Optimization of Power Quality in Grid Connected Photovoltaic Systems

The photovoltaic-grid system is comprised of the following components: a photovoltaic generator, a boost converter, a maximum power point tracking controller, a three-level inverter, an RL filter, and the grid. This system is shown in Figure 1.

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Figure 1. Global system of PVG connected to grid

2.1 Modelling of the photovoltaic generator

The real equivalent circuit design of a photovoltaic cell is illustrated in Figure 2.

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Figure 2. Equivalent circuit of photovoltaic cell

The current-voltage (I-V) characteristic for a PVG cell can be described as follows:

$I=I_{p h}-I_s\left[\left(\exp \frac{V+I \cdot R_s}{m \cdot \frac{K \cdot T}{q}}\right)-1\right]-\frac{V+I \cdot R_s}{R_{s h}}$             (1)

The current-voltage characteristic for a PV panel that has $N_s$ cells connected in series and $N_P$ cells connected in parallel is given by the following expression:

$\begin{gathered}I=N_p \cdot I_{p h}-N_p \cdot I_s\left[\exp \left\langle\left(\frac{1}{m \cdot K \cdot T / q}\right) \cdot\left(\frac{V}{N_s}+\frac{R_s \cdot I}{N_p}\right)\right\rangle-\right. 1]-\frac{N_p}{R_{s h}} \cdot\left(\frac{V}{N_s}+\frac{R_s \cdot I}{N_p}\right)\end{gathered}$             (2)

Photovoltaic panel model. In our study, we chose the Sun Power SPR-305E-WHT-D model for many factors such as accuracy and realism, as the model's characteristics closely resemble real-world solar panels, ensuring accuracy in representative simulations. In addition, our selection is driven by the alignment of specific model characteristics with research objectives, especially when investigating efficiency, energy productivity, or responses to different environmental conditions. Simulink's provision of pre-built libraries for this model further supports this choice, facilitating seamless integration and compatibility into the simulation environment with other system components, simplifying the simulation process. Furthermore, prior use of the Sun Power SPR-305E-WHT-D and its validation in other studies has strengthened our confidence in its consistency and comparability, confirming its suitability for achieving reliable results.

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Figure 3. Irradiation effect on the power-voltage characteristic

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Figure 4. Temperature effect on the power-voltage characteristic

For SunPowerSPR-305E-WHT-D (Neser=5, Nar=66) PV panel, Figure 3 shows the effect of irradiation for the power-voltage characteristic of this PV panel.

Figure 4 illustrates the temperature effect for the power-voltage characteristic of this PV panel.

2.2 Model of boost converter

A DC-DC converter acts as a switch-mode regulator to transform an unregulated DC voltage to a regulated DC output voltage. The regulation is usually achieved through PWM and the switching device commonly used is either a MOSFET or an IGBT. The primary function of a boost DC-DC converter is to increase the DC voltage. The configuration of a DC-DC boost converter with a PV system as the input is depicted in Figure 5. Maximum power is reached when the MPPT algorithm changes and adjusts the duty cycle of the boost DC-DC converter [7].

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Figure 5. Boost converter

The mathematical expressions that control the operation of the converter are presented as follows:

$V_o=\frac{V}{(1-\alpha)}$             (3)

$I_o=I \cdot(1-\alpha)$             (4)

2.3 Three-level inverter models

2.3.1 Model and control of FC inverter

The flying capacitor three-level three-phase inverter is depicted in Figure 6. This term is applied due to the floating nature of the capacitor with respect to the earth's potential. Thus, a three-level flying capacitor inverter consists of four switches, two main capacitors & one auxiliary capacitor in each leg [8].

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Figure 6. Flying capacitor three level inverter (FC) [9]

The output voltage is shown in Table 1.

Table 1. States of one leg of FC inverter

As outlined in Table 1, each leg of the inverter can assume one of three potential switching states: positive (P), Zero (O), or negative(N). Activation of the top two switches (Ti1 and Ti2) results in switching state P and the corresponding output voltage is positive(+Uc/2). When the medium switches Ti2 and Ti3 are turned on switching state is O, and the output voltage is zero. Lastly, when the lower switches (Ti3 and Ti4) are turned on, the switching state becomes N, and the corresponding output voltage is negative(-Uc/2)

For any initial state of FC inverter, the inverter output voltages are giving by:

$V_{A N}=S_1\left(V_{C 1}-V_{C 2}\right)+S_2 V_{C 2}-\frac{V_{C 1}}{2}$             (5)

2.3.2 Model and control of NPC inverter

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Figure 7. Neutral point clamped three level inverter (NPC)

The diagram in Figure 7 displays the detailed configuration of the NPC inverter. The inverter consists of a DC bus and three legs, each of which contains four IGBTs, four free-wheeling diodes, and two clamping diodes. The antiparallel connection of each free-wheeling diode with the power switch forms a reverse conduction path for the current. The DC bus includes two capacitors (C1 and C2), providing the midpoint "O". Capacitors can absorb the power difference between the rectifier and the inverter, and support the dc link. denotes the dc-link voltage [10].

Connection functions. Three connection functions are defined for each leg of the inverter, and each function corresponds to one of the three states of the leg:

$\left\{\begin{array}{l}F_{c 1 j}=F_{1 j} \cdot F_{2 j} \\ F_{c 2 j}=F_{2 j} \cdot F_{3 j} \\ F_{c 3 j}=F_{3 j} \cdot F_{4 j}\end{array}\right.$             (6)

Table 2. States of one leg of NPC inverter

Table 2 demonstrates that each segment of the NPC inverter has the capability to have one of three distinct switching states: P, O, N.

Output voltages. The output voltages of NPC inverter are expressed as follows:

$\left[\begin{array}{l}V_{10} \\ V_{20} \\ V_{30}\end{array}\right]=\left[\begin{array}{lll}F_{c 11} & F_{c 21} & F_{c 31} \\ F_{c 12} & F_{c 22} & F_{c 32} \\ F_{c 13} & F_{c 23} & F_{c 33}\end{array}\right] \cdot\left[\begin{array}{c}\frac{U c}{2} \\ 0 \\ -U c \\ 2\end{array}\right]$             (7)

We define the output voltage vector as follows, based on the voltages $V_{10}$, $V_{20}$ et $V_{30}$:

$V_s=V_{10} e^{j 0}+V_{20} e^{-j 2 \pi / 3}+V_{30} e^{j 2 \pi / 3}$             (8)

$V_s=V_d+j V_q$             (9)

2.3.3 Model and control of ANPC inverter

The fundamental structure of the three-phase, three-level active neutral point clamped (ANPC) inverter is depicted in Figure 8. It is evident that each phase incorporates two supplementary active switches that are connected in reverse parallel with the clamping diodes. Since the modulation strategy is the same for each phase, analysis on one phase leg is sufficient [11].

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Figure 8. Active neutral point clamped three level inverter (ANPC)

For one phase, the relation of switching states and the output voltage is shown in Table 3.

Table 3. States of one leg of ANPC inverter

Table 3 demonstrates that each segment of the ANPC inverter also has the capability to have one of three distinct switching states: P, O, N.

2.4 Filter model

A basic type of filter is the line inductance, commonly referred to as an L-filter (as shown in Figure 9). The ideal characteristic of this filter is that its impedance increases as the frequency increases, thereby increasing the reduction of high-frequency signals. The transfer function matrix of an L-filter in the Laplace domain is simply written as [12]:

$Y_L^s=\left[\begin{array}{cc}\frac{1}{s L_t+R_t} & 0 \\ 0 & \frac{1}{s L_t+R_t}\end{array}\right]$             (10)

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Figure 9. Filter RL

2.5 Main control strategies

The objective of the global system controller is to maximize the power delivered by the PV generator, regulate the DC-link voltage, set a unit power factor and to control the switches of the multilevel inverter.

2.5.1 MPPT control (IC)

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Figure 10. MPPT control (IC)

The MPPT algorithm employs the principle of generating disturbances by varying the cyclic ratio α and monitoring its impact on the power output of the PVG. It utilizes the instantaneous conductance I/V and the incremental conductance dv/di for MPPT. This approach is illustrated in Figure 10.

Figure 11 presents its algorithm.

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Figure 11. IC algorithm [13]

2.5.2 DC bus control

The DC voltage controller is responsible for regulating the DC bus and setting the reference active power, $P_{g~ref }$. The block diagram of the DC voltage control system is displayed in Figure 12.

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Figure 12. DC bus control block diagram

2.5.3 Power control

The expression for active and reactive power $\left(P_g, Q_g\right)$ can be represented using the Park components of the supply voltage $\left(V_{t d}, V_{t q}\right)$ and line current $\left(I_{t d}, I_{t q}\right)$ as indicated below:

$\left\{\begin{array}{l}P_g=V_{t d} \cdot I_{t d}+V_{t q} \cdot I_{t q} \\ Q_g=V_{t d} \cdot I_{t q}-V_{t q} \cdot I_{t d}\end{array}\right.$              (11)

Reference currents $\left(I_{td ref }, I_{tq ref }\right)$ are used to establish the desired reference active and reactive powers $\left(P_{g ref}, Q_{g ref}\right)$, as follows:

$\left\{\begin{array}{l}I_{t d ~ r e f}=\frac{P_{g ~ r e f} \cdot V_{t d}-Q_{g ~r e f} \cdot V_{t q}}{V_{t d}{ }^2+V_{t q}{ }^2} \\ I_{t q ~ r e f}=\frac{P_{g ~ r e f} \cdot V_{t q}+Q_{g ~ r e f} \cdot V_{t d}}{V_{t d}{ }^2+V_{t q}{ }^2}\end{array}\right.$             (12)

A unity power factor refers to a condition in an electrical system where the phase angle between the voltage and current waveforms is zero, resulting in an ideal power factor of 1.

This power factor can be achieved by setting the reactive power reference to zero. Additionally, the system can generate or absorb reactive power by adjusting the reactive power reference to be either negative or positive:

$\left\{\begin{array}{l}Q_{\text {g ref }}<0 \\ Q_{\text {g ref }}>0\end{array}\right.$             (13)

2.5.4 Current control

The execution of vector current control in the park reference frame involves synchronizing the reference with the grid voltage. The electrical equations for the filter ($R_t, L_t$) are detailed as follows:

$\left\{\begin{array}{l}V_{t d}=R_t I_{t d}+L_t \frac{d I_{t d}}{d t}-\omega_s L_t I_{t d}+V_{s d} \\ V_{t q}=R_t I_{t q}+L_t \frac{d I_{t q}}{d t}+\omega_s L_t I_{t q}+V_{s q}\end{array}\right.$             (14)

Current control block diagram is illustrated in Figure 13.

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Figure 13. Current control block diagram

2.5.5 PWM control

Pulse Width Modulation (PWM) is a technique for controlling the switches of a three-phase three-level inverter. The intersective PWM method is a simple way to generate the PWM pulse train in response to a given signal. As illustrated in Figure 14, a sine wave (blue) is compared with a triangle wave (red) and when the triangle wave is less than the sine wave, the PWM output signal (green) is set to a high level (1). Conversely, it is set to a low level (0).

The level switching edge is produced at every moment the sine wave intersects the triangle wave. Thus, the different crossing positions result in variable duty cycle of the output waveform [14].

where:

$\left\{\begin{array}{l}m a=\frac{V_{m .s i n}}{V_{m . t r i}}=0.8 \\ m f=\frac{f_{t r i}}{f_{\text {sin }}}=200\end{array}\right.$             (15)

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Figure 14. PWM principle

Combined, the control strategies establish a complementary relationship, promoting a coordinated and synchronized approach to power generation, conversion, and delivery. MPPT technique plays a pivotal role in optimizing power generation. DC bus control generates a stable voltage, this stable voltage supports efficient PWM modulation. In turn, PWM guarantees that the multi-level inverter output aligns with grid integration standards, which contribute to stable and reliable power supply in the PV system, ensuring its efficient performance in real-world applications.

The study's result highlights the outstanding performance of the ANPC inverter, supported by remarkably low THD values for both current (0.96%) and voltage (43.28%). It is classified as an ideal option for enhancing power quality in grid-connected photovoltaic systems.

The broader implications of the study underscore the critical role of inverter topology in enhancing power quality, indicating the potential for significant improvements in overall performance and reliability and opening up prospects for practical applications, ensuring a cleaner, more stable power supply. Investment in advanced inverter technologies, specifically ANPC, is proposed as a strategic approach to meeting power quality standards and contributing to the sustainability and efficiency of the broader energy infrastructure.

As for future work, the study suggests exploring various inverter models and configurations and investigating emerging technologies and hybrid setups to enhance power quality metrics. It also recommends improving simulation models and considering a wider range of environmental conditions to gain a more comprehensive understanding of inverter performance.