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CN109347089B - Power supply construction optimization method - Google Patents

Power supply construction optimization method Download PDF

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CN109347089B
CN109347089B CN201811038849.2A CN201811038849A CN109347089B CN 109347089 B CN109347089 B CN 109347089B CN 201811038849 A CN201811038849 A CN 201811038849A CN 109347089 B CN109347089 B CN 109347089B
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power supply
power
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CN109347089A (en
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兰洲
孙飞飞
杨升峰
沈志恒
鲍威
朱虹
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Hangzhou Wr Power Technology Co ltd
Economic and Technological Research Institute of State Grid Zhejiang Electric Power Co Ltd
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Hangzhou Wr Power Technology Co ltd
Economic and Technological Research Institute of State Grid Zhejiang Electric Power Co Ltd
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for AC mains or AC distribution networks
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for AC mains or AC distribution networks
    • H02J3/38Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381Dispersed generators
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02PCLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P80/00Climate change mitigation technologies for sector-wide applications
    • Y02P80/10Efficient use of energy, e.g. using compressed air or pressurized fluid as energy carrier

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  • Power Engineering (AREA)
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Abstract

本发明公开了一种电源建设优化方法,涉及电源建设优化领域,目前,电源建设优化常以总费用或年费用最小为目标函数,该方法单一的追求经济性会造成个别线路出现重载或轻载的现象。本发明包括步骤:以最大支路负载比为目标设计目标函数;确定电源规划约束;根据能源发展政策确定各规划水平年电力系统所需要的总装机容量指标,生成新并网边界条件约束;建立基于政策不确定性的电源建设优化模型;采用原‑对偶内点法求解电源建设优化模型;得到电源建设优化方案。本技术方案以电力系统最大支路数负载比为目标函数来评估支路负荷波动,有效避免线路重载和轻载的出现,并加新并网边界条件约束,保障电力系统安全稳定运行和电能质量。

Figure 201811038849

The invention discloses a power supply construction optimization method, which relates to the field of power supply construction optimization. At present, power supply construction optimization often takes the minimum total cost or annual cost as the objective function, and the single pursuit of economy in this method will cause individual lines to appear heavy or light. loading phenomenon. The invention includes the steps of: designing an objective function with the maximum branch load ratio as the target; determining a power supply planning constraint; The power supply construction optimization model based on policy uncertainty; the original-dual interior point method is used to solve the power supply construction optimization model; the power supply construction optimization scheme is obtained. This technical solution takes the load ratio of the maximum number of branches of the power system as the objective function to evaluate the load fluctuation of the branches, effectively avoids the occurrence of heavy and light loads on the line, and adds new grid-connected boundary condition constraints to ensure the safe and stable operation of the power system and energy quality.

Figure 201811038849

Description

Power supply construction optimization method
Technical Field
The invention relates to the field of power supply construction optimization, in particular to a power supply construction optimization method.
Background
At present, the method generally adopted by power supply construction optimization is to take the minimum total cost or annual cost as an objective function. The single pursuit of economy of the method can cause the phenomenon of heavy load or light load of individual lines, the heavy load lines can cause the safety of the power grid to be reduced, and the light load lines can cause the economic operation of the power grid to be poor.
Disclosure of Invention
The technical problem to be solved and the technical task to be solved by the invention are to perfect and improve the prior technical scheme and provide a power supply construction optimization method, aiming at relieving the phenomenon that the single pursuit of economy of the prior power supply construction optimization method causes heavy load or light load of individual lines. Therefore, the invention adopts the following technical scheme.
A power supply construction optimization method is characterized by comprising the following steps:
1) determining an objective function of a power supply planning optimization model, and designing the objective function by taking the maximum branch load ratio as a target;
2) determining power supply planning constraints, wherein the power supply planning constraints comprise node power balance constraints, power flow of a power grid and voltage constraints;
3) acquiring an energy development policy, determining a total installed capacity index required by each planning horizontal year electric power system according to the energy development policy, obtaining the minimum load capacity of a new grid-connected power supply and the maximum load capacity of the new grid-connected power supply, and generating new grid-connected boundary condition constraint, wherein a new grid-connected boundary condition constraint formula is as follows:
Figure GDA0002590514320000011
in the formula (I), the compound is shown in the specification,Sthe minimum load capacity of the new grid-connected power supply is obtained;
Figure GDA0002590514320000021
the maximum load capacity of the new grid-connected power supply is obtained; alpha is alphaiSiTo determine the capacity of the grid-connected power plant;
4) establishing a power supply optimization model based on policy uncertainty according to the objective function, the power supply planning constraint and the new grid-connected boundary condition constraint;
5) solving a power supply construction optimization model by adopting a primary-dual interior point method;
6) and determining the power resource condition, the load distribution condition, the possible development speed and the growth requirement in the planning area according to the solving result of the power supply construction optimization model, and selecting the power plant site with the condition of constructing the power plant to obtain a power supply construction optimization scheme considering policy uncertainty.
As a preferable technical means: in step 1), the objective function of the power supply planning optimization model is:
Figure GDA0002590514320000022
wherein x is a decision vector variable; (x) is an objective function; piThe branch number load ratio of the branch i;
Figure GDA0002590514320000023
the load ratio of the maximum branch number of the branch i is; the load ratio is set to represent the branch load fluctuation limitation so as to avoid the occurrence of heavy load and light load of the line.
As a preferable technical means: in the step 2) of the process,
the node power balance constraint is:
Figure GDA0002590514320000024
in the formula, PiInjecting power for the active power of the node i; qiReactive injection power for node i; j e i represents that the node j is directly connected with the node i, and includes the case that j is equal to i; v is the node amplitude; theta is a nodal phase angle vector; pijActive power of a branch between a node i and a node j; qijThe branch reactive power between the node i and the node j is obtained; sPA non-zero injection node (including PV nodes and PQ nodes) number set for active balance constraint; sQInjecting a PQ node number set for non-zero; sZA node number set is injected for zero;
wherein the node injects power Pij(V, theta) and Qij(V, θ) is:
Pij(V,θ)=ViVj(Gijcosθij+Bijsinθij)
Qij(V,θ)=ViVj(Gijsinθij+Bijcosθij)
wherein j is each branch point of the node i; gijIs the conductance between node i and node j; b isijIs the susceptance between node i and node j; thetaijIs the phase angle difference between node i and node j.
As a preferable technical means: the power flow constraint and the voltage constraint of the power grid comprise:
and (3) branch current carrying capacity constraint:
Figure GDA0002590514320000031
in the formula (I), the compound is shown in the specification,P ijthe lower limit of the current carrying capacity of the branch from the node i to the node j is set;
Figure GDA0002590514320000032
the upper limit of the current carrying capacity of the branch from the node i to the node j is set; the constraint is used for avoiding the light load or heavy load phenomenon of the optimized rear road;
main transformer tidal current direction constraint:
Pzb_ij≤0
in the formula, Pzb_ijThe main transformer power flow direction from the node i to the node j is obtained; the constraint is used for avoiding that active power flows from the voltage phase angle lagging node j to the leading node i;
active restraint of the section:
Figure GDA0002590514320000033
in the formula (I), the compound is shown in the specification,P snapshotthe lower limit of active constraint of the section;
Figure GDA0002590514320000034
the upper limit of active power constraint of the section; the constraint is used for monitoring the power flow of the circuit in the power grid in real time, and the influence of overlarge power flow of the circuit on the stability of a system or a local power grid is avoided;
and non-PV node voltage upper and lower limit inequality constraint:
Figure GDA0002590514320000041
in the formula, Vi minThe lowest voltage amplitude allowed for non-PV node i; vi maxThe highest voltage amplitude allowed for non-PV node i; the constraint is used for the load flow calculation of the optimized power grid to improve the convergence.
As a preferable technical means: in the step 5), when solving by adopting a primal-dual interior point method, introducing a relaxation variable to constrain a function inequality into an equality constraint and a variable inequality constraint;
Figure GDA0002590514320000042
Figure GDA0002590514320000043
grespectively an upper limit and a lower limit; g (x) is an inequality constraint notation;
processing equality constraint conditions by a Lagrange multiplier method, and processing variable inequality constraint conditions by an inner point barrier function method and a constraint step method:
Figure GDA0002590514320000044
wherein p is a barrier factor, and p > 0; the lagrange function is defined as follows:
Figure GDA0002590514320000045
wherein x, l and u are original variable vectors; y, z and w are corresponding Lagrange multiplier vectors, namely dual variable vectors; deriving an optimality condition of the kuen-figure gram after the barrier function is introduced, and solving by using a Newton-Raphson method; initially, an initial barrier factor is taken large enough to ensure the feasibility of the solution, and then the barrier factor is gradually reduced to ensure the optimality of the solution.
Has the advantages that: the embodiment of the invention has the following beneficial effects:
1. on the basis of the traditional power supply planning method, the invention improves both the objective function and the constraint condition of the power supply planning model, and avoids the phenomenon of heavy load or light load of individual circuits. The invention evaluates the branch load fluctuation by taking the maximum branch load ratio of the power system as the objective function, effectively avoids the occurrence of heavy load and light load of the line, and ensures that the branch load rate is relatively balanced and the utilization rate is more reasonable.
2. Analyzing the condition of an energy development policy, adding new grid-connected boundary condition constraints, establishing a power supply construction optimization model based on policy uncertainty, and ensuring safe and stable operation and power quality of a power system.
3. The balance of active power and reactive power of the nodes is considered to ensure that the frequency of the system is stabilized within a specified range and the balance of load and output is ensured; and in the optimal power flow problem, the upper and lower limit constraints of an inequality are added, which is beneficial to the convergence of power grid power flow calculation after optimization.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the drawings in the specification.
As shown in fig. 1, the present invention includes the following steps.
S01: determining to evaluate branch load fluctuation according to the maximum branch number load ratio of the power system, and therefore, the objective function of the power supply planning optimization model is as follows:
Figure GDA0002590514320000051
wherein x is a decision vector variable; (x) is an objective function; piThe branch number load ratio of the branch i;
Figure GDA0002590514320000052
is the maximum branch number load ratio of the branch i. The load ratio is set to reflect the branch load fluctuation limitation, so that the heavy load and the light load of the line can be effectively avoided.
S02: inheriting the balance constraint h (x) of the active power and the reactive power of a node planned by a traditional power supply to be 0, wherein the balance constraint h (x) is generally a node power balance constraint and can be further divided into a node active power balance equation and a reactive power balance equation;
the node power balance equation, the equality constraint is shown as follows:
Figure GDA0002590514320000061
in the formula, PiInjecting power for the active power of the node i; qiReactive injection power for node i; j e i represents that the node j is directly connected with the node i, and includes the case that j is equal to i; v is the node amplitude; theta is a nodal phase angle vector; pijActive power of a branch between a node i and a node j; qijThe branch reactive power between the node i and the node j is obtained; sPA non-zero injection node (including PV nodes and PQ nodes) number set for active balance constraint; sQInjecting a PQ node number set for non-zero; sZA node number set is injected for zeros.
Wherein the node injects power Pij(V, theta) and QijThe specific development of (V, θ) is shown as follows:
Pij(V,θ)=ViVj(Gijcosθij+Bijsinθij)
Qij(V,θ)=ViVj(Gijsinθij+Bijcosθij)
wherein j is each branch point of the node i; gijIs the conductance between node i and node j; b isijIs the susceptance between node i and node j; thetaijIs the phase angle difference between node i and node j.
In power supply optimization planning, inequality constraints
Figure GDA0002590514320000062
The method is an important guarantee for ensuring the safe and reliable operation of the power grid.
Figure GDA0002590514320000063
gRespectively, the upper limit and the lower limit of inequality constraint.
Inequality constraints typically contain many aspects, and the constraints are not the same for different systems; the constraints also differ using different optimization algorithms. Constraints imposed herein include: power flow constraint, voltage constraint, and the like. The detailed description of the various constraints is as follows:
the safe and economic operation equation of the power grid is as follows:
and (3) branch current carrying capacity constraint:
Figure GDA0002590514320000071
in the formula (I), the compound is shown in the specification,P ijthe lower limit of the current carrying capacity of the branch from the node i to the node j is set;
Figure GDA0002590514320000072
the upper limit of the branch current carrying capacity from the node i to the node j. If the load is lower than the lower limit, a branch light load can occur; if the branch load is higher than the upper limit, a branch overload occurs. The condition that the optimization rear road is lightly loaded or heavily loaded can be avoided through the constraint.
Main transformer tidal current direction constraint:
Pzb_ij≤0
in the formula, Pzb_ijThe main transformer power flow direction from the node i to the node j is shown. If less than or equal to 0, it indicates that active power is flowing from the voltage phase angle leading node i to the voltage phase angle lagging node j. Otherwise, the process is reversed. By this constraint, it is possible to avoid that active power flows from the voltage phase angle lagging node j to the leading node i, which does not necessarily cause an accident, but this operation is not normal.
Active restraint of the section:
Figure GDA0002590514320000073
in the formula (I), the compound is shown in the specification,P snapshotthe lower limit of active constraint of the section;
Figure GDA0002590514320000074
the upper limit of active constraint of the section. The power flow of the circuit in the power grid needs to be monitored in real time, and the influence of overlarge power flow of the circuit on the stability of a system or a local power grid is avoided.
And non-PV node voltage upper and lower limit inequality constraint:
to ensure power quality and supply safety, all electrical equipment of the power system must operate near the rated voltage, and the voltage magnitude at the PV node must be given as described above. Therefore, this constraint is mainly for PQ nodes.
Figure GDA0002590514320000075
In the formula, Vi minThe lowest voltage amplitude allowed for non-PV node i; vi maxThe highest voltage magnitude allowed for the non-PV node i. If no constraint is added, the optimized power grid load flow solution is located near the boundary of a feasible domain, and load flow calculation is easy to not converge. Therefore, the constraint has very important significance for the convergence of the load flow calculation of the optimized power grid.
S03: the method comprises the following steps of knowing national relevant energy development policies, determining total installed capacity indexes required by power systems in each planning level year, and adding new grid-connected boundary condition constraints:
new grid-connected power supply boundary conditions:
Figure GDA0002590514320000081
in the formula (I), the compound is shown in the specification,Sthe minimum load capacity of the new grid-connected power supply is obtained;
Figure GDA0002590514320000082
the maximum load capacity of the new grid-connected power supply is obtained; alpha is alphaiSiIn order to determine the capacity of the grid-connected power plant, the safe and stable operation and the electric energy quality of the power system are guaranteed.
S04: establishing a power supply construction optimization model based on policy uncertainty, wherein an objective function of the power supply construction optimization model is a maximum branch number load ratio of an electric power system, equality constraint has node power balance constraint, inequality constraint has branch current carrying capacity constraint, main transformer tidal current direction constraint, section active constraint and non-PV node voltage upper and lower limit inequality constraint, and boundary condition constraint has new grid-connected power supply boundary condition constraint;
s05: and solving the power supply construction optimization model based on the policy uncertainty by adopting a primal-dual interior point method. In the original dual interior point method, the introduction of the relaxation variable eliminates the function inequality constraint, so that the interior point property of the initial solution can be ensured only by giving a proper initial value to the relaxation variable and the corresponding Lagrange multiplier without special calculation for the property. The basic idea is as follows: introducing a relaxation variable to constrain a function inequality into an equality constraint and a variable inequality constraint;
Figure GDA0002590514320000083
processing equality constraint conditions by a Lagrange multiplier method, and processing variable inequality constraint conditions by an inner point barrier function method and a constraint step method;
Figure GDA0002590514320000091
wherein p is a barrier factor, and p > 0. Thus, the lagrangian function is defined as follows:
Figure GDA0002590514320000092
wherein x, l and u are original variable vectors; y, z and w are corresponding lagrange multiplier vectors, i.e. dual variable vectors. And (4) deriving an optimality condition of the kuen-figure gram after the barrier function is introduced, and solving by using a Newton-Raphson method.
S06: determining the power resource condition and the load distribution condition in the planning area, the possible development speed and the growth requirement, solving the model based on a source-dual interior point method, and selecting a power plant site with the condition of building a power plant to obtain a power supply construction optimization scheme based on policy uncertainty.
The power supply construction optimization method provided by the embodiment of the invention has the following characteristics:
firstly, the method firstly searches the load ratio of the maximum branch number of the power system to evaluate the branch load fluctuation; secondly, considering node power balance constraint, power flow constraint and voltage constraint of a power grid; thirdly, analyzing the relevant energy development policy of China, adding new grid-connected boundary condition constraints, and establishing a power supply construction optimization model based on policy uncertainty; and finally, solving the model by using a prime-dual interior point method to obtain a power supply construction optimization scheme based on policy uncertainty. The problem that the traditional method adopts the minimum total cost or annual cost as a target function and single pursuit of economy causes heavy load or light load of individual lines is solved, the safe economy of power construction and the relative balance of branch load rates are improved, the utilization rate is more reasonable, and the safe and stable operation and the electric energy quality of an electric power system are guaranteed.
Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
The above method for optimizing power supply construction shown in fig. 1 is a specific embodiment of the present invention, has shown the outstanding substantive features and significant progress of the present invention, and can be modified equivalently according to the practical use requirements and under the teaching of the present invention, all of which are within the protection scope of the present solution.

Claims (5)

1. A power supply construction optimization method is characterized by comprising the following steps:
1) determining an objective function of a power supply planning optimization model, and designing the objective function by taking the maximum branch load ratio as a target;
2) determining power supply planning constraints, wherein the power supply planning constraints comprise node power balance constraints, power flow constraints and voltage constraints;
3) acquiring an energy development policy, determining a total installed capacity index required by each planning horizontal year electric power system according to the energy development policy, obtaining the minimum load capacity of a new grid-connected power supply and the maximum load capacity of the new grid-connected power supply, and generating new grid-connected boundary condition constraint, wherein a new grid-connected boundary condition constraint formula is as follows:
Figure FDA0002590514310000011
in the formula (I), the compound is shown in the specification,Sthe minimum load capacity of the new grid-connected power supply is obtained;
Figure FDA0002590514310000012
the maximum load capacity of the new grid-connected power supply is obtained; alpha is alphaiSiTo determine the capacity of the grid-connected power plant;
4) establishing a power supply construction optimization model based on policy uncertainty according to the objective function, the power supply planning constraint and the new grid-connected boundary condition constraint;
5) solving a power supply construction optimization model by adopting a primary-dual interior point method;
6) and determining the power resource condition, the load distribution condition, the possible development speed and the growth requirement in the planning area according to the solving result of the power supply construction optimization model, and selecting the power plant site with the condition of constructing the power plant to obtain a power supply construction optimization scheme based on policy uncertainty.
2. The power supply construction optimization method according to claim 1, wherein: in step 1), the objective function of the power supply planning optimization model is:
Figure FDA0002590514310000013
wherein x is a decision vector variable; (x) is an objective function; piThe branch number load ratio of the branch i;
Figure FDA0002590514310000014
the load ratio of the maximum branch number of the branch i is; the load ratio is set to represent the branch load fluctuation limitation so as to avoid the occurrence of heavy load and light load of the line.
3. The power supply construction optimization method according to claim 2, wherein: in the step 2) of the process,
the node power balance constraint is:
Figure FDA0002590514310000021
in the formula, PiInjecting power for the active power of the node i; qiReactive injection power for node i; j e i represents that the node j is directly connected with the node i, and includes the case that j is equal to i; v is the node amplitude; theta is a nodal phase angle vector; pijActive power of a branch between a node i and a node j; qijThe branch reactive power between the node i and the node j is obtained; sPA non-zero injection node number set for active balance constraint; sQIs a non-zero noteEntering a PQ node number set; sZA node number set is injected for zero;
wherein the node injects power Pij(V, theta) and Qij(V, θ) is:
Pij(V,θ)=ViVj(Gijcosθij+Bijsinθij)
Qij(V,θ)=ViVj(Gijsinθij+Bijcosθij)
wherein j is each branch point of the node i; gijIs the conductance between node i and node j; b isijIs the susceptance between node i and node j; thetaijIs the phase angle difference between node i and node j.
4. The power supply construction optimization method according to claim 3, wherein: the power flow constraint and the voltage constraint of the power grid comprise:
and (3) branch current carrying capacity constraint:
Figure FDA0002590514310000022
in the formula (I), the compound is shown in the specification,P ijthe lower limit of the current carrying capacity of the branch from the node i to the node j is set;
Figure FDA0002590514310000023
the upper limit of the current carrying capacity of the branch from the node i to the node j is set; the constraint is used for avoiding the light load or heavy load phenomenon of the optimized rear road;
main transformer tidal current direction constraint:
Pzb_ij≤0
in the formula, Pzb_ijThe main transformer power flow direction from the node i to the node j is obtained; the constraint is used for avoiding that active power flows from the voltage phase angle lagging node j to the leading node i;
active restraint of the section:
Figure FDA0002590514310000031
in the formula (I), the compound is shown in the specification,P snapshotthe lower limit of active constraint of the section;
Figure FDA0002590514310000032
the upper limit of active power constraint of the section; the constraint is used for monitoring the power flow of the circuit in the power grid in real time, and the influence of overlarge power flow of the circuit on the stability of a system or a local power grid is avoided;
and non-PV node voltage upper and lower limit inequality constraint:
Figure FDA0002590514310000033
in the formula, Vi minThe lowest voltage amplitude allowed for non-PV node i; vi maxThe highest voltage amplitude allowed for non-PV node i; the constraint is used for the load flow calculation of the optimized power grid to improve the convergence.
5. The power supply construction optimization method according to claim 4, wherein: in the step 5), when solving by adopting a primal-dual interior point method, introducing a relaxation variable to constrain a function inequality into an equality constraint and a variable inequality constraint;
Figure FDA0002590514310000034
Figure FDA0002590514310000035
grespectively an upper limit and a lower limit; g (x) is an inequality constraint notation;
processing equality constraint conditions by a Lagrange multiplier method, and processing variable inequality constraint conditions by an inner point barrier function method and a constraint step method:
Figure FDA0002590514310000041
wherein p is a barrier factor, and p > 0; the lagrange function is defined as follows:
Figure FDA0002590514310000042
wherein x, l and u are original variable vectors; y, z and w are corresponding Lagrange multiplier vectors, namely dual variable vectors; deriving an optimality condition of the kuen-figure gram after the barrier function is introduced, and solving by using a Newton-Raphson method; initially, an initial barrier factor is taken large enough to ensure the feasibility of the solution, and then the barrier factor is gradually reduced to ensure the optimality of the solution.
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