E-SOP-based interconnected power distribution area voltage optimization regulation and control method

Abstract

The invention discloses an E-SOP-based interconnected power distribution area voltage optimization regulation and control method, and the method comprises the steps: carrying out the analysis of an E-SOP-containing power distribution area interconnection system structure, and constructing an E-SOP mathematical model; establishing a voltage-power sensitivity calculation model, and determining the optimal access position of the E-SOP; an E-SOP interconnected power distribution area planning model with the lowest comprehensive cost as the target is constructed, and the optimal capacity configuration of the E-SOP is determined; establishing a multi-objective function E-SOP interconnection power distribution area operation optimization model and solving the model; and determining the optimal position, capacity and operation scheme of the E-SOP according to the solving result. According to the method, a three-terminal SOP (E-SOP) containing an energy storage system is applied to an interconnection system of a power distribution area, the flexibility and rapidity of a power distribution network can be improved from the multi-dimensional aspects of space, energy and power of a power distribution system, and voltage optimization of the power distribution area is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of voltage management in distribution stations, and in particular to a voltage optimization and control method for distribution stations interconnected based on E-SOP. Background Art

[0002] With the continuous development of modern power systems, distribution substations are an important part of the power system, which directly affects local economic development and the daily quality of life of users. However, the high proportion of distributed generation (DG) represented by photovoltaics and wind turbines and various new types of power-consuming equipment connected to the distribution network have brought more challenges to the safe operation of distribution substations. The complexity of low-voltage distribution networks and the diversity of loads are increasing, and distribution substations are facing problems such as power flow reversal, voltage fluctuations and insufficient power supply capacity.

[0003] Traditional methods of voltage management in distribution substations mainly rely on the regulation of hardware equipment, such as transformer tap changers and capacitor banks. These traditional methods have certain limitations in response speed and flexibility. With the development of power electronics and intelligent control technology, fully controlled power electronic devices, intelligent soft switches (Soft Open Point, SOP) have attracted widespread attention due to their excellent regulation capabilities and fast power transfer performance. Compared with traditional voltage regulation and reactive power compensation methods, it can not only play the role of tie switches to achieve interconnection between distribution substations, but also realize precise control and regulation of voltage in the interconnection of distribution substations to achieve the goal of continuous voltage regulation. Therefore, based on intelligent soft switching technology, low-voltage distribution substations are interconnected and supplied to each other, so as to achieve voltage management in the substation area and improve the power supply level of the substation area from multiple dimensions.

[0004] At present, there are differences in the connection methods, access locations and functions of SOPs used in power systems. Faced with today's complex distribution networks, SOPs are mainly used in medium-voltage distribution networks and low-voltage distribution networks, namely distribution substations. This technology mainly studies the use of SOPs to interconnect different distribution substations, mobilize the power flow of each substation, and improve the flexibility and speed of distribution substations. However, since SOPs only have power exchange control and flow optimization capabilities, and do not have energy supply capabilities, they are paired with energy storage systems (ESS) to supplement the shortcomings of SOPs. Summary of the invention

[0005] In order to solve the problems of voltage fluctuation, load fluctuation and insufficient power supply capacity in distribution substations. The present invention proposes a voltage optimization and control method for interconnected distribution substations based on E-SOP. The three-terminal SOP (E-SOP) containing an energy storage system is applied in the interconnected system of distribution substations. The flexibility and rapidity of the distribution network can be improved from the multi-dimensional aspects of space, energy and power of the distribution system, and the voltage optimization of the distribution substations can be achieved.

[0006] The technical solution adopted by the present invention is:

[0007] The voltage optimization control method of the E-SOP interconnected distribution station area includes the following steps:

[0008] Step 1: Analyze the interconnection system structure of the distribution substation area containing E-SOP and construct the E-SOP mathematical model;

[0009] Step 2: Establish a voltage-power sensitivity calculation model to determine the optimal access location of the E-SOP;

[0010] Step 3: Construct an E-SOP interconnected distribution substation planning model with the goal of minimizing the comprehensive cost and determine the optimal capacity configuration of E-SOP;

[0011] Step 4: Establish and solve the multi-objective function E-SOP interconnected distribution substation operation optimization model;

[0012] Step 5: Determine the optimal location, capacity and operation plan of E-SOP based on the solution results.

[0013] In the step 1, in the E-SOP substation interconnection system, the main power grid is connected to the substation transformers T1, T2 and T3 respectively through equivalent impedances R1+jX1, R2+jX2 and R3+jX3; the output end of each substation transformer is connected to the load, distributed power supply and corresponding voltage source converter in the respective substation, where P1 represents the power of the load and distributed power supply in the substation; the DC output ends of VSC1, VSC2 and VSC3 are connected together through a DC bus, and connected to ESS through a DC-DC converter, and the energy storage system can release or absorb electric energy to the DC bus.

[0014] In the step 1, the three-terminal SOP (E-SOP) containing the energy storage system is a fully controlled power electronic device, including three three-phase back-to-back voltage source converters VSC1, VSC2, and VSC3;

[0015] Take the three-phase back-to-back voltage source converter VSC1 as an example. Figure 4 As shown, the input terminal of VSC1 is connected to the three-phase AC power supply E a 、E b 、E c, each phase power supply is connected to the sum of the equivalent resistance of the line and inductance of each phase, R, which is used to limit the current and reduce the impact; after the three-phase power supply passes through the resistor, the current i a 、i b 、i c Flows through the equivalent inductor L on the AC side; the three-phase circuit is connected to the filter capacitor C1 after the inductor to smooth the output voltage and reduce fluctuations; VSC1 contains a bridge circuit composed of IGBTs to realize the core functions of VSC, and each phase current flows into the bridge structure, and the conversion from AC to DC is realized through the switching operation of the power switch; the DC output end of VSC1 is connected to a DC bus capacitor C2; the output current i1 of VSC1 and the output currents i2 and i3 of VSC2 and VSC3 are connected to the DC bus, and are further connected to the energy storage system ESS through a DC-DC converter.

[0016] In step 1, the three-terminal SOP (E-SOP) containing the energy storage system selects the PQ-PQ-VQ control mode, connects the E-SOP to the interconnected system, and realizes power flow optimization and voltage optimization through power interaction in different distribution stations. During the optimization operation, the active power loss of the E-SOP itself is considered, and its loss is related to the active and reactive power output of the three-terminal SOP (E-SOP) containing the energy storage system.

[0017] In step 1, according to the actual operation mode of the distribution station area, the power of all ports of the three-terminal SOP is balanced with the active power, active loss, and charging and discharging power of the energy storage system (ESS), that is, zero. The power relationship of the port is described as:

[0018]

[0019] Where: P sop,i,t and Q sop,i,t are the active power and reactive power output by the i-th port of the three-terminal E-SOP at time t, respectively; is the active power loss of the i-th port of the three-terminal E-SOP at time t; and are the charging and discharging powers of the ESS in the three-terminal E-SOP at time t; α sop,i is the active power loss coefficient of the i-th port of the three-terminal E-SOP.

[0020] The capacity constraints of the three-terminal E-SOP are as follows:

[0021]

[0022] Where: S sop,i,max is the maximum capacity of the i-th port in the three-terminal E-SOP;

[0023] The active and reactive power constraints of the three-terminal E-SOP are as follows:

[0024]

[0025] Where: are the minimum and maximum values ​​of reactive power at the i-th port in the three-terminal E-SOP, respectively; They are the minimum and maximum active power of the i-th port in the three-terminal E-SOP, respectively.

[0026] The model of the energy storage system in the three-terminal E-SOP is as follows

[0027]

[0028] α ch +α dis ≤1;

[0029] E sop,min ≤E sop,t ≤E sop,max ;

[0030] Where: E sop,t is the amount of electricity of ESS in E-SOP during time period t; ch , β dis are the charge and discharge coefficients of ESS in E-SOP, respectively; are the maximum values ​​of the charging and discharging power of ESS in E-SOP respectively; α ch , α dis are the charging and discharging state values ​​of ESS in E-SOP respectively. ch When the value is 1, it means that the ESS is in charging state. dis When the value is 1, it means that the ESS is in the discharge state; sop,min 、E sop,max are the minimum and maximum power of ESS in E-SOP respectively; △t represents the interval between time point t and time point t-1; E sop,t-1 is the power of ESS in E-SOP during the time period t-1.

[0031] In step 2, according to the voltage drop principle, the voltage expression of any node i is as follows:

[0032]

[0033] Where: U i is the voltage at any node i, U N is the voltage at the balance node, i.e. the transformer output; R i , X i are the resistance and reactance between node i and the equilibrium node respectively; P i , Qi are the active power and reactive power flowing between node i-1 and node i respectively; R k , X k are the resistance and reactance between nodes k and l respectively; n is the total number of nodes in the substation.

[0034] The power of any node in the distribution system will be affected by the power of other nodes, so the losses of transformers, E-SOPs and lines as well as the power injected by other nodes are considered comprehensively;

[0035]

[0036] Where: P T , Q T are respectively the active and reactive losses of the transformer; P sop is the loss of E-SOP; P k , Q k are the injected active and reactive power of node k respectively; P loss,k , Q loss,k are the active and reactive losses between nodes k and l respectively.

[0037] The transformer loss calculation formula is:

[0038]

[0039] Where: P T,m , Q T,m , P 0,m , P k0,m , Q k0,m They are respectively the active loss, reactive loss, no-load active loss, load active loss, and load reactive loss of the transformer m; P T,m,t , Q T,m,t , S r,m is the actual output active power, reactive power and rated capacity of transformer m.

[0040] Based on three interconnected distribution stations and considering the three-phase system, the following system loss calculation formula is considered comprehensively:

[0041]

[0042] Where: P kl , Q kl are the active and reactive powers flowing between node k and node l respectively.

[0043] If the power of node j changes, the voltage of node i will also change accordingly. i Take the derivative and get .

[0044] When k = j:

[0045]

[0046] When k≠j:

[0047]

[0048] Where: P j , Q j are the active and reactive power of node j respectively.

[0049] According to the above calculation formula, the voltage-power sensitivity of each node in the interconnected substation is obtained. Considering both active and reactive power, a comprehensive voltage-power sensitivity is established, and the weight factor is added to comprehensively consider the impact of both aspects on the system to more accurately determine the position of E-SOP.

[0050] The combined voltage-power sensitivity is defined as follows:

[0051]

[0052] Where: CS is the comprehensive sensitivity of voltage active sensitivity and voltage reactive sensitivity; w1 and w2 are the weight coefficients of voltage active sensitivity and voltage reactive sensitivity respectively.

[0053] In step 3, the objective function is to minimize the comprehensive cost of the interconnection system of the distribution substation area in one year, and the expression is as follows:

[0054]

[0055] The meanings of the various parts in the above formula are as follows:

[0056] One year's investment cost

[0057]

[0058] Where: b is the discount rate; y sop is the economic useful life of E-SOP; C sop C is the unit capacity investment cost of installing the SOP in E-SOP; E ss is the investment cost of ESS in E-SOP; S sop,i,max The maximum capacity of the SOP in the E-SOP installed at point i.

[0059] One year's operation and maintenance costs

[0060]

[0061] Where: η sop is the daily operation and maintenance cost coefficient of E-SOP; is the unit capacity operation and maintenance cost of SOP in E-SOP; Ess It is the daily operation and maintenance cost coefficient of ESS in E-SOP.

[0062] One year's loss cost

[0063]

[0064] Where: μ is the electricity price of the interconnected area system; F loss It is the loss of the interconnected substation system in one day.

[0065] In step 3, the optimal capacity configuration is solved by using an ant colony algorithm, and the solution process of the ant colony algorithm includes initialization, path selection, pheromone update and iteration.

[0066] S3.1: Initialization, set the number of ants AN to 30, that is, the number of solutions constructed in each iteration; the initial value of the pheromone concentration τ is 1; the heuristic factor η is set to the inverse of the comprehensive cost, which is used to measure the attractiveness of the loss cost objective function of the distribution substation interconnection system. The calculation formula is as follows:

[0067]

[0068] Pheromone importance parameter α x Controls the ant's reliance on pheromones when selecting the objective function, and its value is 1; the heuristic factor importance parameter β x Controls the ant's reliance on the heuristic factor, with a value of 2; pheromone volatility coefficient ρ x Controls the decay rate of pheromone, its value is 0.6; pheromone increases constant Q x A constant that controls the pheromone increment, with a value of 300.

[0069] S3.2: Ant path selection, each ant starts from the starting point and gradually selects a path according to the probability H ij Build a capacity configuration plan and continuously iterate until a complete plan is formed. When choosing the next capacity configuration, Ant selects the path according to the following formula:

[0070]

[0071] Where: H ij is the probability of an ant moving from node i to node j; τ ij is the pheromone concentration on path (i, j); η ij is the heuristic factor on path (i, j); τ ik is the pheromone concentration of path (i, k); η ikis the heuristic factor on the path (i, k); allowed is the set of capacity configurations that the ants can choose; i, j, and k here represent the nodes on the path respectively.

[0072] S3.3: Calculate the comprehensive cost of each ant's solution. When all ants have completed their paths and found their own capacity configuration solutions, the formula for updating the pheromone concentration is as follows:

[0073]

[0074] Where: is the pheromone added by the qth ant on the path (i, j).

[0075] The definition is as follows:

[0076]

[0077] Where: F q is the comprehensive cost of the path found by the qth ant.

[0078] S3.4: After continuous iterations, check whether the termination condition is met (such as reaching the maximum number of iterations or the comprehensive cost converges). If so, output the optimal solution, otherwise return to step 3.2 to continue iterating. Finally, the capacity configuration solution with the lowest comprehensive cost found in all iterations is taken as the optimal solution.

[0079] In the step 4, a multi-objective function E-SOP interconnected distribution substation operation optimization model is established, and the model is converted into a second-order cone programming model using cone relaxation technology, and solved in combination with YALMIP and GUROBI tools;

[0080] The E-SOP interconnected distribution substation operation optimization model is as follows:

[0081] The operation optimizes the objective functions of minimum voltage deviation and minimum system comprehensive loss, so a multi-objective function is established:

[0082] min[F loss +F v ];

[0083] Where: F v is the voltage deviation objective function of the interconnected substation system, which is as follows:

[0084]

[0085] Where: Ω is the node set of the interconnected substation system; U i,t is the voltage of node i at any time during the day; U r is the rated value of the voltage.

[0086] System comprehensive loss model:

[0087] The comprehensive system loss mainly consists of three parts: SOP loss, transformer loss and line loss.

[0088]

[0089] Constraints:

[0090] ① Transformer constraints are as follows:

[0091]

[0092] ② Network security operation constraints are as follows:

[0093]

[0094] Where: U i,min , U i,max are the maximum and minimum voltage amplitudes of node i; P i,min , P i,max , Q i,min , Q i,max are the maximum and minimum values ​​of active and reactive power of node i respectively;

[0095] ③ The network flow constraints are as follows:

[0096]

[0097]

[0098]

[0099] Where: P k,t , Q k,t are the active power and reactive power injected into node k during period t; U j,t , U k,t are the voltage amplitudes of nodes j and k in time period t; G jk , B jk and G jj , B jj are the mutual conductance, mutual admittance, self-conductance and self-susceptance in the node admittance matrix respectively; θ jk,t is the phase angle difference between nodes j and k; P k,DG , Q k,DG are the active power and reactive power output by DG at node k respectively; P k,LD , Q k,LD are the active power and reactive power injected by the load at node k respectively; I kl,t ,I kl,maxare the current and current amplitude between nodes k and l during period t, respectively.

[0100] In step 4, due to the system comprehensive loss function F loss The constraints of the transformer and the three-terminal E-SOP are non-convex, and the cone relaxation technique is used to transform them into a second-order cone programming model. The details are as follows:

[0101] A new variable z is introduced for each non-convex fractional term, where only the line loss in the system comprehensive loss function is non-convex. kl Considering that the active and reactive power balance equations and the current square constraint contain trigonometric functions, a new variable x is introduced jk,t ,y jk,t 、r jk,t , removing the nonlinearity of the product term and obtaining a new linearized equation. The definitions of the four new variables are shown below.

[0102]

[0103] x jk,t =U j,t U k,t cosθ jk,t

[0104] y jk,t =U j,t U k,t sinθ jk,t

[0105]

[0106] By introducing slack variables, the original non-convex terms are relaxed into linear terms, and the loss function can be redefined as:

[0107]

[0108] The constraints are redefined as:

[0109]

[0110] In addition, the above model should also obey the second-order cone constraints as shown below:

[0111]

[0112] ||(P kl ,Q kl )||2≤z kl U k

[0113] ||(P T,m ,Q T,m )||2≤Sr,m

[0114] ||(P sop,i ,Q sop,i )||2≤S sop,i,max

[0115] Where: ||(P kl ,Q kl )||2 represents P kl and Q kl The second norm (i.e., vector length) of ||(P T,m ,Q T,m )||2 represents P T,m and Q T,m The second norm (i.e., vector length); ||(P sop,i ,Q sop,i )||2 represents P sop,i and Q sop,i The second norm (i.e., the length of the vector).

[0116] By converting the apparent power constraint between nodes k and l, the transformer constraint, and the capacity constraint of the three-terminal E-SOP into second-order cone constraints and retaining other linear constraints, the entire problem is converted into a standard second-order cone programming model. In this way, the convex optimization solver GUROBI tool can be used to efficiently solve the problem.

[0117] The present invention provides a voltage optimization control method based on E-SOP interconnected distribution station area, and the technical effects are as follows:

[0118] 1) The present invention proposes an optimization method for interconnecting distribution substations based on energy storage intelligent soft switches, which effectively solves the problem of voltage fluctuations in distribution substations. The voltage-power sensitivity analysis and optimization model can accurately perform E-SOP site selection and optimal configuration, reduce unnecessary losses, maintain the stability of voltage levels, reduce the risk of equipment failure caused by voltage anomalies, and improve the overall reliability of the system.

[0119] 2) The solution of the present invention aims at the problem of insufficient power supply capacity in the distribution network. Through the site selection and optimal configuration of E-SOP, the flexible interconnection between substations is realized and the power transmission path is optimized. In the scenario of load growth and DG access, the system can effectively improve the power supply capacity, ensure the stability of power supply, and alleviate the risk of local load overload.

[0120] 3) Based on comprehensive consideration of transformer, line and other equipment losses, the present invention proposes a planning model with the lowest comprehensive cost as the goal to ensure the economy of E-SOP capacity configuration. The multi-objective optimization model achieves efficient energy allocation during operation, effectively reduces power grid losses, reduces operation and maintenance costs, and improves the economic benefits of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0121] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0122] Figure 1 This is a diagram of the interconnection system based on E-SOP.

[0123] Figure 2 This is a framework diagram of the voltage optimization and control method for interconnected distribution station areas based on E-SOP.

[0124] Figure 3 This is a flow chart of the voltage optimization control method for interconnected distribution station areas based on E-SOP.

[0125] Figure 4 This is the topological structure diagram of E-SOP.

[0126] Figure 5 This is a voltage-power sensitivity diagram for distribution lines.

[0127] Figure 6 This is a diagram of an IEEE 33-node calculation example in the embodiment.

[0128] Figure 7 It is a comparison chart of the comprehensive system loss under 4 different schemes in the embodiment.

[0129] Figure 8 1 and 1 are the comparison results of the voltages of each node under the three schemes in the embodiment. DETAILED DESCRIPTION

[0130] The voltage optimization control method based on E-SOP interconnected distribution station area includes:

[0131] (I) Overall technical framework:

[0132] Firstly, the structure of the interconnected system of the substation area containing E-SOP was deeply analyzed, and the mathematical model of E-SOP was constructed; secondly, the comprehensive loss characteristics of the substation transformer, line and other equipment were fully considered, and the influence of load fluctuation and DG access on the distribution substation area was combined, and a voltage-power sensitivity calculation model was proposed to determine the optimal access position of E-SOP; then, an E-SOP interconnected distribution substation planning model with the lowest comprehensive cost as the goal was constructed, and the optimal capacity configuration of E-SOP was further determined, taking into account various types of losses in the substation area. The planning results (including site selection and capacity determination) were passed to the operation layer, and the operation of the E-SOP interconnected distribution substation area was optimized by combining the multi-objective function E-SOP interconnected distribution substation operation optimization model.

[0133] Finally, through the simulation example of IEEE 33-node flexible interconnection system and the use of algorithm to solve, the effectiveness and accuracy of the proposed optimization strategy and E-SOP access scheme in improving system voltage and reducing losses are verified. The structure of the E-SOP area interconnection system established by the present invention is as follows: Figure 1 shown.

[0134] The E-SOP substation interconnection system is connected to the substation transformers T1, T2 and T3 respectively through the equivalent impedances R1+jX1, R2+jX2 and R3+jX3 from the main grid; the output end of each substation transformer is connected to the load, distributed power source and corresponding voltage source converter in its own substation, where P1 represents the power of the load and distributed power source in the substation; the DC output ends of VSC1, VSC2 and VSC3 are connected together through the DC bus and connected to the ESS through the DC-DC converter. The energy storage system can release or absorb electric energy to the DC bus.

[0135] (II) Voltage optimization control strategy based on E-SOP interconnected distribution station area:

[0136] The voltage optimization control strategy based on E-SOP interconnected distribution substation mainly consists of two parts: planning layer and operation optimization layer. Figure 2 As shown. The planning layer establishes a voltage-power sensitivity calculation model by comprehensively considering various losses, and incorporates load fluctuations and distributed power output into the model to determine the optimal access location of the final E-SOP. At the same time, an E-SOP interconnected distribution substation planning model that considers investment, operation and maintenance, and loss costs is established to determine the planning plan for E-SOP capacity and pass it to the operation optimization layer. In the operation optimization layer, an E-SOP interconnected distribution substation operation optimization model with system comprehensive loss and node voltage multi-objective function is established to determine the system operation plan.

[0137] When E-SOP is accessed in the distribution station area, active interaction between interconnected stations will be caused and certain reactive compensation will be provided. At the same time, since a large amount of DG is connected in the distribution network and the load also changes with time, the voltage-power sensitivity can be used to assess the sensitivity of node voltage to active power changes in the power system, and the voltage stability of the system when power changes can be judged. Therefore, the present invention establishes a voltage-power sensitivity calculation model, by calculating the sensitivity under different situations, and finally compares and determines the access position of the optimal E-SOP.

[0138] Considering the existence of DG and load fluctuations in the current distribution network, DG and load can be added to the system as the injected power of the node in the calculation of voltage-power sensitivity, and processed to better adapt to the dynamic changes of distributed energy access and load. Since the present invention takes both active and reactive power into consideration, a comprehensive voltage-power sensitivity CS is established, and a weight factor is added to comprehensively consider the impact of both aspects on the system, so as to more accurately determine the position of E-SOP. The larger the calculated CS is, the better the power between systems can be regulated by connecting E-SOP to the node.

[0139] (III) Technical solution verification:

[0140] Figure 3 The operation optimization process of the interconnected distribution substation containing E-SOP is demonstrated. First, the basic parameters of the distribution substation, such as E-SOP, transformer, network line, load and DG prediction, are collected to determine the initial conditions for model establishment and solution; then, a voltage-power sensitivity calculation model is established to optimize the installation position of E-SOP, and its optimal access point is determined based on the calculation results; secondly, an E-SOP interconnected distribution substation planning model with the lowest comprehensive cost as the goal is constructed, and the optimal installation capacity is solved by the ant colony algorithm. In addition, a multi-objective function E-SOP interconnected distribution substation operation optimization model is established, and the cone relaxation technology is used to convert it into a second-order cone programming model, which is solved in combination with YALMIP and GUROBI tools. Finally, the optimal location, capacity and operation plan of E-SOP are determined based on the solution results.

[0141] (IV) Working principle: 1: Structure and model of E-SOP:

[0142] Most technologies now use two-terminal SOP. The three-terminal SOP with ESS mentioned in this paper is also a fully controlled power electronic device, which consists of three three-phase back-to-back voltage source converters VSC1, VSC2, and VSC3. On the basis of the existing three-terminal SOP topology, an ESS is connected in parallel on the DC large capacitor side through a DC-DC converter, making it a more comprehensive and flexible new distribution device. The specific topology is as follows: Figure 4 shown.

[0143] The E-SOP of the present invention selects the control mode of PQ-PQ-VQ, connects it to the interconnected system, and realizes power flow optimization and voltage optimization through power interaction in different stations. Therefore, in the optimization operation process, we need to consider the loss caused by power interaction. The present invention only considers that there is a certain active power loss in E-SOP itself, and its loss is related to the active and reactive power output of E-SOP.

[0144] According to the actual operation mode of the distribution area, the power of all ports of the three-terminal SOP and the sum of the active power, active power loss, and charging and discharging power of the ESS should be balanced, that is, zero. The power relationship of this port can be described as:

[0145]

[0146] Where: P sop,i,t and Q sop,i,t are the active power and reactive power output by the i-th port of the three-terminal E-SOP at time t, respectively; is the active power loss of the i-th port of the three-terminal E-SOP at time t; and are the charging and discharging powers of the ESS in the three-terminal E-SOP at time t; α sop,i is the active power loss coefficient of the i-th port of the three-terminal E-SOP.

[0147] The capacity constraints of the three-terminal E-SOP are as follows:

[0148]

[0149] The active and reactive power constraints of the three-terminal E-SOP are as follows:

[0150]

[0151] Where: S sop,i,max is the maximum capacity of the i-th port in the three-terminal E-SOP; are the minimum and maximum values ​​of reactive power at the i-th port in the three-terminal E-SOP, respectively; They are the minimum and maximum active power of the i-th port in the three-terminal E-SOP, respectively.

[0152] The model of the energy storage system in the three-terminal E-SOP is as follows

[0153]

[0154] α ch +α dis ≤1

[0155] E sop,min ≤E sop,t ≤E sop,max

[0156] Where: E sop,t is the amount of electricity of ESS in E-SOP during time period t; ch , β dis are the charge and discharge coefficients of ESS in E-SOP, respectively; are the maximum values ​​of the charging and discharging power of ESS in E-SOP respectively; αch , α dis are the charging and discharging state values ​​of ESS in E-SOP respectively. ch When the value is 1, it means that the ESS is in charging state. dis When the value is 1, it means that the ESS is in the discharge state; sop,min 、E sop,max They are the minimum and maximum power of ESS in E-SOP respectively.

[0157] 2: Establishment of E-SOP interconnected distribution station area planning model based on voltage-power sensitivity:

[0158] This paper derives the voltage-power sensitivity through the node voltage drop formula, taking into account the losses and characteristics of various devices. Figure 5 Take a simple power distribution circuit as an example.

[0159] According to the voltage drop principle, the voltage expression of any node i is as follows:

[0160]

[0161] Where: U i is the voltage at any node i, U N is the voltage at the balance node, i.e. the transformer output; R i , X i is the resistance and reactance between node i and the equilibrium node; P i , Q i is the active power and reactive power flowing between node i-1 and node i; R k , X k are the resistance and reactance between nodes k and l.

[0162] The power of any node in the distribution system will be affected by the power of other nodes. Therefore, this paper comprehensively considers the losses of transformers, E-SOPs and lines as well as the power injected by other nodes.

[0163]

[0164] Where: P T , Q T are respectively the active and reactive losses of the transformer; P sop is the loss of E-SOP; P k , Q k are the injected active and reactive power of node k respectively; P loss,k , Q loss,k are the active and reactive losses between nodes k and l respectively.

[0165] The transformer loss calculation formula is:

[0166]

[0167] Where: P T,m , Q T,m , P 0,m , P k0,m , Q k0,m They are respectively the active loss, reactive loss, no-load active loss, load active loss, and load reactive loss of transformer m; P T,m,t , Q T,m,t , S r,m is the actual output active power, reactive power and rated capacity of transformer m.

[0168] This article considers three interconnected distribution stations and a three-phase system, so the calculation formula for system loss is comprehensively considered:

[0169]

[0170] Where: P kl , Q kl are the active and reactive power flowing between node k and node l respectively.

[0171] If the power of node j changes, the voltage of node i will also change accordingly, so i Take the derivative and get .

[0172] When k = j

[0173]

[0174] When k≠j

[0175]

[0176] Where: P j , Q j are the active and reactive power of node j respectively.

[0177] According to the above calculation formula, the voltage-power sensitivity of each node in the interconnected substation can be obtained. Since this article takes both active and reactive power into consideration, a comprehensive voltage-power sensitivity is established, and weight factors are added to comprehensively consider the impact of both aspects on the system to more accurately determine the position of E-SOP.

[0178] The combined voltage-power sensitivity is defined as follows:

[0179]

[0180] Where: CS is the comprehensive sensitivity of voltage active sensitivity and voltage reactive sensitivity; w1 and w2 are the weight coefficients of voltage active sensitivity and voltage reactive sensitivity respectively.

[0181] 3: E-SOP interconnected distribution substation planning model based on the lowest comprehensive cost:

[0182] The objective function of the present invention is to minimize the comprehensive cost of the interconnection system of the distribution substation area in one year, and the expression is as follows:

[0183]

[0184] The meaning and detailed introduction of each part of the formula are as follows.

[0185] 3.1: One year's investment costs

[0186]

[0187] Where: b is the discount rate; y sop is the economic useful life of E-SOP; C sop are the unit capacity investment costs of installing the SOP in E-SOP; C Ess It is the investment cost of ESS in E-SOP.

[0188] 3.2: One year's operation and maintenance costs

[0189]

[0190] Where: η sop is the daily operation and maintenance cost coefficient of E-SOP; is the unit capacity operation and maintenance cost of SOP in E-SOP; Ess It is the daily operation and maintenance cost coefficient of ESS in E-SOP.

[0191] 3.3: One year's loss cost

[0192]

[0193] Where: μ is the electricity price of the interconnected area system, F loss It is the loss of the interconnected substation system in one day.

[0194] The loss calculation will be carried out in detail in the next section 4.2.

[0195] 4. E-SOP interconnected distribution substation operation optimization model based on multi-objective function:

[0196] This paper runs the optimization objective function of minimizing voltage deviation and minimizing system comprehensive loss. Therefore, a multi-objective function is established

[0197] min[F loss +Fv ]

[0198] Where: F v is the voltage deviation objective function of the interconnected substation system.

[0199] 4.1: Voltage deviation model:

[0200]

[0201] Where: Ω is the node set of the interconnected substation system; U i,t is the voltage of node i at any time during the day; U r is the rated value of the voltage.

[0202] 4.2: System comprehensive loss model:

[0203] The comprehensive system loss of the distribution substation area based on E-SOP interconnection mainly consists of three parts: SOP loss, transformer loss and line loss.

[0204]

[0205] 5: Constraints:

[0206] The transformer constraints are as follows:

[0207]

[0208] The network security operation constraints are as follows:

[0209]

[0210] The network flow constraints are as follows:

[0211]

[0212]

[0213]

[0214] Where: U i,min , U i,max are the maximum and minimum voltage amplitudes of node i; P i,min , P i,max , Q i,min , Q i,max are the maximum and minimum active and reactive values ​​of node i respectively; P k,t , Q k,t U is the active power and reactive power injected into node k during period t; j,t , U k,t is the voltage amplitude of nodes j and k in period t; G jk , Bjk and G jj , B jj is the mutual conductance, mutual admittance, self-conductance and self-susceptance in the node admittance matrix; θ jk,t is the phase angle difference between nodes j and k; P k,DG , Q k,DG is the active power and reactive power output by DG at node k; P k,LD , Q k,LD I is the active power and reactive power injected by the load at node k; kl,t ,I kl,max is the current and current amplitude between nodes k and l during period t.

[0215] Example:

[0216] The present invention uses an improved IEEE 33-node power distribution system to perform a case analysis on the proposed solution. Figure 6 As shown. Among them, node 1 is the point where the upper power grid is connected, and the other nodes are the access nodes on the high-voltage side of the transformer and the nodes where various devices are connected. The rated voltage of the system is 12.66kV, and all the transformers in the substations are 10kV / 400V. In order to consider the existence of DG and load fluctuations in the current distribution system, this paper connects 3 photovoltaic (PV) power sources and 3 wind turbine (WT) power sources to the distribution system. Among them, PV is located at nodes 14, 20, and 27, and the corresponding installed capacities are 0.8, 0.6, and 0.4MW respectively; WT is located at nodes 4, 24, and 31, and the corresponding installed capacities are 0.7, 0.5, and 0.3MW respectively. All DGs operate at unity power factor. The example parameter settings used in this paper are shown in Table 1, which are SOP-related parameters and ESS parameters in E-SOP, transformer-related parameters, and grid-related parameters.

[0217] Table 1 Example parameter settings

[0218]

[0219]

[0220] Voltage-power sensitivity describes the impact of a small change in power injected or consumed at a node in the system on the voltage of other nodes. Through this analysis, key nodes and weak voltage areas can be effectively identified, thereby optimizing the planning and configuration of distributed energy and E-SOP. At the same time, since reactive power transmission will cause losses, this paper preliminarily screened a group of nodes that meet the requirements of short reactive power transmission as candidate nodes, and calculated the voltage-power sensitivity of these nodes. Table 2 shows the calculation results of voltage-power sensitivity in this paper. It can be concluded that the site selection method proposed in this paper selects nodes 7, 18 and 29 as three-terminal E-SOP access points.

[0221] Table 2 Voltage-power sensitivity of candidate nodes

[0222]

[0223] In order to compare the superiority of the method proposed in this paper, this paper selects the following three schemes for comparison:

[0224] Solution 1: System without E-SOP interconnection;

[0225] Scheme 2: The voltage-power sensitivity site selection method proposed in this paper;

[0226] Solution 3: Only use the system interconnected by SOP;

[0227] Solution 4: Ignore SOP loss, transformer loss and line loss.

[0228] By using the ant colony optimization algorithm to solve the constant capacity model, the optimization results shown in Table 3 were obtained.

[0229] Table 3 Comparison of the fixed capacity results of Scheme 2 and Scheme 4 Unit / MW

[0230]

[0231] As can be seen from Table 3, key factors such as SOP, transformer and line loss are fully considered in the process of solving the model, which makes the capacity allocation between each E-SOP port show certain differences. This processing method makes the calculation results closer to the actual application scenario. Compared with the traditional model that only considers some parameters, it more comprehensively reflects the complexity and constraints of power grid operation. In addition, for the comparative analysis of different schemes, the fixed capacity cost results under four different schemes are shown in Table 4.

[0232] Table 4 Comparison of costs of four schemes Unit / 10,000 yuan

[0233]

[0234] From the results in Table 4, it can be seen that although the system without E-SOP or SOP will not generate additional investment and operation and maintenance costs, its loss cost is higher than that of Scheme 1, Scheme 3 and Scheme 4. This shows that although the connection to SOP will increase investment and operation and maintenance costs, the annual comprehensive cost of the system has dropped significantly. Comparing the annual comprehensive costs of Scheme 2 and Scheme 3, the cost of Scheme 2 is 15.35% lower than that of Scheme 3; at the same time, the cost of Scheme 2 is also 9.3% lower than that of Scheme 4. Therefore, introducing E-SOP for interconnection in the distribution substation system and comprehensively considering the losses of SOP, transformers and lines in operation optimization can effectively reduce the comprehensive cost of the system.

[0235] In order to further verify the superiority of the proposed technology, Figure 7 The comparison of the comprehensive system loss under 4 different schemes is shown. It can be seen intuitively from the figure that the scheme proposed in the present invention (Scheme 3) shows a significant effect in reducing the comprehensive loss of the distribution station area interconnection system, and can reduce the system's average daily loss by 51.7%. In contrast, Schemes 4 and 5 are not very effective in reducing the comprehensive system loss. Although the technical scheme in this article will produce certain losses in SOP, the final comprehensive loss of the area interconnection system is lower than that of other schemes. This shows that the technical scheme proposed in this article has higher application value and practical benefits in optimizing system energy efficiency and reducing energy consumption losses, and is superior to other schemes.

[0236] Figure 8 Demonstrate the effects of Scheme 1, Scheme 2 and Scheme 3 in reducing voltage deviation in distribution station areas. Figure 8 The analysis shows that the voltage deviation of Scheme 2 is significantly reduced compared with Scheme 1 and Scheme 3, which indicates that the introduction of SOP in the distribution substation interconnection system can significantly improve the voltage deviation of each node. Further comparison of the curves of Scheme 2 and Scheme 3 shows that adding ESS to the three-terminal SOP not only helps to balance the active power flow between different substations, but also provides additional energy support for SOP, which reduces the voltage deviation of Scheme 2 by 33.9%.

Claims

1. Based on the E-SOP interconnected distribution station area voltage optimization control method, it is characterized by The following steps are involved: Step 1: Analyze the interconnection system structure of the distribution substation area containing E-SOP and construct the E-SOP mathematical model; Step 2: Establish a voltage-power sensitivity calculation model to determine the optimal access location of the E-SOP; Step 3: Construct an E-SOP interconnected distribution substation planning model with the goal of minimizing the comprehensive cost and determine the optimal capacity configuration of E-SOP; Step 4: Establish and solve the multi-objective function E-SOP interconnected distribution substation operation optimization model; Step 5: Determine the optimal location, capacity and operation plan of E-SOP based on the solution results.

2. According to claim 1, the voltage optimization control method based on E-SOP interconnection distribution station area is characterized in that: In the step 1, in the E-SOP substation interconnection system, the main power grid is connected to the substation transformers T1, T2 and T3 respectively through equivalent impedances R1+jX1, R2+jX2 and R3+jX3; the output end of each substation transformer is connected to the load, distributed power supply and corresponding voltage source converter in the respective substation, where P1 represents the power of the load and distributed power supply in the substation; the DC output ends of VSC1, VSC2 and VSC3 are connected together through a DC bus, and connected to ESS through a DC-DC converter, and the energy storage system can release or absorb electric energy to the DC bus.

3. According to claim 1, the voltage optimization control method based on E-SOP interconnection distribution station area is characterized in that: In step 1, E-SOP is a fully controlled power electronic device, including three three-phase back-to-back voltage source converters VSC1, VSC2, and VSC3; for the three-phase back-to-back voltage source converter VSC1, the input end of VSC1 is connected to the three-phase AC power source E a 、E b 、E c , each phase power supply is connected to the sum of the equivalent resistance of the line and inductance of each phase, R, which is used to limit the current and reduce the impact; after the three-phase power supply passes through the resistor, the current i a 、i b 、i c Flows through the equivalent inductor L on the AC side; the three-phase circuit is connected to the filter capacitor C1 after the inductor; VSC1 contains a bridge circuit composed of IGBTs to realize the core function of VSC, and each phase current flows into the bridge structure, and the conversion from AC to DC is realized through the switching operation of the power switch; the DC output end of VSC1 is connected to a DC bus capacitor C2; the output current i1 of VSC1 and the output currents i2 and i3 of VSC2 and VSC3 are connected to the DC bus, and further connected to the energy storage system ESS through a DC-DC converter.

4. According to claim 3, the voltage optimization control method based on E-SOP interconnection distribution station area is characterized in that: E-SOP selects the PQ-PQ-VQ control mode, connects E-SOP to the interconnected system, and realizes power flow optimization and voltage optimization through power interaction in different distribution stations. During the optimization operation, the active power loss of E-SOP itself is considered, and its loss is related to the active and reactive power output of E-SOP. According to the actual operation mode of the distribution station area, the power of all ports of the three-terminal SOP is balanced with the active power, active loss, and the sum of the charging and discharging power of the energy storage system (ESS), that is, zero; the power relationship of the port is described as: Where: P sop,i,t and Q sop,i,t are the active power and reactive power output by the i-th port of the three-terminal E-SOP at time t, respectively; is the active power loss of the i-th port of the three-terminal E-SOP at time t; and are the charging and discharging powers of the ESS in the three-terminal E-SOP at time t; α sop,i is the active power loss coefficient of the i-th port of the three-terminal E-SOP; The capacity constraints of the three-terminal E-SOP are as follows: Where: S sop,i,max is the maximum capacity of the i-th port in the three-terminal E-SOP; The active and reactive power constraints of the three-terminal E-SOP are as follows: Where: are the minimum and maximum values ​​of reactive power at the i-th port in the three-terminal E-SOP, respectively; are the minimum and maximum active power of the i-th port in the three-terminal E-SOP respectively; The model of the energy storage system in the three-terminal E-SOP is as follows α ch +α dis ≤1； AND sop,min ≤E sop,t ≤E sop,max ; Where: E sop,t is the amount of electricity of ESS in E-SOP during time period t; ch , β dis are the charge and discharge coefficients of ESS in E-SOP, respectively; are the maximum values ​​of the charging and discharging power of ESS in E-SOP respectively; α ch , α dis are the charging and discharging state values ​​of ESS in E-SOP respectively. ch When the value is 1, it means that the ESS is in charging state. dis When the value is 1, it means that the ESS is in the discharge state; sop,min 、E sop,max are the minimum and maximum power of ESS in E-SOP respectively; △t represents the interval between time point t and time point t-1; E sop,t-1 is the power of ESS in E-SOP during the time period t-1.

5. According to claim 1, the voltage optimization control method based on E-SOP interconnection distribution station area is characterized in that: In step 2, according to the voltage drop principle, the voltage expression of any node i is as follows: Where: U i is the voltage at any node i, U N is the voltage at the balance node, i.e. the transformer output; R i , X i are the resistance and reactance between node i and the equilibrium node respectively; P i , Q i are the active power and reactive power flowing between node i-1 and node i respectively; R k , X k are the resistance and reactance between nodes k and l respectively; n is the total number of nodes in the substation; The power of any node in the distribution system will be affected by the power of other nodes, so the losses of transformers, E-SOPs and lines as well as the power injected by other nodes are considered comprehensively; Where: P T , Q T are respectively the active and reactive losses of the transformer; P sop is the loss of E-SOP; P k , Q k are the injected active and reactive power of node k respectively; P loss,k , Q loss,k are the active and reactive losses between nodes k and l respectively; The transformer loss calculation formula is: Where: P T,m , Q T,m , P 0,m , P k0,m , Q k0,m They are respectively the active loss, reactive loss, no-load active loss, load active loss, and load reactive loss of the transformer m; P T,m,t , Q T,m,t , S r,m is the actual output active power, reactive power and rated capacity of transformer m; Based on three interconnected distribution stations and considering the three-phase system, the following system loss calculation formula is considered comprehensively: Where: P kl , Q kl are the active and reactive power flowing between node k and node l respectively; If the power of node j changes, the voltage of node i will also change accordingly. i Take the derivative and get; When k = j: When k≠j: Where: P j , Q j are the active and reactive power of node j respectively; According to the above calculation formula, the voltage-power sensitivity of each node in the interconnected substation is obtained. Considering both active and reactive power, a comprehensive voltage-power sensitivity is established, and the weight factor is added to comprehensively consider the impact of both aspects on the system to more accurately determine the position of E-SOP; The combined voltage-power sensitivity is defined as follows: Where: CS is the comprehensive sensitivity of voltage active sensitivity and voltage reactive sensitivity; w1 and w2 are the weight coefficients of voltage active sensitivity and voltage reactive sensitivity respectively.

6. The voltage optimization control method based on E-SOP interconnection distribution station area according to claim 1 is characterized in that: In step 3, the objective function is to minimize the comprehensive cost of the interconnection system of the distribution substation area in one year, and the expression is as follows: The meanings of the various parts in the above formula are as follows: One year's investment cost Where: b is the discount rate; y sop is the economic useful life of E-SOP; C sop The unit capacity investment cost for installing the SOP in the E-SOP; C E ss is the investment cost of ESS in E-SOP; S sop,i,max The maximum capacity of the SOP in the E-SOP installed at point i; One year's operation and maintenance costs Where: η sop is the daily operation and maintenance cost coefficient of E-SOP; is the unit capacity operation and maintenance cost of SOP in E-SOP; η Ess is the daily operation and maintenance cost coefficient of ESS in E-SOP; One year's loss cost Where: μ is the electricity price of the interconnected area system; F loss It is the loss of the interconnected substation system in one day.

7. The voltage optimization control method based on E-SOP interconnection distribution station area according to claim 1 is characterized in that: In step 3, the optimal capacity configuration is solved by using an ant colony algorithm, and the solution process of the ant colony algorithm includes initialization, path selection, pheromone update and iteration; S3.1: Initialization, set the number of ants AN to 30, that is, the number of solutions constructed in each iteration; the initial value of the pheromone concentration τ is 1; the heuristic factor η is set to the inverse of the comprehensive cost, which is used to measure the attractiveness of the loss cost objective function of the distribution substation interconnection system. The calculation formula is as follows: Pheromone importance parameter α x Controls the ant's reliance on pheromones when selecting the objective function, and its value is 1; the heuristic factor importance parameter β x Controls the ant's reliance on the heuristic factor, with a value of 2; Pheromone volatility coefficient ρ x Controls the decay rate of pheromone, its value is 0.6; pheromone increases constant Q x The constant that controls the pheromone increment is 300; S3.2: Ant path selection, each ant starts from the starting point and gradually selects a path according to the probability H ij Build a capacity configuration plan and continuously iterate until a complete plan is formed; when choosing the next capacity configuration, Ant selects the path according to the following formula: Where: H ij is the probability of an ant moving from node i to node j; τ ij is the pheromone concentration on path (i, j); η ij is the heuristic factor on path (i, j); τ ik is the pheromone concentration of path (i, k); η ik is the heuristic factor on the path (i, k); allowed is the set of capacity configurations that the ants can choose; i, j, and k here represent the nodes on the path respectively; S3.3: Calculate the comprehensive cost of each ant's solution. When all ants have completed their paths and found their own capacity configuration solutions, the formula for updating the pheromone concentration is as follows: Where: The pheromone added by the qth ant on the path (i, j); The definition is as follows: Where: F q is the comprehensive cost of the path found by the qth ant; S3.4: After continuous iterations, check whether the termination conditions are met (such as reaching the maximum number of iterations or the comprehensive cost convergence). If so, output the optimal solution, otherwise return to step 3.2 to continue iterating; finally, the capacity configuration plan with the lowest comprehensive cost found in all iterations is taken as the optimal solution.

8. The voltage optimization control method based on E-SOP interconnection distribution station area according to claim 1 is characterized in that: In the step 4, a multi-objective function E-SOP interconnected distribution substation operation optimization model is established, and the model is converted into a second-order cone programming model using cone relaxation technology, and solved in combination with YALMIP and GUROBI tools; The E-SOP interconnected distribution substation operation optimization model is as follows: The operation optimizes the objective functions of minimum voltage deviation and minimum system comprehensive loss, so a multi-objective function is established: min[F loss +F v ]; Where: F v is the voltage deviation objective function of the interconnected substation system, which is as follows: Where: Ω is the node set of the interconnected substation system; U i,t is the voltage of node i at any time during the day; U r is the rated value of the voltage; System comprehensive loss model: The comprehensive system loss mainly consists of three parts: SOP loss, transformer loss and line loss; 9. The voltage optimization control method based on E-SOP interconnected distribution station area according to claim 8 is characterized in that: The E-SOP interconnected distribution substation operation optimization model includes constraints: ① Transformer constraints are as follows: ② Network security operation constraints are as follows: Where: U i,min , U i,max are the maximum and minimum voltage amplitudes of node i; P i,min , P i,max , Q i,min , Q i,max are the maximum and minimum values ​​of active and reactive power of node i respectively; ③ The network flow constraints are as follows: Where: P k,t , Q k,t are the active power and reactive power injected into node k during period t; U j,t , U k,t are the voltage amplitudes of nodes j and k in time period t; G jk , B jk and G jj , B jj are the mutual conductance, mutual admittance, self-conductance and self-susceptance in the node admittance matrix respectively; θ jk,t is the phase angle difference between nodes j and k; P k,DG , Q k,DG are the active power and reactive power output by DG at node k respectively; P k,LD , Q k,LD are the active power and reactive power injected by the load at node k respectively; I kl,t ,I kl,max are the current and current amplitude between nodes k and l during period t, respectively.

10. The voltage optimization control method based on E-SOP interconnected distribution station area according to claim 9 is characterized in that: In step 4, due to the system comprehensive loss function F loss The constraints of the transformer and the three-terminal E-SOP are non-convex, and the cone relaxation technique is used to transform them into a second-order cone programming model; the details are as follows: A new variable is introduced for each non-convex fractional term, where only the line loss in the system comprehensive loss function is non-convex, and the new variable z is introduced kl ; Considering that the active and reactive power balance equations and the current square constraint contain trigonometric functions, a new variable x is introduced jk,t ,y jk,t 、r jk,t , remove the nonlinearity of the product term and get a new linearized equation; the definitions of the four new variables are as follows; x jk,t =U j,t U k,t cosθ jk,t y jk,t =U j,t U k,t sinθ jk,t By introducing slack variables, the original non-convex terms are relaxed into linear terms, and the loss function can be redefined as: The constraints are redefined as: In addition, the above model should also obey the second-order cone constraints as shown below: ||(P kl ,Q kl )||2≤z kl U k ||(P T,m ,Q T,m )||2≤S r,m ||(P sop,i ,Q sop,i )||2≤S sop,i,max Where: ||(P kl ,Q kl )||2 represents P kl and Q kl The second norm (i.e., vector length) of ||(P T,m ,Q T,m )||2 represents P T,m and Q T,m Two norm; ||(P sop,i ,Q sop,i )||2 represents P sop,i and Q sop,i Two norm; By converting the apparent power constraint between nodes k and l, the transformer constraint and the capacity constraint of the three-terminal E-SOP into second-order cone constraints and retaining other linear constraints, the entire problem is transformed into a standard second-order cone programming model.

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