© The Author(s), published by EDP Sciences, 2024

Nomenclature

RPFC: Rotating power flow controller

MAGA: Multi-scenario adaptive genetic algorithm

FACTS: Flexible AC transmission systems

UPFC: Unified power flow controller

DPFC: Distributed power flow controller

ST: Sen transformer

HUPFC: Hybrid unified power flow controller

RPST: Rotating phase shifting transformer

T_sh, T_h: Shunt transformer, series transformer

α₁, α₂: Rotor angles of RPFC

: Voltage of the shunt transformer

: Voltage of the series transformer

I_s: Sending bus current of RPFC

I_s1: System line current

I_sh: Primary-side current of shunt transformer

Z_s: Primary impedance of transformer

Z_sh: Secondary impedance of transformer

K_sc: Series closure switch

R₁ + jX₁, R₂ + jX₂: Line impedance of bus

I_m: Steady state loop current

R, L: Resistance and inductance of RPFC

P, Q: Line transmitted power

U_RPFCd, U_RPFCq: d-axis and q-axis components of the RPFC output voltage

Z_RPST: Impedance of RPFC

Z_h: Impedance of series transformer

K_sh: Shunt transformer’s ratio

: RPST rotor current

: Stator-side current

U_rotor: Rotor-side voltage

U_stator1, U_stator2: Stator voltages of the two RPSTs

T_RPFC: RPFC equivalent ratio

Z_RPFC: RPFC equivalent impedance

K₁, K₂, K₃: Liaison switch

U_s, U₁, U₂, U₃: Bus voltage

U_N: Nominal system voltage

P_L, Q_L: Loads of the bus

P_DG, Q_DG: Distributed photovoltaic power

∆U: Voltage drop

R₀ + jX₀: Equivalent impedance of the line

U_RPFC: Output voltage of RPFC

K_bp: Parallel bypass switch

P₁ + jQ₁, P₂ + jQ₂: Transmission power of the line

Z_m: Total loop impedance

I_m: Closing loop point current

SP_RPFC: Actual rotational speed of the rotary phase transformer

η: Sampling interval

P_c, P_m: Current values of the crossover and mutation operators

N: Number of generations of the current run

I_max: Maximum current value allowed to pass through the line

P_ref, Q_ref: Set value of transmission power

G, B: Conductance and conductivity in the nodal conductivity matrix

SP_RPFCmax: Limiting rotational speed of the rotary phase transformer

t: System computation time

P_c0, P_m0: Initial values of the crossover and mutation operators

N_f: Number of stagnation

1 Introduction

Green and low-carbon transformation and response to climate change have become world trends and popular aspirations. Clean power sources and loads such as wind power, photovoltaics, energy storage, and electric vehicles will be widely connected to urban distribution grids [1]. Due to the simple grid structure and relatively single control method of the traditional distribution network, it has exposed some problems of its own when faced with diversified sources and loads, such as difficulty in meeting the development needs of regional balance and exacerbating the distribution network voltage and the complexity of power and difficulty of regulation [2]. In response to the main problems faced by the safe operation of active distribution networks, including voltage limit violations [3], dual power supply phase angle difference line closing, and power flow out-of-control phenomena [4], researchers in related fields have proposed many solutions.

In terms of voltage regulation, existing research can be divided into voltage regulation solutions for On-Load Tap Changer (OLTC) [5] and regulation of Distribution Network Synchronous Compensators (DSTATCOM) pressure scheme [6], voltage regulation scheme involving energy storage [7], etc. Literature [8] studied the impact of OLTC dynamic adjustment on voltage stability. The changes in primary voltage and current before and after OLTC dynamic adjustment can be used to monitor the mid-and long-term stability of the voltage, which can improve the voltage safety and stability of the power system. Literature [9] proposed a control strategy for DSTATCOM to participate in automatic voltage control, which coordinates control with remote control signals in constant reactive power mode, steady-state voltage regulation control mode, and transient voltage control mode. Through its reactive power output Control is carried out to support the access point voltage. However, the resistance voltage drop dominates the low-voltage distribution network, so the reactive power voltage regulation method has certain limitations. Literature [10] proposes a control method for distributed energy storage cluster voltage regulation. By constructing a cluster economic voltage regulation model, the optimal timing output of each cluster’s energy storage is determined. The results show that the proposed method can effectively eliminate node voltage deviations.

In terms of flexible loop closing of phase angle difference lines, literature [11] proposes a scheme that combines series phase-shifting transformers (static compensation) and four-quadrant converters (dynamic compensation). In the static compensation link, by adjusting the transformer winding ratio, the combination method generates the voltage vector to be compensated. In the dynamic compensation link, the output voltage amplitude and phase of the four-quadrant converter are flexibly controlled to achieve real-time online voltage compensation. However, due to the limitations of the design structure, the phase-shifting transformer can only cope with the loop closing situation of 30 phase angle differences, which has certain limitations and brings problems such as complex control and high cost to the operation of power electronic equipment in the dynamic compensation link. Literature [12] proposed a phase shifting scheme of Two Core Symmetrical Phase Shifting Transformer (TCPST). By changing the tap position of the secondary winding of the excitation transformer, the voltage amplitude can be kept unchanged. It realizes the function of voltage phase shifting, but it is an on-load tap changer type phase shifter, so it has the disadvantages of slow adjustment speed, discrete adjustment, and short service life.

In terms of power control, intelligent soft switches have better adjustment functions. Its basic structure consists of high-power fully controlled power electronic components [13]. By applying control strategies to the inverters on both sides, the output voltage amplitude of the access point is satisfied and independent control of the phase to achieve bidirectional decoupling control of active and reactive power flowing through interconnected lines. However, the design capacity of the back-to-back intelligent soft switch is determined by the maximum power that the line needs to transfer, so it exhibits large capacity and low cost. Disadvantages of height and large size.

In the 1990s, the General Electric Company of the United States proposed a flexible AC transmission device-RPFC based on traditional transformers and a Rotary Phase Shifting Transformer (RPST) [22], which can flexibly control the line compensation voltage without being affected by the line current influence, thereby providing a new method for economical, flexible, and frequent control of power systems [14]. At present, most research at home and abroad focuses on RPFC steady-state modelling [15] and power flow control of transmission lines [16]. Literature [17] compared the working characteristics of RPFC and unified power flow controller in transmission network power flow control, pointing out that RPFC has great advantages in terms of operation and maintenance, impact resistance, and cost. However, there are few studies on the application of RPFC in low-voltage distribution networks. This is because the traditional distribution network is based on a one-way power distribution network between the power grid and users. Its operation and control mode is relatively passive, and the demand for power flow control is relatively low. Small [18], and with access to large-scale distributed power sources and the continuous development of intelligent motor production and digital control technology [19], RPFC has re-entered people’s field of vision. Literature [20] proposed a phasor synthesis control and loss reduction optimization strategy based on RPFC, which can optimize line losses while satisfying the voltage quality of the station area. Literature [21] proposed a power-voltage-angle three-closed-loop power decoupling control method based on RPFC, which can effectively control the power at the loop closing point of the interconnected distribution network. However, the existing RPFC system is greatly affected by the parameters of the PI controller, so it is urgent to improve the RPFC system with new algorithms to meet the rapid adjustment requirements. Literature [21] proposed the use of variable universe fuzzy PI control to improve the RPFC controller, which effectively improved the response speed and control accuracy. However, its overshoot phenomenon still has a certain impact on the RPFC adjustment speed and the RPFC response. The improvement of speed has now become the main problem faced by the promotion and application of RPFC. Therefore, further research on RPFC control strategies is urgently needed to give full play to the regulatory performance of RPFC in voltage regulation, phase angle difference line flexible loop closing, and power flow control.

Based on the existing literature research results, this article proposes a solution using RPFC for typical application scenarios in active distribution network construction. First, the RPFC topology and working principle are explained, and a simplified circuit voltage source model of RPFC is established. By changing the RPFC parameters, a voltage vector of any size and direction that can be continuously adjusted in the line can be connected. Furthermore, a voltage over-limit control model based on RPFC, a flexible loop closing model for phase angle difference lines, and a power decoupling control model based on instantaneous reactive power theory were constructed. Then, an RPFC system control strategy using MAGA is proposed, which can directly solve the two rotor angles based on the built multi-scenario model, and output the solution results to the servo motor for real-time control of the RPFC. Finally, a simulation model was built and compared with traditional PI-RPFC. The simulation results showed that MAGA-RPFC significantly improved the system operating speed. Relevant research on RPFC is of great significance for improving the carrying capacity and reliability of distributed energy in distribution networks and is an effective supplementary solution for the construction of new active distribution networks in the future.

2 RPFC topology and working principle

2.1 RPFC topology

In the 1990s, General Electric Company of the United States proposed a flexible AC transmission device based on traditional transformers and rotary phase shifting transformers (Rotary Phase Shifting Transformer, RPST) – electromagnetic rotary power controller (Rotary Power Flow Controller, RPFC), which can flexibly control the line compensation voltage without the influence of line current, thus providing a new method for the economic and flexible control of the power system.

An RPFC topology is shown in Figure 1a, where T_sh is a shunt transformer; T_h is a series transformer; RPST1 and RPST2 are spin-transfer phase transformers; and α₁ and α₂ are the rotor angles of the two spin-transfer phase transformers, respectively.

Figure 1 RPFC topology structure. (a) RPFC schematic [18]. (b) RPFC topology diagram.

The rotary phase transfer transformer is the core component of the RPFC, and its working principle is shown in Figure 1b, based on the principle of electromagnetic induction, using two groups of RPST rotor angle rotation, respectively, to synthesize a stator voltage phase with constant amplitude and adjustable phase angle of 360°, and the two voltage phases are superimposed and connected to the secondary side of the series transformer, to inject a series voltage with adjustable amplitude and phase angle in the line.

RPST at rest is similar to a transformer, its stator-side voltage and rotor-side voltage there is a certain ratio relationship, while the phase difference is related to the angle between the stator and rotor α₁ and α₂, for the multi-pole RPST, the rotor angle only needs to be moved to a very small mechanical angle, you can change the voltage phase quantity of the series into the line.

2.2 Working principle

The operating principle of RPFC is shown in Figure 2a, where are the secondary side voltages of the shunt transformer T_sh and are the secondary side voltages of the series transformer T_h.

Figure 2 Working principle of RPFC. (a) RPFC equivalent circuit diagrams (b) RPFC simplified circuit diagram.

The single-phase equivalent circuit of RPFC is shown in Figure 2b, where I_s is the sending bus current of RPFC; I_s1 is the system line current; I_sh is the primary-side current of shunt transformer; Z_s is the primary-side impedance of shunt transformer; Z_sh is the impedance of shunt transformer’s secondary-side; Z_RPST is the impedance of rotary transfer phase transformer imputed to the secondary-side; Z_h is the impedance of series transformer imputed to the primary-side, and k_sh is the shunt transformer’s ratio; is the RPST rotor current; is the stator-side current; U_rotor is the rotor-side voltage; U_stator1 and U_stator2 are the stator voltages of the two RPSTs, respectively; and α₁ and α₂ are the phase-shift angles of the stator and rotor voltages of the two RPSTs, respectively.

Neglecting the transformer excitation current, the following relationship can be obtained according to the traditional transformer analysis methods(1) (2) (3)

In the equation:(4)

Referring to Figure 2a, the stator and rotor voltages of the two RPSTs satisfy the following relationship(5)

Let δ = (α₁ − α₁)/2, φ = (α₁ + α₁)/2, be obtained according to (4) and (5):(6)

Based on the electromagnetic induction theorem, assuming an ideal RPST, there is the active and reactive power emitted or absorbed on the parallel side of the RPST is equal to the active and reactive power absorbed or emitted on the series side, so there is:(7)

In the equation:(8)

Based on (3), (6)–(8) can be calculated to obtain the relationship between the system line current, RPFC stator-side current, RPFC rotor-side current, shunt transformer primary-side current and the RPFC feeder bus current as(9)

Based on (1)–(2) the injection voltage of RPFC can be calculated as(10)

Among them, the expressions and derivation process of T_RPFC and Z_RPFC are shown in Appendix A, so that the simplified circuit model of RPFC can be obtained as shown in Figure 2b, whose series part consists of a controlled ideal voltage source and a variable internal impedance, and the parallel branch is a controlled current source.

According to the RPFC regulation characteristics, it is known that the continuous regulation of the injected line voltage can be accomplished by changing the sizes of α₁ and α₂, thus realising the functions of voltage regulation, phase angle regulation, power control, etc., as shown in Figure 3 for the RPFC line regulation vector diagram.

Figure 3 Line regulation vector diagram of RPFC. (a) Voltage over the lower limit (b) Voltage over the upper limit (c) Power regulation (reactive) (d) Power regulation (active) (e) Phase angle difference line closing loop.

3 Multi-scenario analysis and modelling of active distribution networks

Three scenarios are analysed and modelled for the active distribution network construction, as shown in Figure 4, in which K₁ is the bus switch of bus 1; K₂ is the liaison switch of bus 1 and bus 2; K₃ is the liaison switch of bus 2 and bus 3; U_s1 is the first-end voltage of bus 1; U₁, U₂, and U₃ are the voltage of the grid-connection point of bus 1, bus 2, and bus 3, respectively; P_L and Q_L are loads of the bus, and P_DG and Q_DG are the power issued by the distributed photovoltaic power of bus 1.

Figure 4 Schematic diagram of active distribution grid.

Scenario 1: Voltage overrun at the end of the line due to power back-feeding caused by a high percentage of distributed PV access (K₁).

Scenario 2: Due to factors such as grid layout design, the feeder end of the 35 kV substation comes from the medium-voltage side of the 110 kV substation (triangular connection) and the high-voltage side of the 220 kV substation (star connection), and at this time, there is a phenomenon of a phase angle difference of about 30° between bus 1 and bus 2 (K₂); or due to the asynchrony of the line construction and the development of loads, the phase angle difference between the two ends of the merging loop point exists or due to unsynchronised line construction and load development. At this time, the loop-forming operation will generate a large loop current in the line, affecting the security of the power supply in the distribution network.

Scenario 3: For long-term closed-loop operation lines, when effective power control at the closed-loop point is necessary to ensure reliable operation of the distribution network (K₃).

3.1 Scenario 1: Control model construction

Referring to Figure 5 Feeder 1, when the PV power P is larger and cannot all be consumed locally, the power will be sent backwards to the grid side through the line, and when P₁R + Q₁X < 0, the voltage at the end of the line is higher than the grid-side bus voltage, and with the gradual increase of the proportion of photovoltaic access, there is even a phenomenon of voltage over the upper limit, and at this time, the line voltage relationship can be expressed as follows:(11)

Figure 5 Equivalent circuit diagram of closed-loop grid with RPFC.

In the equation:(12)

Analysing equation (11) and ignoring the less influential imaginary part, the voltage drop ∆U between U_s1 and U_s can then be expressed as:(13)

When RPFC is connected to K₁, the system voltage drop can be expressed as:(14)

At this point, the voltage at the grid point and the regulation target for scenario 1 can be expressed respectively:(15)where U_N is the nominal system voltage.

3.2 Scenario 2: Control model construction

As shown in Figure 5 for a phase angle difference line flexible closed-loop equivalent circuit including RPFC, R₀ + jX₀ is the equivalent impedance of the outer port of the closed-loop line; R₁ + jX₁, R₂ + jX₂ are the line impedance of bus 1 and bus 2, respectively; P₁ + jQ₁, P₂ + jQ₂ are the transmission power of the two lines, respectively; U_RPFC and Z_RPFC is the voltage vector of the line into which RPFC is connected in series and the impedance inside RPFC, respectively; U₁ and U₂ are the voltages of both terminals of RPFC, respectively; and K_sc and K_bp are the series closure switches and parallel bypass switch of RPFC, respectively.

Under the premise that the line parameters within the actual loop closing path, the feeder load before loop closing, and the phase angle difference between the voltages on both sides of the loop closing switch are known, the steady-state loop closing current including RPFC is calculated, and therefore the regulation objective of Scenario 2 (i.e., for the minimum loop closing current) can be expressed as follows:(16)where I_m is the steady state combined loop current after adding RPFC and Z_m is the total loop impedance, where:(17)

3.3 Scenario 3: Control model construction

Referring to Figure 4, the power control model of the K₃ closing loop point including RPFC is analysed, and its equivalent circuit is the same as that of Figure 5, under the single-phase coordinate system, it can be obtained that there exists the following relationship between the circuit equations on both sides of the closing loop point:(18)where R and L are the equivalent resistance and inductance of the Z_RPFC, so that U₁ is fixed on the d-axis as the reference voltage, then we have U_1d = U₁ and U_1q = 0. At this time, the d-axis component and the q-axis component of the line current are:(19)

The expressions for k₁, k₂, k_id and k_iq are given in equation (A5) in Appendix A. In the dq coordinate system, the line power at U₁ in Figure 4 can be calculated from the instantaneous power theory [16] as follows:(20)

Based on equations (19) and (20) after simplified calculation the relationship between U_RPFCq, U_RPFCd and the line transmitted power P, Q can be obtained as:(21)

At this point, the scenario three objective functions can be expressed as:(22)

In the formula, P_ref, Q_ref for the line set transmission power, at this time the joint formula (21), formula (22) can be obtained URPFC series into the line voltage vector amplitude and angle.

3.4 Restrictive condition

3.4.1 Voltage deviation constraints

According to the “power quality power supply voltage deviation” (GB/T 12325-2008) [23], different voltage levels of the line are allowed to pass through the voltage deviation limit is different, to the voltage deviation limit for voltage constraints(23)where ε is the voltage deviation rate limit for the specific voltage level.

3.4.2 Combined loop current constraint

In order to prevent the line current-carrying capacity from crossing the limit for a long period of time during regulation, or from excessive inrush currents due to loop closure leading to equipment burnout or failure, the line current-carrying capacity is constrained as:(24)where I_m is the closing loop point current on the line and I_max is the maximum current value allowed to pass through the line.

3.4.3 Power equation constraints

The equation constraints confirmed by the power equation during distribution network operation are:(25)where G and B are the conductance and conductivity in the nodal conductivity matrix and the other parameters have been described above.

3.4.4 Control precision constraints

According to the operating characteristics of the RPFC, the control accuracy of the two sets of rotary transfer phase transformers is constrained due to the fact that the servomotor controlling the rotor angle rotation belongs to a kind of mechanical regulation, and there is a deviation of other factors such as inertia:(26)where, α₁ and α₂ are the actual angles of the two rotary phase transformers, a_1ref and a_2ref are the control angles of the two rotary phase transformers, and χ is the permissible error of the rotation angle.

3.4.5 Motor speed constraint

Since the rotor angular rotation of the RPFC is a type of operation by means of servomotor drive, there is a constraint on the speed of rotor regulation in the RPFC:(27)where SP_RPFC is the actual rotational speed of the rotary phase transformer and SP_RPFCmax is the limiting rotational speed of the rotary phase transformer.

3.4.6 Cycle time constraint

In the power control condition and voltage regulation condition, the design is that the system collects system parameters every η seconds for calculation, so there are:(28)where t is the system computation time.

3.5 Multi-scene adaptive genetic algorithm solution

According to the principle of the MAGA algorithm and the multi-scene control model of this paper [24], the specific solution steps are as follows:

1) Coding and parameter initialisation. According to the regulation characteristics of the RPFC, its main control parameter is the rotation angle of the two rotary transfer phasor transformers, because the binary coding needs frequent encoding and decoding, which requires a lot of calculations, the real number coding method is used for the solution, which is able to save the solution time, at this time, the corresponding coding of the RPFC can be expressed as [α₁, α₂]. When the control precision c = 0.0001, it satisfies α₁, α₂ ∈ [0.0000, 360.0000].

2) Operation scenario discrimination. Since the RPFC in this paper needs to adapt to different application scenarios, i.e., multiple control objectives. In order to overcome the defects of traditional genetic algorithms that is easy to fall into the local optimal solution under the constraints of multi-scene and multi-objective, we complete the operation scene discrimination through the real-time collection of the distribution system parameters and set the initial value of the crossover and variance parameters of different scenarios for the searching need to satisfy the adaptability of the algorithm to different scenarios.

3) Adaptation calculation. Judge whether the results of the control model satisfy the various constraints under the multi-scene control objective [25], due to the fact that the models of each group have been normalised, if a constraint is not satisfied, the individual fitness function is 1. If they are all satisfied, the fitness value is calculated according to the fitness function of the scenario and the optimal individual fitness in the N population is introduced into the N + 1 population, at the same time, the individuals with fitness of non-1 in the population form the mating pool.

4) Selection of action. Form a roulette wheel according to the size of the fitness of the individuals in the mating pool, the greater the fitness, the greater the chance of being selected, using roulette to randomly select the parents and mothers.

5) Crossover variation action. By using automatically varying crossover probability and mutation probability to control the genetic operation, when the search for the optimal stagnation, increase the mutation probability and crossover probability to help jump out of the limitation solution, easy to find the optimal solution, the specific adaptive mechanism can be expressed as:(29) (30)where P_c and P_m are the current values of the crossover and mutation operators, respectively, P_c0 and P_m0 are the initial values, a ∈ [0, P_c], b ∈ [P_m, 0.1], N is the number of generations of the current run, and N_f is the number of generations when there is a stagnation in the algorithm’s optimisation process.

It can be seen that when other parameters are unchanged, the values of the crossover operator P_c and the mutation operator P_m increase with the increase of N under certain conditions, i.e., when the number of times that the optimal solution remains unchanged exceeds a certain value, the algorithm automatically increases the probability of the crossover and the mutation to jump out of the locally optimal solution, and in this paper, the overall control block diagram of the MAGA-RPFC system is shown in Figure 6, and the flowchart of the improved adaptive genetic algorithm is Figure 7 shown.

Figure 6 Overall control block diagram of MAGA-RPFC system

Figure 7 Algorithm flow chart.

Figure 8 Simulation results of voltage regulation condition. (a) Two control strategies for pressure regulation process (b) Rotor Angle change process of two control strategies.

Figure 9 Flexible loop simulation results.

Figure 10 Simulation results of RPFC regulation when the set power is 0. (a) RPFC control process when the set power is 0 (b) Rotor angle regulation process of RPFC.

Figure 11 The set value changed from 0 to 1 MW in the regulation process. (a) RPFC control process when the set power is 1 MW. (b) Rotor angle regulation process of RPFC.

4 Simulation of an algorithm

According to Figure 4 to build the distribution network structure for simulation and analysis, for the multi-scenario adaptive genetic algorithm proposed in this paper, compared with a PI-RPFC approach, the PI-RPFC control strategy is shown in Figure B1–B3 in Appendix B, the RPFC parameters are shown in Table 1, and the parameters of the improved adaptive genetic algorithm for the three working conditions are shown in Table 2.

4.1 Simulation verification of voltage regulation working conditions

With the increasing number of distributed PV access [26], there has been a daytime power back-feeding caused by the voltage overrun condition, according to Figure 4 grid topology, RPFC access position is K₁, access mode refer to Figure 5. When the line end voltage is located in the normal range, the bypass switch K_bp is in the closed state, at this time the RPFC short-circuit access to the line; the voltage overrun phenomenon occurs after the closure of the K_sc after the disconnection of the K_bp After the RPFC is involved in regulation, the distribution network system parameters are shown in Table 3.

As shown in Figure 8a for the voltage change at the end of the line when the RPFC is put into operation under the two control strategies, it can be seen that the PI-RPFC exhibits a kind of overshooting characteristic, while the MAGA-RPFC, after a short time of computation (the average computation time for the voltage regulation is 0.11 s, which can be neglected in relation to the overall RPFC regulation time), always regulates the voltage at a kind of rated motor speed, so the MAGA-RPFC shows better control accuracy under the same time, the simulation results are shown in Table 1, and the voltage regulation process is shown in Figure 8b.

4.2 Phase angle difference line flexible closed loop working condition simulation verification

As shown in Figure 4, there exists a 30° phase angle difference between the two ends of the K₂ switch, when the distribution line is undergoing reconstruction or overhaul, the power supply to the customer will be interrupted if the power failure is used to transfer the load, however, the direct closing of the line with a 30° phase angle difference will lead to a large closing current, which will lead to the action or damage of the protection equipment, therefore, it is necessary to guarantee the power supply to the customer load in an uninterruptible and flexible way, and the access position of RPFC is at the K₂ switch in Figure 4, and the access method is referred to Figure 5. The RPFC is connected to the K₂ switch in Figure 4, and the access method is referred to in Figure 5. Under normal power supply conditions, the series switch K_sc and the bypass switch K_bp are in the disconnected state, and when the demand for flexible loop closure is raised, the RPFC completes the preparatory work and then K_sc closes, and the system parameters are shown in Table 4.

For phase angle difference line flexible loop closing, the system does not have too high requirements for regulation time, after the demand for loop closing transferring power supply is put forward, RPFC parameter calculations are carried out, and the current changes after loop closing are shown in Figure 9, which shows that the RPFC under the two control strategies shows consistency in loop current suppression of loop closing, and the regulation accuracy of the two control strategies is 0.81%.

4.3 Simulation analysis of power control operating conditions

As shown in Figure 4, in which the K₃ switch is closed, effective power control is required at the closed loop point under the long-term closed-loop operation condition. At this time, the access mode of RPFC at the K₃ switch refers to Figure 5, and the system parameters are shown in Table 5.

In the power control simulation verification, the following experiments are carried out for verification:

1. Before the moment t = 0 s: the series switch K_sc and the bypass switch K_bp are in the disconnected state; and

2. t = 0 s moment: series switch K_sc and bypass switch K_bp are directly closed, at this time, U₂ line flows 0.1865 MW active and 0.3309 MVar reactive power to U₃ line through bypass switch K_bp, which puts forward the power control demand to the RPFC, and the bypass switch K_bp is disconnected, meanwhile, making the power flow in the closed-loop point to be 0. The power control effect under the two control strategies and corresponding changes of RPFC parameters under the two control strategies are shown in Figure 10a, the comparison of simulation results is shown in Table 6, and the simulation regulation process is shown in Figure 10b;

3. t = 60 s: the power control demand is put forward to RPFC, so that U₃ line flows 1 MW active power and 0MVar reactive power to U₂ line, at this time, the power regulation effect and the corresponding RPFC parameter changes are shown in Figure 11a, under two power regulation conditions, the average calculation time of MAGA-RPFC is 0.16 s, which can be ignored compared with the overall regulation time of RPFC. The comparison of simulation results at this time is shown in Table 6, and the simulation regulation process is shown in Figure 11b.

From the simulation results, it can be seen that the RPFC system based on the improved adaptive genetic algorithm exhibits better regulation performance under the three working conditions, and shows faster response speed and control accuracy compared with the RPFC under PI control, which verifies the feasibility and effectiveness of the proposed control strategy.

5 Conclusion

In view of the problems of voltage regulation, flexible loop closing and power regulation encountered in the construction of active distribution networks, a solution of electromagnetic rotating power controller is proposed. Through theoretical analysis and simulation verification, the following conclusions are drawn:

1. The main structure of RPFC is two sets of phase-shifting transformers. By changing the relative angle of the stator and rotor, the continuous adjustment of the injected line voltage is completed. It is an electromagnetic power flow controller, so it has low cost, no harmonics and high reliability. Advantage. Based on the analysis of the working principle and equivalent characteristics of RPFC, a line steady-state voltage source model was established.

2. For different operating scenarios, a voltage over-limit control model based on the RPFC steady-state voltage source, a flexible loop closing model based on the vector synthesis principle, and a power decoupling model based on the instantaneous reactive power theory were constructed, and the MAGA algorithm was used to The multi-scenario control model was solved, and the simulation results verified the effectiveness of the proposed control strategy.

3. Comparing the control performance of PI-RPFC and MAGA-RPFC algorithms, the RPFC system based on MAGA shows better control effects in terms of control accuracy, response time and adjustment stability.

4. In the face of complex active distribution network multi-operation scenarios, the control target can be achieved simply by switching the RPFC control model, which shows good applicability and generalizability, and has certain implications for future active distribution network construction.

This article proposes a multi-scenario solution based on RPFC, but currently, there are certain limitations in its applicable working conditions. With the rapid development of microgrid construction, in the microgrid quasi-synchronous and interconnected operation scenario, compared with the distribution network interconnection power control scenario, the frequency adjustment dimension of RPFC has been added. Therefore, it is necessary to carry out research on quasi-synchronous control of microgrids based on RPFC.

Acknowledgments

This work was done by the Jiangsu Electric Power Co., LTD. Science and technology project (J2022061).

References

Appendix A

RPFC steady state voltage source model

It can be obtained from Figure 2 (A1)

Based on equation (10) it can be obtained(A2)

In the equation:(A3)

At this point, we can get(A4) (A5)

Appendix B

Traditional RPFC control strategy based on PI control

Figure B1 Voltage regulation flow chart of PI-RPFC.

Figure B2 Flexible loop closing flow chart of PI-RPFC.

Figure B3 Flow control flowchart for PI-RPFC.

All Tables

All Figures

	Figure 1 RPFC topology structure. (a) RPFC schematic [18]. (b) RPFC topology diagram.
In the text

	Figure 2 Working principle of RPFC. (a) RPFC equivalent circuit diagrams (b) RPFC simplified circuit diagram.
In the text

	Figure 3 Line regulation vector diagram of RPFC. (a) Voltage over the lower limit (b) Voltage over the upper limit (c) Power regulation (reactive) (d) Power regulation (active) (e) Phase angle difference line closing loop.
In the text

	Figure 4 Schematic diagram of active distribution grid.
In the text

	Figure 5 Equivalent circuit diagram of closed-loop grid with RPFC.
In the text

	Figure 6 Overall control block diagram of MAGA-RPFC system
In the text

	Figure 7 Algorithm flow chart.
In the text

	Figure 8 Simulation results of voltage regulation condition. (a) Two control strategies for pressure regulation process (b) Rotor Angle change process of two control strategies.
In the text

	Figure 9 Flexible loop simulation results.
In the text

	Figure 10 Simulation results of RPFC regulation when the set power is 0. (a) RPFC control process when the set power is 0 (b) Rotor angle regulation process of RPFC.
In the text

	Figure 11 The set value changed from 0 to 1 MW in the regulation process. (a) RPFC control process when the set power is 1 MW. (b) Rotor angle regulation process of RPFC.
In the text

	Figure B1 Voltage regulation flow chart of PI-RPFC.
In the text

	Figure B2 Flexible loop closing flow chart of PI-RPFC.
In the text

	Figure B3 Flow control flowchart for PI-RPFC.
In the text