Suitability of capacitor allocation methods in different kinds of distribution networks

In the context of power systems with “a high percentage of renewable energy” and “a high percentage of power electronic equipment”, reactive power capacitors are demanded to support the voltage and keep the economic operation of the distribution network. Reasonable configuration of reactive power compensation including capacitor location and compensation capacity can keep the system voltage at a reasonable level, improve the system voltage stability, and reduce the network loss. In this paper, a reactive power optimization model based on three capacitor allocation methods, namely the reactive power sensitivity method, the active power loss method, and the voltage stability method, was established. Considering the stability and economy of distribution network operation, the suitability of the different methods in different kinds of distribution networks was evaluated in terms of the indicators of minimizing the network loss, minimizing the voltage offset, and minimizing the system operation cost. The simulation results show that the active power loss method is the most suitable for reducing voltage fluctuations and network losses.


Introduction
For the purpose of achieving the "double carbon" goal, China's pace of low-carbon green energy has accelerated.Up to the end of 2020, renewable energy power generation such as photovoltaic power generation accounted for 42.4% of the total new installed capacity, and renewable energy accounted for 29.5% of the overall power capacity.However, distributed power generation is more stochastic and volatile.The distribution of network loss can be increased significantly and the voltage quality in the grid can be degraded [1].To keep the system voltage at a reasonable level and to improve system voltage stability, and thus reduce network loss [2,3], the effective configuration of reactive power compensation is needed.
To effectively improve the power quality of distribution networks and reduce losses, a lot of studies have been conducted on the optimal configuration of reactive power capacitors in distribution networks.A reactive sensitivity method was proposed to determine the location of reactive capacitors in distribution networks by taking a partial derivation of the node equivalent reactive power by reducing the network active power loss [4].The active power loss method was presented in [5].The full compensation of reactive power was considered at each node of the distribution network in sequence.The total active power losses of the system were ranked.The compensation nodes of the capacitors were quantitatively determined.A voltage stability method was proposed to identify the sensitive points of voltage collapse, which was aimed at obtaining the optimal siting nodes for capacitors [6,7].The existing methods were weighted and a Shannon entropy-based method was proposed to optimize the capacitor location and capacity determination [8].However, the above studies cannot accurately reflect the scope of application of different capacitor optimization allocation methods in different kinds of distribution networks to improve stability and economy.The accuracy of different methods in different kinds of distribution network applications needs to be further studied.
Based on the three capacitor allocation methods, a reactive power optimization model will be built in this paper.The stability and the economy of the distribution network are taken into account.The suitability of the different methods in different kinds of distribution network applications will be studied, in which the indicators of the minimum network loss, the minimum voltage offset, and the minimum system operation cost will be compared.

Determination of compensation position of the capacitor
2.1.1.Reactive sensitivity method.According to the order of values of the system network loss reduced by effective reactive power injected at each node, the top-ranked nodes have higher sensitivity.The node with the highest sensitivity is selected as the node at which the capacitor is stalled for compensation.The sensitivity could be expressed as follows: where Ploss is the active power loss of the distribution network, i is the first node of the branch number concerned, m is the number of system branches, U is the node voltage, Q eff is equivalent reactive power at the concerned node, and Ri is the branch resistance.
2.1.2.Active power loss method.The active power loss method is executed as follows.The full compensation of reactive loads is compensated at every node, respectively, in the system.Power loss is calculated.The active power losses of the radial network are reduced.Reduced power losses for every node are ordered.The node at which the reduced loss is largest is defined as the better choice for capacitor compensation.The node with the most significant loss reduction needed to be compensated by a reactive capacitor.It could be expressed as follows: where j is the last node of the branch number concerned.n is the number of system nodes.

Voltage stability method.
According to the order of the voltage collapse sensitivity of each node, the nodes ranked lower are most sensitive to voltage.Reactive capacitor compensation is needed at the node that is most sensitive to voltage collapse.The voltage collapse could be expressed as follows: where Q eff is effective reactive power at the node concerned, P eff is effective active power at the node concerned, and Xi is the branch reactance.After the capacitor is connected at a selected point to the system, the original distribution of power flow in the system will be changed by its capacity.The minimization of the total network loss cost in the distribution network is taken as the optimization objective, which could be expressed as follows: where P and Q are the active and reactive powers injected at the corresponding node point of the distribution network, respectively, and λp is the cost per unit of electricity.

Constraint equations. (1) Power balance constraints
where Pci and Qci are the active and reactive powers injected at node i. θij is the voltage phase difference between node i and node j.Gij and Bij are the conductance and the susceptance between node i and node j, respectively.
(2) Node voltage constraints , min ,max i ii In this paper, Ui,min is 0.95 UN, and Ui,max is 1.05 UN.UN is the nominated voltage of the distributed network.

Suitability of capacitor allocation methods in different kinds of distribution networks
For the purpose of studying the suitability of different capacitor optimization allocation methods in different types of distribution networks, different distribution models were built based on the IEEE33 node distribution network [9], whose network topology is shown in Figure 1.The simulation was divided into the following four types of distribution networks: Distribution network_1: Primitive network (load factor β = system load/system baseline value, β = 43.69%);Distribution network_2: Lightly loaded network (β = 9.22%); Distribution network_3: Long line-containing network (β =43.69%, l22 =17.62 km); Distribution network_4: Lightly loaded network with a long line (β =9.22%, l22 =17.62 km).(l22 is the branch 22 in the distribution network between node 3 and node 23.) The classical particle swarm algorithm is used to solve the optimal operation [10,11].The reference value of the system power is 10 MVA.The reference voltage value is 12.66 kV.The system load is 3715+j2300 kVA.The upper and lower voltage limits are 1.05 p.u. and 0.95 p.u., respectively.In the actual grid, DGs are usually distributed in remote areas.So, in this paper, DGs are connected to nodes 18, 21, and 33 near the end of the modified network, with capacities of 300 kW, 100 kW, and 200 kW, respectively.The maximum number of iterations is set to be 1000 in the program.The number of populations is set to 200.
IEEE33 node distribution network topology.

Simulation results
Firstly, the initial power flow of the distribution network is determined.Then, the scores of each node for Method_1, Method_2, and Method_3 are listed in Figure 2. Method_1, Method_2, and Method_3 correspond to the reactive sensitivity method, Active power loss method, and Voltage stability method, respectively.The Method_1 and Method_2 score values are sorted from large to small, and the Method_3 score value was sorted from small to large.In distribution network_1, the Method_1 and Method_2 score values of node 30 were the largest, and the Method_3 score value of node 32 was the smallest.In distribution network_2, the Method_1 and Method_2 score values of node 6 were the largest, and the Method_3 score value of node 15 was the smallest.In distribution network_3, the Method_1 score value of node 23 was the largest, and Method_2 score value of node 30 was the largest, and the Method_3 score value of node 25 was the smallest.In Distribution network_4, the Method_1 score value of node 23 was the largest, and Method_2 score value of node 6 was the largest, and the Method_3 score value of node 15 was the smallest.

Suitability evaluation of different configuration methods
On the basis of the three perspectives of the active power loss of the network, average voltage offset, and system operation cost, the suitability indexes of different capacitor optimization allocation methods applied in different kinds of distribution networks were evaluated.The results are shown in Table 1.It could be indicated that Method_1 and Method_2 have the greatest improvement effect on the economic operation of the distribution network with a loss reduction of about 31.55%.Method_3 has a great improvement effect on the overall voltage of the distribution network after compensation in distribution network_1 and distribution network_2.In distribution network_3, Method_2 has the greatest improvement effect on improving the stability and economy of the overall operation of the distribution network with a loss reduction of about 25.62%.The average voltage shift of 3.77% is in the range of permissible voltage fluctuation for distribution network operation after compensation.In distribution network_4, Method_2 has the greatest improvement effect on improving the economic operation of the distribution network with a loss reduction of about 20.83% after compensation.Method_3 has a great improvement effect on the overall voltage of the distribution network.Therefore, for different kinds of distribution networks, the optimization method for determining capacitor allocation based on the amount of change in active power losses is the best choice.

Conclusions
The different kinds of distribution network models have been built by modifying the IEEE33 node distribution system.The position and the optimal capacity of reactive capacitors in the distribution network have been determined by using the reactive power sensitivity method, the active power loss variation method, and the voltage stability method.The three indexes of the minimum network loss, the minimum voltage offset, and the minimum system operation cost have been taken into account.The results show that the optimization method of determining the capacitor configuration based on the variation of active power loss was the best among the three reactive capacitor optimization methods.It is verified that it was the most suitable for different kinds of distribution networks and has the most significant improvement on the stability and economy of the overall operation of the distribution network.

Figure 2 .
Figure 2. Compensated location scores for different methods at each node in different distribution networks.

Table 1 .
Suitability evaluation results of different configuration methods.
c System operating costs: