Distributed power supply auxiliary power distribution network black start method based on wind and light uncertainty

Abstract

The application relates to a kind of distributed power auxiliary power distribution network black start method based on wind light uncertainty, comprising the following steps: obtaining recovery cost weight based on the recovery condition of system line, and obtaining line importance based on line load and node load importance;Determine the distributed power as the starting node;With the starting node as the starting point, the starting order of the distributed power is randomly generated by using genetic algorithm to represent the distributed power;Based on the shortest path algorithm, the random order obtained in step S3 is calculated to obtain multiple starting orders with the shortest path;By establishing a network frame reconstruction optimization model, the objective of the distributed power starting order optimization is set to maximize the important load recovery capacity, and the target network frame is established to minimize the recovery path weight, to obtain the optimal starting order for starting.Compared with the prior art, the application has the advantages of good starting effect, high efficiency, strong safety and the like.

Description

Technical Field

[0001] This invention relates to the field of power distribution networks, and in particular to a black start method for distributed power generation-assisted power distribution networks based on the uncertainties of wind and solar power. Background Technology

[0002] With the large-scale integration of distributed resources such as renewable energy, electric vehicles, energy storage, and flexible loads into the distribution network, the distribution network is gradually exhibiting characteristics such as active and flexible operation, providing flexible resource support for distribution network fault recovery or local self-healing. Research on utilizing distributed generation (DG) to assist the black start of the distribution network can effectively alleviate the problem of insufficient black start power in urban power grids, thereby accelerating the black start process of the transmission and distribution network.

[0003] Currently, scholars both domestically and internationally have conducted extensive research on black start in power grids. Many scholars have carried out feasibility studies on distributed generation (DG) power sources such as photovoltaics, wind power, energy storage, and micro gas turbines in distribution networks as black start sources, and have conducted relevant simulation model demonstrations, providing new directions and progress for black start research. Existing research on black start methods for distribution networks after large-scale power outages mainly falls into three categories: distribution network zoning optimization, grid reconfiguration optimization, and load restoration optimization. For distribution network zoning optimization, it is stipulated that each zoning area must contain at least one black start source, and the source output must match the load capacity to maintain voltage and frequency stability within the system. Some scholars have established distribution network black start zoning optimization models that consider recovery time and safety based on these requirements. For grid reconfiguration optimization, some scholars have established optimization models for the node recovery sequence and recovery path in the distribution network with the goal of maximizing the recovery of important loads and minimizing the weight of recovery lines. However, the impact of DG output characteristics on the black start scheme has not been considered. For load restoration optimization, scholars generally believe that load restoration optimization should be implemented throughout the entire black start process. In the initial stage of black start, while charging the recovery path of the units to be started, a small number of important loads should be connected to maintain the stability of system voltage and frequency. After establishing a stable grid, power supply to some important loads should be restored according to the power output. In summary, existing research on black start of distributed generation (DG) assisted distribution networks only considers distribution network zoning optimization, grid reconfiguration optimization, or load restoration optimization. Black start schemes are often relatively simple and fail to consider the uncertainty of DG output of various types in the distribution network. When formulating black start schemes, the DG start-up sequence, recovery path, and target grid optimization are not considered together. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a black start method for distributed power generation-assisted distribution networks based on the uncertainty of wind and solar power.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] A black start method for distributed generation-assisted distribution networks based on wind and solar uncertainties includes the following steps:

[0007] S1: Obtain the recovery cost weight based on the recovery status of the system lines, and obtain the line importance based on the line load and node load importance;

[0008] S2: Identify the distributed power source to be the startup node;

[0009] S3: Starting from the starting node, use a genetic algorithm to randomly generate chromosomes to represent the startup order of the distributed power source;

[0010] S4: Calculate the random order obtained in step S3 based on the shortest path algorithm to obtain multiple starting orders with the shortest paths;

[0011] S5: By establishing a network reconfiguration optimization model, the objective of optimizing the startup sequence of distributed power sources is set to maximize the recovery capacity of critical loads, and to establish the target network with the minimum recovery path weight, thereby obtaining the optimal startup sequence for startup.

[0012] Preferably, the formula for calculating the recovery cost weight is:

[0013]

[0014] Among them, C n Let Ψ be the recovery cost weight for unit n. L Let c be the set of all lines l in the system. l The weight of the recovery cost for line l; α l A value of 0 indicates that line l has not been restored, α l A value of 1 indicates that line l has been restored.

[0015] Preferably, the formula for calculating the importance of the line is:

[0016]

[0017] Among them, Z l P represents the importance of line l. Li and P Lj Here, represents the load connected to nodes i and j at both ends of line l, respectively; w is the load importance coefficient, with w=10 for primary loads, w=1 for secondary loads, and w=0.1 for tertiary loads; c l The weight of the recovery cost for line l.

[0018] Preferably, step S2 specifically includes:

[0019] The black-start capability of distributed generation is evaluated. Based on the black-start capability, the impact of the start path weight, the start capacity, the frequency and voltage regulation capability, and the load increase speed, the black-start evaluation index of the distributed generation is obtained. The distributed generation with the highest black-start evaluation index is selected as the start node.

[0020] Preferably, the formula for obtaining the black-start evaluation index is:

[0021] δ=λ1a+λ2b+λ3c+λ4d+λ5e

[0022] Where δ is the DG black start evaluation index, λ1, λ2, λ3, λ4, and λ5 are allocation coefficients, and λ1+λ2+λ3+λ4+λ5=1; a is the DG black start capability; b is the influence of the DG start path weight; c is the DG start capacity; d is the DG frequency and voltage regulation capability; and e is the DG load increase speed.

[0023] Preferably, the genetic algorithm in step S3 specifically includes:

[0024] In the genetic algorithm, chromosomes are encoded in binary form, and the restored sequence is represented as chromosomes of length kN, where N is the distributed power source in the power distribution network system, and k is the length of the chromosome segment.

[0025] Chrom = [A1,A2,…,A N ]

[0026] Where Chrom is a permutation of N DGs, A N A chromosome segment of length k;

[0027] After decoding the chromosomes:

[0028] Phen = [B1, B2, ..., B N ]

[0029] Where Phen represents the boot order of DG, B N This represents the start time of the Nth DG.

[0030] Preferably, step S4 specifically includes:

[0031] Given the startup order obtained from S3, the Floyd algorithm is used to search for the shortest path between the corresponding nodes according to the startup order of the distributed power source, and the startup order corresponding to the minimum recovery path weight is obtained:

[0032]

[0033] Where, α l A value of 0 indicates that line l has not been restored, α l A value of 1 indicates that line l has been restored, and Z represents line l.l Ψ represents the importance of line l. L Let be the set of all lines l in the system.

[0034] Preferably, the objective function of the target space frame is:

[0035]

[0036] Among them, Ψ load α is the set of all loads in the system. Li Whether the load on node i has been restored; w i is the load importance coefficient of node i; g is the minimum weight of the recovery path under this startup sequence.

[0037] Preferably, the constraints of the objective function include distributed generation output constraints, power balance constraints, node voltage constraints, line thermal stability limit constraints, and distribution network topology radial structure constraints.

[0038] Preferably, the constraints on the objective function are as follows:

[0039] Distributed power generation output constraints:

[0040]

[0041]

[0042] In the formula: P Gn Q represents the active power output of the nth distributed power source that is started; Gn To start the reactive power output of the nth distributed power source; Ψ N It is the set of all distributed power sources in the system;

[0043] Power balance constraints:

[0044]

[0045] In the formula: α Gn To indicate whether the nth power source has been restored, 0 indicates not restored, and 1 indicates restored. α Li To indicate whether the load at node i has been restored, 0 indicates not restored, and 1 indicates restored. P Li Let Ψ be the load at node i. N Ψ is the set of all distributed power sources in the system. load It is the set of all load nodes in the system;

[0046] Node voltage constraints:

[0047] V i min ≤V i ≤Vi max i∈Ψ load

[0048] In the formula: V i Ψ represents the voltage amplitude at each node in the system. load It is the set of all load nodes in the system;

[0049] Line thermal stability limit constraints:

[0050]

[0051] In the formula: P Tl Ψ represents the active power transmitted in line l. L It is the set of all lines l in the system;

[0052] Distribution network topology radial structure constraints: The distribution network system is a loopless and islanded topology.

[0053] Compared with the prior art, the present invention has the following advantages:

[0054] (1) Existing black-start schemes mainly use large generating units with black-start capabilities to restore system power supply. Often, the restoration of the distribution network needs to be considered after the transmission network is restored, resulting in slow restoration speed and large power outage losses. This invention utilizes the advantages of distributed power sources in the distribution network. After a major power outage, multiple distributed power sources are used to form a local distribution network island operation. Distributed power sources with black-start capabilities supply power to the loads in the distribution network, which can promote the system restoration process, reduce system power outage losses, and thus improve the resilience of the power grid.

[0055] (2) Existing research on black-start network reconfiguration schemes rarely considers the joint optimization of power restoration sequence and line restoration sequence. Often, only one of them is optimized, neglecting the influence of their relationship on the final network reconfiguration result, leading to the result easily getting trapped in local optima. This invention fully considers the relationship between power restoration sequence and line restoration sequence, establishes a joint optimization model for network reconfiguration, and uses a combination of genetic algorithm and Floyd algorithm to obtain the global optimal solution, resulting in good start-up performance and high efficiency. Attached Figure Description

[0056] Figure 1 This is a flowchart of the present invention;

[0057] Figure 2 This is a diagram of the IEEE 33-node distribution network system in an embodiment of the present invention;

[0058] Figure 3 This is a diagram showing the number of available batteries in an electric vehicle charging and swapping station according to an embodiment of the present invention.

[0059] Figure 4 This is a typical daytime wind turbine output diagram in an embodiment of the present invention;

[0060] Figure 5 This is a typical daily photovoltaic power output diagram in an embodiment of the present invention;

[0061] Figure 6 This is a diagram of the black start scheme for the IEEE 33-node distribution network in an embodiment of the present invention; Detailed Implementation

[0062] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Note that the following description of the embodiments is merely illustrative and is not intended to limit its applicability or use, nor is the present invention limited to the following embodiments.

[0063] Example

[0064] A distributed generation-assisted black start method for distribution networks based on wind and solar uncertainties, such as Figure 1 As shown, it includes the following steps:

[0065] S1: Obtain the recovery cost weight based on the recovery status of the system lines, and obtain the line importance based on the line load and node load importance.

[0066] The formula for calculating the recovery cost weight is:

[0067]

[0068] Among them, C n Let Ψ be the recovery cost weight for unit n. L Let c be the set of all lines l in the system. l The weight of the recovery cost for line l; α l A value of 0 indicates that line l has not been restored, α l A value of 1 indicates that line l has been restored.

[0069] The formula for calculating the importance of a line is:

[0070]

[0071] Among them, Z l P represents the importance of line l. Li and P Lj Here, represents the load connected to nodes i and j at both ends of line l, respectively; w is the load importance coefficient, with w=10 for primary loads, w=1 for secondary loads, and w=0.1 for tertiary loads; c l The weight of the recovery cost for line l.

[0072] S2: Determine the distributed power source to be the startup node.

[0073] Step S2 specifically includes:

[0074] The black-start capability of distributed generation (DG) is evaluated. Black-start assessment metrics are derived based on DG's black-start capability, the impact of startup path weights, startup capacity, frequency and voltage regulation capabilities, and load ramp-up speed. The DG with the highest black-start assessment metric is selected as the startup node. The formula for obtaining the black-start assessment metric is:

[0075] δ=λ1a+λ2b+λ3c+λ4d+λ5e

[0076] Where δ is the DG black start evaluation index, λ1, λ2, λ3, λ4, and λ5 are allocation coefficients, and λ1+λ2+λ3+λ4+λ5=1; a is the DG black start capability; b is the influence of the DG start path weight; c is the DG start capacity; d is the DG frequency and voltage regulation capability; and e is the DG load increase speed.

[0077] S3: Starting from the startup node, use a genetic algorithm to randomly generate chromosomes to represent the startup order of the distributed power source.

[0078] Genetic algorithms specifically include:

[0079] In the genetic algorithm, chromosomes are encoded in binary form, and the restored sequence is represented as chromosomes of length kN, where N is the distributed power source in the power distribution network system, and k is the length of the chromosome segment.

[0080] Chrom = [A1,A2,…,A N ]

[0081] Where Chrom is a permutation of N DGs, A N A chromosome segment of length k;

[0082] After decoding the chromosomes:

[0083] Phen = [B1, B2, ..., B N ]

[0084] Where Phen represents the boot order of DG, B N This represents the start time of the Nth DG.

[0085] S4: Calculate the random order obtained in step S3 based on the shortest path algorithm to obtain multiple starting orders with the shortest paths. Using chromosomes randomly generated by a genetic algorithm, the Floyd algorithm is used to select the recovery path with the minimum path weight for each target node. The idea of ​​this algorithm is to find the shortest path from each vertex to other vertices, let L(v i ,v k ) represents point v iv at the point k The shortest path, L(v k ,v j ) represents point v k v at the point j The shortest path, L(v i ,v j ) represents point v i v at the point j The path, then point v i v at the point j The shortest path is:

[0086] min(L(v i ,v k )+L(v k ,v j ),L(v i ,v j )), v k ∈Ψ load

[0087] Specifically, for the startup order obtained by S3, the Floyd algorithm is used to search for the shortest path between the corresponding nodes according to the startup order of the distributed power source, and the startup order corresponding to the minimum recovery path weight is obtained:

[0088]

[0089] Where, α l A value of 0 indicates that line l has not been restored, α l A value of 1 indicates that line l has been restored, and Z represents line l. l Ψ represents the importance of line l. L Let be the set of all lines l in the system.

[0090] S5: By establishing a network reconfiguration optimization model, the objective of optimizing the startup sequence of distributed power sources is set to maximize the recovery capacity of critical loads, and to establish the target network with the minimum recovery path weight, thereby obtaining the optimal startup sequence for startup.

[0091] The objective function of the target network structure is:

[0092]

[0093] Among them, Ψ load α is the set of all loads in the system. Li Whether the load on node i has been restored; w i is the load importance coefficient of node i; g is the minimum weight of the recovery path under this startup sequence.

[0094] The constraints on the objective function include:

[0095] Distributed power generation output constraints:

[0096]

[0097]

[0098] In the formula: P Gn Q represents the active power output of the nth distributed power source that is started; Gn To start the reactive power output of the nth distributed power source; Ψ N It is the set of all distributed power sources in the system;

[0099] Power balance constraints:

[0100]

[0101] In the formula: α Gn To indicate whether the nth power source has been restored, 0 indicates not restored, and 1 indicates restored. α Li To indicate whether the load at node i has been restored, 0 indicates not restored, and 1 indicates restored. P Li Let Ψ be the load at node i. N Ψ is the set of all distributed power sources in the system. load It is the set of all load nodes in the system;

[0102] Node voltage constraints:

[0103] V i min ≤V i ≤V i max i∈Ψ load

[0104] In the formula: V i Ψ represents the voltage amplitude at each node in the system. load It is the set of all load nodes in the system;

[0105] Line thermal stability limit constraints:

[0106]

[0107] In the formula: P Tl Ψ represents the active power transmitted in the line. L It is the set of all lines l in the system;

[0108] Distribution network topology radial structure constraints: The distribution network system is a loopless and islanded topology.

[0109] In this embodiment, as follows Figure 2The improved IEEE 33-node test system shown is a case study demonstrating black start based on the method of this invention. The distribution network system contains 7 distributed generation sources, which are added at nodes 1, 7, 13, 17, 21, 25, and 30, respectively. The parameters of the distributed generation sources are shown in Table 1.

[0110] Table 1 Distributed Power Generation Parameters

[0111]

[0112]

[0113] The electric vehicle charging and battery swapping station can accommodate a maximum of 150 batteries. The number of usable batteries within the station is detailed below. Figure 3 The maximum energy storage capacity is 600kW, and the maximum charging and discharging power per hour is 400kW. When wind turbines and photovoltaics are used as black-start power sources, their maximum output power is affected by weather conditions. Therefore, it is necessary to predict the output of distributed power sources in the future and adjust the output according to the load power deficit. Typical daily output curves for each wind turbine and photovoltaic unit in the distribution network are shown below. Figure 4 , 5 As shown, to simulate power fluctuations in actual situations, this paper superimposes a 10% random power fluctuation onto the typical active power output curve and uses it as the output prediction value of DER. The outage time is selected as a typical scenario for analyzing the black start scheme. The loads at nodes 4, 16, 23, and 31 are critical loads, while some controllable loads exist at nodes 2, 6, 7, 9, 13, 18, 21, 23, 24, 28, 29, and 31.

[0114] according to Figure 4 and Figure 5 The typical power outage times for stroke and solar power output curves are selected as follows:

[0115] When the power outage occurs at 03:00, the available photovoltaic power generation output is 0, the available wind turbine power generation output is low (G1 is about 360KW, G6 is about 420KW), and the number of batteries in the available electric vehicle charging station is close to saturation (about 150 batteries).

[0116] The following section uses DG to represent distributed generation. In the optimization based on genetic algorithm and Floyd algorithm, the number of individuals is set to 50, and the number of iterations is specified as 100. Based on the characteristics of DG, black-start capability is analyzed, and DGs at nodes 2, 3, or 4, which have self-starting capability and good voltage and frequency regulation capabilities, are prioritized for self-starting, driving other power sources to start and supply power to surrounding important loads. The algorithm is called to solve the above scenario, and the black-start schemes are obtained as follows: Figure 6 As shown.

[0117] Analyzing the results in Table 2 for the black-start recovery scheme in a typical scenario, we can conclude that: the power outage occurred at 03:00 AM, at which time most electric vehicle charging and battery swapping stations were idle, and the number of available batteries in these stations was close to saturation. Since the outage occurred at night, photovoltaic output was zero, so the photovoltaic units at nodes 25 and 21 could not participate in the black-start recovery. Simultaneously, since wind turbine output was still available at this time, the wind turbine output was restored to power the system. DG3 is a black-start power source with stable output power and sufficient capacity at this time, so DG3 was prioritized for self-starting. Considering plant power consumption, transmission line losses, and reserving a certain margin, a safe and stable recovery network was established. The other DGs to be started were determined to be DG2, DG4, DG1, and DG6, with a total available DG capacity of 2.38MW in the system. The specific operation process of the black start scheme is shown in the table below. First, DG3 is started, and node 13 is restored. DG3 supplies power to node 13. Then, node 13 supplies power to node 14, restoring the load of node 14. On the one hand, the power supply to the load of node 15 is restored through node 14. On the other hand, the load of node 8 is restored by closing the tie switch between nodes 8 and 14. Then, DG2 is started by restoring node 7. At the same time, node 15 supplies power to node 16. DG4 is started by connecting node 16 to node 17. On the other hand, power is restored to nodes 6 and 20 from DG2. Node 6 restores node 5 and then node 4. Node 20 restores node 19 and then node 18. The output of DG4 restores the power supply to node 32 by closing the tie switch between nodes 17 and 32, thus restoring node 31. Then, DG1 is started from node 18, and DG6 is started from node 31. Finally, nodes 22, 29, 28, 23, and 24 are restored respectively. The entire recovery scheme restored important load nodes 4, 16, 23 and 31, completing the restoration of power supply to all important loads. The startup method of this invention saves black start time and has greater advantages than the traditional scheme of first black start using the transmission network and then restoring power supply to the distribution network from the transmission network.

[0118] Table 2 Power Outage Time 03:00 Black Start Scheme

[0119]

[0120] Obviously, the timing of the power outage will affect the black start scheme of the distribution network, and the DG capacity needs to be configured according to the worst-case power outage scenario to design a black start scheme that meets the needs of most power outage scenarios.

[0121] The above embodiments are merely illustrative and do not constitute a limitation on the scope of the present invention. These embodiments can also be implemented in various other ways, and various omissions, substitutions, and modifications can be made without departing from the technical spirit of the present invention.

Claims

1. A black start method for distributed power generation-assisted distribution networks based on wind and solar uncertainties, characterized in that, Includes the following steps: S1: Obtain the recovery cost weight based on the recovery status of the system lines, and obtain the line importance based on the line load and node load importance; S2: Determine the distributed power source to be the startup node. Step S2 specifically includes: The black start capability of distributed power sources is evaluated. Based on the black start capability, the impact of the start path weight, the start capacity, the frequency and voltage regulation capability, and the load increase speed, the black start evaluation index of distributed power sources is obtained. The distributed power source with the highest black start evaluation index is selected as the start node. S3: Starting from the starting node, use a genetic algorithm to randomly generate chromosomes to represent the startup order of the distributed power source; S4: Calculate the random order obtained in step S3 based on the shortest path algorithm to obtain multiple starting orders with the shortest paths. Step S4 specifically includes: Given the startup order obtained from S3, the Floyd algorithm is used to search for the shortest path between the corresponding nodes according to the startup order of the distributed power source, and the startup order corresponding to the minimum recovery path weight is obtained: in, α l A value of 0 represents a line. l Not recovered. α l 1 represents the line l It has been restored. For the line l The importance of the line, For all lines in the system l The set that constitutes; S5: By establishing a network reconfiguration optimization model, the objective of optimizing the startup sequence of distributed power sources is set to maximize the recovery capacity of critical loads, and to establish the target network with the minimum recovery path weight, thereby obtaining the optimal startup sequence for startup.

2. The distributed power generation-assisted black start method for distribution networks based on wind and solar uncertainties according to claim 1, characterized in that, The formula for calculating the recovery cost weight is as follows: in, For the unit n The recovery cost weight, For all lines in the system l The set that constitutes For the line l The recovery cost weight; α l A value of 0 represents a line. l Not recovered. α l 1 represents the line l It has been restored.

3. The distributed power generation-assisted black start method for distribution networks based on wind and solar uncertainties according to claim 1, characterized in that, The formula for calculating the importance of the line is as follows: in, For the line l The importance of the line, P Li and P Lj The lines are respectively l Two-end nodes i and nodes j The load received; For nodes i Load importance coefficient, For nodes j The load importance coefficient is 10 for Level 1 loads, 1 for Level 2 loads, and 0.1 for Level 3 loads. For the line l The recovery cost weight.

4. The distributed power generation-assisted black start method for distribution networks based on wind and solar uncertainties according to claim 1, characterized in that, The formula for obtaining the black-start evaluation index is as follows: in, δ For DG black start evaluation indicators, λ 1. λ 2. λ 3. λ 4. λ 5 is the allocation coefficient. λ 1+ λ 2+ λ 3+ λ 4+ λ 5 = 1; a For DG black boot capability; b The impact of DG startup path weights; c This is the DG boot capacity; d DG frequency and voltage regulation capability; e The rate at which DG increases its load.

5. The distributed power generation-assisted black start method for distribution networks based on wind and solar uncertainties according to claim 1, characterized in that, The genetic algorithm in step S3 specifically includes: In the genetic algorithm, chromosomes are encoded in binary form, and the restored sequence is represented as chromosomes of length kN, where N is the distributed power source in the power distribution network system, and k is the length of the chromosome segment. Chrom=[A1,A2,…,A N ] Where Chrom is a permutation of N DGs, A N A chromosome segment of length k; After decoding the chromosomes: Phen=[B1,B2,…,B N ] Where Phen represents the boot order of DG, B N This represents the start time of the Nth DG.

6. The distributed power generation-assisted black start method for distribution networks based on wind and solar uncertainties according to claim 1, characterized in that, The objective function of the target network structure is: in, It is the set of all loads in the system; α Li For nodes i Has the load been restored? w i For nodes i Load importance coefficient; g Set the recovery path weight for this startup sequence.

7. The distributed power generation-assisted black start method for distribution networks based on wind and solar uncertainties according to claim 6, characterized in that, The constraints of the objective function include distributed generation output constraints, power balance constraints, node voltage constraints, line thermal stability limit constraints, and distribution network topology radial structure constraints.

8. The distributed power generation-assisted black start method for distribution networks based on wind and solar uncertainties according to claim 7, characterized in that, The constraints on the objective function are specifically as follows: Distributed power generation output constraints: In the formula: P Gn The active power output of the nth distributed power source that is started; Q Gn The reactive power output for starting the nth distributed power source; It is the set of all distributed power sources in the system; Power balance constraints: In the formula: To indicate whether the nth power source has been restored, 0 indicates not restored, and 1 indicates restored. For nodes i The indicator shows whether the load has been restored; 0 indicates no restoration, and 1 indicates restoration. For nodes i Load capacity, It is the set of all distributed power sources in the system. It is the set of all load nodes in the system; Node voltage constraints: In the formula: V i This represents the voltage amplitude at each node in the system; It is the set of all load nodes in the system; Line thermal stability limit constraints: In the formula: P Tl For the line l Active power transmitted in the middle, For all lines in the system l The set that constitutes; Distribution network topology radial structure constraints: The distribution network system is a loopless and islanded topology.

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