In the context of modern power systems, the integration of distributed photovoltaic generation has significantly transformed the operational landscape of distribution networks. The inherent intermittency of solar power, combined with load fluctuations, often leads to voltage deviations at points of common coupling. To address these challenges, we propose a novel coordinated reactive voltage control strategy that leverages the adaptive capabilities of both photovoltaic inverters and magnetically controlled reactors. Our approach is designed to enhance system stability, reduce transmission losses, and maintain voltage profiles within acceptable bounds. Throughout this work, we emphasize the critical role of various types of solar inverter in providing reactive power support, which is essential for effective voltage regulation in high-penetration renewable energy scenarios.
Traditional voltage control methods, such as on-load tap changers, capacitor banks, and static var compensators, often suffer from discrete operation, slow response, or limited flexibility. In contrast, modern types of solar inverter offer continuous reactive power output, enabling more precise and rapid voltage adjustments. However, the coordination between multiple inverters and other reactive power devices remains a complex optimization problem. Our research addresses this gap by introducing a voltage partition-based adaptive weighting scheme for inverters and integrating them with MCRs through an improved quantum particle swarm optimization algorithm. The proposed method ensures that different types of solar inverter can dynamically adjust their reactive power outputs based on real-time voltage conditions, thereby improving overall network performance.
The foundation of our control strategy lies in detecting the voltage at the point of common coupling and determining the appropriate weight coefficients for a composite reactive power control law. This composite law combines voltage-based and power-factor-based control actions. The reactive power output from a photovoltaic inverter is expressed as:
$$Q = \alpha Q_1 + \beta Q_2$$
where $$Q_1$$ represents the reactive power demand derived from the voltage control curve $$Q(U)$$, and $$Q_2$$ corresponds to the reactive power derived from the power factor control curve $$Q(\cos \phi(P))$$. The coefficients $$\alpha$$ and $$\beta$$ are the adaptive weights that sum to unity ($\alpha + \beta = 1$). These weights are dynamically adjusted according to the voltage partition zone in which the system operates. The voltage range is divided into five distinct zones, as illustrated conceptually in our approach. For different types of solar inverter, the same weighting logic can be applied, making the strategy universally applicable.
To implement the adaptive weighting, we define specific voltage thresholds: $$U_{L1}$$ and $$U_{U1}$$ as the lower and upper voltage limits, and $$U_{L0}$$ and $$U_{U0}$$ as the target voltage bounds. The weighting coefficients for each zone are summarized in Table 1.
| Voltage Zone | $$\alpha$$ | $$\beta$$ |
|---|---|---|
| A (U < U_{L0}) | 1 | 0 |
| B (U_{L0} ≤ U < U_{U0}) | $$\frac{U – U_{L0}}{U_{L1} – U_{L0}}$$ | $$1 – \frac{U – U_{L0}}{U_{L1} – U_{L0}}$$ |
| C (U_{L0} ≤ U ≤ U_{U0}) | 0 | 1 |
| D (U_{U0} < U ≤ U_{U1}) | $$\frac{U – U_{U0}}{U_{U1} – U_{U0}}$$ | $$1 – \frac{U – U_{U0}}{U_{U1} – U_{U0}}$$ |
| E (U > U_{U1}) | 1 | 0 |
This adaptive mechanism ensures that when voltage deviations are severe, the inverter prioritizes direct voltage-driven control, whereas under normal conditions, it focuses on maintaining power factor within regulatory limits. The scheme is highly robust and can be implemented across various types of solar inverter, including string inverters, microinverters, and central inverters, provided their reactive power capability is sufficient. For instance, a string connected grid inverter, which is one of the most common types of solar inverter, can easily adopt this control logic due to its built-in power electronics interface. The flexibility of the weighting function allows each inverter to contribute optimally without requiring extensive communication infrastructure.
In parallel with inverter control, we employ a magnetically controlled reactor as a supplementary reactive power compensation device. MCRs offer smooth and continuous regulation of reactive power, making them ideal for steady-state voltage support. The control logic for the MCR is based on voltage deviation. When the bus voltage exceeds the upper limit, the MCR absorbs reactive power (inductive mode); when it falls below the lower limit, the MCR supplies reactive power (capacitive mode). The reactive power adjustment is governed by:
$$\Delta Q = \frac{U_{ref}}{X_r} \Delta U_s$$
where $$\Delta U_s$$ is the voltage deviation at the MCR bus, $$U_{ref}$$ is the reference voltage, and $$X_r$$ is the equivalent reactance. The combination of inverter-based and MCR-based control enables a decentralized yet coordinated approach to voltage regulation. This is particularly beneficial when multiple types of solar inverter are present, as their collective reactive power capacity can be leveraged alongside the MCR for enhanced performance.
To optimize the coordination between photovoltaic inverters and MCRs, we formulate a multi-objective optimization problem. The primary objectives are minimizing active power losses and minimizing voltage deviations across the network. The weighted sum objective function is:
$$\min F = a \frac{P_{\text{loss}}}{P_0} + b \frac{U_{\text{dev}}}{U_0}$$
where $$P_0$$ and $$U_0$$ are the baseline values of power loss and voltage deviation, respectively, and $$a + b = 1$$ are weighting factors indicating the relative importance of each objective. The equality constraints are given by the power flow equations:
$$P_i = U_i \sum_{j \in i} U_j (G_{ij} \cos \theta_{ij} + B_{ij} \sin \theta_{ij})$$
$$Q_i = U_i \sum_{j \in i} U_j (G_{ij} \sin \theta_{ij} + B_{ij} \cos \theta_{ij})$$
Inequality constraints include voltage limits, inverter active power limits, and MCR reactive power limits:
$$U_i^{\min} \leq U_i \leq U_i^{\max}$$
$$P_{\text{pv},i}^{\min} \leq P_{\text{pv},i} \leq P_{\text{pv},i}^{\max}$$
$$Q_{\text{MCR}}^{\min} \leq Q_{\text{MCR}} \leq Q_{\text{MCR}}^{\max}$$
The optimization problem is solved using an improved quantum particle swarm optimization algorithm. QPSO enhances the global search capability of standard PSO by modeling particle states with quantum bits and incorporating a mean best position. The update rule for particle positions is:
$$x_i(t+1) = P_i(t) \pm \alpha(t) | M_{\text{best}}(t) – x_i(t) | \ln\left(\frac{1}{\mu(t)}\right)$$
$$P_i(t) = \psi(t) P_{\text{best},i} + [1-\psi(t)] G_{\text{best},i}$$
$$\alpha(t) = m + n \frac{t_{\max} – t}{t_{\max}}$$
$$M_{\text{best}}(t+1) = \frac{1}{N} \sum_{i=1}^N P_{\text{best},i}$$
where $$\alpha(t)$$ is the contraction-expansion coefficient, dynamically adjusted to balance exploration and exploitation. This improved QPSO algorithm is particularly effective for the nonlinear, constrained optimization inherent in reactive power dispatch. The decision variables include the reactive power outputs of inverters and the MCR. The algorithm efficiently searches the solution space to find the optimal set points, considering the diverse characteristics of different types of solar inverter.
To validate the proposed strategy, we conducted simulations on a modified IEEE 33-bus distribution system. The base voltage is 10 kV and base power is 10 MVA. Photovoltaic systems with a capacity of 2 MW each are integrated at buses 10, 15, 24, and 30. The maximum reactive power output per inverter is 1.2 MVar. The total system load is 3.715 + j2.300 MVA. The voltage target range is set to [0.97, 1.03] p.u., with allowable limits of [0.93, 1.07] p.u.
In the first set of simulations, we considered only inverter reactive power control, without MCR intervention. We evaluated four control strategies under three photovoltaic output levels: 2.0 MW, 1.5 MW, and 0.25 MW. The strategies are: (1) no reactive power output, (2) Q(U) control, (3) Q(cos φ(P)) control, and (4) the proposed Q(U, cos φ(P)) control. Table 2 summarizes the simulation cases.
| Case | PV Output (MW) | Control Strategy |
|---|---|---|
| 1-1 | 2.00 | No reactive power |
| 1-2 | 2.00 | Q(U) |
| 1-3 | 2.00 | Q(cos φ(P)) |
| 1-4 | 2.00 | Q(U, cos φ(P)) |
| 2-1 | 1.50 | No reactive power |
| 2-2 | 1.50 | Q(U) |
| 2-3 | 1.50 | Q(cos φ(P)) |
| 2-4 | 1.50 | Q(U, cos φ(P)) |
| 3-1 | 0.25 | No reactive power |
| 3-2 | 0.25 | Q(U) |
| 3-3 | 0.25 | Q(cos φ(P)) |
| 3-4 | 0.25 | Q(U, cos φ(P)) |
Table 3 presents the total active power loss and average voltage deviation for each case. The results clearly indicate that the proposed composite strategy outperforms the individual strategies in terms of balancing voltage regulation and power loss reduction. For instance, at 2.0 MW output, the average voltage deviation is reduced by 4.28% compared to the no-reactive-power case. The proposed strategy also yields lower losses than the Q(U) strategy, saving 237 kW at high generation levels. These findings confirm that the adaptive weighting approach effectively harnesses the capabilities of different types of solar inverter to achieve superior voltage and loss performance.
| Case | Power Loss (kW) | Average Voltage Deviation (%) |
|---|---|---|
| 1-1 | 524 | 4.28 |
| 1-2 | 1101 | 1.17 |
| 1-3 | 753 | 3.16 |
| 1-4 | 864 | 1.21 |
| 2-1 | 261 | 3.48 |
| 2-2 | 677 | 0.49 |
| 2-3 | 483 | 1.09 |
| 2-4 | 459 | 0.57 |
| 3-1 | 56 | 2.71 |
| 3-2 | 105 | 0.92 |
| 3-3 | 56 | 2.71 |
| 3-4 | 84 | 0.64 |
In the second simulation set, we introduced an MCR at bus 22 with a rating of 5 MVar. The photovoltaic output was fixed at 1.5 MW. We compared three optimization scenarios: (1) PSO optimization with inverters only, (2) improved QPSO optimization with inverters only, and (3) improved QPSO with inverters and MCR coordinated. The weighting factors a and b in the objective function were both set to 0.5, reflecting equal importance of loss minimization and voltage deviation minimization. Table 4 describes these scenarios.
| Scenario | PV Inverters | MCR | Optimization Method |
|---|---|---|---|
| 1 | Participating | Not participating | PSO |
| 2 | Participating | Not participating | Improved QPSO |
| 3 | Participating | Participating | Improved QPSO |
The simulation results for the photovoltaic nodes over a typical day are shown in terms of average voltage deviation in Table 5. The total power losses for scenarios 1, 2, and 3 were 6753.498 kW, 4897.453 kW, and 4090.312 kW, respectively. The coordinated approach significantly reduces losses by up to 2663.186 kW compared to the PSO-based inverter-only case. Moreover, the voltage deviations at photovoltaic nodes 10, 15, 24, and 30 are substantially decreased, with reductions of 1.63%, 2.32%, 0.38%, and 0.49%, respectively. These results underscore the efficacy of coordinating multiple types of solar inverter with MCR for comprehensive reactive power management.
| Scenario | Node 10 (%) | Node 15 (%) | Node 24 (%) | Node 30 (%) |
|---|---|---|---|---|
| 1 | 0.035333 | 0.043981 | 0.010987 | 0.024514 |
| 2 | 0.033903 | 0.040100 | 0.011845 | 0.027847 |
| 3 | 0.019029 | 0.020691 | 0.007221 | 0.019583 |
The proposed voltage partition-based adaptive control strategy demonstrates significant advantages in managing voltage deviations and reducing network losses. The adaptation of weights based on real-time voltage conditions allows for a seamless transition between voltage-driven and power-factor-driven control modes. This flexibility is particularly important given the wide variety of types of solar inverter deployed in modern distribution networks. For example, string inverters, which are among the most common types of solar inverter in residential and commercial installations, can benefit from this strategy due to their inherent reactive power capability. Similarly, microinverters and central inverters can be programmed with the same logic, ensuring system-wide consistency.
Furthermore, the integration of MCR provides an additional degree of freedom for reactive power compensation. Unlike discrete capacitor banks, MCRs offer continuous and fast response, making them ideal for steady-state voltage support. The coordination between inverters and MCR is achieved through the optimization framework, which considers the operational limits of both devices. The improved QPSO algorithm ensures that the solution converges efficiently, avoiding local optima. This is crucial for large-scale networks with numerous types of solar inverter and other controllable devices.
From an economic perspective, the reduction in power losses directly translates to cost savings for utilities and end-users. The improved voltage profile also enhances equipment lifespan and reduces maintenance costs. The proposed method does not require significant hardware upgrades, as it relies on existing inverter capabilities and standard MCR installations. Therefore, it is a cost-effective solution for modernizing distribution network operation. The adaptive nature of the control ensures robustness against system uncertainties, such as varying solar irradiance and load patterns.
In conclusion, we have developed and validated a comprehensive reactive voltage control strategy that integrates adaptive inverter control and MCR optimization. The key findings are as follows:
1. The voltage partition-based adaptive control strategy for photovoltaic inverters effectively balances voltage regulation and power factor maintenance. The composite control law, with dynamically adjusted weights, provides superior performance compared to individual Q(U) or Q(cos φ(P)) strategies. This approach is applicable to various types of solar inverter, including string, micro, and central inverters.
2. The coordination of photovoltaic inverters with MCR significantly reduces active power losses and voltage deviations. In our simulations, total losses decreased by up to 2663.186 kW, and voltage improvements were observed at all photovoltaic nodes. The improved QPSO algorithm outperforms standard PSO in finding optimal set points, demonstrating better convergence and solution quality.
3. The proposed method offers a practical and scalable solution for reactive power management in distribution networks with high photovoltaic penetration. It leverages existing infrastructure and does not necessitate costly new equipment. The continuous compensation capability of MCRs, combined with the flexibility of inverters, provides a powerful tool for maintaining system stability and efficiency.
4. Future work could explore the application of this strategy to transient voltage conditions, as the current focus is on steady-state optimization. Additionally, incorporating advanced communication and real-time data analytics could further enhance the responsiveness of the control system. The impact of different types of solar inverter on the overall performance is also an area deserving deeper investigation, as their efficiency and dynamic characteristics vary.
Overall, our research contributes a novel and effective methodology for voltage control in modern distribution networks. By harnessing the capabilities of multiple types of solar inverter and coordinating them with magnetically controlled reactors, we achieve a harmonious and efficient power system operation that meets the demands of the evolving energy landscape.