As the penetration of distributed photovoltaic (PV) generation continues to increase, voltage violations—both overvoltage and undervoltage—have become a critical challenge for distribution networks, particularly at the terminal distribution transformer (DT) substations. In this paper, I analyze the mechanism of voltage deviation in distribution feeder zones caused by PV integration, and then explore the dual closed-loop control and active/reactive power characteristics of solar inverter systems. Based on these analyses, I propose a voltage regulation strategy for DT substations that leverages the power control capability of the solar inverter. The strategy ensures that the terminal DT substation voltage remains within acceptable limits under various operating conditions. The effectiveness of the proposed control strategy is validated through simulation studies.
In many county-level power grids, due to the scattered load distribution and long supply radius, the tap position of the distribution transformer is often set to a higher level during heavy load periods to maintain the terminal voltage above 198 V. However, when a large number of distributed PV systems are connected via the DT substation, the reverse power flow during high PV generation and low load conditions can cause the voltage to exceed the upper limit of 235.4 V. Conversely, during nighttime when PV output is zero and load is high, the voltage may drop below 198 V. Traditional tap changing requires power outage, which is not a viable real-time solution. Hence, I propose a method that utilizes the solar inverter to dynamically adjust both active and reactive power outputs to regulate the voltage at the point of common coupling (PCC) of the DT substation.
1. Voltage Impact of PV Integration on Distribution Networks
1.1 Impact on 10 kV Feeder Voltage
Consider a radial distribution feeder with N nodes, each having both load and PV generation, as shown in the general topology. The voltage drop from the feeder head (node 0) to node k can be expressed as:
$$
\Delta U_k = \frac{1}{U_N} \sum_{j=1}^{k} \left[ R_j \cdot \sum_{i=j}^{n} (P_{L_j} – P_{PV_i}) + X_j \cdot \sum_{i=j}^{n} (Q_{L_j} – Q_{PV_i}) \right]
$$
where \(U_N\) is the nominal line voltage at the low-voltage side of the DT, \(R_j\) and \(X_j\) are the resistance and reactance from the feeder head to node j, \(P_{L_j}, Q_{L_j}\) are the load active and reactive powers at node j, and \(P_{PV_i}, Q_{PV_i}\) are the PV active and reactive powers at node i.
When PV output exceeds local load, the net power flow reverses, potentially causing voltage rise. The closer the PV is to the feeder end, the more significant the voltage elevation.
1.2 Impact on DT Substation Voltage
For a simplified equivalent circuit of a DT substation with PV:
$$
V_1 = \frac{1}{K} \left( U_0 – \Delta U_k \right) + \frac{1}{V_2} \left[ (P_{PV} – P_L) R + (Q_{PV} – Q_L) X \right]
$$
Here, \(V_1\) is the low-voltage side output voltage of the DT, \(V_2\) is the load-side or inverter-side voltage, \(K\) is the transformer ratio, \(U_0\) is the feeder head voltage, and \(R, X\) are the low-voltage line resistance and reactance.
In practical engineering, the voltage rise due to PV active power injection can be approximated by:
$$
\Delta U = \frac{P R}{U_N}
$$
For example, a 100 kW PV system connected via 200 m of BVV-120 mm² cable (resistance 0.153 Ω/km) causes a voltage rise of:
$$
\Delta U = \frac{100 \times (200 \times 0.153 / 1000)}{0.4} = 7.65 \text{ V}
$$
This rise, combined with the already high tap setting, often leads to overvoltage during light load conditions.
To further illustrate, I built a 5-node distribution network model in MATLAB (parameters: system short-circuit capacity 10 MVA, voltage 10.5 kV, DT capacity 120 kVA, ratio 10 kV/400 V, no-load loss 0.47 kW, short-circuit loss 1.85 kW, no-load current 1.3%, short-circuit voltage 4.0%, line type LGJ-95, length 30 km, 100 kW PV at node 5, 300 kW total load evenly distributed, power factor 0.9). The voltage profiles at different nodes for 100% and 40% load conditions, with and without PV, are summarized in Table 1.
| Node | 100% Load, No PV | 40% Load, No PV | 100% Load, PV connected | 40% Load, PV connected |
|---|---|---|---|---|
| 1 | 228.5 | 231.0 | 228.8 | 231.3 |
| 2 | 224.2 | 229.8 | 225.1 | 230.5 |
| 3 | 220.1 | 228.5 | 221.5 | 229.7 |
| 4 | 216.3 | 227.2 | 218.2 | 228.9 |
| 5 | 212.8 | 226.0 | 215.6 | 228.0 |
The results show that without PV, the voltage at the terminal node drops significantly under heavy load. With PV, the voltage at all nodes rises, and at node 5 (PV connection point) the voltage exceeds 235 V under light load conditions.
2. Solar Inverter Control Mechanism
2.1 Voltage-Current Dual Closed-Loop Control
The solar inverter connects to the DT substation through an LCL filter. The mathematical model in the dq rotating reference frame is:
$$
\begin{cases}
L_0 \frac{di_d(t)}{dt} – L_0 \omega i_q(t) = V_d(t) – e_d(t) – R_0 i_d(t) \\
L_0 \frac{di_q(t)}{dt} + L_0 \omega i_d(t) = V_q(t) – e_q(t) – R_0 i_q(t)
\end{cases}
$$
Transforming to the S-domain yields:
$$
\begin{cases}
V_d(s) = (sL_0 + R_0) i_d(s) – L_0 \omega i_q(s) + e_d(s) \\
V_q(s) = (sL_0 + R_0) i_q(s) + L_0 \omega i_d(s) + e_q(s)
\end{cases}
$$
The dual closed-loop control consists of an outer voltage loop and an inner current loop. The active power \(P\) and reactive power \(Q\) in the dq frame are:
$$
\begin{cases}
P = U_d I_d + U_q I_q \\
Q = U_d I_q – U_q I_d
\end{cases}
$$
By controlling the q-axis current \(I_q\), the solar inverter can independently regulate reactive power, while \(I_d\) regulates active power.
2.2 Active and Reactive Power Capability
The reactive power capability of a solar inverter is constrained by its rated apparent power \(S_{PV}\):
$$
Q_{PV} = \pm \sqrt{S_{PV}^2 – P_{PV}^2}
$$
Figure 1 illustrates the relationship. When the inverter operates at maximum active power (point a), its reactive capacity is zero. By reducing active power, more reactive margin becomes available. For instance, at point b (maximum power), the reactive range is between points c and d. If voltage still exceeds limits, active power curtailment (point f) provides additional reactive capability.
Typically, the solar inverter operates in maximum power point tracking (MPPT) mode. However, when voltage violations occur, the inverter can either absorb reactive power (during overvoltage) or inject reactive power (during undervoltage) to regulate the PCC voltage.
3. Proposed Voltage Regulation Strategy
3.1 Reactive Power Control
I define a target voltage range for the DT substation: [210 V, 235 V]. When the measured voltage \(U\) lies within this range, the inverter maintains its current operating point. If \(U > 235\) V, the solar inverter absorbs reactive power (inductive) to lower the voltage. If \(U < 210\) V, the inverter injects reactive power (capacitive) to raise the voltage. The control curve is shown in Figure 2 (conceptual). The required reactive power change \(\Delta Q\) can be derived from the voltage sensitivity:
$$
\Delta U \approx \frac{R \Delta P + X \Delta Q}{U_N}
$$
Assuming active power remains unchanged, the necessary reactive power adjustment is:
$$
\Delta Q = \frac{U_N \Delta U}{X}
$$
Here, \(X\) is the equivalent reactance between the inverter and the DT substation.
3.2 Active Power Control
If the reactive power capacity is insufficient to bring the voltage back into the target range (e.g., during severe overvoltage with high PV output), active power curtailment is employed. The active power reduction needed is:
$$
\Delta P = \frac{U_N \Delta U}{R}
$$
The solar inverter then limits its active power output accordingly, as illustrated in the active power control curve (Figure 3 conceptual). A threshold voltage \(U_{max}\) is set; when \(U > U_{max}\), active power is reduced linearly or stepwise.
3.3 Integrated Control Flow
The complete control algorithm is as follows:
- Measure the DT substation voltage \(U\) in real time.
- If \(U_{min} \le U \le U_{max}\) (target range), maintain current inverter operation.
- If \(U > U_{max}\):
- Calculate required reactive absorption \(\Delta Q\) using the sensitivity formula.
- If the required \(\Delta Q\) is within inverter capability, send command to adjust \(I_q\) for reactive absorption.
- If not sufficient, calculate active power curtailment \(\Delta P\) and limit active output.
- If \(U < U_{min}\):
- Calculate required reactive injection \(\Delta Q\).
- Send command to adjust \(I_q\) for reactive injection. Even when PV active output is zero (nighttime), the inverter can still provide reactive power up to its rated capacity.
- Return to step 1.
This strategy ensures that the DT substation voltage is always maintained within the desired safe range, regardless of load and PV variations.
4. Simulation Validation
4.1 Simulation Setup
I implemented the proposed strategy in MATLAB/Simulink using the topology shown in Figure 4 (conceptual). The system parameters are listed in Table 2.
| Parameter | Value |
|---|---|
| DT capacity | 120 kVA |
| Distribution voltage | 10/0.4 kV |
| Line impedance | 0.712 + j0.284 Ω/km |
| Inverter rated capacity | 100 kVA |
| Target voltage range | [210 V, 235 V] |
| Feeder length | 30 km (30 nodes) |
| Total load | 2100 kW (evenly distributed) |
| PV location | Node 30 (terminal) |
4.2 Case 1: Light Unchanged, Load Transition from High to Low
In this scenario, solar irradiance is constant, and the load drops from 2100 kW to 420 kW at t=1 s. Without voltage control, the terminal nodes experience overvoltage. With the proposed control, the solar inverter absorbs reactive power and, if necessary, curtails active power to keep voltage within limits. Table 3 summarizes the results.
| Node | Before Load Drop (No Control) | After Load Drop (No Control) | After Load Drop (With Control) |
|---|---|---|---|
| 28 | 234.4 V | 236.5 V | 234.2 V |
| 29 | 234.4 V | 236.7 V | 233.8 V |
| 30 (PV node) | 234.4 V | 236.8 V | 230.3 V |
The control successfully reduced the terminal voltage from 236.8 V to 230.3 V, avoiding overvoltage.
4.3 Case 2: No Solar Irradiance, Load Transition from Low to High
Here, nighttime condition (PV active output = 0) and load increases from 420 kW to 2100 kW at t=1 s. Without control, the voltage at the end of the feeder drops below 198 V. The proposed strategy commands the solar inverter to inject reactive power (capacitive) to support voltage, even though there is no active power generation. Since the inverter has full reactive capacity (100 kvar), it can provide significant voltage support. Results are shown in Table 4.
| Node | Before Load Rise (No Control) | After Load Rise (No Control) | After Load Rise (With Control) |
|---|---|---|---|
| 28 | 223.0 V | 207.2 V | 210.8 V |
| 29 | 223.0 V | 206.8 V | 210.6 V |
| 30 (PV node) | 223.0 V | 206.5 V | 210.4 V |
The control lifted the terminal voltage from 206.5 V to 210.4 V, well above the 210 V lower threshold.
5. Conclusion
In this work, I have addressed the voltage violation problem in distribution transformer substations caused by high penetration of distributed PV. By analyzing the voltage impact mechanism and the control characteristics of solar inverter systems, I developed a practical voltage regulation strategy that leverages both reactive and active power control of the inverter. The key contributions are:
- Derivation of voltage sensitivity formulas for DT substations.
- Utilization of the reactive power capability of the solar inverter as a primary regulation means, with active power curtailment as a secondary measure.
- Implementation of a real-time control algorithm that maintains voltage within the [210 V, 235 V] range under varying load and PV conditions.
Simulation results confirm that the strategy effectively prevents both overvoltage and undervoltage at the terminal substation, even under extreme scenarios such as sudden load changes or zero solar irradiance. The approach is cost-effective as it largely exploits the existing inverter hardware without additional investment. Future work will focus on coordinating multiple solar inverter units in a feeder and incorporating battery energy storage for enhanced flexibility.