# A Novel Coordinated Control System to Reactive Power Compensation of Photovoltaic Inverter Clusters

Authors: Tingzhe Pan
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

With the development of new energy, a cost-effective reactive power compensation scheme is essential to the voltage stability of the power system for small-capacity distributed generation. This paper proposes a coordinated control scheme of inverter cluster which is based on the reactive power support capability of the photovoltaic inverter. Moreover, by using power angle vectors, a reactive power distribution algorithm is proposed to solve the poor power quality of the point of common coupling connecting source and load in the distributed generation station. Simulations verify the performance of the algorithm is better than the conventional static capacity distribute algorithm and dynamic residual margin distribute algorithm. Finally, the effectiveness of the reactive power compensation scheme and distribution strategy for improving power quality and regulation ability proposed in this paper is verified by operation experiments in the actual power station.


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## Body

## 1. Introduction

With the increasing urgency to protect the environment and the deepening of government energy reform, renewable energy such as photovoltaic (PV) and wind power will join in the grid on a large scale in the next few years and gradually replace the traditional power generation to dominate future energy supply. Small-capacity distributed PV cobuilt with factories and buildings is widely adopted for development because of its low construction cost, flexible grid control, and rich construction sites. Distributed and small-capacity PV stations will be a crucial part of the future grid [1–5].As a power generation unit, the inverter is the key equipment of PV power stations (PVPS). With the development of electronics technology, the inverter is evolving in the direction of digitization, intelligence, and multifunction. PV inverters can achieve separate control of active and reactive power through decoupling and have the ability to undertake the power grid frequency and voltage regulation [6–13]. Meanwhile, with the development of digital technology, the control accuracy, conversion efficiency, and response speed of PV inverter will gradually be better than the traditional generator and feeder equipment [14–16].Renewable generation has significant randomness and volatility, so unregulated pure active power output has a major impact on power quality and system stability [12, 17]. Dynamic reactive power control can compensate the system voltage and power factor (PF) in real time, and the traditional way is to configure Static Var Generator (SVG) at the point of common coupling (PCC) of PVPS [18, 19]. However, for small-capacity distributed generation (DG) stations, SVG is expensive and inefficient.Applying inverters to compensate the reactive power while generating energy can achieve the same effect as SVG and can stabilize the feeder voltage and reduce line losses [20–22]. It is a current research hotspot to coordinate and control individual small-capacity inverter groups to achieve the overall superior system performance of PVPS. At present, the industry has proposed a variety of control algorithms for volt/var control (VVC) and has achieved certain results in closed-loop simulation and local experiments [3, 6]. Through sorting and comparison of different VCC algorithms, as shown in Table 1, the problems and research progress motivate the current research work of this paper [23–29].Table 1
VCC algorithm comparison description.
Reactive power compensation program of PVPSAdvantagesDisadvantagesCompensate with SVG/SVC at PCCResponse speed (+++++);power quality at PCC (+++++);simple control (+++);night compensation;High investment costs (+);large power consumption (+);damage rate (+);no station topology optimization (+);Compensate with SVG/SVC at distributed generation node and internal confluence pointResponse speed (+++);power quality at PCC (+++);station topology optimization (++ reduce line loss and improve stability margin);Complex control (++);no night compensation;high investment costs (++);large power consumption (++);damage rate (++);Compensate with SVG/SVC at PCC and inverters at distributed generation nodeResponse speed (++++);power quality at PCC (++++);night compensation;station topology optimization (++)Complex control (++);high investment costs (++);large power consumption (++);damage rate (+);Compensate with inverters actively by embedding PVPS model at generation nodeResponse speed (+++++);no investment costs (+++);no power consumption (+++);damage rate (+++);station topology optimization (+++)Power quality at PCC (+ oscillation caused by over compensation);complex control (+);no night compensation;Compensate with inverters by static allocation of station control system at generation nodePower quality at PCC (++);no investment costs (++++);no power consumption (+++);damage rate (+++);station topology optimization (+++);Response speed (+);complex control (++);no night compensation;Compensate with inverters by dynamic intelligent distribution of station control system at generation nodePower quality at PCC (+++);no investment costs (++++);no power consumption (+++);damage rate (+++);station topology optimization (++++);Response speed (++);complex control (+);no night compensation;(∗better performance with more +).As a distributed group topology, how to allocate each inverter in different states involves active power generation, voltage balance, and compensation effect, which is the key step of using the inverter as the main reactive power source [26, 27]. However, as shown in Table 1, the existing applications mostly consider how to ensure the compensation effect and PVPS revenue, while ignoring the equilibrium problem of DG nodes [30, 31]. And algorithms are mostly based on simulation analysis, ignoring the interference to the environment and sampling data, as well as experimental verification and engineering applications sometimes [32]. Based on this, this paper proposes an algorithm for reactive power equilibrium distribution of parallel devices, which can provide a solution to the existing problems.The technical scheme of using DG devices for system reactive power compensation (RPC) is considered in this paper to reduce the investment cost. On the premise of ensuring the overall compensation effect, an angle length distributed algorithm for the distributed confluence device based on the power angle vector relationship is proposed, to reduce the difference between different devices and improve the system stability. On the other hand, two other low data dimension inverter group reactive power distribution (RPD) algorithms are compared and analyzed, and the effects of different algorithms on voltage equalization and maximum compensation capability are summarized. Simulation results verify the effectiveness of the proposed study. Finally, the angle length distribution algorithm is embedded into the PVPS control system for operation experiments. The long-term operation results prove the feasibility of the technical route and distribution strategy in this paper, which provides an effective and balanced idea of RPC for distributed PVPS.


## 2. Power Model

Due to the shortage of land resources and high investment costs, the construction process of centralized high-voltage PVPS slows down. With the opening of China’s PV grid connection policy and the reduction of PV module cost, increasingly factories and buildings participate in the construction of distributed PV to save electricity costs and participate in power market transactions. The topology of distributed PVPS is shown in Figure1. The power station and load converge at PCC and are jointly subject to the grid power quality assessment [28]. Different PV matrices in the station are converged in PCCPV through transformers. Each PV matrix is composed of different numbers of inverters and PV arrays. Thus, the PVPS is a multigeneration node grouping and hierarchical converging system [32].Figure 1
Topology of distributed PVPS.PV inverter usually operates at a constant PF (usually 1) to improve power generation, which leads to uncontrollable reactive power with the change of light and temperature [12, 22]. Figure 2 shows the statistical status of Hisense PVPS in Foshan, China, with inverters at 0.95 fixed PF running within a week, and the phenomenon that the power station generates electricity with relatively stable PF in PCCPV during the generation period can be seen from the figure. With the periodic increase of power generation at noon every day, the active and reactive power transmitted by PVPS to the high-voltage bus will also undergo periodic changes. Due to the randomness and volatility of PV power generation, this feature does not have a quantifiable law.Figure 2
PF comparison diagram of PVPS without compensation.The influence of reactance of the transmission line betweenPCCPV, PCC, and PCCLoad is ignored in the topology of Figure 1 [28], so formula (1) is satisfied.Under the fixed PF mode, P and Q of PVPS change at the same time atPCCPV, assuming that the load remains unchanged, so the power fluctuation caused by PV will be reflected in the grid, resulting in dramatic changes in Figure 2, especially the fluctuation of active power. This behavior, which does not consider dynamic RPC but only pursues the generation efficiency and fixed operation mode, has caused a serious burden to the power system. With the continuous construction and development of PV industry, as well as the increasing popularity of power substitution and power consumption upgrading, this burden will become more severe in the increasingly high penetration power system. Meanwhile, the continuous bad PF at PCC will cause assessment fines to users [22].(1)PG=PL−P,QG=QL−Q.


## 3. Algorithm

PV inverter can realize the decoupling control of active power and reactive power [7, 11, 12]. The control logic of RPC designing with this paper is shown in Figure 3 [22]. According to the comprehensive status of power quality obtained at PCC, the reactive power ΔQ needing to be regulated is calculated, and then, the reactive power execution of the inverter is obtained through the feeder distribution algorithm and the inverter group distribution algorithm, as well as the power iteration between groups [32]. The scheme in Figure 3 is a dynamic real-time tracking control [28], so the oscillation amplitude of the control effect is related to the interval period between two commands. Assuming that the normally control oscillation will not exceed the system limits, and the safety threshold is set at PCC, the stabilization device will be started when the disturbance exceeds the system requirements. Meanwhile, the inverter is also embedded with the regulation threshold and voltage operation limit in each one to ensure to resist the disturbance during the real-time operation quickly. As the control system of PVPS is very complex and includes LVRT and HVRT, other reconstruction works will not be described in detail in this paper. In short, the RPC effect will eventually converge in the real-time correction control mode.Figure 3
RPC control logic of PVPS.RPD algorithm is related to the overall compensation effect of the inverter as the reactive power source and the balance between different matrices and inverters. This chapter compares and analyzes the compensation ability, operation balance, and stability control ability of three different algorithms.


### 3.1. Ratio Distribute Algorithm

Transformers and inverters have independent static parameters to adapt to the complex field environment. Taking the device capacity as an allocation basis, the static distribution algorithm is designed as shown in Table2. Algorithm 1 does not consider the dynamic operation parameters of devices. Although RPC quantity ΔQ reflects part of the dynamic parameters, the fixed allocation ratio does not play a sufficient role in compensating and balancing when the dynamic parameters of the device group differ greatly, which wastes the group control effect.Table 2
Ratio distribute algorithm of static capacity.
Algorithm 1: Ratio distribute algorithmInput: RPC amountΔQ; transformer capacity matrix CT; inverter capacity matrix CI;Output: transformer reactive power adjustment matrixΔQT; inverter reactive power adjustment matrix ΔQI;(1): Initialize, arrangeCT according to the sequence of transformer grid connection, the length of CT is m , make k=1;(2): Repeat(3): CalculateΔQTk=ΔQ−∑i=1k−1ΔQTi×CTk/∑i=kmCTi, among which k=1, ΔQT1=ΔQ×CT1/∑i=1mCTi;(4): Initialize inverter group under transformer feeder,CIk=fCI, ΔQIk=, j=1;(5): Repeat(6): CalculateΔQIkj=ΔQTk−∑i=1j−1ΔQIki×CIkj/∑i=jnCIki, among which j=1, ΔQIk1=ΔQTk×CIk1/∑i=1nCIki;(7): Updatej=j+1;(8): Untilj=n in CIk;(9): UpdateΔQTk=∑i=1nΔQIki, verify the constraints of formula (2);(10): Updatek=k+1;(11): Untilk=m in CT;The topology of PVPS and the parameters of each device shown in this paper are based on the Foshan Hisense distributed PVPS in China. Define the topology of Figure1 with 5 PV matrixes converging at PCCPV, and [14 13 15 15 15] PV arrays converging at PCCTi separately. Table 3 shows the static capacity parameters of each device, and Table 4 defines the dynamic operation parameters under three typical cases.Table 3
Static parameters of PVPS installation.
ParameterStatic value (rated capacity)/(kW)Transformer[1000 800 1250 1250 1250]PV matrix 1[50 80 80 80 80 80 80 50 80 80 80 80 50 50]PV matrix 2[80 80 80 80 50 50 50 50 80 50 80 50 50]PV matrix 3[80 80 80 80 80 80 80 80 80 80 80 80 80 80 80]PV matrix 4[80 80 80 80 80 80 80 80 80 80 80 80 80 80 80]PV matrix 5[80 80 80 80 80 80 80 80 80 80 80 80 80 80 80]Table 4
Dynamic parameters of PVPS installation.
ParameterDynamic value/(kW)Case 1Case 2Case 3TransformerActive powerAll 0[500 400 625 625 625][900 720 1125 1125 1125]Reactive powerAll 0[500 400 625 625 625]All 0PV matrix 1Active powerAll 0[25 40 40 40 40 40 40 25 40 40 40 40 25 25][45 72 72 72 72 72 72 45 72 72 72 72 45 45]Reactive powerAll 0[25 40 40 40 40 40 40 25 40 40 40 40 25 25]All 0PV matrix 2Active powerAll 0[40 40 40 40 25 25 25 25 40 25 40 25 25][72 72 72 72 45 45 45 45 72 45 72 45 45]Reactive powerAll 0[40 40 40 40 25 25 25 25 40 25 40 25 25]All 0PV matrix 3Active powerAll 0[40 40 40 40 40 40 40 40 40 40 40 40 40 40 40][72 72 72 72 72 72 72 72 72 72 72 72 72 72 72]Reactive powerAll 0[40 40 40 40 40 40 40 40 40 40 40 40 40 40 40]All 0PV matrix 4Active powerAll 0[40 40 40 40 40 40 40 40 40 40 40 40 40 40 40][72 72 72 72 72 72 72 72 72 72 72 72 72 72 72]Reactive powerAll 0[40 40 40 40 40 40 40 40 40 40 40 40 40 40 40]All 0PV matrix 5Active powerAll 0[40 40 40 40 40 40 40 40 40 40 40 40 40 40 40][72 72 72 72 72 72 72 72 72 72 72 72 72 72 72]The relationship between the demand of RPC amountΔQ∈0,C and the actual distribution value meets Formula (2), which is the capacity constraint.(2)∑k=1k=mΔQTk=∑k=1k=m∑j=1j=nΔQIkj≤ΔQ.The greater the difference in the operation state of feeder devices, the more obvious the imbalance of the station system, and the phenomenon of voltage imbalance and power backflow after confluence is more serious. Therefore, the difference of feeder array under the samePCC is an important index to measure the merits and disadvantages of the RPD algorithm. This paper defines the phase difference and power difference as Formulas (3) and (4), where φ is the phase angle, and SS is the apparent power of one device.(3)sφ=∑i=1nφi−φ¯2n.(4)sP=∑i=1nSi−S¯2n.Algorithms in this paper are all implemented in MATLAB 2021a, and the PVPS model in Figure1 is built to calculate the cases in the above table, and the normalized result is shown in Figure 4.Figure 4
The results of algorithm 1 for the case.Since the initial power state of each device in Case 2 and Case 3 is not 0, the reactive power that can be allocated will reach saturation earlier, and the corresponding power difference remains unchanged after saturation, while the power difference in Case 1 continues to increase steadily. The phase difference in Case 2 and Case 3 is larger when the plannedΔQ is small, but when the planned ΔQ is increased to compensate for the initial value difference enough, the phase difference remains at 0.


### 3.2. Residual Margin Algorithm

Define the dynamic parameters of remaining capacitydQ when the inverter is running, as shown in Figure 5. In most cases, the inverters are in state Stime, and the maximum additional RPC dQ can be provided without loss of generating power Ptime, as formula (5), where C is the apparent power of the inverter. Taking dQ as the allocation basis, a one-dimensional dynamic distribution algorithm is designed as shown in Table 5.Figure 5
RPC power vector diagram.Table 5
Residual margin algorithm of one-dimensional dynamic capacity.
Algorithm 2: Residual margin algorithmInput: RPC amountΔQ; transformer capacity matrix CT, transformer real-time active power matrix PT, transformer real-time reactive power matrix QT; inverter capacity matrix CI, inverter real-time active power matrix PI, inverter real-time reactive power matrix QI;Output: transformer reactive power adjustment matrixΔQT; inverter reactive power adjustment matrix ΔQT;(1): Initialize, arrangeCT according to the sequence of transformer grid connection, the length of CT is m, make k=1;(2): Calculate reactive power margin matrix of transformerdQT by formula (5);(3): Repeat(4): CalculateΔQTk=ΔQ−∑i=1k−1ΔQTi×dQTk/∑i=kmdQTi, among which k=1, ΔQT1=ΔQ×dQT1/∑i=1mdQTi;(5): Initialize inverter group under transformer feeder,ΔQIk=, j=1, calculate reactive power margin matrix of inverter dQIk by formula (5);(6): Repeat(7): CalculateΔQIkj=ΔQTk−∑i=1j−1ΔQIki×dQIkj/∑i=jndQIki, among which j=1, ΔQIk1=ΔQTk×dQIk1/∑i=1ndQIki;(8): Updatej=j+1;(9): Untilj=n in dQIk;(10): UpdateΔQTk=∑i=1nΔQIki, verify the constraints of formula (2);(11): Updatek=k+1;(12): Untilk=m in CT;Calculate the cases in Tables3 and 4 through Algorithm 2, and the normalized result is shown in Figure 6. By observing the trend of Figures 4 and 6, the optimization results of Algorithm 2 and Algorithm 1 are basically consistent.(5)dQ=C2−Ptime2−Qtime.Figure 6
The results of algorithm 2 for the case.


### 3.3. Angle Length Distribute Algorithm

In this section, the distribution principle is based on the imbalance degree without considering the power margin. In each RPD, the difference in PF and apparent power between the devices connected at PCC and the lower level is considered to balance the phase angle and power amplitude of different devices.Figure7(a) shows that two devices under one PCC achieve the same PF cosφ¯ by adjusting the reactive power. This adjustment does not change the active power generation P1P1 and P1P2 and ensures the stability of total reactive power: Q1+Q2=Q1′+Q2′. Due to the large number of devices connected to the PCC, the approximate solution of Formula (6) is adopted for the average PF.(6)cosφj¯=∑i=jnPi∑i=jnPi2+∑i=jnQi+ΔQ−∑i=1j−1ΔQi2,j>1,cosφ1¯=∑i=1nPi∑i=1nPi2∑i=1nQi+ΔQ2,j=1.Figure 7
Reactive power adjustment under average angle and length of power. (a) Vector diagram of average angle. (b) Vector diagram of average length.Figure7(b) shows that two devices under one PCC achieve the same apparent power S¯ by adjusting the reactive power. This adjustment will also guarantee the active power generation and the total reactive power: Q1+Q2=Q1″+Q2″, and the average apparent power is calculated by the approximate solution of Formula (7).(7)Sj¯=∑i=jnPi2+∑i=jnQi+ΔQ−∑i=1j−1ΔQi2×Cj∑i=jnCi,j>1,S1¯=∑i=1nPi2+∑i=1nQi+ΔQ2×C1∑i=1nCi,j=1.From Figure7 and Formulas (6) and (7), it can be seen that the angle average or length average reduces the difference between devices in different dimensions, which is conducive to the power convergence of the device group, and reduces the system stability impact caused by the differential fluctuation of distributed nodes. Based on this, the designed algorithm is shown in Table 6.Table 6
Angle length distributed algorithm of multidimensional dynamic capacity.
Algorithm 3: Angle length distributed algorithmInput: RPC amountΔQ; transformer capacity matrix CT, transformer real-time active power matrix PT, transformer real-time reactive power matrix QT; inverter capacity matrix CI, inverter real-time active power matrix PI, inverter real-time reactive power matrix QI;Output: transformer reactive power adjustment matrixΔQT; inverter reactive power adjustment matrix ΔQT;(1): Initialize, arrangeCT according to the sequence of transformer grid connection, the length of CT is m, make k=1;(2): Repeat(3): Calculate average PF matrix of transformercosφTk¯ by formula (6);(4): Calculate apparent power matrix of transformerSTk¯ by formula (7);(5): CalculateΔQTφk=1−cosφTk¯2/cosφTk¯×PTk−QTk;(6): CalculateΔQTsk=STk¯2−PTk2−QTk;(7): Then calculateΔQTk=ΔQTsk+ΔQTφk/2;(8): Initialize inverter group under transformer feeder,ΔQIk=, j=1;(9): Repeat(10): Calculate average PF matrix of invertercosφIkj¯ by formula (6);(11): Calculate apparent power matrix of inverterSIkj¯ by formula (7);(12): CalculateΔQIkφj=1−cosφIkj¯2/cosφIkj¯×PIkj−QIkj;(13): CalculateΔQIksj=SIkj¯2−PIkj2−QIkj;(14): Then calculateΔQIkj=ΔQIkφj+ΔQIksj/2;(15): Updatej=j+1;(16): Untilj=n in CIk;(17): UpdateΔQTk=∑i=1nΔQIki, verify the constraints of formula (2);(18): Updatek=k+1;(19): Untilk=m in CT;Maintain the same environment as Algorithm 1 and Algorithm 2, and simulate Algorithm 3. The normalized result is shown in Figure8. It can be seen from the results that Algorithm 3 is significantly better than the first two algorithms in terms of power imbalance in Case 1, and the power imbalance degree keeps a very low growth rate in most of the planned ΔQΔQ, but the overall change law still remains consistent.Figure 8
The results of algorithm 3 for the case.


### 3.4. Comparison

Through the previous analysis in this chapter, it can be concluded that the three algorithms can solve the basic RPC and have the same distribution law in typical cases. But for the data value of trend expression, as well as the optimization performance in the face of more complex, real-time data changes, and device values with nonequal ratios, a further comparative analysis is needed. The three algorithms compared in this paper are summarized in Table7, and the common features in Table 1 are omitted.Table 7
Comparison and description of algorithms this paper.
AlgorithmAdvantagesDisadvantagesRatio distribute algorithmSimple control (+++)RPC capability (+ΔQ)stability margin (+)balance ability (+ sp)Residual margin algorithmBalance ability (++sp)Complex control (++)RPC capability (+ ΔQ)stability margin (+)Angle length distributed algorithmRPC capability (++ΔQ)stability margin (++)balance ability (+++ sp)Complex control (+)(∗better performance with more +).After meeting the operational constraints of PVPS implanted in the control system, taking the actual operation condition of Foshan Hisense distributed PVPS as the input conditions shown in Figure2, compare and analyze different distribution algorithms as follows. Among them, the upper limit values of RPC quantity ΔQΔQ under different distribution algorithms are compared, as shown in Figure 9.Figure 9
MaximumΔQ comparison of three algorithms.Under the same operation condition, the higher the upper limit value ofΔQΔQ quantity is, the better the distribution and adjustment ability of the algorithm is. Therefore, under the same ΔQΔQ demand, the higher the upper limit value is, the larger the regulation margin of each device in PVPS is, the less PVPS resources needed are called, and the PVPS system will be relatively more stable.Algorithms 1 and 2 are basically consistent in Figures4 and 6, and there is no obvious difference for solving the demand of RPC. This is the reason many PVPS currently use Algorithm 1 with simple calculation and less data dimension to solve inverter cluster RPC. In the unchanged Night period, Algorithm 3 has a minimal margin advantage over algorithms 1 and 2, but it has a significant margin disadvantage at some times in the period of drastic changes, especially in the a.m. start and p.m. end periods. It shows that the imbalance of the system is serious during these drastic periods, and Algorithm 3 sacrifices the ΔQ margin to reduce the imbalance, which is the balance property.The static capacity parameters of the topology in Figure1 are shown in Table 3, and the differences between the unregulated and three RPD algorithms are simulated for the operation state shown in Figure 2 and Figures 10 and 11. The results show that only the transformers have a larger value during the night period, while inverters basically keep 0. This is due to the fact that the inverter stops generating power but the cable laid on low voltage of transformer absorbs small-capacity capacitive power from the grid through the transformer. However, the power is too small to affect the system at the night.Figure 10
Transformer difference comparison of three algorithms inPCCPV.Figure 11
Inverter array difference comparison of three algorithms inPCCTi.The value of plannedΔQΔQ in Figure 11 is uncertain over time. Observing the transformer and PV matrices, it can be found that the spsp of Algorithm 3 is basically smaller than Algorithm 1 and Algorithm 2 during the power generation period, while spsp of Algorithm 1 is larger than Algorithm 2. In addition, for the period when changes drastically at noon in PV matrix, it can be found that even if the RPC is increased by the device, sp is still declining compared to the original sp, indicating that a reasonable distribution algorithm can reduce the device imbalance and stabilize the system auxiliary while completing the RPC.Thesφsφ of Algorithm 3 changes violently when ΔQ is relatively small, and the sφsφ of Algorithm 1, 2, and 3 increase sequentially in the generation period, but it is still controlled within a reasonable range. For the transformer, when the power fluctuates greatly during the noon period, sφ will exceed the original state, but it can be controlled below the original state in other power generation periods. In addition, Algorithm 1 and 2 will produce sφ a sudden change at Day 6 noon, which is caused by the sharp power change and obvious demand of ΔQΔQ at the moment. However, Algorithm 3 will not have such an accident because sφ is considered sφ in the iteration.The PV matrix distribution algorithm can significantly reducesφsφ at the a.m. start and p.m. end time because the inverters use constant PF operation in the original state, so there is no dynamic method corresponding to the sudden change. The PV matrix is increased in most power generation periods after cluster control; however, sφ still maintain a low level at most periods except the noon power generation time, showing that a reasonable distribution algorithm can help to reduce the device imbalance while completing the RPC.In general, the more data dimensions of parameter allocation, the better the comprehensive effect of optimization, and the greater the complexity of calculation. In actual operation, since the influence of length on voltage is greater than angle,spsp is more important than sφ in selection.


## 3.1. Ratio Distribute Algorithm

Transformers and inverters have independent static parameters to adapt to the complex field environment. Taking the device capacity as an allocation basis, the static distribution algorithm is designed as shown in Table2. Algorithm 1 does not consider the dynamic operation parameters of devices. Although RPC quantity ΔQ reflects part of the dynamic parameters, the fixed allocation ratio does not play a sufficient role in compensating and balancing when the dynamic parameters of the device group differ greatly, which wastes the group control effect.Table 2
Ratio distribute algorithm of static capacity.
Algorithm 1: Ratio distribute algorithmInput: RPC amountΔQ; transformer capacity matrix CT; inverter capacity matrix CI;Output: transformer reactive power adjustment matrixΔQT; inverter reactive power adjustment matrix ΔQI;(1): Initialize, arrangeCT according to the sequence of transformer grid connection, the length of CT is m , make k=1;(2): Repeat(3): CalculateΔQTk=ΔQ−∑i=1k−1ΔQTi×CTk/∑i=kmCTi, among which k=1, ΔQT1=ΔQ×CT1/∑i=1mCTi;(4): Initialize inverter group under transformer feeder,CIk=fCI, ΔQIk=, j=1;(5): Repeat(6): CalculateΔQIkj=ΔQTk−∑i=1j−1ΔQIki×CIkj/∑i=jnCIki, among which j=1, ΔQIk1=ΔQTk×CIk1/∑i=1nCIki;(7): Updatej=j+1;(8): Untilj=n in CIk;(9): UpdateΔQTk=∑i=1nΔQIki, verify the constraints of formula (2);(10): Updatek=k+1;(11): Untilk=m in CT;The topology of PVPS and the parameters of each device shown in this paper are based on the Foshan Hisense distributed PVPS in China. Define the topology of Figure1 with 5 PV matrixes converging at PCCPV, and [14 13 15 15 15] PV arrays converging at PCCTi separately. Table 3 shows the static capacity parameters of each device, and Table 4 defines the dynamic operation parameters under three typical cases.Table 3
Static parameters of PVPS installation.
ParameterStatic value (rated capacity)/(kW)Transformer[1000 800 1250 1250 1250]PV matrix 1[50 80 80 80 80 80 80 50 80 80 80 80 50 50]PV matrix 2[80 80 80 80 50 50 50 50 80 50 80 50 50]PV matrix 3[80 80 80 80 80 80 80 80 80 80 80 80 80 80 80]PV matrix 4[80 80 80 80 80 80 80 80 80 80 80 80 80 80 80]PV matrix 5[80 80 80 80 80 80 80 80 80 80 80 80 80 80 80]Table 4
Dynamic parameters of PVPS installation.
ParameterDynamic value/(kW)Case 1Case 2Case 3TransformerActive powerAll 0[500 400 625 625 625][900 720 1125 1125 1125]Reactive powerAll 0[500 400 625 625 625]All 0PV matrix 1Active powerAll 0[25 40 40 40 40 40 40 25 40 40 40 40 25 25][45 72 72 72 72 72 72 45 72 72 72 72 45 45]Reactive powerAll 0[25 40 40 40 40 40 40 25 40 40 40 40 25 25]All 0PV matrix 2Active powerAll 0[40 40 40 40 25 25 25 25 40 25 40 25 25][72 72 72 72 45 45 45 45 72 45 72 45 45]Reactive powerAll 0[40 40 40 40 25 25 25 25 40 25 40 25 25]All 0PV matrix 3Active powerAll 0[40 40 40 40 40 40 40 40 40 40 40 40 40 40 40][72 72 72 72 72 72 72 72 72 72 72 72 72 72 72]Reactive powerAll 0[40 40 40 40 40 40 40 40 40 40 40 40 40 40 40]All 0PV matrix 4Active powerAll 0[40 40 40 40 40 40 40 40 40 40 40 40 40 40 40][72 72 72 72 72 72 72 72 72 72 72 72 72 72 72]Reactive powerAll 0[40 40 40 40 40 40 40 40 40 40 40 40 40 40 40]All 0PV matrix 5Active powerAll 0[40 40 40 40 40 40 40 40 40 40 40 40 40 40 40][72 72 72 72 72 72 72 72 72 72 72 72 72 72 72]The relationship between the demand of RPC amountΔQ∈0,C and the actual distribution value meets Formula (2), which is the capacity constraint.(2)∑k=1k=mΔQTk=∑k=1k=m∑j=1j=nΔQIkj≤ΔQ.The greater the difference in the operation state of feeder devices, the more obvious the imbalance of the station system, and the phenomenon of voltage imbalance and power backflow after confluence is more serious. Therefore, the difference of feeder array under the samePCC is an important index to measure the merits and disadvantages of the RPD algorithm. This paper defines the phase difference and power difference as Formulas (3) and (4), where φ is the phase angle, and SS is the apparent power of one device.(3)sφ=∑i=1nφi−φ¯2n.(4)sP=∑i=1nSi−S¯2n.Algorithms in this paper are all implemented in MATLAB 2021a, and the PVPS model in Figure1 is built to calculate the cases in the above table, and the normalized result is shown in Figure 4.Figure 4
The results of algorithm 1 for the case.Since the initial power state of each device in Case 2 and Case 3 is not 0, the reactive power that can be allocated will reach saturation earlier, and the corresponding power difference remains unchanged after saturation, while the power difference in Case 1 continues to increase steadily. The phase difference in Case 2 and Case 3 is larger when the plannedΔQ is small, but when the planned ΔQ is increased to compensate for the initial value difference enough, the phase difference remains at 0.


## 3.2. Residual Margin Algorithm

Define the dynamic parameters of remaining capacitydQ when the inverter is running, as shown in Figure 5. In most cases, the inverters are in state Stime, and the maximum additional RPC dQ can be provided without loss of generating power Ptime, as formula (5), where C is the apparent power of the inverter. Taking dQ as the allocation basis, a one-dimensional dynamic distribution algorithm is designed as shown in Table 5.Figure 5
RPC power vector diagram.Table 5
Residual margin algorithm of one-dimensional dynamic capacity.
Algorithm 2: Residual margin algorithmInput: RPC amountΔQ; transformer capacity matrix CT, transformer real-time active power matrix PT, transformer real-time reactive power matrix QT; inverter capacity matrix CI, inverter real-time active power matrix PI, inverter real-time reactive power matrix QI;Output: transformer reactive power adjustment matrixΔQT; inverter reactive power adjustment matrix ΔQT;(1): Initialize, arrangeCT according to the sequence of transformer grid connection, the length of CT is m, make k=1;(2): Calculate reactive power margin matrix of transformerdQT by formula (5);(3): Repeat(4): CalculateΔQTk=ΔQ−∑i=1k−1ΔQTi×dQTk/∑i=kmdQTi, among which k=1, ΔQT1=ΔQ×dQT1/∑i=1mdQTi;(5): Initialize inverter group under transformer feeder,ΔQIk=, j=1, calculate reactive power margin matrix of inverter dQIk by formula (5);(6): Repeat(7): CalculateΔQIkj=ΔQTk−∑i=1j−1ΔQIki×dQIkj/∑i=jndQIki, among which j=1, ΔQIk1=ΔQTk×dQIk1/∑i=1ndQIki;(8): Updatej=j+1;(9): Untilj=n in dQIk;(10): UpdateΔQTk=∑i=1nΔQIki, verify the constraints of formula (2);(11): Updatek=k+1;(12): Untilk=m in CT;Calculate the cases in Tables3 and 4 through Algorithm 2, and the normalized result is shown in Figure 6. By observing the trend of Figures 4 and 6, the optimization results of Algorithm 2 and Algorithm 1 are basically consistent.(5)dQ=C2−Ptime2−Qtime.Figure 6
The results of algorithm 2 for the case.


## 3.3. Angle Length Distribute Algorithm

In this section, the distribution principle is based on the imbalance degree without considering the power margin. In each RPD, the difference in PF and apparent power between the devices connected at PCC and the lower level is considered to balance the phase angle and power amplitude of different devices.Figure7(a) shows that two devices under one PCC achieve the same PF cosφ¯ by adjusting the reactive power. This adjustment does not change the active power generation P1P1 and P1P2 and ensures the stability of total reactive power: Q1+Q2=Q1′+Q2′. Due to the large number of devices connected to the PCC, the approximate solution of Formula (6) is adopted for the average PF.(6)cosφj¯=∑i=jnPi∑i=jnPi2+∑i=jnQi+ΔQ−∑i=1j−1ΔQi2,j>1,cosφ1¯=∑i=1nPi∑i=1nPi2∑i=1nQi+ΔQ2,j=1.Figure 7
Reactive power adjustment under average angle and length of power. (a) Vector diagram of average angle. (b) Vector diagram of average length.Figure7(b) shows that two devices under one PCC achieve the same apparent power S¯ by adjusting the reactive power. This adjustment will also guarantee the active power generation and the total reactive power: Q1+Q2=Q1″+Q2″, and the average apparent power is calculated by the approximate solution of Formula (7).(7)Sj¯=∑i=jnPi2+∑i=jnQi+ΔQ−∑i=1j−1ΔQi2×Cj∑i=jnCi,j>1,S1¯=∑i=1nPi2+∑i=1nQi+ΔQ2×C1∑i=1nCi,j=1.From Figure7 and Formulas (6) and (7), it can be seen that the angle average or length average reduces the difference between devices in different dimensions, which is conducive to the power convergence of the device group, and reduces the system stability impact caused by the differential fluctuation of distributed nodes. Based on this, the designed algorithm is shown in Table 6.Table 6
Angle length distributed algorithm of multidimensional dynamic capacity.
Algorithm 3: Angle length distributed algorithmInput: RPC amountΔQ; transformer capacity matrix CT, transformer real-time active power matrix PT, transformer real-time reactive power matrix QT; inverter capacity matrix CI, inverter real-time active power matrix PI, inverter real-time reactive power matrix QI;Output: transformer reactive power adjustment matrixΔQT; inverter reactive power adjustment matrix ΔQT;(1): Initialize, arrangeCT according to the sequence of transformer grid connection, the length of CT is m, make k=1;(2): Repeat(3): Calculate average PF matrix of transformercosφTk¯ by formula (6);(4): Calculate apparent power matrix of transformerSTk¯ by formula (7);(5): CalculateΔQTφk=1−cosφTk¯2/cosφTk¯×PTk−QTk;(6): CalculateΔQTsk=STk¯2−PTk2−QTk;(7): Then calculateΔQTk=ΔQTsk+ΔQTφk/2;(8): Initialize inverter group under transformer feeder,ΔQIk=, j=1;(9): Repeat(10): Calculate average PF matrix of invertercosφIkj¯ by formula (6);(11): Calculate apparent power matrix of inverterSIkj¯ by formula (7);(12): CalculateΔQIkφj=1−cosφIkj¯2/cosφIkj¯×PIkj−QIkj;(13): CalculateΔQIksj=SIkj¯2−PIkj2−QIkj;(14): Then calculateΔQIkj=ΔQIkφj+ΔQIksj/2;(15): Updatej=j+1;(16): Untilj=n in CIk;(17): UpdateΔQTk=∑i=1nΔQIki, verify the constraints of formula (2);(18): Updatek=k+1;(19): Untilk=m in CT;Maintain the same environment as Algorithm 1 and Algorithm 2, and simulate Algorithm 3. The normalized result is shown in Figure8. It can be seen from the results that Algorithm 3 is significantly better than the first two algorithms in terms of power imbalance in Case 1, and the power imbalance degree keeps a very low growth rate in most of the planned ΔQΔQ, but the overall change law still remains consistent.Figure 8
The results of algorithm 3 for the case.


## 3.4. Comparison

Through the previous analysis in this chapter, it can be concluded that the three algorithms can solve the basic RPC and have the same distribution law in typical cases. But for the data value of trend expression, as well as the optimization performance in the face of more complex, real-time data changes, and device values with nonequal ratios, a further comparative analysis is needed. The three algorithms compared in this paper are summarized in Table7, and the common features in Table 1 are omitted.Table 7
Comparison and description of algorithms this paper.
AlgorithmAdvantagesDisadvantagesRatio distribute algorithmSimple control (+++)RPC capability (+ΔQ)stability margin (+)balance ability (+ sp)Residual margin algorithmBalance ability (++sp)Complex control (++)RPC capability (+ ΔQ)stability margin (+)Angle length distributed algorithmRPC capability (++ΔQ)stability margin (++)balance ability (+++ sp)Complex control (+)(∗better performance with more +).After meeting the operational constraints of PVPS implanted in the control system, taking the actual operation condition of Foshan Hisense distributed PVPS as the input conditions shown in Figure2, compare and analyze different distribution algorithms as follows. Among them, the upper limit values of RPC quantity ΔQΔQ under different distribution algorithms are compared, as shown in Figure 9.Figure 9
MaximumΔQ comparison of three algorithms.Under the same operation condition, the higher the upper limit value ofΔQΔQ quantity is, the better the distribution and adjustment ability of the algorithm is. Therefore, under the same ΔQΔQ demand, the higher the upper limit value is, the larger the regulation margin of each device in PVPS is, the less PVPS resources needed are called, and the PVPS system will be relatively more stable.Algorithms 1 and 2 are basically consistent in Figures4 and 6, and there is no obvious difference for solving the demand of RPC. This is the reason many PVPS currently use Algorithm 1 with simple calculation and less data dimension to solve inverter cluster RPC. In the unchanged Night period, Algorithm 3 has a minimal margin advantage over algorithms 1 and 2, but it has a significant margin disadvantage at some times in the period of drastic changes, especially in the a.m. start and p.m. end periods. It shows that the imbalance of the system is serious during these drastic periods, and Algorithm 3 sacrifices the ΔQ margin to reduce the imbalance, which is the balance property.The static capacity parameters of the topology in Figure1 are shown in Table 3, and the differences between the unregulated and three RPD algorithms are simulated for the operation state shown in Figure 2 and Figures 10 and 11. The results show that only the transformers have a larger value during the night period, while inverters basically keep 0. This is due to the fact that the inverter stops generating power but the cable laid on low voltage of transformer absorbs small-capacity capacitive power from the grid through the transformer. However, the power is too small to affect the system at the night.Figure 10
Transformer difference comparison of three algorithms inPCCPV.Figure 11
Inverter array difference comparison of three algorithms inPCCTi.The value of plannedΔQΔQ in Figure 11 is uncertain over time. Observing the transformer and PV matrices, it can be found that the spsp of Algorithm 3 is basically smaller than Algorithm 1 and Algorithm 2 during the power generation period, while spsp of Algorithm 1 is larger than Algorithm 2. In addition, for the period when changes drastically at noon in PV matrix, it can be found that even if the RPC is increased by the device, sp is still declining compared to the original sp, indicating that a reasonable distribution algorithm can reduce the device imbalance and stabilize the system auxiliary while completing the RPC.Thesφsφ of Algorithm 3 changes violently when ΔQ is relatively small, and the sφsφ of Algorithm 1, 2, and 3 increase sequentially in the generation period, but it is still controlled within a reasonable range. For the transformer, when the power fluctuates greatly during the noon period, sφ will exceed the original state, but it can be controlled below the original state in other power generation periods. In addition, Algorithm 1 and 2 will produce sφ a sudden change at Day 6 noon, which is caused by the sharp power change and obvious demand of ΔQΔQ at the moment. However, Algorithm 3 will not have such an accident because sφ is considered sφ in the iteration.The PV matrix distribution algorithm can significantly reducesφsφ at the a.m. start and p.m. end time because the inverters use constant PF operation in the original state, so there is no dynamic method corresponding to the sudden change. The PV matrix is increased in most power generation periods after cluster control; however, sφ still maintain a low level at most periods except the noon power generation time, showing that a reasonable distribution algorithm can help to reduce the device imbalance while completing the RPC.In general, the more data dimensions of parameter allocation, the better the comprehensive effect of optimization, and the greater the complexity of calculation. In actual operation, since the influence of length on voltage is greater than angle,spsp is more important than sφ in selection.


## 4. Experiment

Algorithm 3 is used to test PVPS of the topology in Figure1 in Foshan Hisense, and the device parameters are shown in Table 3. This paper adopts embedded development to realize the control logic in Figure 3 in Code Blocks with Linux system development environment. The control system is shown in Figure 12, which indicates that the work of this paper is a small part of PVPS. The PF comparison after experiment is shown in Figure 13, and by comparing the original conditions of the PVPS shown in Figure 2, it can be found that the PF fluctuation of PCCPVPCCPV and inverter is obvious after the retrofit operation, which is the result of changing the fixed PF operation mode of the inverter group in the original station to the remote reactive power regulation mode. In this mode, the reactive power will not change with the active power generation. The overall reactive power output of the power station has relatively independent characteristics, and the reactive power value is relatively stable, thereby reducing the reactive power demand and suppressing the reactive power fluctuation at PCCPCC. The curve change of QPCCQPCC in Figure 13 is the experimental proof expected by this theory.Figure 12
Schematic diagram of PVPS control system.Figure 13
PF comparison diagram of PVPS under RPC.The modified control system follows the demand ofPCC to generate ΔQΔQ, to improve the PF of PCCPCC. It can be seen from the results that the steady-state PF value increases from 0.95 to 0.97, which significantly improves the power quality of the station and reduces the reactive power pressure of the grid. In this paper, some stable operation constraints such as overvoltage and undervoltage are set during the retrofit of control system, although, which is not described in detail, the retrofit process still includes many other steps besides the algorithm. Due to the factors such as bus voltage and device capacity, the compensation capacity cannot be continuously released. Therefore, the QPVQPV in Figure 13 shows a trapezoidal change. It is worth noting that since the operation experiment in Figure 13 is in summer and Figure 2 is in spring, the sampling environment in Figure 13 is faced with more sufficient illumination and drastic environmental changes, so the active power generation and PF change sharply during some periods. Figure 13 shows the effect after RPC, so it can be inferred that the power quality will be worse if RPC is not used.In Foshan, one PVPS in the same area as Hisense was selected to conduct a control experiment. The operation results of 75 consecutive days were analyzed daily, as shown in Figure14. The cycle Figure 14 is divided into three consecutive stages, and the middle 36–60 days are the retrofit stage of the control system, which may not be representative. It can be seen from the figure that the active daily energy curve of the pilot power station has not deviated at any stage and has always maintained the same power generation law as the comparison power station, which verifies that the technical scheme in this paper does not cause any loss to the power generation. However, the reactive daily energy of the pilot PVPS has increased significantly, which has caused the PF of PCCPCC to decrease, while compensating the reactive power and improving the PF of PCCPCC. The whole process maintains the same operation law as Figure 13, and the experimental operation proves the economy and effectiveness of the technical route proposed in this paper.Figure 14
Control experiment daily diagram of PVPS under RPC.


## 5. Conclusion

In this paper, the influence of distributed PVPS on grid and the owner’s power consumption quality during operation is analyzed, and the advantages of grid-connected inverter in RPC are explained. Three algorithms are designed by using different data dimensions to solve the problem of inverter group reactive power control, and the imbalance evaluation method is defined according to the system equilibrium target. In typical cases, the performance advantages of Algorithm 3 are obtained by comparison and analysis, but the data dimensions and calculation are also relatively complex.Three algorithms are compared and analyzed by using one week’s actual operation data of the power station, and compared with the fixed PF operation of the power generation device, cluster control can not only perform RPC but also reduce the imbalance of the system. The reactive power margin of Algorithm 3 proposed in this paper is low in some periods, which is due to sacrificing a certain margin to reduce the imbalance, butspsp is the lowest, and the sφsφ control does not undergo changes abruptly, so it has more advantages in a comprehensive performance.Through the transformation of the control system to run Algorithm 3 in the actual power station, the experimental results show that the improvement of RPC through the inverter group is an effective way to improve power quality, and it is an important way of VVC in the future intelligent PVPS and high penetration of renewables grid.In the future, consider voltage balance in the algorithm to further refine the control, and use the power generation device group control to adjust the frequency by active power to further improve the frequency characteristics of the grid. Among them, how to coordinate the voltage-frequency control is an important problem. In this paper, the experiment does not perform RPC when the inverter is not generating, but the inverter still has the ability of reactive power output at the moment, so it can consider how to use the nonpower generation period to support the power system economically. The refined management and control of renewables is an important part of constructing the new power system. According to the cluster control idea in this paper, the control, operation and maintenance, communication, and other fields of power stations can be expanded in the future to further promote digital intelligent power stations.



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*Source: 6396345-2022-10-11.xml*