Control Analysis of Building-Integrated Photovoltaic System

Abstract

In this chapter, a photovoltaic system integrated into the building is investigated. The studied structure includes also a battery energy storage system. The overall system is connected to a four-wire AC bus, with the possibility to supply single-phase and three-phase loads. Each equipment is interfaced with a dedicated power converter. This chapter examines the technical operation of all structure components and gives a detailed mathematical study of the DC/AC power converter control in case of two modes, namely, grid connected mode and standalone mode. The investigated control is based on resonant controller. The resonant controller parameters tuning, which is based on the generalized stability margin criterion, is detailed in this chapter. To prove the performance of the proposed control algorithm, several simulation tests developed under PSIM software were performed and then validated by experimental results.

1. Introduction

Nowadays, rooftop photovoltaic systems (PV) and building-integrated photovoltaic (BIPV) systems are becoming well known and commonly used. The growth of these installations is due to their environmental advantages in addition to their social and economic benefits. Indeed, since building electricity consumption accounts for a large proportion of a country’s overall consumption, and tends to increase further for the coming years, local generation offers an ideal solution [1, 2, 3, 4].

Regarding the obstruction of PV systems’ fluctuating aspect, it can be derived in various ways. The integration of battery energy storage system (BESS) is considered as efficient and complementation solution, mainly for standalone microgrids [5]. Urban photovoltaic systems are usually connected to the distribution network, but the operation in standalone is also possible [6, 7].

In order to ameliorate the PV system efficiency, an adequate control strategy should be introduced. In the literature, several control techniques are developed: integral proportional regulators, resonant correctors, hysteresis correctors, sliding mode controls, predictive controls, and so on [8, 9, 10, 11].

This chapter investigates the operation of PV system devoted to building application. It gives an overview of the control of all integrated power converters and then explains in details the control of the DC/AC power converter in both operation modes, namely, standalone mode and grid connected mode. For the grid connected mode, the control must ensure that the AC bus voltage remains within the acceptable range, and for standalone mode the DC/AC converter is controlled to inject generated PV power into the AC-link.

This chapter first outlines overall system description, followed by a review of each power converter control. A detailed mathematical study is dedicated to the DC/AC converter control in grid connected and autonomous modes. Simulation results and experimental validation are subsequently presented.

2. System description

The building solar system structure is given in Figure 1. It is composed of a PV panels in parallel with a battery energy storage system which are linked to a DC bus, a DC/AC power converter, and an LCL filter interfacing between DC and AC bus. Single- and three-phase linear and nonlinear loads are connected to the AC bus.

Figure 1.

Photovoltaic system including BESS.

The linear building loads are modeled by a resistive load, and the nonlinear ones are modeled by a rectifier connected to a capacitive filter at the DC side. This model is conformed to many building loads, similar to televisions, personal computers, and fluorescent lamp ballast [12]. In case of three-phase balanced loads, the neutral current is zero, but since several building loads are single phase and include electronic converters, their waves include harmonics which induce a nonzero neutral current. Regarding neutral wire, the more common considered structures are presented in Figure 2. The first structure is based on DC-link neutral point where the neutral wire is generated via two identical capacitors (Figure 2a). In the second structure, the neutral wire is generated through a Delta/Star grounded transformer as shown in Figure 2b [13]. As to the third configuration, it is based on four-leg power converter (Figure 2c) [14, 15, 16]. In this chapter the structure with transformer is adopted.

Figure 2.

Different structures that integrate the fourth wire.

The PV system presents two operating modes according to the grid state:

• Grid connected mode: this mode is activated when the grid is available. In this case, the power surplus is injected into the grid, and if the consumption is superior to local generation, the power flow will be directed from the grid to loads and eventually to charge batteries according to their stat of charge (SOC).

• Standalone mode: this mode is activated when the grid is absent. In this case, building loads are supplied first by the PV system then if necessary by the BESS. In case of power deficit, the shedding of non-priority loads is carried out.

3. Power converter control

An overview of the control of each converter presented in Figure 2b is subsequently presented.

3.1 BESS DC/DC converter control

Batteries are frequently integrated to PV systems thanks to their special energy characteristics. Indeed, batteries have a high energy density, which ensure long time of stable operation. The charging time and number of cycles depend on the adopted technology.

The battery power flow is bidirectional. In discharge mode, the power is supplied by battery, and in charging mode, the power is absorbed by battery. For both modes, the state of charge limits should be respected to not affect the battery lifetime.

The BESS incorporates a DC/DC power converter that manages battery operation modes according to the appropriate control. A cascade control is adopted, the inner loop regulates the battery current, and the external one regulates the DC-link voltage.

The switches C₁ and C₂ (Figure 3) are controlled individually. In case of battery charging, C₁ is controlled and in case of battery discharging, C₂ is controlled.

Figure 3.

Control strategy of BESS.

3.2 PV DC/DC converter control

The structure of the two-stage power conversion is adopted for the PV system; this configuration is commonly privileged in the majority of the PV systems. The difference with the conventional structure is that the V_dc regulation is ensured by the BESS. As to the control of the DC/DC converter, it aims to ensure Maximum Power Point Tracking (MPPT) (which corresponds to the peak point of the power versus the voltage curve). In the case of this study, the Perturbation and Observation (P&O) algorithm is applied. The inputs of the P&O algorithm are the solar radiation G and the temperature T as shown in Figure 4.

Figure 4.

Control of the PV DC/DC converter.

3.3 DC/AC converter control

3.3.1 Modeling of the DC/AC converter

The output of the DC/AC and the LCL filter are modeled in single phase as shown in Figure 5. According to this figure, the obtained results are expressed as follows:

Figure 5.

LCL filter single-phase modeling.

$$V_c=V_i-L_1{I}_{L1}s$$E1

$$I_c=I_{L1}-I_{L2}$$E2

$$V_c=\frac{1}{C_{f}s}{I}_c$$E3

Based on Eq. (3), the transfer function between the current I_L1 and the voltage (V_i − V_c) is given by the following equation:

$$\frac{I_{L1}}{V_i-V_c}=\frac{1}{L_{1}s}$$E4

According to Eqs. (2) and (3), the transfer function between the voltage V_c and the current (I_L1 − I_L2) is expressed as follows:

$$\frac{V_c}{I_{L1}-I_{L2}}=\frac{1}{C_{f}s}$$E5

The transfer functions given by Eqs. (4) and (5) allow the deduction of the system block diagram given by Figure 6.

Figure 6.

System filter block diagram.

3.3.2 Control of the DC/AC converter

3.3.2.1 Standalone mode

In standalone mode, the DC/AC converter control ensures that the LCL filter capacitor voltages are equal to their references. In that case, the converter control includes two cascade loops as shown in Figure 7. The external loop is based on a resonant controller RC₁ used to regulate the voltage across the LCL filter capacitor. This loop generates at its output the reference current I_c-ref. This current will be added to the current I₂ to provide the inner loop reference current I_1-ref. The inner loop is based on a resonant controller, and in this work, it simplified to a simple gain G. In the following, the tuning of the parameters of the voltage external loop and the current inner loop will be presented and detailed.

Figure 7.

Control strategy of DC/AC converter in the case of standalone mode.

3.3.2.1.1 Tuning of the external loop resonant controller RC₁

For simplification reasons, it is assumed that the internal current loop is faster than the external voltage loop. Thus, it can be approximated equal to the unity by associating it with the PWM function. The following block diagram is then obtained for the determination of the external voltage loop resonant controller parameters as presented in Figure 8.

Figure 8.

Block diagram of the external voltage loop.

According to Figure 4, the open and closed-loop system transfer functions are expressed by Eqs. (7) and (8), respectively. Note that the transfer function of the resonant controller RC₁ is given by Eq. (6):

$$F_{\mathit{CR}1}\left(s\right)=\frac{c_{2c}{s}^2+c_{1c}s+c_{0c}}{s^2+{\omega }_0^2}$$E6

$$F_{\mathit{OL}‐\mathit{Vc}}\left(s\right)=\frac{V_c}{V_{c‐\mathit{ref}}-V_c}=\frac{c_{2c}{s}^2+c_{1c}s+c_{0c}}{C_f{s}^3+C_f{\omega }_0^{2}s}$$E7

$$F_{\mathit{CL}‐\mathit{Vc}}\left(s\right)=\frac{V_c}{V_{c‐\mathit{ref}}}=\frac{c_{2c}{s}^2+c_{1c}s+c_{0c}}{C_f{s}^3+c_{2c}{s}^2+\left(C_f{\omega }_0^2+c_{1c}\right)s+c_{0c}}$$E8

The method chosen for the resonant controller parameters tuning is based on the generalized stability margin criterion [17, 18]. The reference polynomial P_GSMc defined by this criterion is expressed as follows:

$$P_{\mathit{\text{GSMc}}}\left(s\right)={\lambda }_c\left(s+r_c\right)\left(s+r_c+j{\omega }_{\mathit{ic}}\right)\left(s+r_c-j{\omega }_{\mathit{ic}}\right)$$E9

where λ_c, r_c, and ω_ic are the factorization coefficient, the abscissa, and the ordinate in the complex plane. On the other hand, the system characteristic polynomial is deduced from Eq. (8), and it is expressed as follows:

$$P_c\left(s\right)=C_f{s}^3+c_{2c}{s}^2+\left(C_f{\omega }_0^2+c_{1c}\right)s+c_{0c}$$E10

According to the generalized stability margin criterion, the resonant controller parameters are tuned by identifying the characteristic polynomial of the closed-loop system P_c(s) with the reference polynomial P_GSM(s) as shown in Eq. (11):

$$P_{\mathit{\text{GSMc}}}\left(s\right)=P_c\left(s\right)$$E11

The identification of P_GSM(s) and P_c(s) allows the deduction of the current inner loop resonant controller parameters as shown in the following equation:

$$\left\{\begin{array}{l}{c}_{2c}=3r_c{\lambda }_c\\ c_{1c}={\lambda }_c\left(3r_c^2+{\omega }_{\mathit{ic}}^2\right)-C_f{\omega }_0^2\\ c_{0c}={\lambda }_c\left(r_c^3+r_c{\omega }_{\mathit{ic}}^2\right)\\ {\lambda }_c=C_f\end{array}\right.$$E12

We choose r_c equal to 200 and ω_ic equal to ω_g. For C_f equal to 30 μF, the resonant controller RC₁ parameters are given by the following equation:

$$\left\{\begin{array}{l}{c}_{2c}=0.018\\ c_{1c}=3.6\\ c_{0c}=832.17\end{array}\right.$$E13

For the obtained resonant controller parameters, Figure 9 shows the pole maps of F_CL-Vc(s). As shown in this figure, the system is stable and the expected stability margin r_c is obtained. Figure 10 shows the Bode diagram of F_OL-Vc(s). This figure shows that the obtained gain margins G_m and P_m are equal to infinity and 72.8°, respectively. Figure 11 presents the gain of F_CL-Vc(s) and shows that the bandwidth of the external voltage loop is equal to 24 Hz. It should be noted here that the larger is the bandwidth, the faster is the system.

Figure 9.

Pole map of F_CL-Vc(s).

Figure 10.

Bode diagram of F_OL-Vc(s).

Figure 11.

Bode diagram of F_CL-Vc(s).

3.3.2.1.2 Tuning of the inner loop gain G

According to Figure 6, the block diagram of the current inner loop is given by Figure 12.

Figure 12.

Block diagram of the inner current loop.

According to Figure 12, the open and closed-loop transfer functions are given by Eqs. (14) and (15), respectively:

$$F_{\mathit{OL}‐\mathit{IL}1}\left(s\right)=\frac{I_{L1}\left(s\right)}{I_{L1‐\mathit{ref}}\left(s\right)-I_{L1}\left(s\right)}=\frac{G}{L_{1}s}$$E14

$$F_{\mathit{CL}‐\mathit{IL}1}\left(s\right)=\frac{I_{L1}}{I_{L1‐\mathit{ref}}}=\frac{1}{\frac{L_1}{G}s+1}=\frac{1}{1+{\tau }_{i}s}\mathit{\text{where}}{\tau }_i=\frac{L_1}{G}$$E15

The inner current loop must ensure a response time much smaller than the external voltage loop. To this purpose, the gain G is selected so that the real part of the inverse of the closed-loop time constant τ_i is greater than the stability margin chosen for the tuning of the voltage external loop (r_c = 200) as shown in Eq. (16).

$$\frac{1}{{\tau }_i}>>100\Rightarrow \frac{G}{L_1}>>100\Rightarrow G>>0.1$$E16

We select G equal to 10. For this value, Figures 13 and 14 present the pole maps of F_CL-IL(s) and the Bode diagram of F_OL-IL(s), respectively. These figures show that the system is stable and the obtained G_m is equal to infinity and the P_m is equal to 90.3°. Figure 15 presents the gain of F_CL-IL(s) and shows that the bandwidth of the inner current loop is equal to 785 Hz. This value is much higher than the bandwidth of the voltage external loop and shows that the current inner loop is much faster than the voltage external loop.

Figure 13.

Pole map of F_CL-IL(s).

Figure 14.

Bode diagram of F_OL-IL(s).

Figure 15.

Bode diagram of F_CL-IL(s).

3.3.2.2 Grid connected mode

In grid connection operation mode, the DC/AC converter controls power exchange with grid. In this mode, only the current loop is controlled. This loop is based on a resonant controller as shown in Figure 16.

Figure 16.

Control strategy of DC/AC converter in case of grid connected mode.

The simplified block diagram of the current loop is given by Figure 17.

Figure 17.

Block diagram of the current loop.

Based on Figure 17, the open and closed-loop transfer functions are given by Eqs. (18) and (19), respectively. The transfer function of the resonant controller RC₂ is given by Eq. (17):

$$F_{\mathit{CR}2}\left(s\right)=\frac{i_{2i}{s}^2+i_{1i}s+i_{0i}}{s^2+{\omega }_0^2}$$E17

$$F_{\mathit{OL}‐i}\left(s\right)=\frac{I_{L1}}{I_{L1‐\mathit{ref}}-I_{L1}}=\frac{i_{2i}{s}^2+i_{1i}s+i_{0i}{\omega }_0^2}{L_1{s}^3+L_1{\omega }_0^{2}s}$$E18

$$F_{\mathit{CL}‐i}\left(s\right)=\frac{I_{L1}}{I_{L1‐\mathit{ref}}}=\frac{i_{2i}{s}^2+i_{1i}s+i_{0i}}{L_1{s}^3+i_{2i}{s}^2+\left(L_1{\omega }_0^2+i_{1i1}\right)s+i_{0i1}}$$E19

For the tuning of the internal loop resonant controller, the generalized stability margin criterion is considered. The system characteristic polynomial P_i(s) is deduced from Eq. (19), and it is expressed as follows:

$$P_i\left(s\right)=L_1{s}^3+i_{2i}{s}^2+\left(L_1{\omega }_0^2+i_{1i}\right)s+i_{0i}$$E20

The identification between the system characteristic polynomial P_i(s) and the generalized stability margin criterion reference polynomial P_GSMi(s) [Eq. (21)] and the resonant controller RC₂ parameters are deduced as in Eq. (22):

$$P_{\mathit{\text{GSMi}}}\left(s\right)={\lambda }_i\left(s+r_i\right)\left(s+r_i+j{\omega }_{\mathit{ii}}\right)\left(s+r_i-j{\omega }_{\mathit{ii}}\right)$$E21

$$\left\{\begin{array}{l}{i}_{2i}=3r_i{\lambda }_i\\ i_{1i}={\lambda }_i\left(3r_i^2+{\omega }_{\mathit{ii}}^2\right)-L_1{\omega }_0^2\\ i_{0i}={\lambda }_i\left(r_i^3+r_i{\omega }_{\mathit{ii}}^2\right)\\ {\lambda }_i=L_1\end{array}\right.$$E22

We choose r_i equal to 100 and ω_ii equal to ω_g. For L_i equal to 2 mH, the resonant controller RC₂ parameters are given by the following equation:

$$\left\{\begin{array}{l}{i}_{2i}=0.5\\ i_{1i}=60\\ i_{0i}=11870\end{array}\right.$$E23

For the obtained resonant controller parameters, Figure 18 shows the pole map of F_CL-i(s). Based on this figure, the stability margin r_i is equal to the desired one. Figure 19 gives the bode diagram of F_OL-i(s). As mentioned on this figure, the gain margins G_m and P_m are equal to infinity and 79.5°, respectively. Figure 20 presents the gain of F_CL-i(s) and shows that the bandwidth of the internal current loop is equal to 40.8 Hz.

Figure 18.

Pole map of F_CL-i(s).

Figure 19.

Bode diagram of F_OL-i(s).

Figure 20.

Bode diagram of F_CL-i(s).

4. Simulation results

Several simulation tests developed under PSIM software were done. Figure 21 presents the LCL filter capacitor voltage in islanded mode for different values of voltage reference V_c-ref-abc. As shown in this figure, the obtained voltages are equal to their references. Figure 22 presents the power injected into the AC bus during 24 hours; this power corresponds to the PV generation. In this case all the batteries are considered to be charged to their SOC_max. The deduced reference current is presented in Figure 23.

Figure 21.

LCL filter capacitor voltage in islanded mode for different values of voltage reference V_c-ref-abc: (a) V_c-ref-abc = 325 V, (b) V_c-ref-abc = 200 V, (c) V_c-ref-abc = 100 V, and (d) V_c-ref-abc = 30 V.

Figure 22.

Power injected into AC bus in case of connected mode.

Figure 23.

Reference current in case of connected mode.

5. Experimental results

Figure 24 shows the experimental test bench. The used AC/DC converter is from SEMIKRON. Currents and voltages are censored via LEM LV25 and LEM 55LP, respectively, as given in Figure 24. The control algorithm is implemented on the STM32F4 Discovery. The acquisition time is set to 100 μs. Figure 25 presents the LCL filter capacitor voltage in islanded mode for different values of voltage reference V_c-ref-abc. As shown in this figure, the obtained voltages are equal to their references.

Figure 24.

Experimental test bench.

Figure 25.

Experimental results for LCL filter capacitor voltage in islanded mode for different values of voltage reference V_c-ref-abc: (a) V_c-ref-abc = 325 V, (b) V_c-ref-abc = 200 V, (c) V_c-ref-abc = 100 V, and (d) V_c-ref-abc = 30 V.

6. Conclusion

In this chapter, the control of power converters integrated in building solar system is investigated. The studied system is composed of a PV panel in parallel with a battery energy storage system which are linked to a DC bus, a DC/AC power converter, and an LCL filter interfacing between DC and AC bus. Single- and three-phase linear and nonlinear loads are connected to a four-wire AC bus. The neutral wire is generated through a Delta/Star grounded transformer. An overview of the control of each power converter is presented. This chapter focuses on the control of the DC/AC power converter. The resonant controller is adopted. A set of simulation and experimental tests were done to show the efficiency of the studied control algorithm.

Acknowledgments

This work was supported by the Tunisian Ministry of Higher Education and Scientific Research under Grant LSE-ENIT-LR11ES15.