Optimizing Allocation of Distributed Electric Heating for Large-Scale Access Distribution Considering the Influence of Power Quality

Abstract

In this paper, a dual-layer grid comprehensive resource optimizing allocation model is proposed, which considers power quality controlling and load optimization scheduling under large-scale application of distributed electric heating. The upper-layer planning aims to minimize the active power loss of the distribution network, the minimum voltage deviation, and the minimum investment cost of the power quality control device. The capacity configuration of the management device and the number and location of the commutation switch configuration were determined. The lower layer is load optimization scheduling, with the minimum number of action switches and the minimum three-phase imbalance as the planning goals, and the decision variable is the state of the commutation switch. By co-simulation through Matlab and OpenDSS, the improved particle swarm algorithm and genetic algorithm are used for multi-objective optimization and the solution. In this way, the capacity configuration of reactive power compensation and active filter, as well as the installation position and switch state of the commutation switch are optimized and managed. Finally, taking the rural low-voltage distribution network in the Tongzhou District as an example, simulations considering the variation in the distributed electric heating penetration rate in the range of 20–80% are carried out. The calculation example results show that the proposed algorithm is effective, can effectively improve the power factor, reduces the harmonic content of the distribution network and the three-phase unbalance, and significantly improves the distribution network voltage.

1. Introduction

With the increasing problems of environmental pollution and the energy crisis, the state is paying more and more attention to energy conservation, emission reduction, and optimization of energy consumption structures [1]. At present, my country’s air pollution situation is severe, and a large number of scattered coal burning and fuel consumption producers are main factors causing serious smog. China consumes about 700 million to 800 million tons of scattered coal every year, which is mainly used for heating small boilers, industrial small boilers, rural production, living, and other fields, accounting for about 20% of the total coal consumption. A large amount of scattered coal is directly used for combustion without cleaning treatment, resulting in the emission of a large amount of air pollutants. In view of the current severe situation of environmental change, China proposed at the United Nations General Assembly held on 22 September 2020 to strive to peak carbon dioxide emissions by 2030 [2] and to achieve carbon neutrality by 2060. Under the dual pressure of resources and environment, it is urgent to find new alternative heating methods [3]. At present, most heat sources use traditional fossil energy coal-fired boilers, which have great economic advantages, but the continued use of coal-fired boilers for heating will exacerbate the growth of carbon emissions, and coal-fired boilers have no obvious advantages in terms of energy efficiency [4,5]. The air source heat pump has high electric-heat conversion efficiency, and is currently the main “coal-to-electricity” heating energy replacement equipment. The large-scale access of electric heating equipment has brought huge pressure to the stable operation of the distribution network. For example, the Huaibei region of the Anhui Province vigorously promoted electric heating, which caused the power supply voltage in some low-voltage stations to be seriously low during peak electricity consumption periods. Due to the promotion of electric heating projects in Le’an County, Jiangxi Province, a serious three-phase power imbalance occurred. Therefore, large-scale access to distributed electric heating equipment will exacerbate power quality problems, which contain a three-phase unbalance, low voltage, and increased harmonic distortion in the distribution network. In addition, this will greatly affect the safety and reliability of the distribution network. Therefore, it is imperative to grasp the status of power quality problems and propose comprehensive power quality control measures with economic technology.

At present, research on reactive power compensation is carried out from two aspects: the reactive power optimization algorithm and reactive power configuration scheme considering distributed energy access. In terms of the reactive power configuration, the power quality compensation performance varies greatly depending on the installation location of the equipment. When the optimal installation location is selected, it can not only effectively reduce the active power loss but also greatly improve the voltage stability of the distribution network [6,7]. With the increase in the number of installed reactive power compensation devices, the investment cost is high, and the economy is poor. An optimization algorithm is used to select the installation location [8]. In Ref. [9], in order to solve the problem of unstable voltage output at the public connection point after the renewable distributed generation is connected to the distribution network, the static reactive power compensator is connected to generate positive reactive power to the grid to reduce the voltage output at the Point of Common Coupling (PCC). The voltage rises, thereby regulating the phase voltage, while Ref. [10] established a multi-objective particle swarm optimization algorithm based on the particle swarm optimization neural network to predict the load curves of photovoltaic and wind power generation, taking into account the network loss and voltage deviation, and realized the relationship between distributed energy and the static var compensator. Collaborative optimization is required.

Refs. [11,12,13,14] all study the configuration of passive filters. According to the effect of the passive filter after installation, it is found that its filtering effect cannot reach the expected value, and an active filter with a relatively better filtering effect is considered [15]. Refs. [16,17,18] configure active filters. First, Ref. [16] considers the characteristics of various types of harmonic sources, high density, and wide distribution range after the new energy is connected to the grid. Based on the modal analysis method and genetic algorithm, the optimal installation position and capacity of each filter are optimized to improve the filtering effect and economic benefits. Meanwhile, Ref. [17] is based on the current limiting strategy of the parallel Active Power Filter (APF) and realizes the comprehensive protection of the traditional current limiting strategy through the particle swarm multi-objective optimization algorithm. Finally, Ref. [18] takes the optimal configuration of the voltage-detecting active power filter device as the research object. First, the active filter device is installed in zones, and the capacity is optimized by considering various factors such as economy and governance effect. Normalized plane constraints convert multi-objective optimization into single-objective optimization.

In order to deal with the three-phase unbalance problem of the distribution network, the three-phase unbalance compensation method and the method of installing an automatic commutation device are usually used. The control algorithm for unbalance control using the compensation device is relatively complex, and the equipment investment is high. The use of automatic commutation switchgear can carry out real-time treatment of the three-phase unbalance problem in the low-voltage station area at a relatively low cost. Ref. [19] considers the amplitude and phase of the unbalanced current and uses the unbalance degree and commutation times as the objective function to study the control strategy of the intelligent commutation switch. In another study, Ref. [20] analyzes the load dynamic planning of the distribution network where the commutation switch is located. On the basis of optimizing the line load reconnection method, the governance control strategy of the intelligent commutation switch in the distribution network is obtained based on genetic optimization. Finally, Ref. [21] proposes a load balancing control strategy that considers the network topology and the number of switching actions but assumes that the power factor of each user load is the same and also does not consider the phase index.

In terms of optimal configuration mathematical modeling, Ref. [22] decomposes the problem into two parts: the unit commitment problem in the first stage and the linear programming of fuel allocation in the second stage. The solution of random unit commitment under the condition of limited fuel price is obtained by optimization calculation, but only the economic cost and uncertain fuel price are considered. In Ref. [23], the maintenance scheduling and production planning problems of large-scale power plants take reducing the total operating cost as the overall objective function, and consider the two stages of shutdown scheduling and production allocation to solve the optimization problem, but only consider the factor of economic cost. Refs. [24,25] propose a feasible two-stage approach to large-scale energy management problems, taking the case of nuclear power plants periodically shutting down, requiring refueling and maintenance, and established an objective function considering production constraints and operating levels of costs. The solution method in Ref. [24] utilizes Benders’ decomposition to solve the linear programming relaxation of a relaxed version of the problem, using enumerated integer solutions to satisfy the constraints not included. Therefore, this paper can also adopt the method of establishing a two-level programming model. However, many factors such as safety, environmental protection, and economy can be used as optimization indicators, and the two-layer programming method can be combined with the optimization algorithm to realize the solution of the model.

Based on the above considerations, in view of the large-scale decentralized electric heating access, few literatures comprehensively consider the above problems. The steady-state power quality problem that exacerbates the three-phase unbalance is studied. Using co-simulation through Matlab and OpenDSS, this paper proposes a comprehensive resource optimal allocation model of the double-layer power grid considering power quality control and load optimization scheduling.

The upper-level planning is the planning problem of power quality control devices. The planning goal is to minimize the investment cost, operation and maintenance cost, and transformer and line loss costs of the control device. The decision variables are the capacity configuration and commutation of the harmonic control device and reactive power compensation device. The number and position of switch configurations are optimized using an improved particle swarm algorithm. The lower layer is load optimization scheduling, with the minimum number of operating switches and the minimum three-phase unbalance as the planning goals; the decision variable is the state of the commutation switch, and the improved genetic algorithm is used to optimize the solution. Optimized and managed reactive power compensation and active filter capacity configuration, as well as the installation position and switch state of the commutation switch, were considered. Based on the perspective of power quality governance, this paper studies the power quality coping strategies for the large-scale access of power substitute loads, improves the power quality operation level of the distribution network, and reduces the economic losses caused by power quality problems.

2. Analysis of Power Quality Problems and Governance Strategies after Large-Scale Application of Distributed Electric Heating

With the continuous increase in the proportion of electric heating equipment, the connection of a large number of electric heating equipment makes the power load increase significantly, which seriously affects the safe operation of the distribution network. The subsequent power quality problems and power quality control measures are analyzed.

2.1. Analysis of Power Quality Problems

When users do not carry out power quality control and directly connect to the grid, the main impacts on the distribution network are as follows:

(1) In rural areas, long-radiation low-voltage distribution networks are often used, and the grid is weak and covers a wide area [26]. The large-scale connection of electric heating loads to the rural distribution network will deepen the problems of insufficient transformer capacity in rural distribution networks and three-phase imbalance caused by uneven load distribution [27].

(2) With the increase in the access scale of electric heating users, the consumption of reactive power is large, causing the line voltage to drop, and the voltage of each node gradually decreases, making the voltage at the end of the line too low, resulting in the failure of the electric heating equipment to start [28].

The schematic diagram of the voltage drop generation principle on the line of the electric heating equipment is shown in Figure 1. Generally speaking, the equivalent resistance value of the low-voltage distribution line is larger than the equivalent reactance value, and the active power of the distributed electric heating equipment will cause a large amount of voltage drop on the low-voltage line, causing the voltage to drop.

$$\Delta U=\frac{P{R}_L+Q{X}_L}{U_2}$$

(1)

where $\Delta U$ is the voltage drop; $R_L$ is the line resistance; $X_L$ is the line reactance; $P$ is the active power of the electric heating load; $Q$ is the reactive power of the electric heating load; $U_2$ is the line terminal voltage.

(3) When electric heating users are directly connected to the grid without harmonic filtering, as the access scale increases, the total harmonic distortion rate of most nodes will exceed the standard [29].

According to the equivalent diagram of multiple electric heating harmonic sources in Figure 2, when electric heating is applied on a large scale, the superposition of harmonics leads to a high total harmonic distortion rate. When considering the influence of background harmonics, each harmonic source is injected into Point of Common Coupling (PCC). The total h-th harmonic current is shown below.

$${\dot{I}}_{h,\mathrm{L}}={\displaystyle \sum _{m=1}^{\mathrm{M}}{\dot{I}}_{h,\mathrm{L}m}}+\frac{{\dot{U}}_{h,S}}{Z_{h,S}+Z_{h,L}}$$

(2)

where $Z_{h,L}$ is the equivalent harmonic impedance of all loads at the PCC; ${\dot{U}}_{h,S}$ is the background h-order harmonic voltage on the system side; $Z_{h,S}$ is the h-order harmonic impedance of the system; ${\dot{U}}_{h,\mathrm{PCC}}$ is the h-order harmonic voltage at the PCC; ${\dot{I}}_{h,\mathrm{PCC}}$ is the h-order harmonic current at the PCC; ${\dot{I}}_{h,\mathrm{L}1}$, ${\dot{I}}_{h,\mathrm{L}2}$, …, ${\dot{I}}_{h,\mathrm{L}m}$ are the h-order harmonic currents generated by loads; $Z_{h,\mathrm{L}1}$, $Z_{h,\mathrm{L}2}$, …, $Z_{h,\mathrm{Lm}}$ are the h-order harmonic impedances of loads; h is the harmonic order.

2.2. User-Side Power Quality Management Strategy

The main constraints affecting the access scale of distributed electric heating users are harmonic distortion rate, voltage deviation, and three-phase unbalance. Therefore, to improve the power quality and power supply reliability of the large-scale application of distributed electric heating, one should mainly focus on the optimization of the grid structure and the configuration of the power quality control device.

2.2.1. Optimal Design of The Grid Structure

The load ratio refers to the ratio of the actual load of the transformer to its capacity, which is used to reflect the load-carrying capacity of the transformer and whether its operation curve is within the optimal 60–75% range. The design of the electrical system in the electric heating system requires the total power supply equipped with a 10% to 20% margin.

$$X=\frac{{\displaystyle \sum _{i=0}^n{P}_i}}{S}\hspace{1em}(n=1,2,3\cdots N)$$

(3)

where $X$ is the transformer load rate; $P_i$ is the actual average load of the node; $S$ is the transformer capacity; and $n$ is the number of single-phase users.

(1) When the load rate of the low-voltage distribution network transformer has a margin of 10% to 20%, the no-load voltage regulation can be used to increase the node voltage amplitude, thereby improving the power quality of the distribution network. The transformers of the rural distribution network can be regulated without load; the voltage adjustment range is (0.90, 1.10), and the single adjustment gear is 0.025 p.u.

(2) For relatively small villages and relatively concentrated loads, place the newly added transformers in the load center, from the low-voltage outlet of the distribution transformer to each load point, and try to extend radially to the surrounding area, and the power supply radius should not be exceeded.

2.2.2. The Reactive Power Compensation and The Harmonic Control Strategy

Considering the practicability and economy of installing the power quality control device, install the Thyristor Switched Capacitor (TSC) + APF device on the low-voltage distribution system side of the distributed electric heating users nearby to reduce the impact on the power quality of the low-voltage distribution network. The entry is shown in Figure 3.

2.2.3. The Three-Phase Imbalance Management Strategy

In the low-voltage platform area, the low-voltage load on-line automatic commutation device is installed on some branches to reduce the three-phase unbalance of the distribution network. The circuit is shown in Figure 4.

3. Two-Tier Planning Model for the Power Quality Management

The upper-level planning is the planning problem of power quality control devices. The planning goal is to minimize the investment cost, operation and maintenance cost, and transformer and line loss costs of the control device. The decision variables are the capacity configuration and commutation of the harmonic control device and reactive power compensation device. The number and position of switch configuration are also considered; the lower layer is load optimization scheduling, with the minimum number of active switches and the minimum three-phase unbalance as the planning goals, and the decision variable is the state of the commutation switch. After the upper-level planning, the installed capacity of the power quality control device and the number and position of the commutation switches provide the initial conditions for the lower-level planning. The three-phase unbalance and voltage deviation obtained from the lower-level planning are fed back to the upper-level planning, and the upper-level planning can be obtained by recalculation. The total objective function value is then considered.

3.1. Upper-Level Planning: Optimal Configuration Model of Power Quality Control Devices

3.1.1. The Objective Function

Establish a multi-objective optimization model considering the voltage deviation of the distribution network, the total investment cost of the power quality control device, and the minimization of the active power loss of the distribution network. The decision variables are the location, quantity, and capacity of the power quality control device. The objective function for:

$$T=\min ({\omega }_1{f}_V+{\omega }_2{f}_{\cos t}+{\omega }_3{f}_{loss})$$

(4)

$$f_V=\min \Delta U={\displaystyle \sum _{i=1}^N\left|U_i-U_{ref}\right|}$$

(5)

$$f_{\cos t}=\min (C_{APF,\cos \mathrm{t}}+C_{CAP,\cos \mathrm{t}}+C_{SW,\cos \mathrm{t}})$$

(6)

$$f_{loss}={\displaystyle \sum _{i=1}^N{P}_{loss,i}}+{\displaystyle \sum _{k\ne 1}^{}{P}_{loss}^k}$$

(7)

where $U_i$, $U_{ref}$, $\Delta U$ are the node voltage, the voltage limits required by national standards, and the sum of node voltage deviation, respectively; $N$ is the number of nodes; $C_{\cos t}$ is the total investment cost of switchgear and the total cost of operation; $C_{APF,\cos t}$, $C_{CAP,\cos t}$, $C_{SW,\cos t}$ are the investment cost of the active filter equipment, reactive power compensation equipment, and commutation switchgear, respectively; $P_{loss,i}$ is when the line i is in a three-phase unbalanced state; the neutral line will have zero-sequence current flowing, and the active line loss of the three-wire four-wire system, $P_{loss}^k$, is the loss of the k-th harmonic.

• Investment cost of power quality control device:

The investment cost includes the cost of the APF, the cost of the reactive power compensation device, and the cost of the commutation switchgear.

$$C_{APF,\cos t}=\min C_{APF}{I}_{APF}$$

(8)

$$C_{CAP,\cos t}=\min C_{cap}{Q}_C$$

(9)

$$C_{SW,\cos t}=\min C_{SW}{N}_{SW}$$

(10)

where $C_{APF,\cos t}$ is the total investment in APF; $C_{APF}$ is the investment cost per unit current; $I_{APF}$ is the compensation current;$C_{cap,\cos t}$ is the total investment of the reactive power compensation device; $C_{cap}$ is the investment cost per unit capacity; $Q_C$ is the installation capacity of the reactive power compensation device; $C_{SW}$ is the investment cost of a single commutation switch; and $N_{SW}$ is the number of commutation switches installed.

• Calculation formula of unit capacity cost $C$ of the power quality control device:

$$C=C_{inv}+C_{mat}{\displaystyle \sum _{t=0}^{T-1}{\left(\frac{1+\gamma }{1+R}\right)}^t}=C_{inv}\left[1+{\lambda }_{mat}{\displaystyle \sum _{t=0}^{T-1}{\left(\frac{1+\gamma }{1+R}\right)}^t}\right]$$

(11)

where $C_{inv}$ is the initial investment cost per unit capacity of the device; $C_{mat}$ is the annual operation and maintenance cost per unit capacity of the device; ${\lambda }_{mat}$ is the ratio between the annual operation and maintenance cost and the initial investment cost; $\gamma$ is the inflation rate; $R$ is the social discount rate; $T$ is the operating life of the device.

At the same time, regarding the data problem in the cost calculation formula, the following supplements are made below.

(1) The initial investment cost of APF is ¥45/A, and the initial investment cost of the low-voltage reactive power compensation device is ¥25/kvar.

(2) The annual operation and maintenance cost is 5% of the one-time investment cost, ${\lambda }_{mat}=5\%$.

(3) The operating life of the device is 15 years, $T=15$.

(4) The inflation rate is 10%, $\gamma =10\%$; the social discount rate is 3%, $R=3\%$.

3.1.2. Restrictions

The equation constraint is that the power flow of the distribution network remains balanced; that is, the power remains balanced, as shown in Equations (12) and (13).

$$P_i=U_i{\displaystyle \sum _{j=1}^N{U}_j(G_{ij}\cos {\theta }_{ij}+B_{ij}\sin {\theta }_{ij}})\hspace{1em}i,j=1,2,\cdots ,N$$

(12)

$$Q_i=U_i{\displaystyle \sum _{j=1}^N{U}_j(G_{ij}\sin {\theta }_{ij}-B_{ij}\cos {\theta }_{ij}})\hspace{1em}i,j=1,2,\cdots ,N$$

(13)

where $P_i$ is the active power flowing into node i; $Q_i$ is the reactive power flowing into node i; $U_i$ is the voltages of node I; $U_j$ is the voltages of node j; $G_{ij}$ is the conductance between the nodes i and j; $B_{ij}$ is the susceptance between the nodes i and j; ${\theta }_{ij}$ is the voltage phase angle difference between the nodes i and j.

The inequality constraint consists of two parts. The control variable constraint is composed of the amplitude of the generator node voltage and the limit value of the reactive power compensation capacity. The state variable constraint is composed of the node voltage amplitude of the low-voltage distribution network, the power factor at the PCC, the constraint limit of the voltage total harmonic distortion rate and harmonic current, and the constraint limit of the three-phase unbalance degree.

$$\left\{\begin{array}{l}{U}_{Gi,\min }<U_{Gi}<U_{Gi,\max }\hspace{1em}\hspace{1em}(i=1,2,\cdots ,N_G)\\ Q_{C,\min }<Q_C<Q_{C,\max }\\ U_{Li,\min }<U_{Li}<U_{Li,\max }\hspace{1em}\hspace{1em}(i=1,2,\cdots ,N_N)\\ PF\ge 0.96\\ HR{U}_h\le 3.2\%\\ TH{D}_U\le 4\%\\ I_{Ph}\le I_{h0}\\ \epsilon \le 1.3\%\end{array}\right.$$

(14)

where $U_{Gi}$, $U_{Gi\max }$, $U_{Gi\min }$ are the actual voltage amplitude and assessment limit value of the generator node voltage; $Q_C$, $Q_{C,\min }$, $Q_{C,\max }$ are the reactive power compensation capacity actually installed on the user side and its assessment limit; $U_{Li}$, $U_{Li,\min }$, $U_{Li,\max }$ are the voltage amplitude of the actual node i and its assessment limit; $PF$ is the power factor of the PCC when the electric heating user is running; $HR{U}_h$ is the h-th harmonic voltage content rate; $TH{D}_U$ is the voltage total harmonic distortion; $I_{Ph}$ is the actual value of the harmonic current flowing through the PCC of the distribution network; $I_{h0}$ is the harmonic current assessment limit required by the national standard; $\epsilon$ is the three-phase unbalance of the public connection point of the distribution network.

3.1.3. Normalized

The upper-layer multi-objective is normalized, and the judgment matrix method is used to determine the weight of each sub-objective, and the weight vector is shown in Formula (15).

$$W=(0.6370,0.2583,0.1047)$$

(15)

3.2. Lower-Level Planning: Mathematical Model of Load Optimization Regulation

For the three-phase four-wire low-voltage system, the zero-sequence current component and the negative-sequence current component can be decomposed at the same time due to the unbalanced current. Negative-sequence and zero-sequence currents need to be considered at the same time in the calculation. According to the calculation formula of the unbalanced current compensation demand of the compensation device of the Power Supply Society Group Standard T/CPSS10012018, the current imbalance is calculated as shown in Formula (16).

$$I_{\epsilon }\%=\frac{I_{\epsilon }}{I_1}\times 100\%=\frac{\sqrt{I_0^2+I_2^2}}{I_1}\times 100\%$$

(16)

where $I_{\epsilon }\%$ is the unbalanced degree; $I_{\epsilon }$ is the unbalanced current of the low-voltage power grid.

The number of commutations in the low-voltage load on-line automatic commutation device can be determined by the phase sequence state matrix before and after commutation. Define M as the number of actions of the commutation switch.

$$M=K-K_0$$

(17)

where $K_0$ is the initial switching phase sequence state column vector corresponding to the load branch; $K$ is the corresponding switching phase sequence state sequence vector after the load branch is commutated.

Calculate the value of each element $M_i$ in $M$ according to the following expression:

$$M_i=\left\{\begin{array}{l}{M}_i=0,K=K_0\\ M_i=1,K\ne K_0\end{array}\right.\hspace{1em}\hspace{1em}i=1\cdots N_{SW}$$

(18)

Then, the switching adjustment times of each load branch of all low-voltage loads on-line automatic commutation devices in the entire distribution station area can be recorded as:

$$m={\displaystyle \sum _{i=1}^{i=N_{sw}}{M}_i}$$

(19)

The optimal commutation strategy for real-time online control of three-phase load unbalance in the distribution station area can establish a mathematical model by synthesizing the three-phase unbalance degree and the minimum number of commutation switches. The objective function is shown in Equation (20).

$$f={\lambda }_1{I}_{\epsilon }\%+{\lambda }_{2}m$$

(20)

where ${\lambda }_1$ is the weight coefficient of the three-phase unbalance degree, and ${\lambda }_2$ is the weight coefficient of the number of commutation switches.

4. Co-Simulation through Matlab and OpenDSS

4.1. Co-Simulation Platform

Aiming at the problem of optimal allocation of resources after the distributed electric heating is connected to the distribution network on a large scale, a double-layer power quality management model based on the software Matlab and OpenDSS is established, and the solution is solved according to the algorithm. The joint simulation platform is shown in Figure 5.

4.2. The Solution

4.2.1. Upper-Level Planning Coding

The upper layer adopts an adaptive particle swarm optimization algorithm in which the inertia factor automatically changes with the fitness value. The encoding of the particles is shown in the following Formula (21).

$$P_{i,PSO}=[P_{i1}\cdots P_{iN},P_{iN+1},P_{iN+2}]$$

(21)

The first part of the particle indicates whether the switch is installed, which is represented by $P_{i1}~P_{iN}$. When the code is 0, the phase change switch is not installed here, and when the code is 1, the phase change switch is installed. The second part of the particle represents the capacity of reactive power compensation, represented by $P_{iN+1}$; the third part of the particle represents the installed capacity of the APF, represented by $P_{iN+2}$.

4.2.2. Lower-Level Planning Coding

The lower layer is solved by an improved genetic algorithm. In order to adapt to the multi-objective optimal commutation and improve the computational efficiency of the algorithm, this paper improves the coding strategy and proposes a vector gene coding strategy.

• Vector gene coding strategy:

The switching situation of the commutation switch installed on the load branch and the 3-bit binary code are addressed. Therefore, fixed-length binary codes can be used to describe the switching states of switches corresponding to each load branch of the low-voltage load on-line automatic commutation device. If the commutation switch switches the load to phase A (at the same time, it does not switch to phase B or C), the corresponding bit of A can be represented as 1, and the corresponding bits of B and C can be represented as 0. The switching situation of the load branch can be represented by a switching phase sequence state column vector k.

$$k=\left\{\begin{array}{lll}{\left[1\hspace{1em}0\hspace{1em}0\right]}^{\mathrm{T}},& Phase& \mathrm{A}\\ {\left[0\hspace{1em}1\hspace{1em}0\right]}^{\mathrm{T}},& Phase& \mathrm{B}\\ {\left[0\hspace{1em}0\hspace{1em}1\right]}^{\mathrm{T}},& Phase& \mathrm{C}\end{array}\right.$$

(22)

Therefore, the switching situation of the commutation switches installed on all load branches can be represented by a switch phase sequence state matrix. The phase sequence state matrix before and after the switch phase sequence in the low-voltage load on-line automatic commutation device is K₀, K.

$$K_0=\left[k_1^0,k_2^0,k_3^0\dots ,k_n^0\right]$$

(23)

$$K=\left[k_1^{},k_2^{},k_3^{}\dots ,k_n^{}\right]$$

(24)

where $k_i^0,k_i^{}$ are the phase sequence state vectors before and after the i-th branch commutation.

• Genetic manipulation:

Crossover operator: The crossover operation is to replace the entire vector gene without destroying the characteristics of the vector gene.

Mutation operator: Control whether to perform mutation according to the mutation rate. Generally, the mutation rate is 0.001~0.1. When mutation is required, the gene to be mutated is randomly selected. After determining the gene to be mutated, each gene can be in the three gene vectors [1 0 0]^T, [0 1 0]^T, [0 0 1]^T with variation between.

4.2.3. Algorithm Flow

The solution flow chart of the optimization model is shown in Figure 6.

5. Case Analysis

OpenDSS is used to carry out comprehensive simulation modeling of the large-scale electric heating load connection to the distribution network for the rural low-voltage station area line for the coal-to-electricity project. The low-voltage distribution network in Caosi Village, Songzhuang Town, Tongzhou District, Beijing is selected. The short-circuit capacity of this low-voltage station area is 10 MVA, and it is powered by a 315 kVA S11 distribution transformer. The power supply radius of this power supply area is 681 m, and there are five branches, including two long branches, 302 m and 213 m, respectively, and three short branches, 115 m, 190 m, and 77 m, respectively. The wire type between each node is LGJ, and there are 140 households of single-phase users in the station area, which are basically evenly distributed on each phase.

After the coal-to-electricity program was launched, all air source heat pump equipment was installed in the village, and the average power supply capacity of electric heating households was increased from 1 kW to 5 kW. The network distribution diagram and topology diagram are shown in Figure 7.

5.1. Grid Structure Optimization

In order to facilitate the mid-term planning of the station area, that is, the penetration rate is 60%; the connection load of the station area is 280 kW; and the transformer load rate after the large-scale implementation of the coal-to-electricity project is 88.88%. Adjust the tap of the non-excitation voltage regulating transformer to control the voltage within a certain range. In order to facilitate the long-term planning of the station area, that is, when the penetration rate is 80%, the access load of the station area is 476 kW. After the large-scale implementation of the coal-to-electricity process, the transformer load rate is 151.11%, which is seriously overloaded. It is planned to add a 315 kVA distribution transformer of the S13 model to the 06 node, reducing the power supply radius of the station area to 440 m, as shown in Figure 8.

When the penetration rate of the distribution network is 60% and 80%, the three-phase voltage of the distribution network is improved to a certain extent after the capacity-increasing station area treatment measures are adopted. The voltage distribution of each node is shown in Figure 9.

The comparison of the minimum voltage values before and after planning under the 60% and 80% penetration rates after the implementation of the transformer optimization measures is shown in

Table 1. Statistical table of minimum three-phase voltage after optimization of grid structure.

Penetration	Planning Measures	Minimum Voltage Value/p.u.
		Phase A	Phase B	Phase C
60%	Before	0.8745	0.9078	0.8603
	After	0.8994	0.9340	0.8816
80%	Before	0.8962	0.7951	0.6986
	After	1.0213	0.9551	0.9238

. When the penetration rate is 80% and 60%, the minimum per unit value of the distribution network voltage is 0.9238 p.u. and 0.8816 p.u., respectively. Under the condition of the 60% penetration rate, it does not meet the requirements of the distribution network low-voltage limit +7%~−10%, so the short-term connection plan of the electric heating device (that is, the penetration rate is 40% and 20%) still needs to carry out the electric energy quality management plan.

5.2. Power Quality Management Planning

5.2.1. Configuration of Power Quality Control Devices

Large-scale application of distributed electric heating for four application scenarios with a penetration rate of 20~80%, a two-layer plan for the large-scale application of distributed electric heating for steady-state power quality management, is carried out. The reactive power compensation capacity and APF capacity installed at the low-voltage incoming line are shown in

Table 2. Reactive power compensation capacity and APF capacity configuration table.

Penetration	Reactive Power Compensation Capacity/kvar	Harmonic Filter Rate of APF
20%	—	23.24%
40%	—	40.62%
60%	39.32	61.90%
80%	92.01	66.21%

. The number and position configuration of the commutation switches are shown in

Table 3. Number and position of commutation switches.

Penetration	Box Position Number
	①	②	③	④	⑤	⑥	⑦	⑧
20%	8	15	19	16	20	6	—	—
40%	8	15	19	16	20	6	—	—
60%	5	10	8	13	20	19	11	—
80%	4	16	11	8	12	20	7	6

.

According to the load data and the load optimization adjustment model, the load wiring adjustment after the commutation switch action adjustment is shown in

Table 4. Different load access before and after commutation.

Penetration	Planning Measures	Box Position Number
		①	②	③	④	⑤	⑥	⑦	⑧
20%	Before	C	C	C	A	B	A	—	—
	After	A	B	B	A	B	A	—	—
40%	Before	C	C	C	A	B	A	—	—
	After	A	B	A	A	B	A	—	—
60%	Before	B	A	C	C	B	C	C	—
	After	A	A	C	B	B	C	A	—
80%	Before	B	A	C	C	C	B	C	A
	After	A	A	C	C	A	B	C	A

.

5.2.2. Management Situation after Optimal Configuration of Power Quality Devices

After optimization, the voltage distribution comparison of each node before and after treatment under different penetration rate application scenarios is shown in Figure 10. Among them, the minimum per-unit values in different application scenarios with a penetration rate of 20~80% are 0.9745 p.u., 0.9317 p.u., 0.9017 p.u., and 0.9486 p.u., which meet the requirements of the low-voltage distribution network limit +7%~−10%.

The voltage THD improvement effect at the PCC point is better, and the results are shown in Figure 11. With the increase in the access scale of distributed electric heating users, in order to ensure that the voltage total harmonic distortion rate meets the requirements of the national standard, the higher the harmonic filtering rate at the low-voltage public connection point of the distribution network, the penetration rate is 20%. The harmonic voltage content rates of ~80% in different application scenarios are 1.05%, 1.38%, 0.91%, and 0.86% respectively, all of which meet the national standard limit voltage total harmonic distortion rate < 4%.

Install the TSC + APF device on the low-voltage power distribution system side of the electric heating user nearby, taking into account the reactive power compensation and harmonic filtering on the load side. At the same time, distributed management is realized, and the transmission path of the power quality interference of electric heating load in the distribution is reduced, thereby reducing the impact on the power quality of the low-voltage distribution network.

The three-phase unbalance degree, power factor, and minimum voltage per unit value under different large-scale application scenarios before and after treatment are shown in

Table 5. Statistical table of power quality evaluation index.

Penetration	Planning Measures	Three-Phase Unbalance	Power Factor	Minimum Voltage Value/p.u.
				Phase A	Phase B	Phase C
20%	Before	14.87%	0.9732	0.9897	0.9876	0.9688
	After	1.21%	0.9731	0.9745	0.9790	0.9937
40%	Before	12.45%	0.9692	0.9328	0.9679	0.9485
	After	0.96%	0.9694	0.9317	0.9576	0.9601
60%	Before	14.30%	0.9250	0.8994	0.9340	0.8816
	After	1.16%	0.9658	0.9112	0.9159	0.9017
80%	Before	26.66%	0.8648	1.0213	0.9551	0.9238
	After	1.22%	0.9697	0.9796	0.9486	0.9548

. It can be seen that after the treatment, no matter the access scale of electric heating users of 20~80% in any application scenario, the three-phase unbalance degree is less than 1.3%, and the fundamental power factor of the PCC point can reach 0.96 or more.

6. Conclusions

Under the background of the large-scale application of distributed electric heating equipment, the power quality problems existing in the distribution network are aggravated. In view of this situation, after the optimization of the grid structure, a two-layer programming model is established that considers the configuration of the power quality control device and the optimal adjustment of the load of the three-phase automatic commutation device. The model considers the practicability and economy of installing the power quality control device, and installs the TSC + APF device near the low-voltage power distribution system side of the distributed electric heating users to realize distributed management. In addition, the optimal configuration of the number and position of the commutation switches is modeled on the premise of taking into account the economic and power quality control effects, and, at the same time, the optimal regulation of the load is considered to control the three-phase unbalance in the platform area. Finally, it is verified by an example that the governance effect of the model is obvious, which shows the rationality and feasibility of the algorithm.