CN111446713A - Power distribution network reconstruction model optimization method and power distribution network reconstruction method - Google Patents
Power distribution network reconstruction model optimization method and power distribution network reconstruction method Download PDFInfo
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Abstract
The invention discloses a power distribution network reconstruction model optimization method, which comprises a power distribution network reconstruction model preliminary objective function; constructing a preliminary constraint condition; optimizing the preliminary constraint condition to obtain a constraint condition; optimizing the preliminary objective function of the power distribution network reconstruction model to obtain a power distribution network reconstruction model objective function; and the power distribution network reconstruction model objective function and the constraint condition form a final power distribution network reconstruction model. The invention also provides a power distribution network reconstruction method comprising the power distribution network reconstruction model optimization method. The method provided by the invention provides a preventive reconstruction method adaptive to online calculation, fully considers the characteristic that the active power and the reactive power of a power distribution network are not decoupled, realizes voltage warning control of the power distribution network through topology structure optimization of the power distribution network so as to improve the static voltage stability margin of the power distribution network in real time, reduces the operation risk of the power distribution network, and has higher voltage safety for the comprehensive load considering the static voltage characteristic of the load under different load levels than before reconstruction.
Description
Technical Field
The invention relates to a power distribution network safe operation and prevention control technology, in particular to a power distribution network reconstruction model optimization method and a power distribution network reconstruction method.
Background
With the development of economic technology and the improvement of living standard of people, electric energy becomes essential secondary energy in production and life of people, and brings endless convenience to production and life of people. Therefore, stable and reliable operation of the power system becomes one of the most important tasks of the power system.
A small number of normally open contact switches and a large number of normally closed section switches exist in the power distribution network, and the network reconstruction adjusts the operation mode by switching the open-close states of the two types of switches, so that the optimal control, the warning control and the like of the power distribution network can be realized. In recent years, the permeability of distributed power supplies and electric automobiles is continuously improved, and the problem of voltage stability of a power distribution network is more prominent. However, the reactive output of the reactive power compensation devices such as the parallel capacitors decreases with the decrease of the voltage amplitude, which further causes the voltage to continue to drop; the traditional voltage regulation means such as a parallel capacitor, an on-load voltage regulator and the like have the defects of high investment cost, high coordination difficulty and the like. When the power distribution network has no fault and the node-free voltage exceeds the limit, the reconstruction taking the economy as the target can realize the economic operation of the power distribution network and improve the voltage distribution; when the distribution network has no fault but node voltage is out of limit, preventive reconstruction with safety as a target is used as a warning control means, extra investment is not needed, the static voltage stability margin of the distribution network can be effectively improved, and the method has great significance for reducing the operation risk of the distribution network.
At present, some documents propose reconstruction models for solving the problem of voltage stability of the power distribution network, but the proposed reconstruction models are greatly influenced by the accuracy of load prediction or are conservative for ensuring the voltage safety of the power distribution network in a long-time scale. On the other hand, the switch decision variables are more in the reconstruction process of the actual power distribution network, and a strict mathematical model belongs to nonlinear non-convex programming and is a nondeterministic polynomial problem. The problems of power distribution network reconstruction, fault location and the like are solved by the multi-application group intelligent optimization algorithm at present, but a large number of infeasible solutions which do not meet network topology constraints are easily generated in the optimization process, the optimization efficiency is influenced, the algorithm randomness is strong, the stable optimization performance and the constant optimization time cannot be guaranteed, and the requirements of real-time online calculation cannot be met.
The perception of the operation state of the power grid is the basis for evaluating the static voltage stability margin of the power distribution network and realizing the controllable operation risk of the power distribution network through reconstruction. Currently, research results for evaluating the static voltage stability margin of a power distribution network often ignore the influence of active power on node voltage.
It should be noted that the resistance value of the transmission line is much smaller than the reactance value, and the voltage distribution is mainly determined by the reactive power; however, for a power distribution network with non-decoupled active and reactive power, both active power and reactive power can affect the node voltage, and particularly for medium and low voltage distribution lines with resistance values close to or larger than reactance values (cable lines), the coupling relation is more obvious, and the influence of the active power on the voltage cannot be ignored. In addition, the node static voltage stability is greatly influenced by load characteristics, the existing related documents take the load static voltage characteristics into account less, and the accuracy of the static voltage stability margin evaluation of the power distribution network is difficult to guarantee.
Disclosure of Invention
One of the purposes of the invention is to provide a power distribution network reconstruction model optimization method which fully considers the active and reactive decoupling characteristics of a power distribution network, improves the static voltage stability margin of the power distribution network and takes the static voltage characteristics of a load into consideration.
The invention also aims to provide a power distribution network reconstruction method comprising the power distribution network reconstruction model optimization method.
The power distribution network reconstruction model optimization method provided by the invention comprises the following steps:
s1, constructing a power distribution network reconstruction model preliminary objective function taking the minimization of the static voltage stability margin index of the power distribution network as an objective function;
s2, constructing a preliminary constraint condition of a preliminary objective function of a power distribution network reconstruction model;
s3, optimizing the preliminary constraint condition constructed in the step S2 to obtain a constraint condition;
s4, optimizing the preliminary objective function of the power distribution network reconstruction model constructed in the step S1 to obtain a power distribution network reconstruction model objective function;
and S5, forming a final power distribution network reconstruction model by the power distribution network reconstruction model objective function obtained after the optimization in the step S4 and the constraint condition obtained after the optimization in the step S3.
Step S1, constructing a preliminary objective function of the power distribution network reconstruction model with the power distribution network static voltage stability margin index minimized as an objective function, specifically, using the following equation as the preliminary objective function:
min SVSM
in the formula, SVSM is the static voltage stability margin index of the power distribution network, and
i is a set of all nodes except the system master station node; viIs the voltage vector of node i; pi+1The active power of the branch (i, i +1) flowing into the node i +1 is input into the node i; qi+1The idle work of the branch (i, i +1) of the node i flowing into the node i + 1; r isi,i+1Is the real part of the impedance of branch (i, i + 1); x is the number ofi,i+1Is the imaginary impedance of branch (i, i + 1).
Step S2, where the preliminary constraint condition for constructing the preliminary objective function of the power distribution network reconstruction model specifically adopts the following equation as the preliminary constraint condition:
f(x,SGL)＝0
g(x,SGL)≤0
in the formula
Switching a state variable for branch k, and
it is indicated that the branch is closed,
indicating a branch disconnection; phi is aLIs the set of all branches; n isbThe total number of nodes of the power distribution network; n issThe number of the root nodes of the power distribution network; x is a running state variable of the power distribution network; sGLInjecting power for the node; f (x, S)GL) 0 is the flow constraint of the whole power grid; g (x, S)GL) And the operation constraint of the whole power grid is less than or equal to 0.
Optimizing the preliminary constraint condition constructed in the step S2 in the step S3 to obtain a constraint condition, specifically, optimizing by using the following steps:
A. the open state of the switch is recorded as '1', the closed state of the switch is recorded as '0', and then the state variable x of the switch in the ring in the power gridiSatisfaction formula
B. Define auxiliary variable κ (i, j) ═ x (i) · x (j)
Relaxing the discrete variables in the step A into continuous variables, and constructing a quadratic equality constraint model [ x (i) ± x (j)]21, thereby converting to a complement relationship of 0 ≦ x (i) ⊥ x (j) ≧ 0, wherein ⊥ is vertical complement;
C. according to the results of step A and step B, the initial constraint conditions
Conversion to equivalence
D. And (3) setting that all branches in the network have no mutual inductance, and expressing a node admittance matrix Y of the system as follows:
wherein A is a node incidence matrix; e is an identity matrix;
is a diagonal matrix of switching variables; y isbIs an original admittance matrix and simultaneously is a diagonal matrix, and the diagonal elements are corresponding branch admittance yk；
E. According to the power balance condition, f (x, S) in the preliminary constraint condition is divided intoGL) Conversion to f (x, S) 0GL,Y)＝0。
Step S4, optimizing the preliminary objective function of the power distribution network reconstruction model constructed in step S1 to obtain a power distribution network reconstruction model objective function, specifically, optimizing by using the following steps:
a. introducing new auxiliary constraints
Smoothing the power distribution network reconstruction model:
wherein M is a set punishment parameter and must be large enough to ensure the punishment effect of the new auxiliary constraint;
a vector reflecting the relation between any two switch variables in the basic loop;
b. and (3) fusing inequality constraints into the objective function by adopting a penalty function method, thereby obtaining a power distribution network reconstruction model objective function shown by the following formula:
in the formula, SVSM is a static voltage stability margin index of the power distribution network; skIs the complex power flowing into branch k; skmaxMaximum allowed for branch k; stThe current complex power value of the transformer t is obtained; stmaxIs the maximum load capacity of the transformer t; viIs the voltage at node i; vminIs the lower limit of the node voltage amplitude; vmaxIs the upper limit of the node voltage amplitude;
is taken as the value of the branch switch state, and
l P(s) is the branch switch number set of the s-th basic loop, L P is the number of basic loops, M1～M6In order to set the first punishment parameter to the sixth punishment parameter, and the first punishment parameter to the sixth punishment parameter must be large enough to ensure the constraint effect, the method of the invention takes 100.
The invention also discloses a power distribution network reconstruction method comprising the power distribution network reconstruction model optimization method, and the method further comprises the following steps:
and S6, solving the final power distribution network reconstruction model formed in the step S5, and reconstructing the power grid according to the obtained solving result.
According to the power distribution network reconstruction model optimization method and the power distribution network reconstruction method, the power distribution network static voltage stability margin is taken as a core index, so that the voltage stability of the method is better, the reconstructed network has higher voltage safety than the network before reconstruction under different load levels for the comprehensive load considering the load static voltage characteristics, and the reliability, the practicability and the accuracy are also considered simultaneously.
Drawings
FIG. 1 is a schematic method flow diagram of the optimization method of the present invention.
Fig. 2 is a schematic flow chart of the reconstruction method of the present invention.
Fig. 3 is a single line schematic diagram of a 69-node actual power distribution system in accordance with an embodiment of the method of the present invention.
Fig. 4 shows the distribution of the optimization results of the harmony algorithm of the embodiment of the method of the present invention.
FIG. 5 is a schematic diagram of the relationship between VSI-min and load factor according to an embodiment of the method of the present invention.
FIG. 6 is a diagram illustrating the relationship between V-min and load factor according to an embodiment of the method of the present invention.
FIG. 7 is a schematic diagram of minimum node voltage distributions for each time section before and after control by the method of the present invention.
Detailed Description
According to the invention, the voltage warning control of the power distribution network is realized through the optimization of the topological structure of the power distribution network, so that the static voltage stability margin of the power distribution network is improved in real time, and the operation risk of the power distribution network is reduced. Therefore, the technical scheme adopted by the invention is that the distribution network online preventive reconstruction method for improving the static voltage stability margin comprises the following steps: the static voltage stability margin evaluation index considering the decoupling characteristic of the active power and the reactive power of the power distribution network is established, and the influence of the active power and the reactive power on the voltage can be effectively reflected. And constructing a distribution network reconstruction model by taking the maximum static voltage stability margin of the distribution network as a target and fully considering the load static voltage characteristic. The method comprises the steps of utilizing complementary constraint to relax discrete variables into continuous variables, constructing a reconstruction complementary constraint model, replacing complementary constraint conditions by introducing an auxiliary penalty function, adding inequality constraint into an objective function through a boundary-crossing penalty function, and establishing a distribution network reconstruction complementary constraint smooth model, is convenient to solve by using a mature nonlinear programming method, avoids directly solving the discrete variables, can greatly reduce the solving difficulty and the solving time, has good numerical stability, and is suitable for on-line calculation.
FIG. 1 is a schematic flow chart of the method of the present invention: the power distribution network reconstruction model optimization method provided by the invention comprises the following steps:
s1, constructing a power distribution network reconstruction model preliminary objective function taking the minimization of the static voltage stability margin index of the power distribution network as an objective function; specifically, the following formula is adopted as a preliminary objective function:
min SVSM
in the formula, SVSM is the static voltage stability margin index of the power distribution network, and
i is a set of all nodes except the system master station node; viIs the voltage vector of node i; pi+1The active power of the branch (i, i +1) flowing into the node i +1 is input into the node i; qi+1The idle work of the branch (i, i +1) of the node i flowing into the node i + 1; r isi,i+1Is the real part of the impedance of branch (i, i + 1); x is the number ofi,i+1Is the imaginary impedance of branch (i, i + 1);
s2, constructing a preliminary constraint condition of a preliminary objective function of a power distribution network reconstruction model; specifically, the following formula is adopted as a preliminary constraint condition:
f(x,SGL)＝0
g(x,SGL)≤0
in the formula
Switching a state variable for branch k, and
it is indicated that the branch is closed,
indicating a branch disconnection; phi is aLIs the set of all branches; n isbThe total number of nodes of the power distribution network; n issThe number of the root nodes of the power distribution network; x is a running state variable of the power distribution network; sGLInjecting power for the node;f(x,SGL) 0 is the flow constraint of the whole power grid; g (x, S)GL) The operation constraint of the whole power grid is less than or equal to 0;
in order to protect and set and reduce short-circuit current, the power distribution network is generally required to run radially, namely, no annular topological structure exists in the network, so that constraint conditions exist
f(x,SGL) 0 is the power flow constraint of the power grid; g (x, S)GL) The operation constraint of the power grid is less than or equal to 0;
s3, optimizing the preliminary constraint condition constructed in the step S2 to obtain a constraint condition; specifically, the method comprises the following steps:
A. because the values of the state variables of the branches in the ring are not independent but have relevance, if the open state of the switch is recorded as '1' and the closed state of the switch is recorded as '0', the state variable x of the switch in the ring is in the power gridiSatisfaction formula
B. Define auxiliary variable κ (i, j) ═ x (i) · x (j)
Relaxing the discrete variable in the step A into a continuous variable by using the characteristic that the switch state x (i) in the ring can only take 0 or 1 and has strong correlation, and constructing a quadratic equality constraint model [ x (i) +/-x (j)]21 is ═ 1; final obtainable x (i)2+x(j)2X 2x (i) x (j) 1, and x (i) x (j) 0, it can be converted into a complementary relationship 0 ≦ x (i) ⊥ x (j) ≧ 0, wherein ⊥ is vertical complementary;
C. according to the results of step A and step B, the initial constraint conditions
Conversion to equivalence
Wherein the first stepOne equation ensures that at most one switch in the loop takes a value of 1, and the second equation ensures that at least one switch in the loop takes a value of 1;
D. and setting that all branches in the network have no mutual inductance, and expressing a node admittance matrix Y when the Newton-Raphson method calculates the power flow as follows:
wherein A is a node incidence matrix; e is an identity matrix;
is a diagonal matrix of switching variables; y isbIs an original admittance matrix and simultaneously is a diagonal matrix, and the diagonal elements are corresponding branch admittance yk；
E. According to the power balance condition, f (x, S) in the preliminary constraint condition is divided intoGL) Conversion to f (x, S) 0GLY) is 0; namely, the active and reactive network losses of the system are not only functions of the node voltage amplitude and angle, but also related to the node admittance matrix;
and (3) integrating the constraint conditions into a model, and assuming that each branch on the feeder line is provided with a switch, subtracting the number of the branches which are not positioned in any ring from the total number of the branches to obtain a switch variable dimension n, so as to form a complementary constraint distribution network reconstruction model:
the model is a complementary constraint distribution network reconstruction model type, a discrete decision space is relaxed into a continuous decision space, and meanwhile, a complementary constraint condition can ensure that a variable is finally converged to 0 or 1, so that the model can be optimized in the continuous space, and the decision complexity of distribution network reconstruction can be effectively reduced;
s4, optimizing the preliminary objective function of the power distribution network reconstruction model constructed in the step S1 to obtain a power distribution network reconstruction model objective function; specifically, the method comprises the following steps:
a. the complementary constraint problem canThe line domain structure does not meet the nonlinear programming constraint specification; because the optimal decision under the KKT condition of the distribution network reconstruction model strictly meets the complementary relaxation condition, new auxiliary constraint is introduced
Smoothing the power distribution network reconstruction model:
wherein M is a set punishment parameter and must be large enough to ensure the punishment effect of the new auxiliary constraint;
a vector reflecting the relation between any two switch variables in the basic loop;
b. since the optimal decision must be in
Obtaining, therefore, the smooth distribution network reconstruction model needs to be ensured in the optimization process
Gradually converging to 0, and fusing inequality constraints into the objective function by adopting a penalty function method, so as to obtain a power distribution network reconstruction model objective function shown by the following formula:
in the formula, SVSM is a static voltage stability margin index of the power distribution network; skIs the complex power flowing into branch k; skmaxMaximum allowed for branch k; stThe current complex power value of the transformer t is obtained; stmaxIs the maximum load capacity of the transformer t; viIs the voltage at node i; vminIs the lower limit of the node voltage amplitude; vmaxIs the upper limit of the node voltage amplitude;
is taken as the value of the branch switch state, and
l P(s) is the branch switch number set of the s-th basic loop, L P is the number of basic loops, M1～M6In order to set a first punishment parameter to a sixth punishment parameter, and the first punishment parameter to the sixth punishment parameter must be large enough to ensure the constraint effect, the method of the invention takes 100;
and S5, forming a final power distribution network reconstruction model by the power distribution network reconstruction model objective function obtained after the optimization in the step S4 and the constraint condition obtained after the optimization in the step S3.
Fig. 2 is a schematic flow chart of the reconstruction method of the present invention: the power distribution network reconstruction method comprising the power distribution network reconstruction model optimization method disclosed by the invention comprises the following steps of:
s1, constructing a power distribution network reconstruction model preliminary objective function taking the minimization of the static voltage stability margin index of the power distribution network as an objective function;
s2, constructing a preliminary constraint condition of a preliminary objective function of a power distribution network reconstruction model;
s3, optimizing the preliminary constraint condition constructed in the step S2 to obtain a constraint condition;
s4, optimizing the preliminary objective function of the power distribution network reconstruction model constructed in the step S1 to obtain a power distribution network reconstruction model objective function;
s5, forming a final power distribution network reconstruction model by the power distribution network reconstruction model objective function obtained after the optimization in the step S4 and the constraint condition obtained after the optimization in the step S3;
and S6, solving the final power distribution network reconstruction model formed in the step S5, and reconstructing the power grid according to the obtained solving result.
The process of the invention is further illustrated below with reference to one example:
the PG & E69 node actual power distribution system (see figure 3) comprises 69 sectional branches and 5 connecting branches, and the total load is 3802.19+ j2694.60kVA. The reference value of the three-phase power is 10MVA, and the reference value of the line voltage is 12.66 kV. Considering the static voltage characteristic of the load, the proportion of the constant power load is 40%, and the proportion of the constant current load and the proportion of the constant impedance load are both 30%.
The results before and after reconstitution are shown in table 1.
TABLE 1 comparison of results before and after reconstruction of PG & E69 node power distribution system
Therefore, the static voltage stability margin of the reconstructed network is obviously improved, and the network loss is reduced by 88.4 kW. Table 1 also compares the solution time of the invention and the harmony algorithm, the optimization process of the algorithm of the invention only needs 16.1s, and the optimality of the solution can be ensured by one-time operation; and the harmony algorithm needs to be operated for many times in order to ensure the optimality of the solution, and the time consumed by 50 times of operation is 505.4s, so that the algorithm is obviously more suitable for online calculation.
In order to further verify the effectiveness of the model and the rapidity of the reconstruction method, the PG & E69 node actual power distribution system is respectively subjected to economic reconstruction through the harmony algorithm and the method, and meanwhile, related parameters of the harmony algorithm are modified, which is shown in Table 2. The comparison results are shown in table 3.
TABLE 2 Harmony Algorithm parameters
| Harmonic algorithm parameters | Harmonic algorithm | |
| HMS | ||
| 10 | 30 | |
| HMCR | 0.85 | 0.9 |
| PAR | 0.3 | 0.45 |
| Number of interations | 250 | 350 |
TABLE 3 comparison of reconstruction results for two algorithms
It can be known that the reconstructed network loss is 91.7kW, the minimum value of the node static voltage stability index is 0.710, although the network loss is reduced by 15.1kW compared with the network loss of the invention, the network loss rate is reduced by only 0.4%, the minimum value of the node voltage stability index is reduced by 0.089 compared with the invention, the safety distance between the real-time running state and the dangerous state of the power distribution network is smaller, and the capability of the system for dealing with voltage instability is weaker.
The scheme obtained by the model has better voltage stability, greatly improves the economy, has smaller difference with the network loss obtained by economy reconstruction, is more suitable for oil field power distribution networks which mainly use quasi-periodic fluctuation loads such as pumping units, and is suitable for scenes with frequent fluctuation and larger instability risk of the voltages of power distribution networks with large occupation ratio of asynchronous rotary distributed power supplies and power distribution networks with concentrated electric vehicle users. In addition, since nodes 45, 46 and 47 are all unloaded, the effect of disconnecting branches 44-45, 45-46, 46-47 or 47-48 is the same, and therefore, although the harmony algorithm is not consistent with the optimization scheme of the method of the present invention, the network loss is the same. It can be easily found that by modifying the harmony algorithm parameters, the global optimization capability of the algorithm is improved, but at the expense of optimization time.
Because the determination of the initial solution and the search of the new solution of the intelligent algorithm have certain randomness, the stability of weak values seriously influences the judgment of the optimal solution. Fig. 4 shows the distribution of the optimal solution fitness obtained each time the harmony algorithm is continuously run for 50 times. In 50 calculations, the number of times of searching the global optimal solution is only 17, and the optimization efficiency is 34%, which indicates that the optimization efficiency is low.
Table 4 shows the minimum values of the maximum load, the minimum node voltage, and the voltage stability index that the system can bear under the critical operating conditions of the constant power load, the constant current load, the constant impedance load, and the integrated load after the objective function is reconstructed according to the present invention.
TABLE 4 Critical operating Condition comparison of different types of loads after reconstruction
After the critical load is crossed, the smaller load is increased, so that voltage collapse occurs, and the power flow cannot be converged. It can be seen that the critical load of the constant impedance load is the smallest, the critical load of the constant current load is the largest, the constant power load critical value is located between the two, and the critical value of the combined load is related to the composition and proportion of the different types of loads.
For the integrated load considering the static voltage characteristic of the load, the change conditions of the minimum value of the node voltage stability index and the minimum value of the node voltage with the increase of the load before and after reconstruction are respectively shown in fig. 5 and fig. 6. Therefore, the reconstructed network has higher voltage safety under different load levels than before reconstruction.
The online safety early warning and prevention control system of the power distribution network based on the method is used as an important function module of the self-healing control system of the intelligent power distribution network, and is applied and tested in the self-healing control system demonstration project of the intelligent power distribution network in a high and new technology service area. The self-healing control master station system of the intelligent power distribution network is connected with 4 transformer substations and 23 10kV lines in a financial region to carry out demonstration engineering construction. Typical daily voltage distribution of an actual distribution network of a power grid is shown in fig. 7, voltage distribution without preventive measures is adopted, and the lower limit of the minimum value of node voltages of sections 10, 17, 18, 19 and 20 is lower than 0.93; when the static voltage stability margin is lower than the safety warning line, the preventive network reconstruction is triggered, the static voltage safety level of the system can be improved on line, and the potential safety hazard of the power distribution network is effectively reduced or eliminated.
Aiming at the power distribution network with non-decoupled active and reactive power, the established evaluation index of the static voltage stability margin of the power distribution network considering the influence of the active power can effectively improve the evaluation accuracy; the smooth complementary reconstruction model based on complementary constraint makes decisions by using a nonlinear programming method, has strong real-time performance and good stability, is suitable for online calculation, and can be used as an online preventive control strategy to effectively improve the static voltage stability margin of the power distribution network so as to meet the safety margin requirement of the power distribution network operation in real time.
Claims (6)
1. A power distribution network reconstruction model optimization method comprises the following steps:
s1, constructing a power distribution network reconstruction model preliminary objective function taking the minimization of the static voltage stability margin index of the power distribution network as an objective function;
s2, constructing a preliminary constraint condition of a preliminary objective function of a power distribution network reconstruction model;
s3, optimizing the preliminary constraint condition constructed in the step S2 to obtain a constraint condition;
s4, optimizing the preliminary objective function of the power distribution network reconstruction model constructed in the step S1 to obtain a power distribution network reconstruction model objective function;
and S5, forming a final power distribution network reconstruction model by the power distribution network reconstruction model objective function obtained after the optimization in the step S4 and the constraint condition obtained after the optimization in the step S3.
2. The power distribution network reconstruction model optimization method according to claim 1, wherein the step S1 is implemented by constructing a preliminary objective function of the power distribution network reconstruction model with the power distribution network static voltage stability margin index minimized as an objective function, specifically by using the following equation as the preliminary objective function:
min SVSM
in the formula, SVSM is the static voltage stability margin index of the power distribution network, and
i is a set of all nodes except the system master station node; viIs the voltage vector of node i; pi+1The active power of the branch (i, i +1) flowing into the node i +1 is input into the node i; qi+1The idle work of the branch (i, i +1) of the node i flowing into the node i + 1; r isi,i+1Is the real part of the impedance of branch (i, i + 1); x is the number ofi,i+1Is the imaginary impedance of branch (i, i + 1).
3. The power distribution network reconstruction model optimization method according to claim 2, wherein the preliminary constraint condition for constructing the preliminary objective function of the power distribution network reconstruction model in step S2 specifically adopts the following equation as the preliminary constraint condition:
f(x,SGL)＝0
g(x,SGL)≤0
in the formula
Switching a state variable for branch k, and
it is indicated that the branch is closed,
indicating a branch disconnection; phi is aLIs the set of all branches; n isbThe total number of nodes of the power distribution network; n issThe number of the root nodes of the power distribution network; x is a running state variable of the power distribution network; sGLInjecting power for the node; f (x, S)GL) 0 is the flow constraint of the whole power grid; g (x, S)GL) And the operation constraint of the whole power grid is less than or equal to 0.
4. The power distribution network reconstruction model optimization method according to claim 3, wherein the step S3 is performed to optimize the preliminary constraint condition constructed in the step S2, so as to obtain the constraint condition, specifically, the following steps are performed to optimize:
A. the open state of the switch is recorded as '1', the closed state of the switch is recorded as '0', and then the state variable x of the switch in the ring in the power gridiSatisfaction formula
B. Defining auxiliary variables
Relaxing the discrete variables in the step A into continuous variables, and constructing a quadratic equality constraint model [ x (i) ± x (j)]21, thereby converting to a complement relationship of 0 ≦ x (i) ⊥ x (j) ≧ 0, wherein ⊥ is vertical complement;
C. according to the results of step A and step B, the initial constraint conditions
Conversion to equivalence
D. And (3) setting that all branches in the network have no mutual inductance, and expressing a node admittance matrix Y of the system as follows:
wherein A is a node incidence matrix; e is an identity matrix;
is a diagonal matrix of switching variables; y isbIs an original admittance matrix and at the same timeIs a diagonal matrix, and the diagonal elements are the corresponding branch admittance yk；
E. According to the power balance condition, f (x, S) in the preliminary constraint condition is divided intoGL) Conversion to f (x, S) 0GL,Y)＝0。
5. The power distribution network reconstruction model optimization method according to claim 4, wherein the step S4 is performed to optimize the preliminary objective function of the power distribution network reconstruction model constructed in the step S1, so as to obtain the power distribution network reconstruction model objective function, and specifically, the method comprises the following steps:
a. introducing new auxiliary constraints
Smoothing the power distribution network reconstruction model:
wherein M is a set punishment parameter;
a vector reflecting the relation between any two switch variables in the basic loop;
b. and (3) fusing inequality constraints into the objective function by adopting a penalty function method, thereby obtaining a power distribution network reconstruction model objective function shown by the following formula:
in the formula, SVSM is a static voltage stability margin index of the power distribution network; skIs the complex power flowing into branch k; skmaxMaximum allowed for branch k; stThe current complex power value of the transformer t is obtained; stmaxIs the maximum load capacity of the transformer t; viIs the voltage at node i; vminIs the lower limit of the node voltage amplitude; vmaxIs the upper limit of the node voltage amplitude;
is taken as the value of the branch switch state, and
l P(s) is the branch switch number set of the s-th basic loop, L P is the number of basic loops, M1～M6The first penalty parameter to the sixth penalty parameter are set.
6. A power distribution network reconstruction method comprising the power distribution network reconstruction model optimization method according to any one of claims 1 to 5, and characterized by further comprising the steps of:
and S6, solving the final power distribution network reconstruction model formed in the step S5, and reconstructing the power grid according to the obtained solving result.
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| CN116090218A (en) * | 2023-01-10 | 2023-05-09 | 国网湖南省电力有限公司 | Distribution network distributed photovoltaic admission capacity calculation method and system |
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| CN116090218A (en) * | 2023-01-10 | 2023-05-09 | 国网湖南省电力有限公司 | Distribution network distributed photovoltaic admission capacity calculation method and system |
| CN116090218B (en) * | 2023-01-10 | 2024-06-04 | 国网湖南省电力有限公司 | Distribution network distributed photovoltaic admission capacity calculation method and system |
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