Power distribution system unit cluster net rack extension planning method and device based on reliability explicit constraint matrix reduction

Abstract

The invention discloses a power distribution system unit cluster net rack extension planning method and device based on reliability explicit constraint matrix reduction, and the method comprises the following steps: firstly, obtaining the system data of a to-be-planned region, and determining related parameters; secondly, a reliability explicit calculation method capable of reducing the matrix scale is adopted, an MILP model of multi-contact power distribution system unit cluster expansion planning is constructed, and an objective function calculation expression and various constraints are provided; comprising power flow constraints and network topology constraints considering network reconstruction under normal and fault conditions, virtual topology constraints under normal and fault conditions, and reliability index calculation equations and constraints; and finally, based on the input parameters, solving the MILP model by using a solver to obtain main line and tie line planning results of the to-be-planned region in each stage in the future. Aiming at the medium-voltage power distribution network and considering the reliability requirement of the planning area, the invention provides the multi-stage planning method for the power supply unit cluster in the power distribution network taking a multi-contact form as a target networking structure, an investment scheme can be determined in each planning stage, and the reliability and the economical efficiency of the planning are favorably improved.

Description

Technical Field

[0001] The present invention relates to the field of distribution network grid expansion planning, and particularly relates to a method and device for distribution system unit cluster grid expansion planning based on reliability explicit constraint matrix reduction, which is applicable to the grid expansion planning work of China's distribution system. Background Art

[0002] In a new urban distribution system, the load characteristics are diverse and the density is relatively high, with high reliability requirements. The penetration rate of distributed new energy is gradually increasing, resulting in problems such as undirectional power flow and voltage over-limit in the distribution network. The main goal of distribution network planning is to meet the growing demand of power sources and loads. The grid structure of the distribution network is the most important factor affecting the system function and characteristics. In the existing distribution network grid planning, the target network structure is mainly a radial network or a single-loop network, which is difficult to meet the high reliability requirements in some areas and has great limitations. The multi-connected network structure can give full play to the potential of flexible load demand response, improve the power supply safety and reliability of the grid, and adapt to the large-scale access of power sources and loads. Therefore, it is necessary to adopt a multi-connected network structure in the future urban distribution system planning. At the same time, in order to meet the economic and reliability requirements of the distribution network planning model, the reliability of the planned grid needs to be evaluated during the optimization process of the distribution network planning model. Research shows that multi-stage planning is more economical than single-stage planning. Therefore, it is very necessary to propose a multi-stage expansion planning method for a multi-connected distribution network.

[0003] In the existing research on grid planning considering reliability, some literature adopts the "N-1" load rate constraint, uses the grid-based planning method, conducts step-by-step planning, divides power supply units and routes wires based on the decomposition steps, and adopts the "N-1" rigid reliability constraint in reliability calculation. Under the transfer demand, the maximum allowable load rate of equipment is obtained. This method ensures the load transfer demand under single-branch or bus faults, but it needs to consider that the power grid rigidly meets the N-1 verification at peak load times, which is prone to the problem of excessive margin. Another part of the literature calculates reliability indicators and converts them into reliability costs included in the objective function. First, a heuristic algorithm is used to generate the grid topology, and then the reliability is calculated through a simulation algorithm to evaluate the reliability cost and iteratively solve for the optimal grid. Since the load failure rate and failure time are related to the network topology, and the reliability calculation requires the network topology to be clearly defined in advance, the above literature decouples and solves the grid topology decision and reliability evaluation, but this method cannot guarantee the global optimum. On this basis, some literature proposes an explicit expression for reliability calculation that can be used in distribution network planning and operation, expressing the reliability indicators in terms of branch failure rates and branch power flows, but this method does not consider load transfer using tie lines, that is, it is considered that the downstream of the faulty branch needs to repair the fault before power can be restored. Subsequently, there is literature on multi-stage expansion planning of distribution networks, considering network reconfiguration, calculating reliability using explicit expressions and using them as constraints. However, this literature only considers the single-tie situation; on the other hand, this literature enumerates the affected states of each load node under any branch fault and introduces a large number of decision variables to represent reliability indicators, making the model difficult to solve.

[0004] To sum up, in the existing research on multi-stage expansion planning of distribution networks considering network reconfiguration, the main lines and tie lines are regarded as the same variable for planning, and the accurate position of the tie lines cannot be obtained. Moreover, the reliability is calculated by introducing variables to represent the power supply status of loads before and after faults, with a large number of variables and high calculation difficulty. Summary of the Invention

[0005] To overcome the problems in the prior art, the present invention proposes a method for expanding the grid of distribution system unit clusters based on reducing the size of the explicit reliability constraint matrix.

[0006] The implementation method of the present invention is as follows:

[0007] A method for expanding the grid of distribution system unit clusters based on reducing the size of the explicit reliability constraint matrix specifically includes the following steps:

[0008] Obtain the system data of the area to be planned and determine relevant parameters;

[0009] Based on the explicit reliability constraint that can reduce the matrix size, construct a mixed integer linear programming MILP model for multi-tie distribution network expansion planning, which model includes the calculation expression of the objective function and various constraint conditions;

[0010] Solve the constructed MILP model according to the obtained system data and the determined relevant parameters to obtain the equipment planning results in each stage of the area to be planned.

[0011] Moreover, the system data of the area to be planned and the determined relevant parameters specifically include:

[0012] Technical system data: node load demand, line impedance, operation limit;

[0013] Economic system data: equipment investment and operation cost, electricity price;

[0014] Reliability index calculation data: equipment failure rate, maintenance time, switch switching time;

[0015] Reliability cost calculation data: power outage loss parameter.

[0016] Moreover, the objective function is the present value of the total cost, specifically including:

[0017] The objective function includes minimizing the present value of the total planning cost, including investment cost, operation and maintenance cost, and reliability cost:

[0018]

[0019] In the formula, T represents the total number of planning stages; t represents any stage in the planning process; Represents the present value calculation factor of the investment cost in stage t; Is the present value calculation factor of the operation cost and reliability cost in stage t; Represents the investment cost in stage t; Represents the investment cost in stage t;

[0020]

[0021] In the formula, τt represents the total number of planning stages;

[0022]

[0023] RRC t = ωEENS t (6)

[0024] In the formula, Is the investment cost and maintenance cost for constructing the standby line a ∈ Λ C Of, Is the investment cost and maintenance cost for constructing the tie line, Is the investment cost and maintenance cost for constructing the standby transformer a ∈ Λ T Of, Denote the investment cost and maintenance cost of building a substation at node S; binary variables respectively represent whether to build a spare line a at branch ij, whether to install a spare transformer a at feeder f, and whether to build a new substation at node S at the beginning of stage t. When the superscript is 0, it represents the construction status in the initial stage; in formula (5), The superscript T of represents the number of planning stages. This vector is a 1*T dimensional unit vector, with only the position corresponding to stage t being 1 and other positions being 0; is used to indicate that the equipment can be used for operation during its life cycle after construction. The superscript represents the spare line a built in the τ-th stage, and the subscript is the built equipment. This vector is a T*1 dimensional unit vector, with only the working time of the corresponding built equipment being 1, that is, from the τ-th position to position 1, and other positions being 0, is the full life cycle service life of the equipment, represents the remaining life of the equipment, corresponding to the first position to position 1, is the remaining life of the existing equipment at the initial stage of construction; in formula (6), ω is the reliability cost coefficient, and EENS is the expected system un-supplied energy;

[0025] For the lines to be built, the lines and transformers that need to be replaced, the spare equipment is selective and can be represented by a. For each equipment, it has its own life cycle, and use The vector can represent its life cycle after construction in a certain stage, then the remaining life of the existing equipment can be represented; when calculating the operation and maintenance costs, it is necessary to simulate the operation in each stage during the construction period, and use the vector The operation and maintenance costs of each stage can be selected.

[0026] Moreover, the various types of constraint conditions include:

[0027] (1) Equipment construction and usage constraints, specifically including:

[0028]

[0029] In the formula, and respectively represent whether to build line ij at stage t and its line capacity; represents whether there is a transformer at feeder f at stage t; respectively represent the resistance, reactance of line ij and the failure rate of the fault branch xy; γ, Ψ F , Ψ S , are respectively the branch set, feeder set, substation node set and transformer set of substation nodes;

[0030] Equations (7)-(8) represent the construction and commissioning life of lines and transformers; Equations (9)-(12) calculate the line capacity, resistance, reactance, and failure rate; Equation (13) indicates that a transformer can only be constructed when there is an existing substation, and Equation (14) indicates that a substation can only be constructed once;

[0031] (2) Power flow constraints considering network reconfiguration under normal and fault conditions, specifically including:

[0032]

[0033] In the formula, M is a number greater than or equal to 10; γ is the set of branches; the superscript xy represents different scenarios, xy = NO indicates no fault at this time and the system is operating normally, xy = γ indicates the operation of the system under the fault of branch γ; is a 0-1 variable indicating whether the line is connected under normal and fault conditions. It is 1 if the line is connected, otherwise it is not;

[0034] This part of the constraint is the power flow constraint under normal operation and fault conditions in the average load scenario of each stage; Equations (15)-(18) are power flow equations ignoring the loss term. When it indicates that branch ij is disconnected in scenario xy, then constraint (17) fails; Equations (21)-(22) are line capacity constraints; Equations (23)-(24) are transformer capacity constraints; Equation (27) indicates that a line can only be connected when it is constructed; Equation (28) represents the isolation of the fault branch;

[0035] (3) Network topology constraints, specifically including:

[0036]

[0037] In the formula, LPM i,t is a 0-1 variable indicating whether the node is in the power supply path. If node i is connected to any branch, it is 1, otherwise it is 0; is a 0-1 variable indicating whether the feeder is at the head of the power supply path of branch ij. If it is at the head, it is 1, otherwise it is 0; is a 0-1 variable indicating whether branch ij' is on the power supply path connected to ij;

[0038] Equations (29)-(31) are the network radial operation constraints for normal and fault scenarios, and equations (32)-(34) are the constraints for determining the feeder at the head of each branch; equation (29) indicates that when any branch connected to a node is connected, the node is on the power supply path; equation (30) ensures that each node is powered by only one branch under each scenario. It can be proved by graph theory that the above constraints can ensure the radial operation of the network; equation (32) means that only one feeder is at the head of the power supply path of each branch; equation (34) means that all branches on the power supply path where only the head of the feeder is connected to the branch are connected, can be set to 1;

[0039] (4) Virtual power flow constraints, specifically including:

[0040]

[0041] In the formula, is the number of users served by node N, represents the number of users served by line ij, represents the number of users served by the substation node;

[0042] The virtual power flow equation constraint constructs a lossless network with the same topology as the original one. The demand of each node is the number of connected users. Based on this, the number of users served downstream of each line can be calculated to calculate SAIDI and SAIFI;

[0043] (5) Reliability index calculation and constraints, specifically including:

[0044]

[0045]

[0046] In the formula, α ij is the line length, λ ij is the unit line failure rate, is the repair time after the line fails, is the switch operation time after the line fails, are respectively the load that cannot be restored to power through network reconfiguration downstream of the fault line, the load that can be restored to power through switch operation upstream of the fault line, and the load that can be restored to power through tie switch operation downstream of the fault line; are respectively the number of users that cannot be restored to power through network reconfiguration downstream of the fault line, the number of users that can be restored to power through switch operation upstream of the fault line, and the number of users that can be restored to power through tie switch operation downstream of the fault line; EENS t 、SAIDI t 、SAIFI tThey are the expected un-energized energy, system average interruption duration, and system average interruption frequency at stage t, respectively; and are the reliability requirements for each stage;

[0047] In the process of reliability calculation, the following assumptions are made:

[0048] Assumption 1: Only single-branch interruption faults are considered in the reliability calculation process;

[0049] Assumption 2: The meshed distribution network operates radially, and sectional switches are equipped at both ends of each branch; when a fault occurs in a certain branch, the circuit breaker at the head of the power supply path where the fault branch is located disconnects, and the whole line loses power. Then, the fault branch is isolated, and the upstream of the branch can restore power supply through the action of the switch. Through network reconfiguration, the power supply demand of the downstream load of the fault can be restored to the greatest extent. Finally, after the fault repair time of this branch, the original system topology is restored, and normal power supply is restored;

[0050] Based on the above assumptions, the interruptions experienced by the upstream load of the fault branch and the load that can be restored to power supply through network reconfiguration downstream after the fault are switch operation interruptions, that is, the power outage time is The interruption experienced by the load downstream of the branch that cannot be restored to power supply through network reconfiguration is a switch operation - restoration interruption, that is, the power outage time is

[0051] For the approximate calculation of reliability indicators, line losses are ignored, and it is considered that the branch tidal flow during normal operation is the downstream load; Equations (39) to (43) calculate the reliability indicator EENS t ; Equations (44) to (48) calculate the reliability indicator SAIDI t ; Equations (49) to (50) calculate the reliability indicator SAIFI t ; Equations (51) to (53) constrain the reliability indicators for each stage.

[0052] Moreover, according to the obtained system data and determined relevant parameters, the constructed MILP model is solved to obtain the equipment planning results for each stage in the area to be planned. The specific steps include:

[0053] According to the obtained system data and determined relevant parameters, the constructed MILP model is solved to obtain the equipment planning results for each stage in the area to be planned and output.

[0054] A distribution system unit cluster network expansion planning device based on reliability explicit constraint matrix reduction includes:

[0055] An acquisition module, which acquires the system data of the area to be planned and determines relevant parameters;

[0056] A model construction module constructs a mixed-integer linear programming (MILP) model for the multi-connected distribution network expansion planning based on the reliability explicit constraints that can reduce the matrix scale. The model includes the calculation expressions of the objective function and various constraint conditions.

[0057] An output module solves the constructed MILP model according to the obtained system data and determined relevant parameters, and obtains the equipment planning results in each stage of the area to be planned.

[0058] Moreover, the constraint conditions in the model construction module include:

[0059] ① Constraints on equipment construction and usage

[0060] ② Power flow constraints considering network reconfiguration under normal and fault conditions

[0061] ③ Network topology constraints

[0062] ④ Virtual power flow constraints

[0063] ⑤ Reliability index calculation and constraints.

[0064] A computer-readable storage medium stores computer instructions, and when the computer instructions run, they execute the steps of the method for expanding the grid framework of the distribution system unit cluster based on reliability explicit constraint matrix reduction.

[0065] The beneficial effects of the present invention are:

[0066] 1. The present invention improves on the existing research, proposes a reliability explicit expression method and a multi-stage planning method for multi-connected structures considering post-fault network reconfiguration, and improves the existing research model to reduce variables, which can improve the calculation efficiency. By using the proposed device and inputting the data of the area to be planned, the optimal planning results in each stage can be obtained. While meeting the reliability by adopting the multi-connected structure and reliability constraints, the economy is improved, and since the adopted model is a MILP model, the global optimal solution can be obtained.

[0067] 2. The present invention takes the power supply unit cluster in the distribution system as a unit and proposes a network framework expansion planning method for the power supply unit cluster based on the reduction of the reliability explicit constraint matrix. The power supply unit cluster is a power supply unit formed by the interconnection of multiple feeders. On the basis of the above research, on the one hand, the usage and connectivity of the main line and the tie line are accurately modeled, and the set of candidate tie lines is expanded. Taking the multi-tie line form as the target network structure, the nodes in the middle and at the end of the line can be used as tie line nodes, and the network reconstruction constraints in the multi-tie line networking form are written. On the other hand, a new calculation method is used to represent the reliability index. It is only necessary to clarify the feeder to which each branch belongs and the downstream load of each branch during normal operation, and the virtual power flow is used to calculate the number of users downstream of each branch, without additionally representing the operating conditions of each node before and after the fault, so as to simplify the variable dimension and improve the calculation speed.

[0068] 3. The present invention proposes a network framework expansion planning method and device for the power supply unit cluster based on the reduction of the reliability explicit constraint matrix. In terms of tie line optimization, the construction and connectivity of the main line and the tie line are accurately modeled using decision variables and constraints, and the set of candidate tie lines is expanded. Taking the multi-tie line form as the target network structure, the nodes in the middle and at the end of the line can be used as tie line nodes and can be used to transfer the load during fault operation, and the power flow constraints in the multi-tie line networking form are written. On the other hand, the downstream load of each branch is represented according to the lossless power flow equation, and the virtual power flow is used to calculate the number of users downstream of each branch, and then the downstream load and the number of users of each branch before and after the fault are calculated, and the explicit expression of the reliability index is written accordingly, so as to simplify the variable dimension and improve the calculation speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] In order to more clearly illustrate the technical solutions of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0070] Figure 1 It is a schematic diagram of the framework of the network framework expansion planning method for the distribution system unit cluster based on the reduction of the reliability explicit constraint matrix in this embodiment;

[0071] Figure 2 It is a schematic diagram of the framework of the network framework expansion planning model for the distribution system unit cluster based on the reduction of the reliability explicit constraint matrix in this embodiment;

[0072] Figure 3 It is a schematic diagram of the network framework expansion planning device for the distribution system unit cluster based on the reduction of the reliability explicit constraint matrix in this embodiment;

[0073] Figure 4Schematic diagram of the 54-node system in this embodiment;

[0074] Figure 5 Schematic diagram of the planning results of each stage for the multi-stage planning of the 54-node system in this embodiment. Detailed implementation manners

[0075] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0076] As Figures 1 to 3 shown, the present invention proposes a method and device for expanding the grid framework of a distribution system unit cluster based on reliability explicit constraint matrix reduction. In combination with specific embodiments, the specific content of this method includes:

[0077] First, obtain the system data and related parameters of the area to be planned, including technical system data: node load demand, line impedance, operation limit; economic system data: equipment investment and operation cost, electricity price; reliability index calculation data: equipment failure rate, repair time, switch switching time; reliability cost calculation data: power outage loss parameter;

[0078] Secondly, construct a grid framework expansion planning model for a distribution system unit cluster based on reliability explicit constraint matrix reduction, propose the calculation expression of the objective function, including investment cost, operation cost, and reliability cost, convert each cost into present value, and propose various constraints, including equipment construction and usage constraints, power flow constraints considering network reconfiguration under normal and fault conditions, network topology constraints, virtual power flow constraints, reliability index calculation and constraints;

[0079] Finally, based on the input parameters, use the Cplex solver to solve the MILP model to obtain the main line and tie line planning results of the area to be planned in each future stage.

[0080] (1) Objective function

[0081] The objective function is to minimize the present value of the total planning cost, including investment cost, operation and maintenance cost, and reliability cost:

[0082]

[0083] In the formula, T represents the total number of planning stages; t represents any stage in the planning process; represents the present value calculation factor of the investment cost in stage t; is the present value calculation factor of the operating cost and reliability cost for stage t; represents the investment cost for stage t; represents the investment cost for stage t;

[0084]

[0085] In the formula, τt represents the total number of planning stages;

[0086]

[0087] RRC t = ωEENS t (6)

[0088] In the formula, is the investment cost and maintenance cost for constructing the standby line a ∈ Λ C ; is the investment cost and maintenance cost for constructing the tie line; is the investment cost and maintenance cost for constructing the standby transformer a ∈ Λ T ; represents the investment cost and maintenance cost for constructing a substation at node S; The binary variable respectively represent whether to construct the standby line a at the branch ij, whether to install the standby transformer a at the feeder f, and whether to build a new substation at node S at the beginning of stage t. When the superscript is 0, it represents the construction status in the initial stage; In formula (5), The superscript T of represents the number of planning stages. This vector is a 1*T-dimensional unit vector, with only the position corresponding to stage t being 1 and other positions being 0; is used to represent that the equipment can be used for operation during its life cycle after construction. The superscript represents the standby line a constructed in the τth stage, and the subscript is the constructed equipment. This vector is a T*1-dimensional unit vector, with only the working time of the corresponding constructed equipment being 1, that is, from the τth position to position 1, and other positions being 0, is the full life cycle service life of the equipment, represents the remaining life of the equipment, corresponding to the 1st position to position 1, is the remaining life of the existing equipment at the initial stage of construction; In formula (6), ω is the reliability cost coefficient, and EENS is the expected energy not supplied by the system.

[0089] It should be noted that for the lines to be built, the lines and transformers that need to be replaced, the standby equipment is selective and can be represented by a. For each equipment, it has its own life cycle, and the vector can represent its life cycle after construction in a certain stage, The remaining life of the existing equipment can be represented. When calculating the operation and maintenance costs, it is necessary to simulate the operation in each stage during the construction period, and use the vector to select the operation and maintenance costs in each stage.

[0090] (2) Constraint conditions

[0091] The constraint conditions of the multi-connected form distribution network multi-stage expansion planning model include equipment construction and usage constraints, power flow constraints considering network reconfiguration under normal and fault conditions, network topology constraints, virtual power flow constraints, reliability index calculation and constraints. Among them, the equipment construction situation is used to represent the construction and usage status of the equipment, so that the equipment constructed in a certain stage can be put into use during its life cycle; the power flow constraints considering network reconfiguration under normal and fault conditions can be used to represent the power flow of each branch on the one hand, and on the other hand, make the planning results meet the safe operation constraints under normal and fault conditions; the network topology constraints can be used to ensure the radiality of the network during operation; the virtual power flow constraints are used to represent the head feeder of the power supply path where each branch is located during normal operation, and represent the number of users downstream of each branch; the reliability index calculation and constraints explicitly express the reliability index with the variables represented in the above constraints and constrain it.

[0092] 1) Equipment construction and usage constraints

[0093]

[0094]

[0095] In the formula, and respectively represent whether the line ij is constructed in the t stage and its line capacity; represents whether the feeder f has a transformer in the t stage; respectively represent the resistance, reactance of the line ij and the failure rate of the fault branch xy; γ, Ψ F , Ψ S , are respectively the branch set, feeder set, substation node set and transformer set of substation nodes.

[0096] Equations (7)-(8) represent the construction and available service life of the line and the transformer; equations (9)-(12) calculate the line capacity, resistance, reactance and failure rate; equation (13) means that the transformer can only be constructed when there is an existing substation, and equation (14) means that the substation can only be constructed once.

[0097] 2) Power flow constraints considering network reconfiguration under normal and fault conditions

[0098]

[0099]

[0100] Wherein, M is a sufficiently large number; γ is a set of branches; the superscript xy represents different scenarios, xy = NO indicates no fault at this time and the system is operating normally, and xy = γ indicates the operating condition of the system under the fault of branch γ; is a 0-1 variable, indicating whether the line is connected under normal and fault conditions. It is 1 if the line is connected, otherwise it is not.

[0101] This part of the constraint is the power flow constraint under normal and fault conditions in the average load scenario of each stage. Equations (15)-(18) are power flow equations ignoring the loss term. When indicates that branch ij is disconnected in scenario xy, then constraint (17) fails; equations (21)-(22) are line capacity constraints; equations (23)-(24) are transformer capacity constraints; equation (27) indicates that the line can only be connected when it is built; equation (28) represents the isolation of the fault branch.

[0102] 3) Network topology constraint

[0103]

[0104]

[0105] Wherein, LPM i,t is a 0-1 variable, indicating whether the node is in the power supply path. If node i is connected to any branch, it is 1, otherwise it is 0; is a 0-1 variable, indicating the feeder whether it is at the head of the power supply path of branch ij. If it is at the head, it is 1, otherwise it is 0; is a 0-1 variable, indicating whether branch ij' is on the power supply path connected to ij.

[0106] Equations (29)-(31) are the network radial operation constraints for normal and fault scenarios, and equations (32)-(34) are the constraints for determining the feeder at the head of each branch. Equation (29) indicates that when any branch connected to the node is connected, the node is on the power supply path; equation (30) ensures that each node is powered by only one branch in each scenario. It can be proved by graph theory that the above constraints can ensure the radial operation of the network; equation (32) indicates that each branch has only one feeder at the head of its power supply path; equation (34) indicates that only when all branches on the power supply path where the head of the feeder is connected to the branch are connected, can it be set to 1.

[0107] 4) Virtual power flow constraint

[0108]

[0109] Wherein, is the number of users carried by node N, represents the number of users carried by line ij, represents the number of users supplied by the substation node.

[0110] The virtual power flow equation constraint constructs a lossless network with the same topology as the original one. The demand of each node is the number of connected users. Based on this, the number of users carried downstream of each line can be calculated to calculate SAIDI and SAIFI.

[0111] 5) Reliability index calculation and constraints

[0112]

[0113] Wherein, α ij is the line length, λ ij is the unit line failure rate, is the repair time after the failure of this line, is the switching operation time after the failure of this line, are respectively the load amounts that cannot be restored to power supply through network reconfiguration downstream of the fault line, the load amounts that can be restored to power supply through switching operation upstream of the fault line, and the load amounts that can be restored to power supply through the operation of the tie switch downstream of the fault line after the failure of branch ij; are respectively the number of users that cannot be restored to power supply through network reconfiguration downstream of the fault line, the number of users that can be restored to power supply through switching operation upstream of the fault line, and the number of users that can be restored to power supply through the operation of the tie switch downstream of the fault line after the failure of branch ij; EENS t SAIDI t SAIFI t are respectively the expected unsupplied energy, system average interruption duration, and system average interruption frequency at stage t; and are the reliability requirements for each stage.

[0114] In the process of reliability calculation, the following assumptions are made:

[0115] Assumption 1: Only single-branch interruption faults are considered in the reliability calculation process;

[0116] Assumption 2: The meshed distribution network operates radially, and sectional switches are equipped at both ends of each branch. When a fault occurs in a certain branch, the circuit breaker at the head end of the power supply path where the fault branch is located is disconnected, and the entire line is powered off. Then, the fault branch is isolated. The upstream of the branch can be restored to power supply through switching operation. Through network reconfiguration, the power supply demand of the load downstream of the fault can be restored to the greatest extent. Finally, after the fault repair time of this branch, the original system topology is restored and normal power supply is restored.

[0117] Based on the above assumptions, the interruptions experienced by the upstream load of the faulty branch and the load downstream that can be restored by network reconfiguration after a fault are switch - action interruptions, that is, the power outage time is The interruptions experienced by the load downstream of the branch that cannot be restored by network reconfiguration are switch - action - restoration interruptions, that is, the power outage time is

[0118] For the approximate calculation of reliability indices, ignoring line losses, it is considered that the branch power flow during normal operation is the downstream load. Equations (39) to (43) calculate the reliability index EENS t ; Equations (44) to (48) calculate the reliability index SAIDI t ; Equations (49) to (50) calculate the reliability index SAIFI t ; Equations (51) to (53) constrain the reliability indices at each stage.

[0119] Through the above objective function and constraints, a multi - stage expansion planning model for a multi - tie distribution network is obtained. This model is a MILP model and can use the Cplex solver to obtain the global optimal solution, thereby obtaining a multi - stage expansion planning scheme for the multi - tie distribution network, while meeting the reliability requirements of power distribution.

[0120] The embodiment of the present invention also proposes a distribution system unit cluster network expansion planning device based on the reduction of the reliability explicit constraint matrix, which is used to obtain the expansion planning results at each stage. The device includes:

[0121] A distribution system unit cluster network expansion planning device based on the reduction of the reliability explicit constraint matrix, including:

[0122] An acquisition module, which acquires the system data of the area to be planned and determines relevant parameters;

[0123] A model construction module, which constructs a mixed - integer linear programming MILP model for the expansion planning of a multi - tie distribution network based on the reliability explicit constraints with a reducible matrix scale. This model includes the calculation expressions of the objective function and various constraint conditions;

[0124] An output module, which directly solves the constructed MILP model according to the obtained system data and the input parameters of the determined relevant parameters, and obtains the equipment planning results at each stage of the area to be planned.

[0125] Moreover, the constraint conditions in the model construction module include:

[0126] ① Constraints on equipment construction and usage

[0127] ② Power flow constraints considering network reconfiguration under normal and fault conditions

[0128] ③ Network topology constraint

[0129] ④ Virtual power flow constraint

[0130] ⑤ Reliability index calculation and constraint

[0131] A computer-readable storage medium stores computer instructions thereon, and when the computer instructions run, they execute the steps of a distribution system unit cluster network expansion planning method based on reliability explicit constraint matrix reduction.

[0132] An embodiment of the present invention further provides a computer-readable storage medium storing computer instructions thereon, characterized in that when the computer instructions run, they execute the steps of the above-mentioned distribution system unit cluster network expansion planning method based on reliability explicit constraint matrix reduction.

[0133] Use a 54-node system to verify the effectiveness of the method and device proposed in this paper. As Figure 4 shown, the system consists of 50 load nodes, 4 substation nodes and 63 branches. System data, investment and maintenance cost coefficients, load demand data, conductor and transformer lifetimes can be obtained from existing research literature. Among them, the base values of power and voltage are 1 MVA and 13.5 kV respectively, and the currency used is US dollars. There are two transformer alternative schemes and line alternative schemes. The feeder failure rate is set to 0.1 / year / km, the repair interruption time and the switch operation only interruption time are 3 hours and 0.5 hours respectively. The load conditions are modeled with three load levels, and the load factors correspond to 70%, 83% and 100% of the peak demand respectively. Investment decisions are made within a 10-year planning period, divided into 5 stages, each stage lasting for two years, the annual interest rate is 10%, and the unit reliability cost ω is set to 10 $ / MWh.

[0134] The device uses CPLEX 12.5, with an Intel Core i7-7700 processor built-in, a frequency of 3.60 GHz, and a memory of 32 GB, and uses MATPOWER to calculate the power flow.

[0135] Table 1 lists the detailed planning results and reliability indicators for each stage. Figure 5 For the final planning result, a total of two new substations, 4 transformers, 45 main lines and 11 tie lines are built.

[0136]

[0137] It can be seen from Table 1 that the planning results of each stage meet the reliability constraints and have high reliability requirements. From Figure 5It can be seen that the finally generated grid scheme is a multi-connection scheme, which can flexibly transfer loads after a fault to fully improve the reliability of the distribution network. Using the model and solution method of this paper, the solution time is 23 minutes and 46 seconds, while using the solution method of existing research, the solution time is 52 minutes and 34 seconds, and a multi-connection scheme cannot be generated. Therefore, by using the proposed device and inputting the data of the area to be planned, the optimal results of each stage of planning can be obtained. While meeting the reliability with a multi-connection structure and reliability constraints, the economy is improved, and since the model used is a MILP model, a global optimal solution can be obtained.

[0138] It should be understood that each part of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, any one or a combination of the following techniques well known in the art can be used: discrete logic circuits having logic gate circuits for implementing logical functions on data signals, application specific integrated circuits having appropriate combinational logic gate circuits, programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), etc.

[0139] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0140] In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, the features defined with "first" and "second" can explicitly or implicitly include at least one of these features. In the description of the present invention, the meaning of "a plurality" is at least two, such as two, three, etc., unless otherwise specifically defined.

[0141] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for planning the expansion of distribution system unit cluster grid based on reliability explicit constraint matrix reduction, characterized in that: The specific steps include: Obtain system data for the area to be planned and determine relevant parameters; Based on the reliability explicit constraint that can reduce the matrix size, a mixed integer linear programming MILP model for multi-interconnection distribution network expansion planning is constructed. The model includes the objective function calculation expression and various constraint conditions. According to the obtained system data and the determined related parameters, the constructed MILP model is solved to obtain the equipment planning results of the area to be planned at each stage.

2. According to claim 1, a method for planning the expansion of a distribution system unit cluster grid based on reliability explicit constraint matrix reduction, characterized in that: The system data of the area to be planned and the related parameters to be determined specifically include: Technical system data: node load requirements, line impedance, operating limitations; Economic system data: equipment investment and operating costs, electricity prices; Reliability index calculation data: equipment failure rate, maintenance time, switch switching time; Reliability cost calculation data: power outage loss parameters.

3. The method for planning the expansion of a distribution system unit cluster grid based on reliability explicit constraint matrix reduction according to claim 1, characterized in that: The objective function is the present value of the total cost, which specifically includes: The objective function includes minimizing the present value of the total planning cost, including investment cost, operation and maintenance cost, and reliability cost: Where T represents the total number of planning stages; t represents any stage in the planning process; Represents the present value calculation factor of the investment cost at stage t; is the present value calculation factor of the operation cost and reliability cost in stage t; represents the investment cost at stage t; represents the investment cost at stage t; Where τt represents the total number of planning stages; RRC t =ωEENS t (6) In the formula, To build a backup line a∈Λ C investment cost and maintenance cost, The investment and maintenance costs of building interconnection lines are To build a backup transformer a∈Λ T investment cost and maintenance cost, Represents the investment cost and maintenance cost of building a substation at node S; binary variable They respectively indicate whether a backup line a is built at branch ij, whether a backup transformer a is installed at feeder f, and whether a new substation is built at node S at the beginning of stage t. The superscript 0 indicates the construction status in the initial stage. In formula (5), The superscript T of represents the number of planning stages. The vector is a unit vector of 1*T dimension. Only the position corresponding to the t stage is 1, and the other positions are 0. It is used to indicate that the equipment can be used for operation within its life cycle after construction. The superscript represents the spare line a constructed in the τth stage, and the subscript is the constructed equipment. The vector is a unit vector of dimension T*1. Only when the working time of the constructed equipment is 1, that is, the working time of the τth to τth stage is 1, the working time of the τth to τth stage is 1. Position 1, other positions are 0, For the full life cycle of the equipment, Indicates the remaining life of the device, corresponding to digits 1 to Position 1, is the remaining life of the existing equipment at the initial stage of construction; in formula (6), ω is the reliability cost coefficient, and EENS is the expected system unsupplied energy; For lines to be built, lines to be replaced, and transformers, the backup equipment is selective, which can be represented by a. Each device has its own life cycle, which can be represented by The vector can represent its life cycle after construction at a certain stage. The remaining life of the existing equipment can be expressed; when calculating the operation and maintenance costs, it is necessary to simulate the operation of each stage during the construction period, using vector The operation and maintenance costs for each stage can be selected.

4. The method for planning the expansion of a power distribution system unit cluster grid based on reliability explicit constraint matrix reduction according to claim 1, characterized in that: The various constraints include: (1) Equipment construction and usage constraints, including: In the formula, and They respectively indicate whether line ij is constructed and its line capacity in stage t; Indicates whether there is a transformer in feeder f at stage t; They represent the resistance and reactance of line ij and the fault rate of fault branch xy respectively; γ, Ψ F , S , They are the branch set, feeder set, substation node set and transformer set of substation nodes; Formulas (7)-(8) represent the construction and service life of the line and transformer; Formulas (9)-(12) calculate the line capacity, resistance, reactance and failure rate; Formula (13) indicates that the transformer can only be built when there is an existing substation, and Formula (14) indicates that the substation can only be built once; (2) Power flow constraints taking into account network reconstruction under normal and fault conditions, including: Where M is a number greater than or equal to 10; γ is a branch set; the superscript xy represents different scenarios, xy=NO means there is no fault at this time and the system is running normally, and xy=γ represents the operation of the system under the fault of the γ branch; It is a 0-1 variable, indicating whether the line is connected in normal and fault conditions. If it is 1, it means the line is connected, otherwise it is not connected; This part of the constraints is the power flow constraints under the load average scenario of each stage, normal operation and fault conditions; Equations (15)-(18) are the power flow equations ignoring the loss term. When , it means that branch ij is disconnected under scenario xy, then constraint (17) becomes invalid; equations (21)-(22) are line capacity constraints; equations (23)-(24) are transformer capacity constraints; equation (27) indicates that the line can be connected only when it is under construction; equation (28) indicates that the fault branch is isolated; (3) Network topology constraints, including: Where, LPM i,t is a 0-1 variable, indicating whether the node is in the power supply path. If node i is connected to any branch, it is 1, otherwise it is 0; is a 0-1 variable, indicating the feeder Whether it is at the beginning of the power supply path of branch ij, if it is at the beginning, it is 1, otherwise it is 0; is a 0-1 variable, indicating whether the branch ij' is On the power supply path connected to ij; Formulas (29)-(31) are the radial operation constraints of the network under normal and fault scenarios, and formulas (32)-(34) are the constraints for determining the feeder at the head end of each branch. Formula (29) indicates that when any branch connected to a node is connected, the node is on the power supply path. Formula (30) ensures that each node is powered by only one branch in each scenario. It can be proved by graph theory that the above constraints can ensure the radial operation of the network. Formula (32) indicates that each branch has only one feeder at the head end of its power supply path. Formula (34) indicates that all branches on the power supply path connected to the branch only when the feeder head end is connected are connected. Can be set to 1; (4) Virtual power flow constraints, including: In the formula, is the number of users served by node N, Indicates the number of users carried by line ij, Indicates the number of users served by the substation node; The virtual power flow equation constraint constructs a lossless network with the same topology as the original one. The demand of each node is the number of connected users. Based on this, the number of users carried by each line downstream can be calculated to calculate SAIDI and SAIFI. (5) Reliability index calculation and constraints, including: In the formula, α ij is the line length, λ ij is the unit line failure rate, is the repair time after the line failure, is the switch action time after the line fails, They are respectively the load amount located downstream of the faulty line that cannot be restored through network reconstruction after the branch ij fails, the load amount located upstream of the faulty line that can be restored through switch action, and the load amount located downstream of the faulty line that can be restored through contact switch action; They are the number of users downstream of the faulty line who cannot recover power through network reconstruction after branch ij fails, the number of users upstream of the faulty line who can recover power through switch action, and the number of users downstream of the faulty line who can recover power through contact switch action; EENS t 、SAIDI t 、SAIFI t They are the expected unsupplied energy, the average power outage time of the system and the average power outage frequency of the system in period t respectively; and Reliability requirements for each stage; During the reliability calculation, the following assumptions are made: Assumption 1: Only single-branch interruption failure is considered in the reliability calculation process; Assumption 2: The mesh distribution network operates radially, and each branch is equipped with a sectionalizer at both ends. When a branch fails, the circuit breaker at the head end of the power supply path where the faulty branch is located is disconnected, and the entire line is powered off. The faulty branch is then isolated, and the upstream branch can restore power supply through switch action. The power supply demand of the downstream load can be restored to the greatest extent through network reconstruction. Finally, after the fault repair time of the branch, the original system topology is restored and normal power supply is restored. Based on the above assumptions, the interruption experienced by the upstream load of the faulty branch and the downstream load that can be restored through network reconstruction after the fault is a switch action interruption, that is, the power outage time is The loads downstream of the branch that cannot be restored through network reconstruction experience a switch action-restore interruption, that is, the power outage time is The reliability index is approximately calculated by ignoring the line loss and assuming that the branch flow during normal operation is the downstream load. Equations (39) to (43) calculate the reliability index EENS t ; Equations (44) to (48) calculate the reliability index SAIDI t ; Equations (49) to (50) calculate the reliability index SAIFI t ; Equations (51) to (53) constrain the reliability indicators of each stage.

5. The method for planning the expansion of a distribution system unit cluster grid based on reliability explicit constraint matrix reduction according to claim 1, characterized in that: According to the obtained system data and the determined related parameters, the constructed MILP model is solved to obtain the equipment planning results of the planned area at each stage. The specific steps include: According to the obtained system data and the determined related parameters, the constructed MILP model is solved to obtain and output the equipment planning results of the area to be planned at each stage.

6. A distribution system unit cluster grid expansion planning device based on reliability explicit constraint matrix reduction, characterized in that: include: Acquisition module, to obtain system data of the area to be planned and determine relevant parameters; The model building module builds a mixed integer linear programming MILP model for multi-interconnection distribution network expansion planning based on explicit reliability constraints that can reduce the matrix size. The model includes the objective function calculation expression and various constraints. The output module solves the constructed MILP model according to the obtained system data and the determined related parameters to obtain the equipment planning results of the area to be planned at each stage.

7. The device for planning the expansion of a power distribution system unit cluster grid based on reliability explicit constraint matrix reduction according to claim 6, characterized in that: The constraints in the model building module include: ① Equipment construction and usage constraints ② Power flow constraints taking into account network reconstruction under normal and fault conditions ③ Network topology constraints ④ Virtual power flow constraints ⑤ Calculation and constraints of reliability indicators.

8. A computer-readable storage medium having computer instructions stored thereon, characterized in that: When the computer instructions are executed, the steps of a method for planning distribution system unit cluster grid expansion based on reliability explicit constraint matrix reduction as described in any one of claims 1 to 5 are executed.

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