2. The TCCC/VRFB compensator

The TCCC/VRFB compensator is composed of the vanadium redox flow battery and the thyristor converter with commutated capacitors; both of them are explained below.

## 2.1. Vanadium redox flow battery

increase when the penetration level is high, compromising the operation security and reliability of MGs [2, 3]. The traditional solution is to increase the reserve generation of conventional power plants, what causes a noneconomic dispatch. Other solutions are provided by the manufacturers of wind turbines, employing both the speed and the pitch control systems as methods of supplying power reserve for frequency support and power generation smoothing on variable-speed wind turbines [4–6]. However, these solutions depend on the operating point of the wind turbine and are less efficient than that provided by an energy storage system (ESS). The output power of wind generators is reduced in order to gain controllability, but sacrificing a part of the free wind energy and consequently increasing the more expensive

ESS can be employed in order to improve the frequency stability of MGs with high wind power penetration. In this sense, several previous works focus on the problems caused by wind generation and how an ESS can effectively solve them [7–11]. However, these solutions are limited according to the amount of energy stored by the used ESS. Nowadays, a promising low-cost, large stationary advanced ESS for these applications is the vanadium redox flow battery (VRFB),

The incorporation of the VRFB into MGs requires a power conditioning system (PCS) and appropriate control strategy to manage the power flow between the VRFB and the utility system [12, 13]. Many solutions using PCS for long-term ESS have been proposed and listed in Ref. [15], a bidirectional single-phase inverter with a DC/AC converter connects a battery energy storage system (BESS) to the AC grid. Additionally, an integrated nonlinear control strategy is proposed both to control converters and to manage the power flow direction between the BESS and a stiff grid. In Ref. [16], a DC-DC converter system is presented based on an input-series/output-parallel dual active bridge structure, in a full modular design. The proposed converter is dedicated to interface a DC voltage network with a battery-based energy storage device. In Ref. [17], a non-isolated online uninterruptible power supply (UPS) is presented. The proposed system consists of bridgeless boost rectifier, battery charger/discharger, and an inverter. For the inverter, a new control method is developed, which regulates the output voltage for both linear and nonlinear loads. In Ref. [18], a grid-connected hybrid PV-wind-battery system with a bidirectional DC/DC chopper is presented. The control strategy manages the power flow from different sources, provides generation reserve to the grid, charges the battery, and satisfies the load demand. The work presented in Ref. [19] proposes a PCS for zinc-bromine (Zn-Br) flow battery-based energy storage system. The PCS consists of four DC-DC converters, one DC-AC inverter, and a battery management system. The battery control strategy including the PCS and the stripping operation is described to perform the

The proposals mentioned above offer practical solutions to connect the VRFB to the AC network. However, much less has been done particularly on the utilization of the VRFB in emerging grid-interactive AC MGs, although major benefits apply [20]. Moreover, none of the aforementioned work has discussed strategies to stabilize the active power flow of wind farms employing long-term ESS and to contribute to the frequency control when faults occur in the

output power of conventional generators to cover the same power demand.

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which presents high-speed response and overload capacity characteristics [12–14].

charging and the discharging of the flow battery in steady state.

electrical system.

The VRFB is an electrochemical ESS which consists of two electrolytes stored in two separate tanks. The electrolytes are formed by sulfuric acid with active vanadium species in different oxidation states: V4/V5 redox couple (catholyte) and V2/V3 redox couple (anolyte). These liquids circulate through the cell stack by pumps. The stack consists of several cells, each of which contains two half-cells that are separated by a proton exchange membrane (PEM). The electrochemical reactions take place in the half-cells, and then inert carbon felt polymer composite electrodes are employed in order to charge or discharge the battery through an external DC current. The general scheme of the VRFB is represented in Figure 1(a).

The half-cell of the VRFB performs two simultaneous chemical reactions; these reactions occur on both sides of the membrane as shown in Figure 1(b). During the charge process, the positive electrolyte (catholyte) delivers electrons to the negative electrolyte (anolyte) through

Figure 1. Vanadium redox flow battery: (a) general scheme and (b) chemical reactions.

the external circuit. Therefore, the oxidation occurs in the catholyte, and the reduction occurs in the anolyte. During the discharge process, the flow of electrons is reversed; the oxidation takes place in the anolyte and the reduction in the catholyte.

The battery produces a nominal cell potential of approximately 1.25 V. By connecting many cells into a "stack," the terminal voltage is obtained. The current density through the cell and the stack voltage establish the power available, while the supply of charged electrolyte to the stack establishes the energy available. So, the rated power and the energy stored can be upgraded by increasing or decreasing the stack and the electrolyte tank, respectively [22–24].

#### 2.2. Model of the VRFB

The VRFB model is composed by the stack model and the mechanical model, as shown in Figure 2. The complete model of the VRFB was developed in Ref. [22]. The stack model calculates the state of charge (SOC) of the electrolyte and the terminal stack voltage (Ustack). These values depend on the initial SOC and the stack current (Istack). On the other hand, the mechanical model calculates the hydraulic losses caused by the electrolyte flow rate (Q). This flow rate is produced by two DC machines that drive the pumps. Therefore, the stack current is calculated from the difference between the terminal VRFB current (IVRFB) and the pump current consumption (Ipump).

#### 2.2.1. VRFB stack model

The proposed electrochemical model of the VRFB calculates two gains in order to obtain the stack voltage Ustack and the effective current Ief. These parameters are the voltage and current gains (Kv, Kc), and they are obtained by solving (Eqs. (1) and (2)). Note that Kc and Kv gains depend on the stack current, the experimental efficiency curves (Figure 3) [23, 24], and the operating condition (charge or discharge):

$$K\_{\rm c,charge} = \eta\_c K\_{\rm c,discharge} = \eta\_c \frac{\left(1 + \eta\_v\right)}{\left(1 + \eta\_c\right)}\tag{1}$$

$$K\_{v,charge} = \frac{K\_{v,discharge}}{\eta\_v} = \frac{\left(1 + \eta\_c\right)}{\left(1 + \eta\_e\right)}\tag{2}$$

Figure 2. Mathematic model of the VRFB.

the external circuit. Therefore, the oxidation occurs in the catholyte, and the reduction occurs in the anolyte. During the discharge process, the flow of electrons is reversed; the oxidation

The battery produces a nominal cell potential of approximately 1.25 V. By connecting many cells into a "stack," the terminal voltage is obtained. The current density through the cell and the stack voltage establish the power available, while the supply of charged electrolyte to the stack establishes the energy available. So, the rated power and the energy stored can be upgraded by increasing or decreasing the stack and the electrolyte tank, respectively

takes place in the anolyte and the reduction in the catholyte.

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Figure 1. Vanadium redox flow battery: (a) general scheme and (b) chemical reactions.

[22–24].

Figure 3. Voltage, coulombic, and energy efficiencies of the VRFB stack.

The effective stack current and the terminal stack voltage are obtained with (Eqs. (3) and (4)):

$$I\_{\mathfrak{e}f} = \mathcal{K}\_{\mathfrak{e}} I\_{\text{stack}} \tag{3}$$

$$
\mathcal{U}\_{stack} = \mathcal{K}\_v \mathcal{U}\_{eq} \tag{4}
$$

The equilibrium voltage (Ueq) can be calculated employing the Nernst equation (Eq. (5)) [25–28]:

$$\mathcal{U}\_{eq} = N\_{cell} \left[ \mathcal{U}\_0 + \frac{2RT}{F} \ln \left( \frac{\text{SOC}}{1 - \text{SOC}} \right) \right] \tag{5}$$

where U<sup>0</sup> is the internal cell voltage when the SOC is 0.5 pu, Ncell is the number of cells in series connection, F is the Faraday constant, T is the absolute temperature, and R is the gas constant. The value of SOC depends on the effective stack power, the storage capacity (Emax), and the initial conditions (SOC0) (Eq. (6)) [29]:

$$\text{SOC} = \text{SOC}\_0 + \int \frac{-\mathcal{U}\_{eq} I\_{cf}}{E\_{\text{max}}} dt \tag{6}$$

#### 2.2.2. Mechanical model

The mechanical model of the VRFB system is developed in Ref. [30]. This model consists of an analytical part and a numerical part. The analytical part models the pipes, bends, valves, tanks, and pumps. The numerical part describes the more complex stack hydraulic circuit. In addition to the mechanical model, in this work it is suggested to incorporate the equivalent DC current consumption of the pumps (Ipump). Therefore, the value of Ipump represents the mechanical losses of the VRFB system (Eq. (7)):

$$I\_{pump} = \frac{P\_{2pumps}}{\mathcal{U}\_{stack}}\tag{7}$$

#### 2.3. Thyristor converter with commutated capacitors

A DC/AC bidirectional converter is required in order to connect the VRFB to the MG. In this regard, a 12-pulse thyristor converter with commutated capacitors on the AC side (TCCC) is proposed for controlling the active power flow of the VRFB [21]. The TCCC operates as a current source. Therefore, the polarization voltage of the VRFB stack determines the voltage at the DC bus (Vconv). As a result, the connection between the VRFB and the TCCC does not require a DC/DC chopper. Figure 4 shows the proposed PCS unit for the VRFB system.

The most important aspects of the proposed PCS are:


The TCCC contains tuned filters to smooth the AC current harmonics of order 12n � 1. Additionally, the reactive power required by the thyristor converter is provided by these filters. From Figures 2 and 4, the following equalities are obtained:

Figure 4. The proposed PCS unit (TCCC).

The effective stack current and the terminal stack voltage are obtained with (Eqs. (3) and (4)):

The equilibrium voltage (Ueq) can be calculated employing the Nernst equation (Eq. (5)) [25–28]:

2RT

where U<sup>0</sup> is the internal cell voltage when the SOC is 0.5 pu, Ncell is the number of cells in series connection, F is the Faraday constant, T is the absolute temperature, and R is the gas constant. The value of SOC depends on the effective stack power, the storage capacity (Emax), and the

The mechanical model of the VRFB system is developed in Ref. [30]. This model consists of an analytical part and a numerical part. The analytical part models the pipes, bends, valves, tanks, and pumps. The numerical part describes the more complex stack hydraulic circuit. In addition to the mechanical model, in this work it is suggested to incorporate the equivalent DC

<sup>F</sup> ln SOC 1 � SOC

> ð �UeqIef Emax

� � � �

Ueq ¼ Ncell U<sup>0</sup> þ

Figure 3. Voltage, coulombic, and energy efficiencies of the VRFB stack.

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SOC ¼ SOC<sup>0</sup> þ

initial conditions (SOC0) (Eq. (6)) [29]:

2.2.2. Mechanical model

Ief ¼ KcIstack (3)

Ustack ¼ KvUeq (4)

dt (6)

(5)

$$I\_{VRFB} = I\_{stack} + I\_{pump} = I\_{conv} \tag{8}$$

$$V\_{conv} = \mathcal{U}\_{stack}\tag{9}$$

Eq. (8) shows that the VRFB terminal current is imposed by the converter current, whereas (Eq. (9)) demonstrates that the TCCC terminal voltage is the polarization voltage of the VRFB. The calculation of the TCCC current at the DC bus is obtained from Ref. [31]:

$$V\_{conv} = b \frac{3}{\pi} \sqrt{2} V\_{i,RMS} \cos \alpha - \frac{3}{\pi} (\mathbf{x}\_t - \mathbf{x}\_c) I\_{conv} \tag{10}$$

where xt and xc are the transformer and capacitor (Ccon) reactance, respectively; Vi,RMS is the RMS voltage of the TCCC at the AC bus; α is the firing angle of the converter; and b is a sign factor which determines the operation mode of the converter: +1 for rectifier operation mode (0 < α < π/2) and �1 for inverter operation mode (π/2 < α < π). The DC current at VRFB terminals is obtained solving (Eqs. (8))–(10)):

$$I\_{VRFB} = \frac{b}{(\mathbf{x}\_t - \mathbf{x}\_c)} \left(\sqrt{2}V\_{i,RMS}\cos\left|\mathbf{x} - \frac{\pi}{3}\mathcal{U}\_{stack}\right.\tag{11}$$

Considering constant values of Vi,RMS and Ustack, IVRFB decreases when α increases, while in rectifier operation mode, and IVRFB increases when α increases during inverter operation mode.

#### 3. Control system of the TCCC

In this section a new multilevel control system has been developed for the TCCC unit; this control system has its own control objectives for each hierarchical control level [9]. The proposed multilevel control system is shown in Figure 5, which is composed of three parts: a lowlevel control system, a mid-level control system, and a high-level control system.

The low-level and mid-level control systems are fully developed in Ref. [21], whereas the highlevel control system (left side of Figure 5) is presented below which represents the main contribution of this work.

Figure 5. New control system of the TCCC.

#### 3.1. High-level control system

IVRFB ¼ Istack þ Ipump ¼ Iconv (8)

<sup>3</sup> Ustack

Eq. (8) shows that the VRFB terminal current is imposed by the converter current, whereas (Eq. (9)) demonstrates that the TCCC terminal voltage is the polarization voltage of the VRFB.

<sup>p</sup> Vi,RMS cos <sup>α</sup> � <sup>3</sup>

where xt and xc are the transformer and capacitor (Ccon) reactance, respectively; Vi,RMS is the RMS voltage of the TCCC at the AC bus; α is the firing angle of the converter; and b is a sign factor which determines the operation mode of the converter: +1 for rectifier operation mode (0 < α < π/2) and �1 for inverter operation mode (π/2 < α < π). The DC current at VRFB terminals

> ffiffiffi 2

Considering constant values of Vi,RMS and Ustack, IVRFB decreases when α increases, while in rectifier operation mode, and IVRFB increases when α increases during inverter operation mode.

In this section a new multilevel control system has been developed for the TCCC unit; this control system has its own control objectives for each hierarchical control level [9]. The proposed multilevel control system is shown in Figure 5, which is composed of three parts: a low-

The low-level and mid-level control systems are fully developed in Ref. [21], whereas the highlevel control system (left side of Figure 5) is presented below which represents the main

level control system, a mid-level control system, and a high-level control system.

<sup>p</sup> Vi,RMS cos <sup>∝</sup> � <sup>π</sup>

� �

The calculation of the TCCC current at the DC bus is obtained from Ref. [31]:

π ffiffiffi 2

Vconv <sup>¼</sup> <sup>b</sup> <sup>3</sup>

IVRFB <sup>¼</sup> <sup>b</sup>

ð Þ xt � xc

is obtained solving (Eqs. (8))–(10)):

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3. Control system of the TCCC

contribution of this work.

Figure 5. New control system of the TCCC.

Vconv ¼ Ustack (9)

<sup>π</sup> ð Þ xt � xc Iconv (10)

(11)

The high-level control system is responsible for determining the active power exchange between the TCCC and the utility system. The goal of the control algorithm is to perform the load leveling of the wind generation and to provide the generation reserve required for frequency regulation. This controller is composed of three parallel control loops: the loadleveling controller, the PFC regulator, and the SFC regulator. The aim of the load-leveling controller is to eliminate the turbulent component of the wind power (Pw). So, a first-order filter with a cutoff frequency at one cycle/hour is employed in order to obtain the diurnal and synoptic component of the wind power (Pwds) [32, 33]. The difference between Pwds and Pw is the compensation power PLL that must be supplied or absorbed by the TCCC/VRFB unit. The load-leveling controller is always active, thus allowing for improvement in the power quality of the electric utility grid with wind generators.

On the contrary, the PFC and SFC regulators are only active when significant frequency deviations arise, contributing to recover the rated system frequency and thus improving the grid security. These controllers are in charge of minimizing the magnitude and duration of system disturbances by damping power oscillations. The purpose of this is to keep the system frequency between minimum and maximum levels during the transient dynamics. This is accomplished by measuring the frequency error Δf, which is proportional to the rate of change of the generator angle dδ/dt involved and consequently directly represents the power oscillation of the system. The value of Δf enters to proportional and proportional-integral (PI) control schemes, in order to calculate the generation reserve required to perform the PFC and SFC (PPFC, PSFC), respectively. In the PFC regulator, a dead-band block is incorporated within the control loop with the purpose of managing the participation of the TCCC/VRFB in the frequency control of the utility system. The low-pass filters are employed to eliminate the noise signal. Finally, the three components are added together to obtain the converter reference power Pconv,ref.

#### 3.2. Mid-level and low-level control system

The mid-level control and the low-level control systems operate the TCCC as a controlled current source. The control algorithm is shown in Figure 5. The mid-level control system calculates the DC reference current (Iconv,ref) by comparing the reference power Pconv,ref with the converter power (Pconv). The nonlinearity of the converter at low current is eliminated by a dead zone block. In the low-level control system, the reference firing angle (αord) for the thyristors is calculated from the reference current Iconv,ref and the converter current (Iconv). Then, the value of αord enters to a 12-pulse generator in order to produce the firing pulses for the TCCC [31, 34].
