This section explores a novel active and reactive power control for ES by a local signal manipulation. A control loop is designed to achieve two objectives. One is to maintain constant real power to the critical load, regardless of the fluctuations in available power from renewable energy sources. Another is to regulate critical load voltage during voltage fluctuations. These objectives are accomplished by designing two control loops for real power control and voltage control to inject the ES voltage at the required phase angle.

The combined operation of the PI controllers is used to estimate the voltage ( v s d ) to be injected in phase with the non-critical load branch current, corresponding to the amount of active power available and PCC voltage. Another main function is to determine the phase angle of the injected voltage. Reference data-PCC voltage Vs* and real power available P* are taken, and the current data of the same quantities are calculated. The supplementary information about angular frequency and phase angle of voltage vector is determined using enhanced phase-locked loop (EPLL). EPLL is chosen due to its simplicity, accuracy, and fast outputs for changing load conditions. These are given as inputs to the controller to generate a reference signal for pulse width modulation (PWM) generator. A full-bridge inverter is employed to generate the essential ES voltage. Bipolar pulse width modulation (Wu et al., 2014) is implemented to produce the vital gate signals to the four switches per the reference signal generated by the designed PQ controller.

PCC voltage has two components. PCC voltage and currents with peak values V s , I s are, respectively, v s ( t ) = V s ⁡ cos ( ω t + ∅ ) , (1) i s ( t ) = I s ⁡ cos ( ω t + φ ) , (2) where ϕ and φ are the initial phases of PCC voltage and current, ω is the angular frequency, and the apparent power consumed by the electric spring system is S ˜ = v s i s ∗ , (3) S ˜ = ( v s d +   j v s q ) ( i s d −   j i s q ) . (4) v s d , v s q are the components of PCC voltage, v s in the d-q rotating frame. Similarly, i s d , i s q are the components of the PCC current, i s in the d-q rotating frame: P i n = v s d i s d +   v s q i s q , (5) Q i n = v s q i s d − v s d i s q . (6)

If the d-axis of the rotating frame is aligned along the PCC voltage vector, then it can be rewritten as P i n = v s d i s d , (7) Q i n = − v s d i s q . (8) P i n , Q i n are calculated where Fourier Transforms are used to extract the peak values and phase angles from the detected quantities of v s , i s as given by Munoz et al. (2012). After calculating the real and imaginary ES voltage terms v s d , v s q using the innermost control loops, a d q / α β transformation (Golestan and Guerrero, 2015) is applied to generate the sinusoidal inverter reference voltage to be injected into the grid as given by the following equations: V s d q ( t ) = V s α β ( t ) e − j ∅ , (9) o r , V s α β ( t ) = V s d q ( t ) e j ∅ , (10) V s α β ( t ) = V s d q ( t )   ( cos ∅ + j ⁡ sin ∅ ) , (11) o r , V s α β ( t ) = ( V s d + j V s q ) ( cos ∅ + j ⁡ sin ∅ ) , (12) V s α + j V s β = ( V s d + j V s q ) ( cos ∅ + j ⁡ sin ∅ ) , (13) where V s α = V s d ⁡ cos ∅ − V s q ⁡ sin ∅ . (14)

Since the proposed ES is applied to a single-phase system, the reference voltage is the calculated α reference command, whereas the β reference command is discarded. This is adopted because the β component can be emulated with a 90 0 phase shift of the α component. This power control method has the following features:

• Eliminates the need to identify the data of grid voltage.

RMS value and the instantaneous phase of the critical load voltage are detected by the RMS and EPLL blocks, respectively. The powers P i n , Q i n are controlled by separate proportional-integral (PI) regulators. Specifically, the regulator in the d-axis controls P i n and that one in the q-axis controls Q i n . The output signals of the PI regulators in both the loops are processed through the inverse dq-to-aß transformation to get the modulation signal, v α . A bipolar pulse width modulation scheme is implemented to obtain drive signals for the VSI just after a limiter.

With reference to Eqs. 1, 2, the total apparent power consumed by the ES system is S ˜ = P i n + j Q i n . (15)

For implementation in modeling, actual powers consumed are calculated as detailed in Figure 2: P i n = V s I s ( cos ( ∅ − φ ) t ) , (16) Q i n = V s I s ( sin ( ∅ − φ ) t ) . (17) P i n , Q i n are calculated with PCC voltage and currents considered in the d-q rotating frame.

If V C r i t , R C r i t , X C r i t are the RMS voltage, resistance, and reactance parameters of critical load, then powers of the critical and non-critical loads are determined from the load impedance values, RMS, then powers of the critical and non-critical loads are determined as:

Real power of critical load: P C r i t = V c r i t 2 R C r i t . (18)

Reactive power of critical load: Q C r i t = V c r i t 2 X C r i t . (19)

The PV array is the combination of the PV modules. The primary element is the PV cell, which converts solar power to electrical power. Alrahim Shannan et al. (2013) detailed the different modeling of the PV cell as single diode model, two diode models, and multiple diode model. In this work single diode model of a PV cell is considered. I _pv is the photocurrent. D₁ is an anti-parallel diode, R_p is leakage resistance, and R_s is contact resistance. V is the output voltage of the single cell, and the output current of cell I is given in Eq. 20: I = I p v − I D 1 − ( V + I R s R p ) , (20) I D 1 = I o 1 [ exp ( q ( V + I R S ) A 1 K T ) − 1 ] , (21) I p v = [ I s c r + K i ( T k − T r e f k ) ] × λ 1000 . (22)

Here, λ is the irradiation of solar, I_scr is cell shorted current, and T_k and T_refk are the actual and standard temperature. K is the temperature coefficient of short-circuit current (A/K), A₁ is the ideality factors of the diodes. q is the charge of the electron, and I_o1 are the reverse saturation currents of diodes. Eq. 21is modified for the PV module as given in Eq. 22. I = N p I P V − N p I D 1 − ( V + I R s R p ) , (23) I = N p I P V − N p I 01 [ e x p { q ( V + I R s ) N s A 1 K T } − 1 ] − ( V + I R s R p ) . (24)

Here, N_s and N_p are the numbers of cells cascaded and shunted in the module. The PV module current is given in Eq. 24. These modules are connected in cascaded and shunted to meet the voltage and power rating. They form a PV array. The PV array current is given as follows: I = N p p I P V − N p p I 01 [ e x p { q ( V + I R s ( N s s N p p ) ) N s A 1 K T } − 1 ] − [ V + I R s ( N s s N p p ) R p ( N s s N p p ) ] , (25) where N_ss and N_pp are the numbers of series-connected and parallel-connected modules. The standard KC200GT data sheet parameters used to do the PV array simulation are given in Table 1.

Generally, a DC–DC boost converter is employed to increase the output voltage. It is shown in Figure 3. The inductor stores energy when the switch is ON, the stored energy is released to the load when it is OFF. MPPT controller generates reference voltage. The error voltage is given as input to the PI controller to generate a reference voltage signal for PWM control. It generates pulses to the boost converter and enables the boost converter to obtain the maximum power from the PV panel and maintain fixed DC link voltage. The ripple in DC link voltage is reduced by a capacitor filter given by Sano and Fujita (2008).

The performance of PV-ES is examined for changes in solar irradiation levels and reference power. Throughout the simulation time, the PCC voltage is maintained at a rated value of 230 V, whereas the reference power is decreased from 8 to 4 kW at t = 2 s. It is correlated with the change in solar irradiation from 900 to 600 W/m². The output of the boost converter is also reduced from 600 to 380 V. Subsequently, power flow between ES and PV is affected by the value of reference power. When reference power is 8 kW, the power flow from PV to ES is 1.1 kW. When reference power is reduced to 4 kW, power flow from PV to ES is also reduced to 600 W. This is illustrated in Figure 8A.

It is observed that, with the controller action, net real power absorbed by the smart load seamlessly tracks the reference power very accurately, as shown in Figure 8B. There is a steady-state error in tracking the reference power between the time intervals of 1.25–1.5 s due to the dynamics in the PV system. When the reference power changes, there is a transient time of 1 s. A peak overshoot of 1 kW from the steady-state value (4 kW) occurs at t = 2 s due to the large change in the reference power. The power absorbed by the critical load is maintained constant at 3.3 kW with a small transient operation at 2 s, as shown in Figure 8C. Steady-state errors during 1.25–1.5 s and from 1.75 to 2 s are cause by the transients in the PV power.

This section investigates a comparison of the performance of the electric springs when fed by DC and PV sources. Tracking of reference power and voltage regulation is investigated under sag and swell conditions in the PCC voltage. The key points are transient time and peak overshoot.

Comparative analysis between the operations of ES when fed from the PV source and a DC source is numerically tabulated in Table 2. From Figure 9, it is observed that during voltage regulation, the time taken to track reference power is the same as that for both configurations. However, their performances for tracking reference power differ slightly under changes in voltage, as illustrated in Figure 10. In contrast, their performance is noticeably different to track variations in reference power as illustrated in Figure 11. Tracking reference power by PV- ES is better than DC-ES by 0.14 s.

Table 2 also compares these two configurations in terms of peak overshoot and settling time during the voltage regulation. Transient time is controlled alike with both sources, whereas peak overshoot differs by 0.2 V during voltage sag.