SOCreload situated between the fully charge condition and the minimum threshold, SOCm.

$$\rm LPS(t) = \left(P\_{\rm PL}\left(t\right) + P\_{\rm NPL}\left(t\right)\right) \cdot \Delta t \quad \text{for} \quad \rm SOC\_m < SOC(t) < SOC\_{nload} \tag{5}$$

More refined and complex strategies can be adopted to reduce as far as possible the LPSP on privileged loads, e.g. it is possible to disconnect the NPL when the battery SOC(t) exceed an imposed threshold, SOCNPL, higher than SOCm. In such way , the remaining energy stored in the battery is used to supply only the PL if the renewable energy is not enough and the design equations (4) became the following.

( ) () () () ( ) ( ) () () () ( ) ( ) () () () ( ) PL NPL gen NPL nbat PL NPL gen NPL nbat NPL PL NPL gen NPL nbat if P t P t t P t t SOC(t) SOC C /100 LPS(t) P t P t t P t t SOC(t) SOC C /100 for 100% SOC(t) SOC if P t P t t P t t SOC(t) SOC C /100 LPS(t) 0 + ⋅Δ > ⋅Δ + − ⋅ = + ⋅Δ − ⋅Δ − − ⋅ > > + ⋅Δ ≤ ⋅Δ + − ⋅ = () () ( ) () () () ( ) () () ( ) PL gen m nbat NPL PL gen m nbat NPL m PL gen m nbat NPL if P t t P t t SOC(t) SOC C /100 LPS(t) P t t P t t P t t SOC(t) SOC C /100 for SOC SOC(t) SOC if P t t P t t SOC(t) SOC C /100 LPS(t) P (t) ⋅Δ > ⋅Δ + − ⋅ = ⋅Δ + ⋅Δ − ⋅Δ − − ⋅ > > ⋅Δ ≤ ⋅Δ + − ⋅ = ( ) () () PL NPL Δ⋅+= SOCfor,ttPtP)t(LPS <sup>m</sup> << SOC)t(SOC reload (6)

Analysing the (6), it can be seen that the LPSP, in stand alone systems supplied by a generically hybrid renewable power plants with a storage systems, depends mainly on two design aspects: sizing of the renewable generators and of the storage system and to the control strategies adopted for the energy management.

A compromise between the power quality of the electrical supply and the costs of the system should be reached in the designing of renewable power plants in particular the use of a fuel generation unit to supply the load in case of a lack of energy from the renewable energy sources and the storage system can decrease the LPSP of the system up to zero.
