Performance Analysis of Solar PV-UPQC for Enhanced Power Quality

The purpose of this research is to improve the power quality of distributed generating systems by suggesting a three-phase, one-stage PV-UPQC in Figure 1. This study aims to enhance the power quality of distributed producing systems. System design and setup, control strategies, modelling and simulation, and optimization approaches make up the methodology's framework.

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Figure 1. Block schematic for the PV-UPQC system

3.1 System design and configuration

In the PV-UPQC system, shunt and series compensators are positioned back-to-back and linked by a common DC link. Using shunt compensators, photovoltaic array electricity is harnessed to lower load current harmonics; to compensate for voltage dips and spikes, the series compensator connects to the grid and injects the necessary voltage in series [28].

3.1.1 Voltage magnitude of DC-link and DC-bus capacitor rating

The DC-link voltage is calculated using Eq. (1), which approximates 677.69 V. Under Standard Test Conditions (STC), the PV array must run at its MPPT voltage of 700 V. The DC-bus capacitor value, derived from Eq. (2), is 9.8 mF with a constant "K" of 0.1 and an overloading factor "a" of 1.2. Under dynamic circumstances, these characteristics guarantee the DC-link voltage's stability [18, 19].

$V_{d c}=\frac{2 \sqrt{2} V_{L L}}{\sqrt{3} m}$     (1)

where, m is the depth of modulation (considered equal to 1).

V_LL is the grid line voltage (415 V).

$C_{d c}=\frac{3 k a V_{p h} I_{s h} t}{0.5 *\left(V_{d c}^2-V_{d c 1}^2\right)}$     (2)

3.1.2 Shunt compensation inductor interface inductor (L_f)

The interfacing inductor value for the shunt compensator is calculated using Eq. (3), yielding approximately 723.3 μH, rounded to 1 mH for practical purposes. The DC-link voltage is roughly 700 V, and the selected switching frequency is 10 kHz [19].

$L_f=\frac{\sqrt{3} m V_{d c}}{12 a f_{s h} I_{c r, p p}}$     (3)

3.1.3 Series injection transformer

The series injection transformer's ratings are determined by the PV-UPQC's total capacity. The turn ratio, calculated with Eq. (4) and Eq. (5), is approximately 3.33, rounded to 3. Grid current and the current flowing via series VSC are equal [18]. With a sag condition of 0.3 pu, the supply current is 29.414A, resulting in an accomplished 6.5 kVA rating for the injection transformer.

$K_{S E}=V_{v s c} / V_{S E}$     (4)

$S_{S E}=3 V_{S E} I_{S E s a g}$     (5)

3.1.4 Interfacing inductor of series compensator (L_r)

Eq. (6) is used to rate the series compensator's interface inductor, yielding a value of 4.3 mH. Under varied load circumstances, this inductor keeps the series compensator stable and effective [29].

$L_r=\frac{\sqrt{3} * m V_{d c} K_{S E}}{12 a f_{s e} I_r}$     (6)

where, I_r is the inductor current ripple, which is assumed to be 20% of grid current (i.e., 5.88), f_se is the switching frequency, ‘m’ is the depth of modulation, and a is the pu value of maximal overload. In this case, 4.3 mH is the chosen value, with m=1, a=1.2, f_se=10 kHz, V_dc=700 V, and 20% ripple current.

3.2 Control strategy

A PID controller, fine-tuned with the help of an MLNN, is at the heart of the control approach. MLNN is particularly well-suited for improving PID controllers in Solar PV-UPQC systems due to its ability to handle complex nonlinear dynamics and adapt to changing operating conditions. Because of its adaptive learning capabilities, it can modify PID parameters in real-time, ensuring consistent performance even in the presence of load variations, harmonics, and voltage fluctuations. Unlike other AI techniques like fuzzy logic, which lacks generality, or evolutionary algorithms, which are computationally intensive for real-time applications, MLNN provides a balance between accuracy and efficiency. Furthermore, it offers excellent forecast accuracy for error dynamics, enabling faster convergence and better control outcomes. Because of its widespread use and proven efficacy in similar control applications, it is likewise a reliable and validated solution for this circumstance. Figure 2 shows the shunt compensator control structure, which maximizes power output by operating the PV array at its highest power point [18].

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Figure 2. Control diagram of the shunt compensator

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Figure 3. Control diagram of the series compensator

The DC component is removed by means of a moving average filter. in order to avoid compromising dynamic performance. Eq. (7) provides the transfer function for the moving average filter.

$\operatorname{MAF}(s)=\frac{1-\mathrm{e}^{-T w s}}{T w s}$     (7)

The moving average filter's $T_w$ window length is given in Eq. (7). The d-axis current $T_w$ is maintained at half of the fundamental time interval since its lowest harmonic is a double-harmonic component [15]. The filter has integer multiples of window length for zero gain and unity DC gain. The PV array's corresponding current component Eq. (8) is provided as

$I_{p v g}=\frac{2}{3} \frac{P_{p v}}{V_s}$     (8)

The PV array power is shown here [16], and the PCC voltage's magnitude is indicated by Vs. The Eq. (9) reflects the grid current in the d-axis.

$I_{s d}^*=I_{L d f}+I_{l o s s}-I_{p v g}$     (9)

The DC component $I_{L d f}$, or the important reference component, is produced by filtering the d-component of the load current, $I_{s d^*}$, as shown in Eq. (9). Figure 3 depicts the series compensator's control structure. The output power of the solar PV system is expressed as

$P=V I$     (10)

Eq. (10) provides the improved power when the voltage and current change, and when the small terms are ignored, the corresponding Eq. (11) is provided.

$P+\Delta P=(I+\Delta I) \cdot(V+\Delta V)$     (11)

$\Delta P=\Delta I * V+\Delta V * I$     (12)

Since ΔP has to be zero at the peak in Eq. (12), the source's dynamic impedance Eq. (13) is given as

$\Delta I / \Delta V=-I / V$     (13)

3.2.1 Bacterial Foraging Optimization (BFO) with MPPT

Figure 4 illustrates the BFO algorithm, involving chemotaxis, swarming, reproduction, and elimination processes. The movement of bacteria, described by Eq. (14), and their repulsion mechanism, outlined in Eq. (15), and the fitness of every bacterium is determined and arranged following the chemotaxis and swarming processes in Eq. (16), contribute to the optimization of voltage and power parameters in the MPPT system [27].

$\begin{gathered}H_i(j+1, k, l) =H_i(j, k, l)+\Delta(i) / \sqrt{\Delta^T(i)} \sqrt{\Delta(i)} Y(i) n\end{gathered}$     (14)

$U_i(j+1, k, l)=U_i(j, k, l)+U_{c c}\left(H_i(j, k, l)\right.$     (15)

$U_{i_{\text {health }}}=\sum_{i=1}^{N c} U_i(j, k, l)$     (16)

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Figure 4. Flow chart of BFO

3.2.2 PID controller optimization

The PID controller's transfer function is represented by Eq. (17), here k_p, k_i, and k_d are the proportional, derivative, and integral gains, respectively. Eq. (18) details the error function used to assess the controller’s performance [30]. The PID gains are optimized using MLNN to ensure robust and stable control, as shown in Figure 5.

$C_{P I D}=k_p+k_i / v+k_d v$     (17)

$e_b(t)=K_p \frac{d \alpha(t)}{d t}=K_b \omega(t)$     (18)

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Figure 5. MLNN-based PID tuning system

The summing function's objective is to total the product of the inputs, weights, and bias. On the other hand, the following formula applies if there is a bias in the neurons of the network.

This is explained by Eq. (19), Eq. (20), and Eq. (21).

$Q_a=\sum_{i=1}^n\left[\alpha_{i j} * p_i(k)\right]+\operatorname{bias}_{i j}$     (19)

where, pi(k) is the total number of neuron inputs, αij connection weight linking to the neuron.

$f(p)=1 / 1+\exp ^{-Q}$     (20)

As such, the data from the training phase should not be used in the MLNN-PID validation and/or testing phases.

$Y_i(t)=1 / 1+\exp ^{-\left[Q_a\right]}$     (21)

The Eq. (22) is used to assess Mean square error (MSE) and the representation of $A_P$ is the expected output, $A_P{ }^*$ is the actual output, and n is the total number of occurrences.

$M S E=\frac{1}{n} \sum\left(A_p-A_p^*\right)^2$     (22)

The suggested work trains a single-layer feed-forward back propagation MLNN for DC-Link balancing [26].

3.3 Simulation and modeling

MATLAB-Simulink is used to create the PV-UPQC model, which incorporates the suggested control schemes and optimization methodologies. The model simulates various grid and load conditions, including different irradiance levels (200 to 1000 W/m²), linear irradiance (1000 W/m²), and unbalanced load scenarios.

3.3.1 Simulation of grid and load conditions

The model accounts for varying irradiance levels and load unbalances to assess the effectiveness of the PV-UPQC's ability to sustain power quality.

3.3.2 Performance evaluation

The simulation results are compared against standard performance metrics to validate the effectiveness of the proposed PV-UPQC design [19].