In modern power systems, the integration of photovoltaic (PV) systems has become increasingly prevalent due to the global shift toward renewable energy sources. However, this integration often leads to voltage instability and exceedance issues, particularly at the points of connection, which can compromise grid reliability and efficiency. The primary challenge arises from the fluctuating nature of solar power generation, causing voltage rises that exceed permissible limits, especially under varying load conditions. Traditional methods for reactive voltage regulation struggle to adapt to complex scenarios, such as multiple PV connection points or dynamic line impedance changes, resulting in suboptimal performance. To address these limitations, I propose a novel approach based on power control of solar inverters, which leverages linear calculations and an improved optimization algorithm to achieve effective voltage regulation. This method not only mitigates voltage exceedance but also enhances overall grid stability by optimizing the active and reactive power outputs of solar inverters.
The core of this approach lies in analyzing the impact of PV grid integration on voltage profiles and subsequently controlling the solar inverter power through a structured process. By dividing the control into three distinct stages—reactive power compensation, maximum power adjustment, and power curtailment—the method ensures adaptive management of inverter outputs. The control adjustments for active and reactive power are derived mathematically, forming the basis for a target function that minimizes unnecessary power reductions while maintaining voltage within safe bounds. An improved chaotic genetic algorithm is employed to solve this function, providing efficient and robust regulation outcomes. Through extensive testing, this method demonstrates significant improvements in voltage stability and reduction in network losses, making it a viable solution for modern power grids with high PV penetration.
Analysis of Voltage Exceedance Due to PV Grid Integration
When PV systems are connected to the grid, they typically operate at unity power factor to maximize power output, but this can lead to voltage rise at the connection points. The magnitude of this voltage increase depends on factors such as the impedance of the distribution lines, the load profile, and the penetration level of PV sources. To quantify this effect, consider a grid with $n$ load nodes, where a PV source is connected at node $k$. The voltage at this node, denoted as $U_k$, is influenced by the active power $P_{DG,k}$ and reactive power $Q_{DG,k}$ injected by the PV system. The main bus voltage is represented as $U_o$, with line impedance parameters including resistance $R_o$ and reactance $X_o$ for the main circuit, and equivalent resistance $R_i$ and reactance $X_i$ for the $i$-th line segment. The load power at each segment is given by $P_{L,i} + jQ_{L,i}$.
The voltage drop at the PV connection point $k$ after grid integration can be expressed as:
$$ \Delta U_k = \frac{\sum_{j=1}^{k} (R_j P_{DG,k} + X_j Q_{DG,k})}{U_N} $$
where $U_N$ is the nominal voltage, and $R_j$ and $X_j$ are the equivalent resistance and reactance of the $j$-th line segment, respectively. The percentage voltage loss, $U_k\%$, is used to derive the voltage rise rates due to active and reactive power, denoted as $\mu_{P,k}$ and $\mu_{Q,k}$, respectively:
$$ \mu_{P,k} = \frac{\partial U_k\%}{\partial P_{DG,k}} $$
$$ \mu_{Q,k} = \frac{\partial U_k\%}{\partial Q_{DG,k}} $$
These relationships highlight that the power output of solar inverters directly affects the local voltage, necessitating precise control to prevent exceedance. For instance, higher $P_{DG,k}$ values can exacerbate voltage rises, particularly in weak grids with high impedance. Thus, understanding these dynamics is crucial for designing effective regulation strategies.
Power Control of Solar Inverters
To regulate voltage, the proposed method focuses on controlling the power output of solar inverters through a linear calculation approach divided into three stages. This ensures that the inverter operates within its capacity while adjusting active and reactive power to maintain voltage stability. The control adjustments, $P_{PV,s}$ and $Q_{PV,s}$, for active and reactive power, respectively, are computed based on the voltage conditions at the connection point.
Reactive Power Compensation Stage
In normal operation, solar inverters operate at maximum power point tracking (MPPT) mode, but this can cause voltage to exceed limits. At this stage, the voltage $U_k$ at the PV connection point must satisfy:
$$ U_k = U_o – \frac{R_k P_j + X_k Q_j}{U_N} $$
where $P_j$ and $Q_j$ are the active and reactive power outputs during compensation. The goal is to adjust $Q_{DG,k}$ to bring $U_k$ close to the target voltage $U_{k,lim}$, which is defined as:
$$ U_{k,lim} = U_o – \frac{R_k P_j + X_k Q_{PV,b}}{U_N} $$
Here, $Q_{PV,b}$ represents the inductive reactive power output by the solar inverter when $U_k$ decreases to $U_{k,lim}$. Combining these equations, the required reactive power adjustment is derived as:
$$ Q_{PV,b} = \frac{(U_o – U_{k,lim}) U_N – R_k P_j}{X_k} $$
If the solar inverter’s apparent power $S$ reaches its maximum $S_{max}$ and voltage exceedance persists, the control proceeds to the next stage.
Maximum Power Adjustment Stage
When the inverter operates at maximum capacity, the power factor angle $\theta_{lim}$ is adjusted to control voltage. The voltage $U_k$ must meet:
$$ U_k = U_o – \frac{R_k P_{PV,i} + X_k Q_{PV,i}}{U_N} $$
where $P_{PV,i}$ and $Q_{PV,i}$ are the active and reactive power outputs of the $i$-th PV source. The target is to achieve $U_{k,lim}$ by modifying the power factor, leading to:
$$ U_{k,lim} = U_o – \frac{R_k P_{PV,i} + X_k Q_{PV,i}}{U_N} $$
The adjusted active power output at time $t$, $P_{PV,t}$, is calculated as:
$$ P_{PV,t} = S_{max} \cos(\theta_{lim}) $$
$$ \theta_{lim} = \arctan\left(\frac{Q_{PV,i}}{P_{PV,i}}\right) $$
This stage ensures that the inverter remains within its thermal limits while contributing to voltage regulation.
Power Curtailment Stage
If voltage exceedance continues after the previous stages, active power curtailment is applied. At the maximum power factor angle $\theta_{max}$, the voltage $U_k$ is given by:
$$ U_k = U_o – \frac{R_k P_{PV,i} + X_k Q_{PV,i}}{U_N} $$
and the target voltage $U_{k,lim}$ is achieved through:
$$ U_{k,lim} = U_o – \frac{R_k P_{PV,s} + X_k Q_{PV,i}}{U_N} $$
where $P_{PV,s}$ is the curtailed active power, computed as:
$$ P_{PV,s} = \frac{(U_o – U_{k,lim}) U_N – X_k Q_{PV,i}}{R_k} $$
This stage prioritizes voltage stability over maximum power generation, ensuring grid safety.
Calculation of Control Adjustments
The final control adjustments for the solar inverter’s active and reactive power are determined by combining the outcomes of the three stages. The adjustments $P_{PV,s}$ and $Q_{PV,s}$ are expressed as:
$$ P_{PV,s} = f(U_{k,s}, U_{k,m}, U_{k,1}) $$
$$ Q_{PV,s} = g(U_{k,s}, U_{k,m}, U_{k,1}) $$
where $U_{k,s}$ is the voltage after curtailment, $U_{k,m}$ is the voltage at $\theta_{lim}$, and $U_{k,1}$ is the voltage at $\theta_{max}$. These adjustments form the basis for the subsequent voltage regulation step.
Implementation of Grid Reactive Voltage Regulation
Using the control adjustments $P_{PV,s}$ and $Q_{PV,s}$, the grid reactive voltage regulation is formulated as an optimization problem. The objective function aims to minimize the total reactive power adjustment across all solar inverters while reducing active power curtailment when possible. The target function is defined as:
$$ \min \left( \sum_{i=1}^{N} Q_{PV,s,i} + \alpha \sum_{i=1}^{N} P_{PV,s,i} \right) $$
where $N$ is the number of solar inverters, and $\alpha$ is a weighting factor that penalizes active power curtailment. The constraints include:
- Solar Inverter Capacity Constraint: The apparent power $S_i$ of each inverter must not exceed its rated capacity $S_{max,i}$:
$$ S_i = \sqrt{P_{PV,i}^2 + Q_{PV,i}^2} \leq S_{max,i} $$ - Active Power Constraint: The active power output of each PV source is bounded by:
$$ 0 \leq P_{PV,i} \leq P_{PV,max,i} $$ - Power Flow Constraint: The nodal power balance must be maintained:
$$ P_{i,c} = \sum_{j} U_i U_j (G_{ij} \cos \delta_{ij} + B_{ij} \sin \delta_{ij}) $$
$$ Q_{i,c} = \sum_{j} U_i U_j (G_{ij} \sin \delta_{ij} – B_{ij} \cos \delta_{ij}) $$
where $P_{i,c}$ and $Q_{i,c}$ are the active and reactive power at node $i$, $U_i$ and $U_j$ are voltages at nodes $i$ and $j$, $G_{ij}$ and $B_{ij}$ are the conductance and susceptance of line $ij$, and $\delta_{ij}$ is the phase angle difference. - Voltage Constraint: The voltage at each node must remain within permissible limits:
$$ U_{min} \leq U_i \leq U_{max} $$
To solve this optimization problem, an improved chaotic genetic algorithm is employed. This algorithm enhances convergence and avoids local optima by incorporating chaotic sequences for population initialization and mutation. The steps include encoding the control variables, evaluating fitness based on the objective function, and applying chaotic crossover and mutation operations. The output is the optimal set of $P_{PV,s}$ and $Q_{PV,s}$ values that achieve voltage regulation while minimizing network losses.
Experimental Results and Analysis
To validate the proposed method, tests were conducted on a 220 V PV-integrated distribution network with three solar inverters, each with a maximum apparent power of 2.5 MVA and an active power output of 2.48 MW. The network comprised 29 nodes connected by overhead lines with an average spacing of 65 meters. Key parameters are summarized in Table 1.
| Parameter | Value |
|---|---|
| Upper Voltage Limit (p.u.) | 1.01 |
| Minimum Inverter Power Factor | 0.98 |
| Line Equivalent Resistance (Ω) | 75 |
| Line Equivalent Inductance (mH) | 12.5 |
| Active Power Output (kW) | 10 |
First, the impact of PV integration on voltage was analyzed under normal, light-load, and heavy-load conditions. The voltage variations over time are shown in Table 2, indicating significant exceedance issues, particularly under light and heavy loads, with peaks up to 1.63 p.u.
| Time (s) | Normal Load (p.u.) | Light Load (p.u.) | Heavy Load (p.u.) |
|---|---|---|---|
| 1 | 1.03 | 1.05 | 1.11 |
| 2 | 1.02 | 1.03 | 1.28 |
| 3 | 1.04 | 1.25 | 1.26 |
| 4 | 1.03 | 1.04 | 1.33 |
| 5 | 1.03 | 1.16 | 1.14 |
| 6 | 1.04 | 1.13 | 1.06 |
| 7 | 1.02 | 1.21 | 1.22 |
| 8 | 1.01 | 1.44 | 1.19 |
| 9 | 1.05 | 1.13 | 1.48 |
| 10 | 1.03 | 1.59 | 1.63 |
The proposed method was then applied to control the solar inverter power, and the local voltage results were compared before and after control. As shown in Figure 1, without control, voltage exhibited significant fluctuations and exceedance, especially under increasing load ratios. After applying the method, the voltage stabilized around 220 V, with no notable exceedance, demonstrating the effectiveness of solar inverter power control.
Further tests evaluated the control performance across the three stages. Table 3 presents the voltage magnitude and solar inverter power outcomes at each stage. Without control, voltage reached 1.076 p.u., with the inverter operating near its maximum capacity. After reactive power compensation, voltage decreased to 1.059 p.u., and further reductions were achieved in the maximum power adjustment and curtailment stages, ultimately reaching 1.012 p.u. The inverter power was efficiently managed, dropping to 2.42 MVA after curtailment, confirming that the method successfully regulates voltage through precise control of solar inverters.
| Control Stage | Voltage Magnitude (p.u.) | Inverter Power (MVA) |
|---|---|---|
| No Control | 1.076 | 2.48 |
| Reactive Power Compensation | 1.059 | 2.51 |
| Maximum Power Adjustment | 1.057 | 2.51 |
| Power Curtailment | 1.012 | 2.42 |
Additionally, the method’s ability to prevent voltage exceedance was assessed under varying PV power fluctuations. As illustrated in Figure 2, the number of nodes experiencing voltage exceedance remained below three, and the voltage fluctuation rate was consistently under 1.25%, highlighting the robustness of the approach. This is crucial for maintaining grid stability in scenarios with high PV variability.
Finally, the impact on network losses was examined. Figure 3 shows the network loss results for 10 randomly selected nodes after regulation. The losses were significantly reduced, all falling below 5.9 kW/h, compared to pre-regulation levels that often exceeded 15.5 kW/h. This underscores the method’s efficacy in enhancing grid efficiency while ensuring voltage stability.
Conclusion
In this paper, I have presented a reactive voltage regulation method for power grids that utilizes power control of solar inverters. By analyzing the voltage impact of PV integration and implementing a three-stage control process, the method effectively derives adjustments for active and reactive power. The optimization via an improved chaotic genetic algorithm ensures minimal power curtailment and enhanced voltage stability. Experimental results confirm that the approach successfully mitigates voltage exceedance, reduces fluctuations, and lowers network losses, making it a practical solution for grids with high solar penetration. Future work could explore integration with smart grid technologies and real-time monitoring systems to further improve adaptability and performance.