Application of Voltage Optimization Strategy for Rotary Power Flow Controllers in Loop Closing of Distribution Networks

Abstract

To mitigate voltage limit issues in the operation of a novel electromagnetic voltage regulation device, this paper presents a flexible loop-closing control strategy with voltage optimization. The approach uses a two-stage path optimization: in the first stage, the voltage phase at the loop-closing point is adjusted to ensure smooth operation, while in the second stage, the voltage magnitude is optimized to prevent voltage limits and achieve seamless regulation. By integrating phase angle difference calculations with coordinated rotation angle control, the simulation results show that this strategy reduces loop-closing current by approximately 95.87% compared to direct loop closing, decreases voltage fluctuations by around 50.0% compared to traditional methods, and shortens operation time by 40.14%. This approach significantly enhances system stability and response speed, effectively addressing the issue of excessive loop-closing current caused by voltage deviations at distribution network tie switches.

1. Introduction

To enhance power supply reliability in distribution networks, open-loop operation is typically employed within a closed-loop design [1,2]. During equipment maintenance, loop-closing transfer operations are necessary to enable uninterrupted load transfer. Prior to loop-closing, a voltage difference exists at the loop-closing point, which diminishes to zero upon completing the operation. Due to the presence of various inertia elements in the system, the loop-closing process may cause oscillations that gradually decay until the system reaches a new steady state, simultaneously generating a current through the loop-closing switch, commonly referred to as loop current [3,4].

The voltage requirements at the loop-closing point are as follows: the phase sequence at both ends of the loop must be consistent; the maximum voltage magnitude difference between the two ends should not exceed 20%; and the phase difference between the voltages at the loop-closing point should not exceed 20°. However, with the increasing integration of distributed energy sources, the voltage magnitude and phase difference across the tie switch grow, resulting in higher loop currents. If the loop current surpasses the relay protection device’s threshold, the loop-closing process may fail, jeopardizing grid safety and power supply reliability [5]. The loop current’s magnitude and characteristics are crucial for assessing system stability and response [6]. Thus, proactive adjustments to the voltage magnitude and phase difference at the loop-closing point are essential to mitigate the loop current’s impact on the system.

One method to suppress loop current involves leveraging intelligent algorithms [7,8,9], which utilize existing grid equipment to enhance the radial distribution network’s configuration, thereby improving loop-closing conditions and facilitating system recovery after faults. Reference [10] introduces a decentralized approach using a multi-agent system, factoring in customer priorities and distributed generators, while addressing operational constraints in both intact and restored feeder sections to achieve loop restoration. Meanwhile, Reference [11] proposes a multi-objective evolutionary algorithm for service restoration, emphasizing the use of remote-controlled switches and effectively managing distribution systems without simplifying the network topology. However, the limitation of these methods lies in the fact that when dealing with large-scale systems, the computational complexity increases significantly, and the feasibility and implementation difficulty of the algorithms also rise.

Another method involves using phase shifters and other adjustment devices to precisely regulate voltage magnitude and phase at the loop-closing point. For instance, in cases where a 30° phase difference caused by star and delta connections hinders loop-closing, Reference [12] proposes a flexible control device utilizing a thyristor-controlled phase-shifting transformer to manage significant voltage and phase discrepancies. Similarly, Reference [13] examines the operation of phase-shifting transformer devices, enhances their design to optimize voltage quality, and suggests a strategy for smooth regulation in scenarios with substantial phase differences. Although these methods can effectively adjust voltage and phase differences, they still face the challenge of not achieving smooth regulation. Furthermore, these methods inherently rely on power electronic devices, which results in relatively higher costs and increased maintenance complexity.

For multi-factor adjustments, power flow control capabilities are essential. Reference [14] proposes a loop-closing device that meets the demand for non-interruptible load transfer under extreme conditions and proposes adjustment schemes for both AC and DC sides, effectively reducing the impact of loop current. Reference [15] studies the application of static var generators in voltage regulation and non-interruptible loop-closing operations and proposes strategies for non-interruptible load transfer under voltage disturbances.

Although these control devices can effectively suppress loop current, power electronic devices are expensive and difficult to maintain, and some devices can only handle single loop-closing scenarios, which have certain limitations. The Rotary Power Flow Controller (RPFC), as a new type of electromagnetic flexible interconnection device, can continuously control the voltage magnitude and phase of the line and has broad application potential [16,17]. The RPFC consists of two rotary phase shifting transformers (RPSTs), with their primary windings connected in parallel to the power supply, and the secondary windings connected in series with the line. Driven by servo motors, the stator windings of the two RPSTs rotate by a certain angle, generating a series voltage with continuously adjustable amplitude and phase. Regarding the basic characteristics and modeling of RPFC, Reference [18] analyzes the power control characteristics of the RPFC, highlighting its advantages of low cost, high durability, and reliability, making it a promising option for applications. References [19,20] systematically studies the modeling and application of RPFC, focusing on its physical structure and mathematical models, and verifying its potential to enhance power system security and stability. Regarding the planning and optimization applications of RPFC in distribution networks, Reference [21] proposes a planning method combining RPFC and energy routers to address energy imbalance and voltage distribution challenges, validating its effectiveness through a two-layer optimization model. Reference [22] enhances RPFC’s PQ decoupling control by introducing variable speed and fuzzy PI adjustments, resolving oscillation and overshoot issues. Regarding the applications of RPFC in reactive power compensation and voltage regulation, Reference [23] develops a steady-state mathematical model and dual closed-loop control strategy for RPFC, enabling bidirectional reactive power regulation and validating its dynamic performance. Reference [24] proposes an RPFC-based co-phase power supply compensation method for electrified railways, using a dual closed-loop control strategy and verifying its effectiveness through simulation. Reference [25] introduces an RPFC-based rolling optimization strategy for bidirectional voltage regulation and loss reduction, improving system stability and reliability. Regarding the applications of RPFC in loop-closing control, Reference [26] proposes a virtual power-based RPFC loop-closing control method to regulate voltage seamlessly at the loop-closing point, preventing system misjudgment and ensuring safe and stable operation. Reference [27] constructs a steady-state power decoupling control model for RPFC based on instantaneous reactive power theory. It addresses the coordination of rotary phase transformers with a two-stage speed control scheme, demonstrating effective performance for flexible loop-closing operations.

This study introduces a flexible loop-closing approach using a two-stage optimal path tailored for RPFC applications in distribution networks. The key contributions of this work are summarized as follows:

• A two-stage optimal path-based RPFC loop-closing control strategy is proposed, focusing on adjusting voltage phase and magnitude at the loop-closing point to prevent the voltage fluctuations commonly seen in traditional methods.
• A phase angle difference calculation and rotation angle coordination control method are proposed, dynamically adjusting the RPFC rotation angle setpoint, significantly improving the stability and response speed of the loop-closing operation.
• Comparative simulations confirm the practicality and reliability of the proposed method, demonstrating the considerable potential of RPFC in enabling flexible loop-closing operations within distribution networks.

The paper is structured as follows: Section 2 explains the fundamental working principle of RPFC. Section 3 outlines the two-stage optimal path-based RPFC loop-closing control strategy. Section 4 provides simulation results and analysis, while Section 5 summarizes the conclusions.

2. Basic Principle of RPFC

To prevent excessive loop-closing currents during the process, it is generally necessary to ensure that the voltage difference at the loop-closing point remains within a reasonable range. Figure 1 demonstrates a typical loop-closing scenario in a distribution network. The green switches in the figure indicate that the loop-closing current is small, and the loop can be directly closed. The red switches indicate that the loop-closing current is large, and the loop cannot be directly closed. The arrows represent the load or the next-level network. As shown, switches B1 and B3 are positioned at either end of the same feeder, resulting in a relatively small voltage difference at the loop-closing point. On the other hand, switches B2 and B4 connect feeders from different substations, leading to a more pronounced voltage difference. Additionally, switch B5 connects feeders originating from transformers with distinct connection groups, introducing a 30° phase shift and creating a larger voltage difference at the loop-closing point.

This paper employs RPFC to minimize the voltage difference at the loop-closing point, effectively reducing the loop-closing current. The RPFC is composed of two RPSTs, as illustrated in its main circuit in Figure 2. In the figure, the red and blue arrows represent the stator voltages of the two RPSTs, the black dashed arrows represent their corresponding set values, and the green arrow represents their combined voltage, which is the RPFC output voltage. In the diagram, U₁ represents the sending-end voltage of the line where the RPFC is installed; U₂ and U₃ denote the voltages at the loop-closing point; ΔU is the RPFC output voltage; U_st1 and U_st2 are the stator voltages of RPST1 and RPST2, respectively; k is the turn ratio of the stator and rotor windings of the RPST; a₁ and a₂ are the rotation angles of the two RPSTs; and QF_b is the tie switch; Z_eq is the equivalent impedance; j indicates the phase of the output voltage, and d refers to the angle between the output voltage and the stator voltage. The sending-end voltage U₁ excites the RPFC to generate constant amplitude stator voltages U_st1 and U_st2, which are combined to produce an adjustable output voltage with flexible amplitude and phase control, thus enabling precise regulation of the left-end voltage at the loop-closing point.

In addition, the power limitation of the RPFC is closely related to its capacity, similar to the working principle of a transformer. Due to the star and delta connection on the primary and secondary sides, the harmonic components in the RPFC output voltage are very small, resulting in low total harmonic distortion (THD). This gives the RPFC a significant advantage in power quality, effectively reducing harmonic pollution and ensuring stable system operation. Therefore, the power limitation of the RPFC is primarily determined by its design capacity, while providing efficient voltage regulation and low harmonic distortion.

The RPFC is modeled as a controlled voltage source DU in series with an equivalent impedance Z_eq. Under standard operating conditions, the stator voltages of the RPFC have equal magnitudes, denoted as U_st1 = U_st2 = U_st. Therefore, δ, between the stator voltage and the output voltage is given by:

$$\delta =\arccos ({\displaystyle \frac{\mathrm{\Delta }\mathit{U}}{2{\mathit{U}}_{\mathrm{st}}}})$$

(1)

The RPFC calculates the output voltage amplitude and phase setpoints, ΔU_set and φ_set, based on the phasor relationship between U₁ and U₃. These output voltage setpoints are then converted into the corresponding rotation angle setpoints α_{a_set} and α_{b_set} for the two rotary phase shifters:

$$\left\{\begin{array}{l}{\alpha }_{\mathrm{a}\_\mathrm{set}}={\phi }_{\mathrm{set}}+{\delta }_{\mathrm{set}}\\ {\alpha }_{\mathrm{b}\_\mathrm{set}}={\phi }_{\mathrm{set}}-{\delta }_{\mathrm{set}}\end{array}\right.$$

(2)

3. RPFC Loop-Closing Control Strategy

3.1. Two-Stage Operation Path for Output Voltage

The operational path planning for the RPFC output voltage is illustrated in Figure 3, where b and g denote the voltage phases of U₂ and U₃, respectively. The planning process is divided into two stages. The primary goal of the first stage is to align the voltage magnitude and phase at the loop-closing point, ensuring β = γ. The constraint in this stage is to ensure that the magnitudes of U₂ and U₁ remain equal throughout the process, i.e., U₂ = U₁. Therefore, in the first stage, the output voltage is required to follow the arc path ADB, with the output voltage magnitude and phase setpoints as follows:

$$\left\{\begin{array}{l}\mathrm{\Delta }{U}_{\mathrm{set}1}=2U_1\sin {\displaystyle \frac{{\beta }_{\mathrm{set}}}{2}}\\ {\phi }_{\mathrm{set}1}=90+{\displaystyle \frac{{\beta }_{\mathrm{set}}}{2}}\end{array}\right.$$

(3)

The setpoint β_set for the RPFC, depending on different operational periods, can be divided into the following three processes:

$$\left\{\begin{array}{ll}{\beta }_{\mathrm{set}}=0\hfill & t<t_1\hfill \\ {\beta }_{\mathrm{set}}=k_{\mathrm{r}}(t-t_1)\hfill & t_1\le t<t_2\hfill \\ {\beta }_{\mathrm{set}}=\gamma \hfill & t\le t_2\hfill \end{array}\right.$$

(4)

In this equation, t₁ and t₂ denote the initial moments of the first and second stages; k_r represents the rate of change in the phase setpoint β_set. When t < t₁, the RPFC is in its initial state, and the two stator voltages differ by 180°, resulting in zero output voltage, and the node voltage U₂ = U₁. When β = β_set = γ, the first stage of the RPFC operation concludes, and it transitions to the second stage.

The second stage aims to equalize the voltage magnitudes at both ends of the loop-closing point, ensuring U₂ = U₃. The constraint during this stage is to maintain consistent phase alignment, i.e., β = γ. Therefore, in the second stage, the RPFC output voltage is required to follow the path of BC, with the output voltage magnitude and phase setpoints expressed as follows:

$$\left\{\begin{array}{l}\mathrm{\Delta }{\mathit{U}}_{\mathrm{set}2}=\mathrm{abs}({\mathit{U}}_3-{\mathit{U}}_1)\\ {\phi }_{\mathrm{set}2}=\arg ({\mathit{U}}_3-{\mathit{U}}_1)\end{array}\right.$$

(5)

The phase setpoint remains unchanged, i.e., β = β_set = γ, while the magnitude setpoint is U_{2_set} = U₃. When the voltage magnitudes satisfy U₂ = U_{2_set} = U₃, the second stage of RPFC operation concludes, ensuring zero voltage difference at the loop-closing point.

3.2. Rotation Angle Coordination Control Method

Figure 4 illustrates the RPFC rotation angle coordination control process. In the figure, θ_1a denotes the initial angle between the stator voltage U_st10 and U_{sta_set}, while θ_2b represents the initial angle between U_st20 and U_{stb_set}. The control system compares the initial positions of the two stator voltages with their respective setpoints and selects the closest stator voltage setpoint as the target value. This approach helps to reduce the operation time and prevent voltage limit violations during the control process.

If the initial state satisfies θ_1a < 180°-θ_2b, U_{sta_set} and U_{stb_set} are chosen as the stator voltage setpoints for RPST1 and RPST2, respectively. Accordingly, the rotation angle setpoints α_{1_set} and α_{2_set} are determined as follows:

$$\left\{\begin{array}{l}{\alpha }_{1\_\mathrm{set}}={\alpha }_{\mathrm{a}\_\mathrm{set}}={\phi }_{\mathrm{set}}+{\delta }_{\mathrm{set}}\\ {\alpha }_{2\_\mathrm{set}}={\alpha }_{\mathrm{b}\_\mathrm{set}}={\phi }_{\mathrm{set}}-{\delta }_{\mathrm{set}}\end{array}\right.$$

(6)

Similarly, if θ_1a > 180°-θ_2b, U_{stb_set} is assigned as the stator voltage setpoint for RPST1, while U_{sta_set} is assigned for RPST2. As a result, the rotation angle setpoints α_{1_set} and α_{2_set} are given by:

$$\left\{\begin{array}{l}{\alpha }_{1\_\mathrm{set}}={\alpha }_{\mathrm{b}\_\mathrm{set}}={\phi }_{\mathrm{set}}-{\delta }_{\mathrm{set}}\\ {\alpha }_{2\_\mathrm{set}}={\alpha }_{\mathrm{a}\_\mathrm{set}}={\phi }_{\mathrm{set}}+{\delta }_{\mathrm{set}}\end{array}\right.$$

(7)

Depending on the operating conditions, select either Equation (6) or Equation (7) as the setpoint for the RPFC rotation angles, and adjust α₁ and α₂ accordingly. This ensures continuous control of the output voltage’s magnitude and phase until the voltages at the loop-closing point satisfy the requirements of the distribution network.

In summary, the RPFC flexible loop-closing control strategy involves the following four steps, as illustrated in Figure 5.

• First-stage path planning. The RPFC aims to align the voltage phases at the loop-closing point, ensuring equal voltage magnitudes throughout the process.
• Second-stage path planning: The RPFC focuses on equalizing voltage magnitudes at the loop-closing point, maintaining consistent phases during the operation.
• Phase angle difference calculation: Determine the set angle δ_set between the stator and output voltages using Equation (1).
• Rotation angle coordination control: Compare the initial positions of the two stator voltages with their setpoints, and select the closest stator voltage setpoint as the target value.

By meticulously planning the RPFC output voltage’s operating path, this strategy successfully eliminates the voltage difference at the loop-closing point, ensuring the distribution network operates reliably.

4. RPFC Flexible Loop-Closing Simulation

4.1. Loop-Closing Simulation Scenario

Taking a specific loop-closing network as an example, its network topology and load distribution are shown in Figure 6. The loop network consists of multiple feeders, each with an impedance of (0.11 + j0.15) Ω/km, with the lengths of the feeders marked in the figure. The load power at each node is expressed in MVA, representing the power demand at different nodes. The electromotive forces are denoted as E₁ and E₂, where E₁ is 10 kV at a 10° phase, and E₂ is 10 kV at a 40° phase. The specific parameters of the RPFC are listed in

Table 1. Simulation parameters of RPFC.

	Capacity /MVA	Voltage Level/kV		Turn Ratio	Rated Speed °/s
		Primary	Secondary
RPST1	2.0	10	2.9	3.44	6
RPST2	2.0	10	2.9	3.44	6
RPFC	4.0	10	5.8	1.72	6

.

4.2. Loop-Closing Performance Analysis

Figure 7 and Figure 8 illustrate the voltage magnitude and phase angle waveforms at the loop-closing point under different control strategies, while Figure 9 depicts the loop-closing current waveforms. Figure 10 and Figure 11 present the output voltage waveforms under various control strategies. These figures clearly demonstrate the changes in voltage, phase, and current under different strategies, further reflecting the effectiveness of each strategy. In the figures, Dq represents the phase angle difference between the voltages at both ends of the loop-closing point. The subscripts “dr,” “tr,” and “op” represent direct loop-closing, the control method proposed in the literature [26], and the new control strategy proposed in this paper, respectively. The corresponding voltage and current data are summarized in

Table 2. Voltage and current metrics across various control strategies.

Parameters	Direct Loop-Closing	Method in Reference [26]	Proposed Method
U2/kV	5.01	5.31	5.32
U3/kV	5.32	5.32	5.32
Dq/°	31.35	0.11	0.10
I/A	295.36	12.20	12.18

, providing key performance indicators for different methods. A detailed comparative analysis of these three loop-closing methods is provided below, highlighting their respective strengths, weaknesses, and applicable scenarios.

For the direct loop-closing method, the voltage magnitudes at the loop-closing point are U_{2_dr} = 5.01 kV and U_{3_dr} = 5.32 kV, with a phase difference of Δθ_dr = 31.35°. At t = 17.0 s, QF_b is directly closed, resulting in the voltages on both sides dropping to 4.97 kV and the loop-closing current I_tr reaching 295.36 A. This current value far exceeds the safety threshold, failing to meet the loop-closing conditions and causing system instability. The main issue with the direct loop-closing method is that it does not account for the interaction between voltage and current, leading to excessive voltage fluctuations and high loop-closing currents. This not only violates the stability requirements of the power system but also risks triggering relay protection malfunctions, further compromising system safety. Therefore, although the direct loop-closing method is simple to operate, its lack of coordinated voltage and current control severely limits its practical applicability, as it is prone to voltage violations.

When operating with the loop-closing control strategy from the literature [26], RPFC starts operating at t = 2 s. The voltage magnitude at the end U_{3_tr} reaches 5.32 kV, and the loop-closing condition is met at t = 23.64 s, at which point QF_b is closed, resulting in a loop-closing current I_tr of 12.20 A. The voltage U_{2_tr} increases from 5.01 kV to 5.31 kV, with a peak of 5.61 kV and a trough of 4.99 kV during operation. The phase difference Δθ_tr decreases from 31.35° to 0.11°, with a trough of −5.28° during the process. Although this method reduces the loop-closing current by approximately 95.87% compared to direct loop-closing, it experiences significant voltage fluctuations, which impact system stability.

With the loop-closing control strategy proposed in the literature [26], the RPFC begins operating at t = 2 s. The voltage magnitude U_{3_tr} gradually increases to 5.32 kV, and the loop-closing condition is met at t = 23.64 s, at which point QF_b is closed, resulting in a loop-closing current of I_tr = 12.20 A. During the process, the voltage U_{2_tr} increases from 5.01 kV to 5.31 kV, with a peak of 5.61 kV and a trough of 4.99 kV. The phase difference Δθ_tr decreases from 31.35° to 0.11°, with a minimum value of −5.28° during the process. Compared to the direct loop-closing method, this strategy significantly reduces the loop-closing current by approximately 95.87%. However, despite the significant reduction in current, the method in the literature [26] exhibits substantial voltage fluctuations during the loop-closing process, which negatively impact system stability. These fluctuations not only affect the normal operation of equipment but can also disrupt subsequent voltage regulation and power distribution. As such, although this method performs well in reducing current, its limitations in voltage control restrict its applicability.

Under the RPFC loop-closing control strategy proposed in this paper, the voltage magnitude U_{3_op} stabilizes at 5.32 kV, and the loop-closing condition is met at t = 14.15 s. After QF_b is closed, the loop-closing current I_op is 12.18 A. The voltage U_{2_op} increases from 5.01 kV to 5.32 kV, with minimal fluctuations, and the phase difference Δθ_op decreases from 31.35° to 0.10°. Compared to the method in the literature [26], the proposed strategy not only achieves a similar reduction in loop-closing current but also reduces voltage fluctuations by approximately 50.0% and shortens the operation time by 40.14%. This method not only improves operational efficiency but also ensures zero voltage difference at the loop-closing point, guaranteeing the stability and reliability of the distribution network.

Figure 10 and Figure 11 further illustrate the differences in voltage and phase waveforms under the two methods. Notably, both methods share the same initial and final steady-state values for voltage and phase, but their adjustment processes differ significantly. In Figure 10, the traditional method exhibits significant voltage fluctuations, with the voltage rising from 0 V to a peak of 3400 V, then falling to a steady value of 2809.34 V. This indicates poor voltage control, as the method fails to achieve a smooth transition. In contrast, the proposed strategy uses an optimized control approach that allows the output voltage to directly stabilize at the target value without overshooting, ensuring fast and stable voltage regulation.

Similarly, in Figure 11, the phase adjustment process of the traditional method is slower due to a lack of optimized control over the phase angle. The method does not prioritize the nearest path for adjustment, resulting in inefficiencies. In contrast, the proposed strategy adjusts the phase more efficiently, even though it involves a temporary dip followed by a rise. Specifically, the phase decreases from 90° to 84.3° and then increases to 94.98°. During this process, the small output voltage amplitude ensures negligible impact on the terminal voltage, maintaining overall stability. Overall, the proposed strategy significantly accelerates the phase adjustment process while ensuring voltage stability, demonstrating its effectiveness in enhancing power system stability and reliability.

The key difference lies in the fact that the method in the literature [26] does not take voltage stability into consideration during the loop-closing process. As a result, it is highly susceptible to voltage violations, as evidenced by the significant voltage swings and the failure to maintain voltage within the acceptable limits. In contrast, the proposed RPFC method not only reduces the loop-closing current but also ensures that voltage remains within the required limits, thereby maintaining system stability. By effectively controlling both current and voltage, the RPFC strategy ensures a reliable and stable operation of the distribution network, making it a more robust solution compared to the method in the literature [26].

5. Conclusions

This paper presents a flexible loop-closing control strategy for the RPFC, utilizing a two-stage optimal path planning approach to mitigate potential voltage limit issues during active loop-closing operations. The main conclusions are as follows:

• The proposed strategy effectively minimizes voltage fluctuations and current surges during loop-closing by optimizing the transitions of voltage magnitude and phase. This approach helps to prevent voltage limit violations, ensuring stable operation during the loop-closing process and avoiding system instability caused by voltage fluctuations.
• As an independent device, the RPFC can perform loop-closing control without relying on other system equipment (such as auxiliary voltage sources or distributed energy sources) for coordination. This characteristic makes RPFC more flexible and convenient for practical applications, reducing dependency on other devices and enhancing system operational efficiency and stability.
• Compared to traditional methods, the proposed control strategy significantly shortens the loop-closing time. Through rotational angle coordination control, the adjustment path of RPFC output voltage is optimized, effectively improving the response speed of loop-closing operations and ensuring quick restoration of the power grid.
• As an electromagnetic device, the RPFC offers excellent tolerance and low maintenance costs, but its operational efficiency may be slightly slower compared to power electronic devices. This limitation makes RPFC more suitable for long-term stable operation in scenarios where extremely fast response times are not critical, though it remains a reliable solution for many applications requiring flexible loop-closing control.
• Future research could focus on strengthening the application of RPFC after loop-closing, especially in its role in power flow distribution and scheduling within the entire power system. Further research could also explore how to integrate RPFC with energy storage systems, distributed energy sources, and other power system technologies to optimize configuration and collaborative scheduling, thereby enhancing the flexibility and stability of the grid.