4.1.1. System and Control Parameters

Figure 10 and Table 3 show the PV system and its converter parameters. The controller gains of the PV system are designed using the method discussed in Reference [34]. The internal current loop is designed first, which gives *k*1pv and *k*2pv, and then the external loop is designed that includes the design of *k*3pv, *k*4pv,*k*5pv, and *k*6pv. In the design of the external loop, all the dynamics of the internal loop are carried along. Therefore, unlike common practice, the internal loop is not limited to be several times faster than the external loop. In our study, the PV operates at MPPT using perturb and observe (P&O) algorithm [35]. However, this is not a requirement for the proposed BES controller.

**Figure 10.** PV converter system and its control.

**Table 3.** Parameters of PV system.


The objective is to obtain the desired ramp rate of 30 %/minute ≈ 75 W/s from the combined PV-BES system. Table 4 shows the parameters of the BES system and its converter. The gains of the power control loop of the BES controller are designed based on the method discussed in Section 3.3.1. Figure 11a shows the plot of the closed loop poles of the power loop on changing *q*i's. Here, *q*<sup>1</sup> and *q*<sup>2</sup> are subsequently increased between 10−<sup>3</sup> →102.5 and 10−<sup>6</sup> →10<sup>−</sup>4, respectively. The reference power of the BES for the ramp control is calculated by using the method mentioned in Section 3.3.2. For the SOC control loop, the control gains are designed based on the method presented in Section 3.3.3. Figure 11b shows the plot of the closed loop poles of the SOC loop on changing *qi*'s. Here, *q*<sup>1</sup> and *q*<sup>2</sup> are increased between 10−1.5 →102.5 and 10<sup>0</sup> →107.75, respectively. Table <sup>4</sup> shows the controller gains and the location of the poles for both the power control loop and the SOC control loop. The poles of the SOC control loop are selected such that its speed is several times slower than the ramp rate calculator.

The system and control parameters of the dc/ac converter are adopted based on the conventional voltage source converter (VSC) and vector control method [36–38] to regulate the dc voltage at 600 V. This ensures exchange of power between the dc and ac system in a desired way. The synchronous generator is simulated using the method proposed in Reference [39].

**Table 4.** BES system parameters.

#### 4.1.2. Results and Discussion

The simulation scenario to study the impact of abrupt PV disturbances is defined as follows. The solar intensity is initially at 1000 W/m<sup>2</sup> and the system is operating at steady state. The PV system supplies 14.2 kW power and there is 1.4 kW power from the ac to the dc system. At *t*=5.0 s, the solar intensity drops from 1000 W/m<sup>2</sup> to 250 W/m2 in a fraction of a second that drops the PV power to 3.42 kW. At *t*=50 s, the solar intensity goes back abruptly to 1000 W/m2.

Figure 12 shows the output power response of the system. There is a sudden change in the power injected to the dc system (and then flowing into the ac system) when BES is not used. The BES smoothes down those changes and establishes an output power ramp at the desired rate. Figure 13 shows the transient response details of the PV, the BES, and the combined output powers. It confirms that the BES quickly compensates for the PV power practically without a delay.

**Figure 12.** Top: solar irradiance, Bottom: powers of the PV and BES system response to the solar irradiance.

**Figure 13.** Power transients of the PV-BES system to PV disturbances.

Figure 14 shows the voltage and frequency transients at point of common coupling (PCC) of the dc and the ac system in response to the abrupt PV disturbances. The BES has reduced the peak and duration of both dc and ac voltage transients. The ac voltage (rms) experiences a peak fluctuation of close to 5.5 V (close to 5%) without the BES, and the BES limits the fluctuations within 0.1 V (practically zero). The BES has also improved the transients in the system frequency. Figure 15 shows the voltage transients at different buses in the dc system. The BES reduces the voltage transients across the entire dc system. Without the BES, this disturbances causes voltage fluctuations with peaks of over 10%. The BES reduces the peak of the transients to about 1%, and damps out the oscillations quickly. Over ten times improvement is achieved.

**Figure 14.** Voltage and frequency due to the abrupt PV disturbances.

**Figure 15.** Dc system voltages due to the abrupt PV disturbances.

The ac current of the grid dc/ac converter is shown in Figure 16. When the PV power drops, the ac system supplies the deficit power to the dc system in the absence of the BES. With the proposed BES, the ac current has smooth transitions. Figure 17 shows the SOC of the BES in response to the abrupt PV disturbances. The SOC controller slowly regulates the SOC to the reference value after the disturbance is taken care without affecting the ramping behavior of the BES.

**Figure 16.** Inverter's ac current due to the abrupt PV disturbances.

**Figure 17.** SOC of the BES during and after the abrupt PV disturbances.
