A novel single-phase grounding fault voltage full compensation topology based on antiphase transformer

Multi-tap and multi-capacitors type arc suppression coils are commonly used in distribution systems. Due to their low compensation accuracy and limited arc suppression capability, it is hardly to avoid personal safety accidents and wildﬁres absolutely. In this paper, a novel single-phase grounding fault voltage full compensation topology based on antiphase transformer is proposed, which is composed by an antiphase transformer, a phase-selection switch and a multi-tap single-phase voltage regulator. The proposed topology can control the neutral point voltage, thus cause the fault voltage being zero. By this way, the lack of arc suppression coil is overcome. The novel compensation topology features low costs, high precision of fault voltage compensation. The principle of the novel compensation topology is explained. The mathematical expressions of residual voltage and current are derived in detail. Finally, the simulation model and experimental platform were built. The results show that the proposed novel compensation topology can effectively make up for the shortcomings of traditional arc suppression coils when it is used with them.


INTRODUCTION
Distribution network is deeply penetrated into the densely populated areas of the customer. The power distribution network is characterized by a large amount of equipment, a wide coverage, and a complicated operating environment, which cause ground faults occurring frequently. Research and investigation results show that single-phase grounding faults account for around 85% of the faults in the distribution network [1,2]. If the singlephase grounding fault is not suppressed in time, it is easy to cause arc grounding, and even cause phase-to-phase grounding short-circuit fault, which will seriously threaten the safety of personal safety and reliable operation of the power grid. When a single-phase grounding fault occurs, the solid grounding system will trip instantly [3]. Resonant grounding system can use arc suppression coil (ASC) to generate a zero-sequence compensating current to remove the impermanent single phase grounding faults by compensating the fault residual current without tripping the circuit breaker. And it is generally concluded that  [4][5][6][7]. However, the residual voltage and residual current caused by grounding faults in the distribution network still seriously threaten personal safety, which has caused serious electric shock casualties' accidents in recent years [8].
The main reason for this problem is that most of the ASCs that have been installed and used at present are multi-tap and multi-capacitors type ASCs, which have limited fault voltage and current suppression capabilities. Take China's Jiangxi Province as an example. Statistics made by Jiangxi Electric Power Research Institute shows that among the installed ASCs, the proportion of multi-tap and multi-capacitors type ASCs is as high as 88.5% [9]. The Chinese standard of overvoltage protection and insulation coordination for AC electrical installation indicate that, the number of taps of the traditional ASC is limited, so that the output current difference of each tap usually exceeds 3 A [3]. In this way, the fault voltage will exceed personal safety voltage under large grounding resistances. Furthermore, many kinds of ASCs can only suppress the fault current to below 10 A, which may cause wildfires or personal safety accident [3,10,11].
To realize high-precision regulation of ASC, continuously adjustable ASCs have been proposed, such as Magnetically Controlled Reactor [12][13][14][15]. However, the practical applications of these new ASCs are still relatively less for theirs costs and drawback of non-linear magnetization characteristic of the core which will induce additional harmonics in the current flowing through the grounding point.
The ASC is essentially a current arc suppression device. In recent years, the voltage arc suppression method has become a new development direction. The grounding arc elimination technologies developed on transfer grounding arc suppression method has been gradually promoted [16][17][18]. However, this method may promote arc combustion under some grounding faults with small grounding resistances.
The active arc suppression device (ASD) is emerged recently for its theoretical ability to completely compensate the fault current [19][20][21][22]. While, the costs are relatively high, for the using of large-capacity electronic devices.
In view of these, a novel single-phase grounding fault voltage full compensation topology based on antiphase transformer is proposed in this paper. Firstly, the antiphase voltage of the fault phase is obtained by an antiphase transformer. Then, a multitap single-phase voltage regulator (MSVR) is used to compensate the output voltage error of the antiphase transformer.
In this paper, the basic principle of this novel full voltage compensation topology for single-phase grounding fault is explained. The detailed mathematical expressions for the optimal transformation ratio of the MSVR and the maximum residual voltage under this condition are deduced. In addition, the compensation effect and characteristics of antiphase transformer under different reactance parameters are qualitatively analysed. The simulation model is based on PSCAD/EMTDC. And an experimental prototype is built at laboratory. The simulation and experiment results show that the proposed topology features low costs and high precision, which can effectively make up for the shortcomings of traditional ASCs when they are used simultaneously.

PRINCIPLE OF FULL COMPENSATION FOR SINGLE-PHASE GROUNDING FAULT
Since the line impedances have little impact on the equivalent circuit of the distribution network model, they can be ignored in the modelling of single-phase grounding fault arc suppression research [5,[10][11][12][13][14][15][16][17][18][19]. Assume that a grounding fault occurs on phase C. To better explain the principle, a schematic diagram of a typical distribution network grounded by a full compensation device is shown in Figure 1.
Where E j ( j = A, B, C ) and U j are the three phase supply voltages, the three phase to ground voltages of the distribution network, respectively; U N is the neutral point voltage; I L_ j and FIGURE 1 Schematic diagram of full compensation arc suppression for single-phase ground fault in distribution network I G _ j are the three phase load currents and ground currents of the distribution network, respectively; Y j is the phase-to-ground distributed admittance; R d is the ground-fault resistance; U d and I d are the fault voltage and fault current, respectively; the compensation current injected into the distribution network is denoted by I Z .
Ignoring the reactance of the transmission line, I d can be expressed as To achieve the full compensation of the single-phase grounding fault current, the voltage of the fault phase needs to be zero.
That is, U c should be zero, and the neutral point voltage U N should satisfy Considering Equations (1) and (2) comprehensively, it can be gotten that by controlling the voltage source to generate a voltage with the same value and opposite direction as the supply voltage of the fault phase, the fault voltage U d and fault current I d can be suppressed to zero at the same time. This is the basic principle of full compensation for single-phase grounding fault based on voltage arc suppression method.

Full compensation topology of single-phase grounding fault based on antiphase transformer
A novel voltage full compensation topology of single-phase grounding fault based on antiphase transformer is shown in Figure 2, which can be used to control the neutral point voltage. The topology consists of an antiphase transformer, a MSVR, and a group of phase-selection switch.
Where I L is the compensation current of ASC injected into the distribution network.
When a single-phase grounding fault occurs on phase j (j = A, B, C). The antiphase transformer, which with Yyn6 connection group, can reverse the phase supply voltage from E j to −E ′ j . While, −E ′ j is deviated from the −E j for the existence of transformer leakage reactance. The MSVR is used to compensate the deviation between −E ′ j and −E j . The phase-selection switch is used to select the fault phase and connect the antiphase transformer and the MSVR. The specific phase selection methods can be referred to in terms of studies on faulty phase selection [23][24][25]. Finally, the neutral point voltage can be adjusted to U N = −E j , which satisfies Equation (2), and thus the fault voltage is fully compensated.
The capacity of the antiphase transformer and MSVR can be greatly reduced by reusing existing ASC, which is more economical. Note that, the antiphase transformer described in this part consists of a transformer with a connection group of Yyn6. Actually, there are many other combinations that can be used to compose an antiphase transformer, such as the Dy11 and Dy7 connection group.

DEVIATION ADJUSTMENT
According to Figures 1 and 2, the equivalent circuit diagram of grounding fault voltage full compensation topology based on antiphase transformer is shown in Figure 3.
Where Z L is the inductive reactance of ASC; E COM is the open circuit voltage of point N to ground, which is used to equalize the output voltage of antiphase transformer and MSVR; Z COM is the equal inductance of antiphase transformer and MSVR.
In three phase power system, all phase-to-ground distributed admittances are basically the same. So, Figure 3 can be simplified to Figure 4.
When the grounding fault voltage is fully compensated, I d = 0. So, the fault branch circuit can be treated as open circuit. Then Figure 4 can be further simplified to Figure 5.
According to Equation (2), when the ground fault voltage is compensated fully, one gets  Set the ratio of the antiphase transformer and the MSVR as m and n respectively. After the C-phase is selected by phaseselection switch, the A-phase and B-phase of the secondary winding of the antiphase transformer are open circuits. The secondary side current of antiphase transformer I C _Sec is Note that I C _Sec is also the input current of primary side of the MSVR. According to the symmetrical component method, the sequence currents of the secondary winding of the antiphase where I C _Sec+ , I C _Sec− and I C _Sec0 are the positive, negative and zero sequence components of I C _Sec , respectively. Viewed from the secondary winding of the antiphase transformer, the complex sequence network diagram is as shown in Figure 6, where, Z 1Σ , Z 2Σ , and Z 0Σ are the sum values of positive, negative and zero sequences of Z COM and Z E , respectively.
Where −E C × m in Figure 6 is the supply voltage to the secondary winding of the antiphase transformer.
Suppose the equivalent reactance of the antiphase transformer and the MSVR from the primary side is X T 11 and X T21 , respectively, which can be obtained from the data plate. Ignoring the magnetizing reactance, Z 1Σ , Z 2Σ , and Z 0Σ are According to Figure 6, we can have Combine Equation (5) to Equation (7), one gets Simplified Equation (8) yields By solving Equation (9), and setting m = 1, we can obtain the optimum ratio of the MSVR n th_opt . In this condition, the residual voltage is suppressed to zero.
In Equation (10), when the ASC is overcompensated, n th_opt takes the positive solution, otherwise it takes the negative solution. The calculated value of n th_opt can be used as a reference for the design of the MSVR. Z E is suggested to be measured at regular intervals, and then manually calibrated the tap of the MSVR to work near the n th_opt , and ensure that the topology can be directly put into use when a ground fault occurs. In engineering, the MSVR can be manual set to the optimal tap according to the power system parameters at route electricity overhauling, for the reason that parameters of the distribution networks, such as Y A , Y B , Y C , remain basically the same during an overhaul period.

Modelling of residual voltage under MSVR
In engineering, it is difficult to achieve stepless voltage adjustment. That is, the ratio of the MSVR may not equal n th_opt exactly.
Setting the ratio difference between each tap position of the MSVR k. The theoretical and actual optimal open-circuit voltage under the optimal tap position of MSVR are E COM , E ′ COM , respectively. We can get Note that, the function round(x) means to get the nearest whole number of x. Further, we can get the residual compensation voltage Thus, the range of are The MSVR is designed according to the VR-8 single-phase feeder voltage regulator standard, which supports 32-taps highprecision voltage regulation with 0.625% accuracy for each tap selection. Based on Equation (13), the value of can be further specified in the range of Equation (14).
Based on Figures 4 and 5, using Norton's theorems to calculate U N Residual voltage of faulty phase C is It is further obtained that the expression of the residual voltage U C considering the voltage deviation (17) acquires its maximum value. Since then, we obtain the mathematical expression for the maximum residual voltage of the MSVR. Further, simply divide the maximum residual voltage by the ground resistance to obtain the maximum residual current.
In the three-phase three-wire distribution system, a singlephase grounding fault results in the increases of the neutral voltage to phase-to-neutral value, which is an inherent phenomenon of the grid. So, the insulation requirement of the neutral point is higher, and should be considered in the design [5,10]. Thus, making the line-to-earth voltages of unfaulty phases increase to the line-to-line value, which is also an inherent phenomenon of the grid and has nothing to do with the proposed topology. However, the phase-to-phase voltages of the grid are unchanged during the faulty period, which can ensure the normal operation of power-consuming equipment after being converted by the distribution transformer.

Analysis of residual voltage under MSVR
Equation (17) not only shows the influence of the MSVR on the residual voltage, but also shows the effect of voltage angle deviations caused by the load loss of the antiphase transformer and MSVR. To make Equation (17) easier to analyse and discuss, we need to give some necessary system parameter values. Let the phase-to-phase voltage of the distribution network is 10 kV, and the grounding capacitance of each phase is 3.3 µF. When the antiphase transformer works with an ASC (overcompensation of 5%), the capacity of the transformer and voltage regulator is set to 100 kVA and 35 kVA, respectively. In two conditions that the load loss of the MSVR and the antiphase transformer are 1%, 0%, respectively, the maximum residual voltage according to Equation (17) is shown in Figure 7.
As can be seen from Figure 7 that the leakage reactance has less influence on the maximum residual voltage, especially when The graph of maximum residual voltage the ground resistance is large. The residual voltage is below 20 V when the load loss is zero. When the load loss increases to 1%, the residual voltage below 30 V, which is still under the personal safety voltage 36 V.
Further, according to Equation (17), plotting the maximum residual current, which is shown in Figure 8.
In Figure 8(a), the mini-figures (1)-(4) are local detail graphs, their physical meanings and units represented by the x, y, and z axes are the same as those of the main graphs In Figure 8(b). The colour spectrum for the mini-figures (1), (2) are the same, and the colour spectrum for the mini-figures (3), (4) are the same.
It can be seen from Figure 8 that for metal-grounding, the residual current decreases significantly as the leakage reactance of the proposed topology increases. When the load loss is 0%, the proposed compensation topology with the ASC can suppress the metal-grounding residual current to below 100 mA, Also, when the load loss is 1%, the metal-grounding residual current is below 200 mA, which is far less than that of only the ASC, as it only aims to suppress the residual current to below 10 A.

Costs comparison with existing methods
A large number of multi-tap and multi-capacitors type ASCs have been installed to the distribution system. They need to be retrofitted to improve the compensation precision and compen- Set the original multi-tap and multi-capacitors type ASCs compensation capacity to 630 kVA, which can compensate for 100 A of fault current. This capacity is a common capacity in practical applications. Since the ASC can compensate the grounding fault current to below 10 A, the recommended capacity of active compensation device and antiphase transformer does not exceed 60 kVA. In the costing process, the price of the equipment is obtained by checking the market price and consulting with the equipment manufacturer, and is settled in $. The costs of four schemes are listed in Table 1 (The detailed calculation is shown in Appendix 1).
It can be seen from Table 1 that the modification costs of Scheme 1, Scheme 2, Scheme 3 and Scheme 4 are 26,932.5 $, 19,237.5 $, 12,004.2 $ and 6694.65 $ respectively. Therefore, from the perspective of costs, the solution proposed in this article is the most cost-effective.
Note that, when a single-phase grounding fault occurs, the ASC and the proposed topology are immediately activated, so that the fault voltage can be well compensated, and the distribution system can be allowed to operate during the faulty period for 1-2 h, so the circuit breaker will not be tripped immediately [3,[10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. After a certain delay, the phase selection switch of the proposed topology trips. If the fault arc has been extinguished, and the zero-sequence current of the system is close to the unfaulty one, which is a lower value, the fault can be distinguished as an impermanent single-phase grounding fault; if the fault arc reignites, the fault can be distinguished as a permanent one. Then, the distribution system needs to identify the faulty branch, isolating it by circuit breaker, and await artificial repair [3,5].
The proposed topology can well suppress the fault point voltage and ensure the safety of the faulty phase. Even in special circumstances, the circuit breaker acted immediately, then the faulty phase voltage immediately declines to 0. At this time, there is no longer a needer for the proposed device to be activated.
Different from the working principle of ASC, which is to compensate the capacitive earth fault current by injecting an inductive current, the arc suppression principle of the proposed topology is to control the neutral point voltage. So, the uses of this topology will not affect the off tuning degree of the ASC or generate resonance in the network.

Result and analysis of simulation
The PSCAD/EMTDC simulation platform is used to simulate and analyse the novel voltage full compensation topology of single-phase grounding fault based on antiphase transformer. The specific parameters of the simulation model are shown in Table 2.
Taking a certain bus section of Shanghai Nantong Substation as the simulation object, the voltage level is 10 kV, and the distributed capacitance of one phase is 3.3 µF.
Select the ground resistance as 100 Ω and the transformer leakage reactance as 0.1 pu. A grounding fault occurs on phase C at 0.2 s, and the proposed topology is put into operation at 0.4 s. According to the parameters in Table 2, a simulation model based on the antiphase transformer is built. The simulation result is shown in Figure 9.
As shown in Figure 9, the direction of the compensation voltage generated by the proposed topology is reverse to the direction of the supply voltage of phase C, and the amplitude is very similar. This is consistent with the analysis in Part 2.1. The voltage difference of each tap of the MSVR is 37 V, the best tap corresponding to the secondary side voltage of the MSVR is 5.957 kV. After the grounding fault occurs, the ASC immediately compensated the fault current, and the RMS values of residual voltage and residual current is 89.66 V and 0.897 A, respectively. After the proposed topology is connected, the RMS values of residual voltage and residual current drop to 9.5 V and 0.095 A, respectively. When only the ASC works, the fault voltage and fault current suppression rates are both 94.77%. When the ASC and the proposed topology work together, the fault voltage and current suppression rates are both 99.45%. It can be seen that after connecting the proposed topology, the residual voltage and residual current value are both further reduced by 89.4% compare to those when the ASC works alone. By this way, the fault  On the basis of the models described above, the leakage reactance of the antiphase transformer and MSVR are set as 0.06, 0.07, 0.08, 0.09 and 0.1, respectively. The corresponding simulations are run respectively. Figure 10 shows the comparison between E COM and E ′ COM . As shown in Figure 10, the value of E COM is obtained by multiplying the optimal ratio n th_opt by the primary side rated voltage of the MSVR (5773 V). The E ′ COM is obtained by manually adjusting the ratio rate of MSVR in simulation model to satisfy Equation (11). It can be seen from Figure 10 that E COM is very close to E ′ COM , which verifies the compensation effect of the proposed topology.
In the above simulation model, setting the grounding resistance to be 1, 50, 200, 600, 1000 Ω, respectively. Under these conditions, the maximum residual voltage under the step adjustment of the MSVR is obtained. The results of the theoretical and actual simulation values of the maximum residual voltage are shown in Figure 11.
It can be seen from Figure 11 that the theoretical value and the simulated value are very similar, thus verifying the robustness of the proposed topology.

Result and analysis of experiment
An experimental prototype is built to further verify the correctness and effectiveness of the compensation topology proposed in this paper. The physical prototype as shown in Figure 12.
The experimental prototype is a scaled model with actual working conditions, and its parameters correspond to the simulation parameters. The phase-to-phase supply voltage of power grid is 0.38 kV, and the grounding capacitance is 3.3 µF. The MSVR is a sliding type autotransformer with a wide range of adjustable output voltage. The value of grounding resistance in the simulation and experiment part of this paper is based on engineering practice experience. The grounding resistance in the actual project can be referred to [27], which provides the equivalent grounding resistances when a single-phase grounding fault occurs in different grounding environments, as shown in Table 3.
The typical ground resistance ranges from 100 to 500 Ω. This paper finally selected 100, 500 and 1000 Ω in the experiment part to simulate a single-phase grounding fault occurs on the surface of reinforced concreted, wet grass, dry asphalt or sand,  respectively. This is also the grounding resistance range that is normally selected by other scholars in simulations and experiments of this field [10,24]. The specific parameters of the antiphase transformer are shown in Table 4. In this experiment, the MSVR is adjusted to the optimum tap position with a gap difference of 2 V initially. Then, the C-phase grounding fault occurs at 0 s. After 120 ms, the ASC put into work (Note: Actually, the ASC should have immediately put into work, the delayed inputs are set for ease of analysis). After a further 120 ms, the proposed topology is engaged.

FIGURE 13
Experimental results of compensation topology based on antiphase transformer with ASC (overcompensation of 52.7%) Figure 13 shows the experimental waveforms of the compensation topology based on antiphase transformer under different grounding resistances. Set the ASC to be overcompensation of 52.7% (that is 0.67 H).
When the grounding resistance is 100 Ω, it can be seen from Figure 13(a1) and (a2) that the effective value of the fundamental wave of the fault voltage is 67.08 V after the fault occurs, and the effective value of the fundamental wave of the fault current is 667.8 mA. When only the ASC works, the residual voltage is 35.87 V, the residual current is 358.3 mA. The fault voltage and fault current suppression rates are 46.53% and 46.35%, respectively. After put into the proposed topology, the residual voltage drops to 2.76 V, the residual current dropped to 24.46 mA. The fault voltage and fault current suppression rates are 95.89% and 96.34%, respectively.
When the ground resistance is 500 Ω, it can be seen from Figure 13  When the ground resistance is 1000 Ω, it can be seen from Figure 13(c) that the fault voltage and current are 228.9 V and 229.8 mA, after the fault occurred. When only the ASC works, the residual voltage and current are 216.5 V and 216 mA, respectively. The fault voltage and fault current suppression rates are 5.42% and 6.01%, respectively. After the proposed topology is engaged, the residual voltage and current drop to 2.45 V and 2.64 mA, respectively. The fault voltage and fault current suppression rates are 98.93% and 98.85%, respectively.
As can be seen from the Figure 13 that when the proposed compensation topology works with the ASC in the experimental prototype, residual voltage and residual current value decline significantly. Moreover, the fault suppression capability of the ASC is greatly improved by the proposed topology, thus verifying the correctness of the simulation result in the simulation part of this paper.
The above experiments are repeated in other two working conditions: the reactance of the ASC is overcompensation of 2.3% (that is 1 H) and under compensation of 100% (without the ASC). The fault voltage and current suppression rates result are as shown in Figure 14.
From Figure 14(a,b), it can be seen that when only ASC works, the suppression rate of fault voltage will decrease significantly as the grounding resistance increases. When the ground resistance is 1000 Ω, even in the case of the ASC overcompensated of 2.3%, the fault voltage suppression rate is only 65.37%. After the proposed topology is engaged, the fault voltage suppression rate is significantly increasing to over 96% and the fault voltage suppression effect is obvious. As a current suppression method, when the ground resistance is large, the uses of ASC will leave a large fault residual voltage. So, the proposed compensation method based on the antiphase transformer can be used as a voltage arc suppression method, and make up for the deficiency of ASC.
As Figure 14(c) shows that even the proposed topology works alone without the ASC, it can also obtain well fault voltage suppression rate in the different grounding resistances.
It can be seen from Figure 14(d,e) that regardless of the grounding resistance of 1000 or 100 Ω, and regardless of the differences ASC tuning-off degree, the fault voltage suppression effect of the proposed topology is obvious.
Note that, this paper does not simulate arc grounding fault. The reason is that, after the proposed device is activated, the fault voltage can be well compensated, and the resistance grounding fault will not be evolved into arc grounding fault. Even in special circumstances that arc grounding occurs, because the characteristic of arc grounding is that the grounding resistance is time variable and non-linear, and the proposed topology has a good suppression effect on different grounding resistances, it can also extinguish the arc.

CONCLUSION
The traditional multi-tap and multi-capacitor ASCs have low compensation accuracy and limited arc suppression capability, so that it is hardly to completely avoid personal safety accidents and wildfires. For this reason, this paper proposes a novel single-phase ground fault voltage full compensation topology based on antiphase transformer. The novel topology makes up the shortcomings of the traditional multi-tap and multi-capacitance ASCs, and greatly improves the fault voltage and current suppression capabilities. As a modification scheme for the traditional multi-tap and multi-capacitor ASCs, the proposed topology can balance costs and compensation effect compared with other arc suppression methods.

APPENDIX I: Cost Comparison with Existing Methods
Before comparing the various methods, a brief overview of them is in order.

Practical Requirements
A large number of multi-tap and multi-capacitors type arc suppression coils(ASCs) have been installed to the distribution system, because of their low compensation precision, they cannot completely avoid the occurrence of personal safety accidents and wildfires. These distribution systems with multi-tap and multi-capacitors type ASCs need to be retrofitted to improve the compensation precision and improve the compensation effect. The 4 modification schemes given here are as follows.

Schemes
Scheme 1: Adopt continuously regulating ASC instead of multitap and multi-capacitors type ASCs. Scheme 2: Adopt fault transfer arc extinguishing equipment instead of tap-regulating ASCs.
Scheme 3: Add active compensation device, used in conjunction with the original multi-tap and multi-capacitors type ASCs. Scheme 4: Add the proposed topology, used in conjunction with the original multi-tap and multi-capacitors type ASCs.

Key Parameters of the Application Case
Set the original ASC compensation capacity to 630kVA, which can compensates for 100A of fault current. This capacity is a common capacity in practical applications. Since the ASC can compensate for grounding fault current below to 10A, the recommended capacity for the addition of active compensation device and antiphase transformer does not exceed 3 * 10A ≈ 57.7kVA). In the costing process, the price of the equipments are obtained by checking the market price and consulting with the equipment manufacturer, and is settled in $.

Cost Comparison
The price of a 630 kVA tap-regulating ASC device is about 30,780 $. The price of Magnetically Controlled Reactor (MCR) of the same capacity is 46,170 $, and the price of a fault transfer arc extinguishing equipment is 15,390 to 23,085 $. Therefore, for scheme 1, deducting the original devices which are reusable (such as grounding transformer), the modification cost is about 23,085 to 30,780 $. For scheme 2, the modification cost is about 15,390 to 23,085 $. Scheme 3 and scheme 4 are modified in a similar way and are compared in detail below.
As shown in Fig. A1, the main equipment to be added to Scheme 3 is an active compensator (60kVA), a DC power for active compensator (60kVA), and a coupling transformer (60kVA). As shown in Fig. A2, for the topology proposed in this paper the main equipment to be added is an antiphase transformer (180 kVA), 3 phase-selection switch (using 63 kVA  Table A1.
From Table A1, we can further calculate that the average annual cost of Scheme 3 is 600.21 $, and the total cost over 20 years is 12,004.2 $, while the average annual cost of Scheme 4 is 334.7325 $, and the total cost over 20 years is 6,694.65 $.

Cost Comparison Summary
The modification costs of Scheme 1, Scheme 2, Scheme 3 and Scheme 4 are 26,932.5 $, 19,237.5 $, 12,004.2 $ and 6,694.65 $ respectively. Therefore, from the perspective of cost, the solution proposed in this article is the most cost-effective.