CN113364054B - Power distribution network interval network reconstruction model optimization method based on second order cone relaxation method - Google Patents
Power distribution network interval network reconstruction model optimization method based on second order cone relaxation method Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
- H02J3/48—Controlling the sharing of the in-phase component
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
- H02J3/50—Controlling the sharing of the out-of-phase component
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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Abstract
The invention provides a power distribution network interval network reconstruction model optimization method based on a second order cone relaxation method, and belongs to the field of power distribution network interval network reconstruction of a power system. Firstly, establishing a deterministic network reconstruction model of a power distribution network, which is formed by an objective function and constraint conditions, then establishing state variables in the model as interval numbers, and converting the deterministic network reconstruction model into an interval optimization model; and converting the interval optimization model into a deterministic optimization model through Relative Distance Measure (RDM) interval operation, and solving the model by using a mixed integer second order cone relaxation method to obtain a reconstruction result of the power distribution network interval network. The optimization method can avoid the statistical requirement and subjective assumption distribution of a large amount of historical data of a probability method and a fuzzy number theory method, can comprehensively reflect the real condition of the operation of the power distribution network, and has higher application value.
Description
Technical Field
The invention belongs to the field of power system distribution network interval network reconstruction, and particularly relates to a power system distribution network interval network reconstruction model optimization method based on a second order cone relaxation method.
Background
The network reconstruction of the power distribution network enables the power distribution network to operate in a more reliable and economical mode by changing the topology structure of the power distribution network, so that the network reconstruction has very important significance for the stable operation of a power system. Because the network reconstruction model of the power distribution network belongs to the mixed integer nonlinear programming problem, the solution is very difficult, and the solution process is easy to fail. The optimization of the existing power distribution network interval network reconstruction model has the following defects:
(1) When the statistical information of the power distribution network is insufficient or unavailable, a probability method and a fuzzy number theory method cannot be adopted.
(2) The existing optimization method can only solve the deterministic or worst situation, so that the optimization result lacks of the injection of uncertainty of the power distribution network to be comprehensively considered.
In contrast, the interval optimization mathematical theory can comprehensively overcome the two defects, and is reflected in:
(1) The interval optimization mathematical theory does not need to know the statistical information of the power distribution network data, but only focuses on the feasible range of the uncertainty of the power distribution network. It can be seen that it is much easier to find a viable range for a distribution network for which data statistics need to be grasped. This is one of the advantages of interval optimization mathematical theory.
(2) Interval optimization mathematical theory focuses not only on a specific scenario, but its interval may be able to characterize all cases of the system.
However, at present, no power distribution network interval network reconstruction model optimization technology utilizing an interval optimization mathematical theory exists, so that the reliability of power distribution network uncertainty reconstruction needs to be improved, and an interval optimization method of the power distribution network reconstruction model based on the interval optimization mathematical theory is researched.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a power distribution network interval network reconstruction model optimization method based on a second-order cone relaxation method. The optimization method provided by the invention can avoid the statistical requirement and subjective assumption distribution of a large amount of historical data of a probability method and a fuzzy number theory method, can comprehensively reflect the real condition of the operation of the power distribution network, and has higher application value.
The invention provides a power distribution network interval network reconstruction model optimization method based on a second order cone relaxation method, which is characterized in that the method firstly establishes a power distribution network deterministic network reconstruction model formed by an objective function and constraint conditions, then establishes state variables in the model as interval numbers, and converts the deterministic network reconstruction model into an interval optimization model; and converting the interval optimization model into a deterministic optimization model through relative distance measure RDM interval operation, and solving the model by using a mixed integer second order cone relaxation method to obtain a reconstruction result of the power distribution network interval network. The method comprises the following steps:
1) Establishing a deterministic network reconstruction model of the power distribution network, wherein the model consists of an objective function and constraint conditions; the method comprises the following specific steps:
1-1) modeling an objective function, expressed as follows:
Wherein, The resistance of the s phase in the branch ij; /(I)For the current square of s phase in branch ij, s= { a, b, c };
1-2) determining constraint conditions of the model, wherein the constraint conditions are as follows:
Switching state constraint of the power distribution network branch circuit;
xij∈{0,1} (2)
Wherein x ij is the switching state of the branch ij, and 1 represents the input of the branch ij;
a power distribution network Distflow tide constraint;
Wherein, Active power and reactive power of s phase in branch ij are respectively; /(I)The active injection power and the reactive injection power of the s phase at the node j are respectively; /(I)The current amplitude at branch ij for s-phase; /(I)Reactance at branch ij for s-phase; v i s,The square of the voltage amplitude of s phase at node i, j, s= { a, b, c }; k (j) is a set of nodes connected to node j;
Radial operation condition constraint of the power distribution network;
Wherein n is the total number of nodes of the power distribution network; n root is the number of power generation nodes; k (i) is a set of nodes connected to node i; constraint of safe operation conditions of the power distribution network;
Wherein, The upper limit of the current amplitude of the branch ij is s phase; v l,Vu is the lower limit and the upper limit of the square of the node voltage amplitude respectively;
2) State variables in the model of step 1) The corresponding interval numbers are respectively established as shown in the formula (7):
Wherein, The lower limit and the upper limit of the current amplitude of the s phase in the branch ij are respectively set; v i s,The lower limit and the upper limit of the square of the voltage amplitude of the s phase at the node i are respectively set; /(I)The lower limit and the upper limit of the active power of the s phase in the branch ij are respectively set; the lower limit and the upper limit of the reactive power of the s phase in the branch ij are respectively set; /(I) The lower limit and the upper limit of the active injection power of the s phase at the node j are respectively; /(I)The lower limit and the upper limit of the reactive power injection of the s phase at the node j are respectively s= { a, b, c };
The deterministic network reconstruction model established in step 1) is converted into the following interval optimization model:
s.t.xij∈{0,1} (9)
3) Converting the interval optimization model in the step 2) into a deterministic optimization model through RDM interval operation, wherein the expression is as follows:
s.t.xij∈{0,1} (15)
Wherein, () RDM represents the RDM form of the corresponding parameter; is an RDM variable corresponding to the current magnitude of the s-phase in branch ij; /(I) Is an RDM variable corresponding to the current magnitude of the s-phase in branch ij; /(I)Is an RDM variable corresponding to the voltage magnitude of the s-phase at node i; /(I)Injecting reactive power RDM variables at node j for the corresponding s-phase; /(I)Is the RDM variable corresponding to the active power of the s phase in the branch ij; /(I)For RDM variable corresponding to the reactive power of s phase at branch ij, s= { a, b, c };
4) Converting the deterministic optimization model of the step 3); comprising the following steps:
the convex relaxation of the nonlinear term is performed on the last three terms in the formula (20) by using a large M method:
Wherein M is a positive number;
The formulas (16) and (17) are rewritten as:
Relaxing the voltage equation (28) by a large M method;
when any branch is open, the voltage constraint equation (28) is rewritten as:
Wherein, subscripts i and j are the head end node and the tail end node of the disconnected branch;
after transformation by RDM interval calculation, the lower bound function and the upper bound function of the objective function formula (14) are respectively shown as follows:
5) Solving the model converted in the step 4) by using a mixed integer second order cone relaxation method MISOCP; the method comprises the following specific steps:
5-1) pairs by RDM calculation Performing relaxation conversion, and the constraint equation after conversion is as follows:
Wherein b is the number of branches;
5-2) solving by using MISOCP method, the specific steps are as follows:
5-2-1) ream Step 3) conversion of the objective function of the optimization model to
5-2-2) Solving an objective functionSimultaneously satisfying the constraint formulas (15), (22) - (25), (26) - (27),
(29) (31) Obtaining the current switching state of the power distribution network branch circuit
5-2-3) According to the current switching state of the distribution network branchAnd obtaining the interval form/>, of the current network loss through RDM interval calculationAnd get the/>, of each closed branchAndUpdating the/>, of each disconnected branchAndWhereinIs the maximum allowed current of s phase in branch ij;
5-2-4) the branches obtained in step 5-2-3) Substituting the constraint type (20);
5-2-5) solving the optimization model of the step 3) to obtain updated switching states of the power distribution network branches By RDM interval power flow calculation, the interval form/>, of updated network loss is given
5-2-6) Making a decision on the results of steps 5-2-3) and 5-2-5):
If it is OutputAs the optimal result of switching the branch circuit of the power distribution network; if mid [ loss 2]<mid[loss1 ], outputAs the optimal result of switching the branch circuit of the power distribution network; if mid [ loss 2]>mid[loss1 ], outputAs the optimal result of switching the branch circuit of the power distribution network;
and (5) finishing the reconstruction and optimization of the power distribution network interval network.
The power distribution network interval network reconstruction model optimization method based on the second order cone relaxation method provided by the invention has the advantages that:
1. According to theorem of upper and lower function boundary optimization of interval optimization, the invention provides a distribution network RDM interval reconstruction model, and the model can comprehensively consider fluctuation of distribution network interval injection power and new energy.
2. The invention provides a method for solving a reconstruction model of a power distribution network interval by using an RDM-MISOCP method. The method comprehensively considers the optimization results of the upper and lower boundary functions of the network loss interval of the power distribution network, and can ensure the optimality of the output result according to the comparison rule of the interval number.
3. The interval method provided by the invention can avoid the statistical requirement and subjective assumption distribution of a large amount of historical data of a probability method and a fuzzy number theory method, can comprehensively reflect the actual condition of the operation of the power distribution network, and has higher application value.
Detailed Description
The invention provides a power distribution network interval network reconstruction model optimization method based on a second order cone relaxation method, which comprises the steps of firstly establishing a traditional deterministic network reconstruction model of a power distribution network, which is composed of an objective function and constraint conditions, then establishing state variables in the model as interval numbers, and converting the traditional deterministic network reconstruction model into an interval optimization model; and converting the interval optimization model into a deterministic optimization model through relative distance measure RDM interval operation, and solving the model by using a mixed integer second order cone relaxation method to obtain a reconstruction result of the power distribution network interval network. The method comprises the following steps:
1) And (3) establishing a traditional deterministic network reconstruction model of the power distribution network, wherein the model is composed of an objective function and constraint conditions. The method comprises the following specific steps:
1-1) establishing an objective function of a model;
the objective function reconstructed by the power distribution network is the minimum network loss, and under the condition of neglecting three-phase coupling, the expression of the objective function is as follows:
Wherein, The resistance of the s phase in the branch ij; /(I)The current square of s phase in branch ij, s= { a, b, c }.
1-2) Determining constraint conditions of the model, wherein the constraint conditions are as follows:
Switching state constraint of the power distribution network branch circuit;
xij∈{0,1} (2)
Wherein x ij is the switching state of the branch ij, and 1 represents the input of the branch ij.
A power distribution network Distflow tide constraint;
Wherein, Active power and reactive power of s phase in branch ij are respectively; /(I)The active injection power and the reactive injection power of the s phase at the node j are respectively; /(I)The current amplitude at branch ij for s-phase; /(I)Reactance at branch ij for s-phase; v i s,The square of the voltage amplitude of s phase at node i, j, s= { a, b, c }; k (j) is the set of nodes connected to node j.
Radial operation condition constraint of the power distribution network;
Wherein n is the total number of nodes of the power distribution network; n root is the number of power generation nodes; k (i) is a set of nodes connected to node i.
Constraint of safe operation conditions of the power distribution network;
Wherein, The upper limit of the current amplitude of the branch ij is s phase; v l,Vu is the lower and upper limits of the square of the node voltage amplitude, respectively.
2) Due to the uncertainty factors existing in the load and the generator of the power distribution network, the state variables in the model of the step 1) are determinedThe corresponding interval numbers are respectively established as shown in the formula (7):
Wherein, The lower limit and the upper limit of the current amplitude of the s phase in the branch ij are respectively set; v i s,The lower limit and the upper limit of the square of the voltage amplitude of the s phase at the node i are respectively set; /(I)The lower limit and the upper limit of the active power of the s phase in the branch ij are respectively set; the lower limit and the upper limit of the reactive power of the s phase in the branch ij are respectively set; /(I) The lower limit and the upper limit of the active injection power of the s phase at the node j are respectively; /(I)The lower and upper limits of the reactive injection power of s phase at node j, s= { a, b, c }, respectively.
The traditional deterministic network reconstruction model established in step 1) is converted into the following interval optimization model:
s.t.xij∈{0,1} (9)
3) Converting the interval optimization model in the step 2) into a deterministic optimization model through RDM interval operation, wherein the expression is as follows:
s.t.xij∈{0,1} (15)
Wherein, () RDM represents the RDM form of the corresponding parameter; is an RDM variable corresponding to the current magnitude of the s-phase in branch ij; /(I) Is an RDM variable corresponding to the current magnitude of the s-phase in branch ij; /(I)Is an RDM variable corresponding to the voltage magnitude of the s-phase at node i; /(I)Injecting reactive power RDM variables at node j for the corresponding s-phase; /(I)Is the RDM variable corresponding to the active power of the s phase in the branch ij; /(I)For RDM variable corresponding to the reactive power of s phase in branch ij, s= { a, b, c }.
4) Since the model in step 3) is a nonlinear programming model, solving is difficult. The present invention thus utilizes a linear relaxation approach to solve this model. The latter three terms in the non-convex constraint type (20) containing the switch variable in the model are subjected to convex relaxation of the nonlinear term by using a large M method:
wherein M is a relatively large positive value, so that the value should be reasonably selected in order to avoid the influence on the calculation efficiency of the optimization algorithm due to the expansion of the optimizing space. The M value of this example was 10.
After the nonlinear term is relaxed, the power flow constraint conditions (16) and (17) can be rewritten as:
after processing, the voltage constraint becomes an inequality constraint because the constraints of the head-end voltage and the tail-end voltage no longer exist when a certain branch is disconnected. Therefore, relaxation of the voltage equation by the large M method is required.
When one leg is open, the voltage constraint equation (28) can be rewritten as:
Wherein, subscripts i and j are the head end node and the tail end node of the disconnected branch;
After transformation by RDM interval calculation, the lower bound function and the upper bound function of the objective function formula (14) are as follows:
Thus, finding the optimal solution of the original object becomes finding the appropriate one The lower bound function f low and the upper bound function f up are simultaneously optimized. From the two functional expressions of equation (30), the lower bound function f low contains the upper bound function f up, so we can actually find the optimal solution for f up. But since the objective function of f up contains a nonlinear termAnd the method is not easy to directly solve. To this end, a mixed integer second order cone relaxation Method (MISOCP) is presented herein for solving.
5) Solving the model converted in the step 4) by using a mixed integer second order cone relaxation method MISOCP; the method comprises the following specific steps:
5-1) first pair by RDM calculation Performing relaxation conversion, and the constraint equation after conversion is as follows:
Wherein n is the number of nodes and b is the number of branches.
5-2) Solving by using MISOCP method, the specific steps are as follows:
5-2-1) ream Step 3) conversion of the objective function of the optimization model to
5-2-2) Solving an objective functionSimultaneously satisfying constraint (14), (22) - (25), (26) - (27), (29), (31) to obtain the current switching state/>, of the power distribution network branch
5-2-3) According to the current switching state of the distribution network branchAnd obtaining the interval form/>, of the current network loss through RDM interval calculationAnd get the/>, of each closed branchAnd
Updating for each disconnected branchAndWhereinIs the maximum allowed current of s-phase in branch ij.
5-2-4) The method obtained in step 5-2-3)Substituting constraint (20).
5-2-5) Solving the optimization model of the step 3), and outputting updated switching states of the power distribution network branchesBy RDM interval power flow calculation, the interval form/>, of updated network loss is given
5-2-6) Making a decision on the results of steps 5-2-3) and 5-2-5):
If it is OutputAs the optimal result of switching the branch circuit of the power distribution network; if mid [ loss 2]<mid[loss1 ], outputAs the optimal result of switching the branch circuit of the power distribution network; if mid [ loss 2]>mid[loss1 ], outputAnd taking the result as an optimal switching result of the power distribution network branch circuit.
And (5) finishing the reconstruction and optimization of the power distribution network interval network.
Claims (1)
1. The method is characterized in that firstly, a deterministic network reconstruction model of the power distribution network, which is composed of an objective function and constraint conditions, is established, then state variables in the model are established as interval numbers, and the deterministic network reconstruction model is converted into an interval optimization model; converting the interval optimization model into a deterministic optimization model through relative distance measure RDM interval operation, and solving the model by using a mixed integer second order cone relaxation method to obtain a reconstruction result of the power distribution network interval network;
the method comprises the following steps:
1) Establishing a deterministic network reconstruction model of the power distribution network, wherein the model consists of an objective function and constraint conditions; the method comprises the following specific steps:
1-1) modeling an objective function, expressed as follows:
Wherein, The resistance of the s phase in the branch ij; /(I)For the current square of s phase in branch ij, s= { a, b, c };
1-2) determining constraint conditions of the model, wherein the constraint conditions are as follows:
Switching state constraint of the power distribution network branch circuit;
xij∈{0,1} (2)
Wherein x ij is the switching state of the branch ij, and 1 represents the input of the branch ij;
a power distribution network Distflow tide constraint;
Wherein, Active power and reactive power of s phase in branch ij are respectively; /(I)The active injection power and the reactive injection power of the s phase at the node j are respectively; /(I)The current amplitude at branch ij for s-phase; /(I)Reactance at branch ij for s-phase; The square of the voltage amplitude of s phase at node i, j, s= { a, b, c }; k (j) is a set of nodes connected to node j;
Radial operation condition constraint of the power distribution network;
Wherein n is the total number of nodes of the power distribution network; n root is the number of power generation nodes; k (i) is a set of nodes connected to node i;
constraint of safe operation conditions of the power distribution network;
Wherein, The upper limit of the current amplitude of the branch ij is s phase; v l,Vu is the lower limit and the upper limit of the square of the node voltage amplitude respectively;
2) State variables in the model of step 1) The corresponding interval numbers are respectively established as shown in the formula (7):
Wherein, The lower limit and the upper limit of the current amplitude of the s phase in the branch ij are respectively set; /(I)The lower limit and the upper limit of the square of the voltage amplitude of the s phase at the node i are respectively set; /(I)The lower limit and the upper limit of the active power of the s phase in the branch ij are respectively set; /(I)The lower limit and the upper limit of the reactive power of the s phase in the branch ij are respectively set; /(I)The lower limit and the upper limit of the active injection power of the s phase at the node j are respectively; /(I)The lower limit and the upper limit of the reactive power injection of the s phase at the node j are respectively s= { a, b, c };
The deterministic network reconstruction model established in step 1) is converted into the following interval optimization model:
s.t.xij∈{0,1} (9)
3) Converting the interval optimization model in the step 2) into a deterministic optimization model through RDM interval operation, wherein the expression is as follows:
s.t.xij∈{0,1} (15)
Wherein, () RDM represents the RDM form of the corresponding parameter; is an RDM variable corresponding to the current magnitude of the s-phase in branch ij; is an RDM variable corresponding to the current magnitude of the s-phase in branch ij; /(I) Is an RDM variable corresponding to the voltage magnitude of the s-phase at node i; /(I)Injecting reactive power RDM variables at node j for the corresponding s-phase; /(I)Is the RDM variable corresponding to the active power of the s phase in the branch ij; /(I)For RDM variable corresponding to the reactive power of s phase at branch ij, s= { a, b, c };
4) Converting the deterministic optimization model of the step 3); comprising the following steps:
the convex relaxation of the nonlinear term is performed on the last three terms in the formula (20) by using a large M method:
Wherein M is a positive number;
The formulas (16) and (17) are rewritten as:
Relaxing the voltage equation (28) by a large M method;
when any branch is open, the voltage constraint equation (28) is rewritten as:
Wherein, subscripts i and j are the head end node and the tail end node of the disconnected branch;
after transformation by RDM interval calculation, the lower bound function and the upper bound function of the objective function formula (14) are respectively shown as follows:
5) Solving the model converted in the step 4) by using a mixed integer second order cone relaxation method MISOCP; the method comprises the following specific steps:
5-1) pairs by RDM calculation Performing relaxation conversion, and the constraint equation after conversion is as follows:
Wherein b is the number of branches;
5-2) solving by using MISOCP method, the specific steps are as follows:
5-2-1) ream Step 3) conversion of the objective function of the optimization model to
5-2-2) Solving an objective functionSimultaneously satisfying constraint (15), (22) - (25), (26) - (27), (29), (31) to obtain the current switching state/>, of the power distribution network branch
5-2-3) According to the current switching state of the distribution network branchAnd obtaining the interval form/>, of the current network loss through RDM interval calculationAnd get the/>, of each closed branchAndUpdating the/>, of each disconnected branchAndWhereinIs the maximum allowed current of s phase in branch ij;
5-2-4) the branches obtained in step 5-2-3) Substituting the constraint type (20);
5-2-5) solving the optimization model of the step 3) to obtain updated switching states of the power distribution network branches By RDM interval power flow calculation, the interval form/>, of updated network loss is given
5-2-6) Making a decision on the results of steps 5-2-3) and 5-2-5):
If it is OutputAs the optimal result of switching the branch circuit of the power distribution network; if mid [ loss 2]<mid[loss1 ], outputAs the optimal result of switching the branch circuit of the power distribution network; if mid [ loss 2]>mid[loss1 ], outputAs the optimal result of switching the branch circuit of the power distribution network;
and (5) finishing the reconstruction and optimization of the power distribution network interval network.
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| A Fault Recovery Strategy of Distribution Network Based on Mixed-integer Second-order Cone Programming;C. Ma等;2020 5th Asia Conference on Power and Electrical Engineering (ACPEE);20200708;全文 * |
| 二阶锥松弛在配电网最优潮流计算中的应用;陈怀毅;胡英坤;杨毅;范舟;;电气应用;20200115(01);全文 * |
| 基于 DistFlow 的含分布式电源配电网优化重构模型;姚 艳，许家玉，崔勤越;能源互联网;20200131(第1期);全文 * |
| 基于DistFlow的含分布式电源配电网优化重构模型;姚艳;许家玉;崔勤越;;能源工程;20200220(01);全文 * |
| 基于二阶锥松弛和Big-M法的配电网分布式电源优化配置;刘健辰;刘山林;;电网技术;20180504(08);全文 * |
| 基于二阶锥规划的有源配电网SNOP电压无功时序控制方法;赵金利;李雨薇;李鹏;冀浩然;王成山;吴建中;;高电压技术;20160718(07);全文 * |
| 负荷变化不确定性的配电网络重构 区间评价方法;王成山, 王守相;中 国 电 机 工 程 学 报;20020531;第22卷(第5期);全文 * |
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