Design and Implementation of the Battery Energy Storage System in DC Micro-Grid Systems

Abstract

The design and implementation of the battery energy storage system in DC micro-grid systems is demonstrated in this paper. The battery energy storage system (BESS) is an important part of a DC micro-grid because renewable energy generation sources are fluctuating. The BESS can provide energy while the renewable energy is absent in the DC micro-grid. The circuit topology of the proposed BESS will be introduced. The design of the voltage controller and the current controller for the battery charger/discharger are also illustrated. Finally, experimental results are provided to validate the performance of the BESS.

1. Introduction

Reducing carbon emissions and mitigating the global warming are the main advantages of using renewable energy [1,2,3]. However, renewable energy fluctuates with its environmental parameters. Therefore, an AC microgrid [4,5,6] and a DC microgrid [7,8,9] are implemented to treat this issue. Renewable energy in a microgrid can be solar or wind power. Extra electricity can be stored in an energy storage system [10,11,12,13]. If the renewable energy sources are absent, the micro-grid will be stabilized via the energy storage system. In this paper, the battery energy storage system (BESS) is designed and implemented in a DC micro-grid.

Takagi-Sugeno Fuzzy [14], proposed by Takagi and Sugeno, is a control system based on fuzzy-logic. In T-S Fuzzy systems, a nonlinear system can be resembled by linear sub-systems. The controllers of the T-S Fuzzy system are designed on the concept of parallel-distributed compensation (PDC) [15]. Lyapunov theorem [16] can be applied to prove the stability of a T-S Fuzzy control system. The stability specifications are displayed in the form of linear matrix inequality (LMI). The T-S Fuzzy control applied to the DC-DC converter can be classified as buck [17] and boost [18] converters. Nevertheless, the non-ideal characteristics of the circuit elements are not treated in the literature. The non-ideal circuit elements are treated in this research to increase control precision and performance.

A battery energy storage system in DC micro-grid systems is designed and implemented. A BESS consists of the battery and the charger/discharger. A buck converter, combined with a boost converter, is implemented as the charger/discharger. If the battery needs to be charged, the buck converter is operated as a charger. Furthermore, the boost converter is operated as a discharger to release electric energy. In this paper, the BESS in the DC micro-grid system is first illustrated. Next, the circuit topology, considering non-ideal circuit models, is demonstrated. After that, the state equations of the BESS are obtained through the state-space average scheme. Then, the voltage and current controllers of the BESS are designed via T-S Fuzzy controls. The system stability of the BESS is proved and verified. The control performances of the voltage controller and current controller are validated by experimental results.

2. System Configuration

The system configuration of the DC micro-grid is shown in Figure 1. The developed battery energy storage system consists of the battery and the bidirectional DC/DC converter. Figure 2 shows the circuit configuration of the battery charger/discharger. The buck converter and boost converter is combined to form the bidirectional converter. In charging mode, the buck converter is operated with (M₁, D₂), while in discharging mode, the boost converter is operated with (M₂, D₁). The non-ideal circuit elements are included in the circuit configuration. The non-ideal elements include the equivalent series resistance (ESR) of the power switch ($R_M$), the ESR of the inductor ($R_L$), the ESR of the capacitor ($R_{C_B}$, $R_{C_{DC}}$), and the forward conduction voltage of the diode ($V_D$). Inductance current $i_L$, DC-link voltage $V_{DC}$ and battery voltage $V_B$ are used to determine the duty ratio of the power switches. The feedback signals are sampled by the analog-to-digital converter (ADC). The control of the bidirectional DC/DC converter is digitally realized via the microcontroller Renesas RX62T.

3. Operation Modes and State Equations

3.1. Charging Mode

At charging mode, the power switch M₂ is kept off. The duty ratio of the power switch M₁ is controlled to regulate the inductance current. When M₁ is turned on, the inductance will be magnetized and the inductance current rises. When M₁ is turned off, the diode D₂ will be forced to turn on. Then the inductance is de-magnetized and the inductance current will fall.

The state space average scheme can be used to find the state equations of charging mode:

$$\left[\begin{array}{c}{\dot{i}}_L\\ {\dot{V}}_{C_B}\end{array}\right]=\left[\begin{array}{cc}-\frac{1}{L}\left(R_L+\frac{R{R}_{C_B}}{R+R_{C_B}}\right)& -\frac{R}{L(R+R_{C_B})}\\ \frac{R}{C_B(R+R_{C_B})}& -\frac{1}{C_B(R+R_{C_B})}\end{array}\right]\left[\begin{array}{c}{i}_L\\ V_{C_B}\end{array}\right]+\left[\begin{array}{c}\frac{1}{L}\left(V_{DC}+V_D-i_L{R}_M\right)\\ 0\end{array}\right]D+\left[\begin{array}{c}-\frac{V_D}{L}\\ 0\end{array}\right]$$

(1)

where R is the load resistance and D is the duty ratio of M₁. The output is the inductance current:

$$y=i_L=\left[\begin{array}{cc}1& 0\end{array}\right]\left[\begin{array}{c}{i}_L\\ V_{C_B}\end{array}\right]$$

(2)

3.2. Discharging Mode

At discharging mode, the power switch M₁ is kept off. The duty ratio of the power switch M₂ is controlled to regulate the output voltage. When M₂ is turned on, the inductance current rises. When M₂ is turned off, the diode D₁ will be forced to turn on. Then, the inductance current falls.

The state space average scheme is also used to find the state equations of discharging mode:

$$\begin{array}{l}\left[\begin{array}{c}{\dot{i}}_L\\ {\dot{V}}_{C_{DC}}\end{array}\right]=\left[\begin{array}{cc}-\frac{1}{L}\left(R_L+\frac{R{R}_{C_{DC}}}{R+R_{C_{DC}}}\right)& -\frac{R}{L(R+R_{C_{DC}})}\\ \frac{R}{C_{DC}(R+R_{C_{DC}})}& -\frac{1}{C_{DC}(R+R_{C_{DC}})}\end{array}\right]\left[\begin{array}{c}{i}_L\\ V_{C_{DC}}\end{array}\right]\\ +\left[\begin{array}{c}\frac{1}{L}\left[V_D+\left(\frac{R{R}_{C_{DC}}}{R+R_{C_{DC}}}-R_M\right)i_L+\frac{R}{R+R_{C_{DC}}}{V}_{C_{DC}}\right]\\ -\frac{1}{C_{DC}(R+R_{C_{DC}})}{i}_L\end{array}\right]D+\left[\begin{array}{c}\frac{V_B-V_D}{L}\\ 0\end{array}\right]\end{array}$$

(3)

where D is the duty ratio of M₁. The output is the DC-link voltage:

$$y=V_{DC}=\left[\begin{array}{cc}\frac{R{R}_{C_{DC}}}{R+R_{C_{DC}}}& \frac{R}{R+R_{C_{DC}}}\end{array}\right]\left[\begin{array}{c}{i}_L\\ V_{C_{DC}}\end{array}\right]-\frac{R{R}_{C_{DC}}}{R+R_{C_{DC}}}{i}_{L}D$$

(4)

4. Design of Current Controller and Voltage Controller

In charging/discharging mode, the current/voltage tracking error will converge to zero by defining a new state variable:

$$x_{err}(t)={\displaystyle \int (r-y(t))dt}$$

(5)

where r is desired value of inductance current for charger and output voltage for discharger.

By combining Equations (1), (2) and (5), the expanded state equations of the charger can be obtained as:

$$\left[\begin{array}{c}{\dot{i}}_L\\ {\dot{V}}_{C_B}\\ {\dot{x}}_{err}\end{array}\right]=\left[\begin{array}{ccc}-\frac{1}{L}\left(R_L+\frac{R{R}_{C_B}}{R+R_{C_B}}\right)& -\frac{R}{L(R+R_{C_B})}& 0\\ \frac{R}{C_B(R+R_{C_B})}& -\frac{1}{C_B(R+R_{C_B})}& 0\\ -\frac{R{R}_{C_B}}{R+R_{C_B}}& -\frac{R}{R+R_{C_B}}& 0\end{array}\right]\left[\begin{array}{c}{i}_L\\ V_{C_B}\\ x_{err}\end{array}\right]+\left[\begin{array}{c}\frac{1}{L}\left(V_{DC}+V_D-i_L{R}_M\right)\\ 0\\ 0\end{array}\right]D+\left[\begin{array}{c}-\frac{V_D}{L}\\ 0\\ r\end{array}\right]$$

(6)

$$y=\left[\begin{array}{ccc}1& 0& 0\end{array}\right]\left[\begin{array}{c}{i}_L\\ V_{C_B}\\ x_{err}\end{array}\right]$$

(7)

Furthermore, by combining Equations (3)–(5), the expanded state equations of the discharger can be obtained as:

$$\begin{array}{l}\left[\begin{array}{c}{\dot{i}}_L\\ {\dot{V}}_{C_{DC}}\\ {\dot{x}}_{err}\end{array}\right]=\left[\begin{array}{ccc}-\frac{1}{L}\left(R_L+\frac{R{R}_{C_{DC}}}{R+R_{C_{DC}}}\right)& -\frac{R}{L(R+R_{C_{DC}})}& 0\\ \frac{R}{C_{DC}(R+R_{C_{DC}})}& -\frac{1}{C_{DC}(R+R_{C_{DC}})}& 0\\ -\frac{R{R}_{C_{DC}}}{R+R_{C_{DC}}}& -\frac{R}{R+R_{C_{DC}}}& 0\end{array}\right]\left[\begin{array}{c}{i}_L\\ V_{C_{DC}}\\ x_{err}\end{array}\right]\\ +\left[\begin{array}{c}\frac{1}{L}\left[V_D+\left(\frac{R{R}_{C_{DC}}}{R+R_{C_{DC}}}-R_M\right)i_L+\frac{R}{R+R_{C_{DC}}}{V}_{C_{DC}}\right]\\ -\frac{1}{C_{DC}(R+R_{C_{DC}})}{i}_L\\ \frac{R{R}_{C_{DC}}}{R+R_{C_{DC}}}{i}_L\end{array}\right]D+\left[\begin{array}{c}\frac{V_B-V_D}{L}\\ 0\\ r\end{array}\right]\end{array}$$

(8)

$$y=V_{DC}=\left[\begin{array}{ccc}\frac{R{R}_{C_{DC}}}{R+R_{C_{DC}}}& \frac{R}{R+R_{C_{DC}}}& 0\end{array}\right]\left[\begin{array}{c}{i}_L\\ V_{C_{DC}}\\ x_{err}\end{array}\right]-\frac{R{R}_{C_{DC}}}{R+R_{C_{DC}}}{i}_{L}D$$

(9)

For convenience, Equations (6) and (8) are represented in general state-equation form:

$$\dot{x}(t)=Ax(t)+Bu(t)+Ev(t)$$

(10)

where v(t) are the disturbances of the system.

In the T-S fuzzy models, the nonlinear BESS are represented by linear sub-systems according to the model rules:

Model rules i: If z₁(t) is M_i1 and … and z_p(t) is M_ip, then

$$\dot{x}(t)=A_{i}x(t)+B_{i}u(t)$$

(11)

where u(t) are the control inputs, x(t) are the state variables, A_i, B_i are the state matrices of the sub-systems, M_ip is the fuzzy set. In charging mode, i_L is chosen as z_p(t). In discharging mode, i_L, V_CDC are chosen as z_p(t). The T-S fuzzy system of the BESS can be expressed after defuzzification:

$$\dot{x}(t)={\displaystyle {\sum }_{i=1}^r{h}_i(z(t))\left\{A_{i}x(t)+B_{i}u(t)\right\}}$$

(12)

where:

$$h_i(z(t))=\frac{{\displaystyle {\prod }_{j=1}^r{M}_{ij}(z_j(t))}}{{\displaystyle {\sum }_{i=1}^r{\displaystyle {\prod }_{j=1}^r{M}_{ij}(z_j(t))}}}$$

(13)

and M_ij(z_j(t)) is the grad of membership.

The PDC controllers of the BESS are expressed as:

Control rules i: If Z₁(t) is M_i1 and … and z_p(t) is M_ip, then

$$u(t)=-{\displaystyle {\sum }_{i=1}^r{h}_i(z(t))F_{i}x(t)}$$

(14)

By substituting (14) into (12), the close-loop system are obtained:

$$\dot{x}(t)={\displaystyle {\sum }_{i=1}^r{\displaystyle {\sum }_{j=1}^r{h}_i(z(t))h_j(z(t))\left\{A_i-B_i{F}_j\right\}x(t)}}$$

(15)

According to state Equation (10), the BESS T-S fuzzy system with disturbances is found:

$$\begin{array}{l}\dot{x}(t)={\displaystyle {\sum }_{i=1}^r{h}_i(z(t))\left\{A_{i}x(t)+B_{i}u(t)+E_{i}v(t)\right\}}\\ y(t)={\displaystyle {\sum }_{i=1}^r{h}_i(z(t))C_{i}x(t)}\end{array}$$

(16)

To suppress the disturbances, the $H_{\infty }$ performance index is defined:

$$\underset{{\Vert v(t)\Vert }_2\ne 0}{\sup }\frac{{\Vert y(t)\Vert }_2}{{\Vert v(t)\Vert }_2}\le \gamma ,0\le \gamma \le 1$$

(17)

where γ is the disturbance suppression ability index.

To analyze the stability of the designed current and voltage controller, Lyapunov theorem [19] is applied to find the following LMI condition:

$$\left[\begin{array}{ccc}X{A}_i^T-M_j^T{B}_i^T+A_{i}X-B_i{M}_j& E_i& -X{C}_i^T\\ E_i^T& -{\gamma }^{2}I& 0\\ -C_{j}X& 0& -I\end{array}\right]<0,i\le j$$

(18)

where X is a positive definite matrix and X = P⁻¹, M_j = F_jX.

5. Results and Discussions

Table 1. Specifications of the BESS.

Rated power	2 kW	VD	1.5 V
Inductance	1.97 mH	RM	0.079 Ù
Input voltage	380 V (DC)	Input capacitance	560 µF
Output voltage	100 V (DC)	Output capacitance	440 µF

lists the specifications of the BESS.

For buck mode, the $H_{\infty }$ performance index is selected as $\gamma =0.7$. For boost mode, the $H_{\infty }$ performance index is selected as $\gamma =0.8$. The controller gains $F_i$ are obtained by using the LMI toolbox in MATLAB.

5.1. Charging Mode

The load resistance is constant and the input voltage V_DC is 380 V. The current commands are 5 A and 20 A. The inductance current and battery voltage at current command 5 A, load = 20 Ù (500 W), and current command 20 A, load = 5 Ù (2 kW) are shown in Figure 3a,b, respectively. It can be found that the inductance current can accurately track the command.

Next, the load is constant (10 Ù) and the input voltage V_DC is also 380 V. The current command is variable 5 A → 10 A → 5 A. Figure 4 shows the inductance current and battery voltage with current command variation. It is clear that the inductance current tracks the command accurately.

5.2. Discharging Mode

The load resistance is constant and the input battery voltage V_B is 100 V. Figure 5a,b shows the inductance current and DC-link voltage at load = 250 Ù (577.6 W) and 135.7 Ù (1.06 kW), respectively. It is obvious that the DC-link voltage can exactly track the command 380 V.

Next, the input voltage V_B is 100 V, and the load is variable 250 Ù → 135.7 Ù → 250 Ù. Figure 6a,b shows the inductance current and DC-link voltage under load variation 300 Ù → 150 Ù and 150 Ù → 300 Ù. It can be seen that the DC-link voltage is well regulated under load variation.

6. Conclusions

A battery energy storage system in DC micro-grid systems is designed and implemented. T-S Fuzzy current control and voltage control of the BESS is introduced. The system stability with disturbance suppression ability is analyzed and shown. The performance of the current controller and voltage controller is verified via experimental results.