In the context of the evolving power system, the integration of distributed photovoltaic generation has been increasing steadily. While this reduces long-distance transmission costs and offers benefits such as low investment and short construction periods, it also introduces significant challenges, particularly concerning voltage regulation. The inherent variability of photovoltaic output and load profiles often leads to voltage violations at the point of common coupling. To address this, we propose a coordinated control scheme that leverages the reactive power capabilities of photovoltaic inverters and a magnetically controlled reactor. This paper details a method based on adaptive voltage partition weights for the coordinated reactive voltage control of distribution networks.
Our research presents a two-pronged approach. First, we develop a control strategy for photovoltaic inverters that adaptively determines reactive power output based on the voltage at the grid connection point. This strategy integrates different types of solar inverters’ control logics, combining voltage-dependent reactive power control and power factor-dependent reactive power control through a dynamic weighting system. Second, we establish an optimization model that minimizes voltage deviation and active power loss. This model is solved using an improved quantum particle swarm optimization algorithm to coordinate the reactive power output of photovoltaic inverters and the magnetically controlled reactor. The effectiveness of our method is validated through simulations on a modified IEEE 33-bus system.
The proposed inverter control strategy operates by detecting the voltage at the point of common coupling and classifying it into distinct zones. For each zone, a unique weighting coefficient is assigned to the two control modes—Q(U) and Q(cos φ (P))—resulting in a composite reactive power command. This adaptive approach allows for a smooth transition between different types of solar inverters’ operating modes, optimizing both voltage support and power factor. When the voltage is within the target range, the power factor control dominates. As voltage deviates, the weight shifts towards direct voltage-reactive power feedback, ensuring a rapid and effective response.
In the optimization phase, we consider the combined impact of photovoltaic inverters and the magnetically controlled reactor. The objective function is a weighted sum of the normalized active power loss and voltage deviation. The constraints include power flow equations, voltage limits, and the capacity limits of the reactive power sources. For this multi-objective optimization problem, we employ an improved quantum particle swarm optimization algorithm. This algorithm enhances the search capability and convergence accuracy compared to the standard particle swarm optimization, effectively avoiding local optima. The optimization determines the optimal reactive power output for the magnetically controlled reactor and the photovoltaic inverters, which represent different types of solar inverters in the system.
The reactive power output of the photovoltaic inverter, representing one of the key types of solar inverters, is determined by the following equation:
$$
Q = \alpha Q_1 + \beta Q_2
$$
Where \(Q_1\) is the reactive power command from the Q(U) control, \(Q_2\) is from the Q(cos φ (P)) control, and \(\alpha\) and \(\beta\) are the adaptive weights with \(\alpha + \beta = 1\). The specific values of these weights are determined by the voltage zone, as summarized in Table 1.
| Voltage Zone | Control Mode | \(\alpha\) (Weight for Q(U)) | \(\beta\) (Weight for Q(cos φ (P))) |
|---|---|---|---|
| A (Low Voltage) | Reactive Power Control | 1 | 0 |
| B (Low Range) | Reactive Power Control | \(\frac{U – U_{L0}}{U_{L1} – U_{L0}}\) | \(1 – \frac{U – U_{L0}}{U_{L1} – U_{L0}}\) |
| C (Target Range) | Reactive Power Control | 0 | 1 |
| D (High Range) | Reactive Power Control | \(\frac{U – U_{U0}}{U_{U1} – U_{U0}}\) | \(1 – \frac{U – U_{U0}}{U_{U1} – U_{U0}}\) |
| E (High Voltage) | Reactive & Active Power Control | 1 | 0 |
The reactive power control for the magnetically controlled reactor is based on a voltage-reactive power droop characteristic. Its output is adjusted to maintain voltage within acceptable limits, and the amount of adjustment is given by:
$$
\Delta Q = \frac{U_{ref}}{X_r} \Delta U_s
$$
Where \(\Delta Q\) is the change in reactive power output, \(\Delta U_s\) is the change in voltage at the point of common coupling, \(U_{ref}\) is the voltage reference, and \(X_r\) is the equivalent reactance of the system. The magnetically controlled reactor provides continuous reactive power compensation, acting as a slow but large-capacity source that complements the faster, more distributed control of the different types of solar inverters.
The multi-objective optimization problem is formulated to minimize both active power loss and voltage deviation. The objective function for this reactive power optimization is:
$$
\min F = a \frac{P_{loss}}{P_0} + b \frac{U_{dev}}{U_0}
$$
Where \(P_{loss}\) is the active power loss, \(U_{dev}\) is the total voltage deviation, \(P_0\) and \(U_0\) are their respective base values, and \(a\) and \(b\) are weighting factors. The constraints for this problem are the power flow equations and the capacity limits of the photovoltaic inverters and the magnetically controlled reactor. The improved quantum particle swarm optimization algorithm updates the position of each particle as follows:
$$
x_i(t+1) = P_i(t) \pm \alpha(t) \left| M_{best}(t) – x_i(t) \right| \ln\left(\frac{1}{\mu(t)}\right)
$$
$$
P_i(t) = \psi(t) P_{best,i} + \left[1 – \psi(t)\right] G_{best,i}
$$
$$
\alpha(t) = m + n \frac{t_{max} – t}{t_{max}}
$$
Our simulation case studies provide quantitative evidence of the method’s efficacy. In the first case, we compared the performance of different control strategies for the different types of solar inverters. Table 2 summarizes the results for the system under various photovoltaic output levels.
| PV Output (MW) | Control Strategy | Network Loss (kW) | Avg Voltage Deviation (%) |
|---|---|---|---|
| 2.00 | No Reactive Power | 524 | 4.28 |
| Q(U) Control | 1101 | 1.17 | |
| Q(cos φ (P)) Control | 753 | 3.16 | |
| Q(U, cos φ (P)) Control | 864 | 1.21 | |
| 1.50 | No Reactive Power | 261 | 3.48 |
| Q(U) Control | 677 | 0.49 | |
| Q(cos φ (P)) Control | 483 | 1.09 | |
| Q(U, cos φ (P)) Control | 459 | 0.57 | |
| 0.25 | No Reactive Power | 56 | 2.71 |
| Q(U) Control | 105 | 0.92 | |
| Q(cos φ (P)) Control | 56 | 2.71 | |
| Q(U, cos φ (P)) Control | 84 | 0.64 |
The results in Table 2 clearly show that our proposed Q(U, cos φ (P)) strategy provides a superior balance between network loss and voltage deviation compared to individual control methods, effectively harnessing the capabilities of the different types of solar inverters. For instance, at 2 MW output, it reduces the average voltage deviation by 4.28% compared to the base case, while incurring significantly lower losses than the Q(U) strategy.
In the second case study, we introduced a magnetically controlled reactor and performed a daily reactive power optimization. The improvements in voltage profiles at the photovoltaic-integrated nodes are shown in Table 3. This table highlights the performance of the Improved QPSO algorithm in coordinating the magnetically controlled reactor and the different types of solar inverters.
| Node | Scenario 1 (PSO, No MCR) | Scenario 2 (Improved QPSO, No MCR) | Scenario 3 (Improved QPSO, With MCR) |
|---|---|---|---|
| 10 | 0.035333 | 0.033903 | 0.019029 |
| 15 | 0.043981 | 0.040100 | 0.020691 |
| 24 | 0.010987 | 0.011845 | 0.007221 |
| 30 | 0.024514 | 0.027847 | 0.019583 |
The data in Table 3 demonstrates that the coordination of the magnetically controlled reactor with the different types of solar inverters, optimized by the Improved QPSO, leads to a substantial reduction in voltage deviation. The total network loss was also most effectively reduced in this scenario, showing a decrease of 2,663.186 kW compared to the scenario with only photovoltaic inverters and 807.141 kW compared to the scenario without the magnetically controlled reactor.
In conclusion, our adaptive voltage partition weight control method for different types of solar inverters provides a robust and efficient solution for local voltage regulation. By dynamically balancing voltage-reactive power feedback and power factor control, this strategy effectively maintains voltage within a narrow band while optimizing network losses. The coordination of these inverters with a magnetically controlled reactor, guided by an improved quantum particle swarm optimization algorithm, further enhances the system’s performance. This integrated approach significantly reduces both voltage deviations and active power losses, demonstrating the synergistic benefits of combining distributed and centralized reactive power resources. The continuous compensation capability of the magnetically controlled reactor, when paired with the fast-acting control of the different types of solar inverters, presents a promising avenue for improving the stability and economic efficiency of modern distribution networks with high photovoltaic penetration.