CN105186541A - Regional power grid reactive power optimization method based on limit tidal current - Google Patents

Abstract

The invention discloses a reactive power optimization method for regional power grids based on limit currents. The weight coefficient of the voltage deviation rate and the gate power factor, and obtain the weighted sum of the voltage deviation rate and the weight coefficient of the gate power factor; judge whether the weighted sum is greater than the engineering threshold. The present invention can adapt to the reactive power allocation requirements under different load modes, and adopts the PQ-PV node type conversion mode and the mode of relaxing the transformer stall constraint according to the characteristics of the feasible domain of the optimization problem under different load modes, and then expands the reactive power configuration, etc. The optimization space of the problem ensures that the reactive power configuration of the power system can fully meet the load demand in theory.

Description

A Reactive Power Optimization Method for Regional Power Grid Based on Limit Power Flow

technical field

The invention relates to the technical field of reactive power control in electric power systems, in particular to a reactive power optimization method for regional power grids based on limit current flow.

Background technique

With the rapid development of power grid construction, the coverage of the power grid is continuously expanding, and the structure is becoming more and more complex. The stability, safety and reliability of the power grid operation have become more important. At present, although the power dispatching, automation department, relay protection, operation and maintenance, communication and other departments of the power supply company perform their duties, they also need to work together. Timely and accurate acquisition of relevant power grid operation information can greatly improve their work efficiency. At the same time, all departments can play Advantages in their respective professional fields, better cooperation with each other to ensure the normal operation of the power grid; open dispatch data sharing channels, establish an information network that is not limited by time and region, strengthen the support and collaboration of various departments for dispatch work, and give full play to all work links It lays a solid foundation for establishing a more harmonious and efficient working mode, and is an important guarantee for the normal operation of the power grid.

Reactive power optimization of regional power grid is an important means to ensure the economical and safe operation of the power grid, maintain a certain voltage level and reduce network loss. In the case of satisfying constraints such as power flow equation constraints, node voltage constraints, and generator output constraints, reactive power optimization can achieve the minimum active power loss of the system, the best voltage quality, the lowest operating cost, or voltage stability by adjusting the distribution of reactive power flow. The goal with the greatest margin.

At present, under the requirements of provincial and regional integrated coordinated control, the power factor of the high-voltage side of the main transformer in the regional power grid is generally low, and the capacity of the parallel reactive power compensation equipment does not match the system requirements, resulting in a low voltage qualification rate, transmission, The serious loss of electric energy in the distribution network brings challenges to the operation safety and service life of the equipment. According to the current research process and operation experience at home and abroad, the problem of reactive power optimization is summarized, which mainly includes two aspects: 1) The existing reactive power configuration can meet the needs of the system or the system is in a small load mode, the transformer gear limit and the capacitor The limitation of switching and cutting times further limits the feasible region, but there is always an optimal solution. If the optimization method is not selected properly, only a suboptimal solution may be found; 2) The existing reactive power configuration cannot meet the load demand at all or the system is under load. In the large mode, the optimal solution is not within the feasible region under the cooperation of the existing parameters, so the result of optimization is often a boundary value, and the system voltage or reactive power exceeds the limit seriously.

For problem 1) domestic and foreign scholars have proposed various improved algorithms, such as genetic algorithm, hybrid algorithm based on genetic algorithm and interior point method, primal-dual interior point method, etc., which can better solve the problems of calculation accuracy and convergence, but The amount of calculation is large and the complexity is high, and its application in large-scale power grids needs further research; for problem 2) the existing reactive power optimization cannot solve the problem. For regional power grids, reactive power planning is relatively conservative and cannot be used for system operation. Provide a more economical and secure physical basis.

Based on the above problems, it is necessary to seek a solution to the mismatch between the current reactive power configuration and system requirements, and provide a technical basis for adding reactive power equipment configuration and capacity selection, thereby improving the economy and safety of power grid operation.

Contents of the invention

The purpose of the present invention is to provide a reactive power optimization method of regional power grid based on limit current.

In order to achieve the above purpose, one embodiment of the present invention provides the power flow calculation by collecting the power information of the regional power grid, and obtaining the result of the power flow calculation;

According to the power flow calculation results, the voltage offset rate and gate power factor are obtained;

Determine the weight coefficient of the voltage offset rate and the gate power factor, and obtain the weighted sum of the voltage offset rate and the weight coefficient of the gate power factor;

Judging whether the weighted sum is greater than the engineering threshold;

When the weighted sum is greater than the engineering threshold, the load node of the regional power grid is converted from the PQ node to the PV node, and the power deficit load node and the total power deficit are obtained;

Converting the power deficit load node from a PV node to a PQ node, and judging whether the voltage offset rate and the gate power factor after the load node conversion are improved;

When the voltage deviation rate and the gate power factor are not improved, the load node PQ node in the regional power grid is converted into a PV node; power optimization;

When the weighted sum is not greater than the engineering threshold, relax the gear limit of the transformer; and then optimize the reactive power.

Preferably, the load nodes for converting PQ nodes into PV nodes in the regional power grid include 10KV nodes and 30KV nodes.

Preferably, the power deficit load node is converted from the PV node to the PQ node step by step; the power gap load node is gradually converted from the PV node to the PQ node. The method is: whenever a load node is restored, the voltage after the load node conversion is judged Whether the offset rate and gate power factor are improved.

Preferably, the objective function of the reactive power optimization model is:

$\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; K</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; \&cup;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; \&Delta;P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

Among them, ΔP _i is the active power loss of electrical components; λ is the weight coefficient; V _ispec is the expected voltage value of node i; V _imax is the maximum voltage value of node i.

Preferably, the constraints of reactive power optimization include equality constraints and inequality constraints, and the inequality constraints include control variable constraints and state variable constraints.

Preferably, the function of the equality constraint is:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;\; U</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;\; U</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>\end{array}\right.$

Among them, P _i and Q _i are the injected power of node i; U _j is the node voltage amplitude; θ _ij is the phase angle difference between nodes i and j.

Preferably, the function of state variable constraints is:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}<span\; class="notranslate">\; \}</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; K</span>}}\end{array}\right.$

Among them, Q _Gmin and Q _Gmax are the upper and lower limits of the reactive output of the generator; U _min and U _max are the upper and lower limits of the node voltage; Q _Timin and Q _Timax are the upper and lower limits of the reactive power of the high voltage side of the gateway transformer.

Preferably, the function to control variable constraints is:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right.$

Among them, parallel capacitor Q _Ci ∈ N _C '; transformer gear T _Ki ∈ N _T ; and represents the upper limit of the slack, and Indicates the lower limit of the amount of relaxation;

and adding constraints as:

$\left\{\begin{array}{c}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\\ {\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}\\ {\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.$

in, and Indicates the upper and lower limits of transformer gear slack; T _Ki ′ is the step size of transformer gear; and Indicates the upper and lower limits of the slack of capacitor capacity; Q _Ci ′ is the capacity of a group of capacitors; s ₁ , s ₂ , y ₁ , y ₂ ∈ Z.

Preferably, the result of reactive power optimization is

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ,</span>\\ {\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; 10</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; 10</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\\ {\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; 10</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; 10</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; .</span>\end{array}$

In summary, the present invention has the following advantages:

In order to meet the requirements of reactive power allocation under different load modes, the present invention adopts the PQ-PV node type conversion mode and the mode of relaxing the transformer stall constraint according to the characteristics of the feasible region of the optimization problem under different load modes, so as to ensure the reactive power of the power system The configuration fully meets the load demand in theory, and then expands the optimization space of the original problem, adjusts the iterative direction of the optimization power flow to make the problem enter the solution domain, and obtains the nodes with unreasonable reactive power configuration and the corresponding Capacity; at the same time, under the operation of this node conversion mode, the entire power grid is in the limit state of reactive power compensation that takes into account both safety and economy, and the reactive power optimization flow at this time is called the limit flow.

1) Safety and economic characteristics. When building the model, the present invention takes the system active power loss and voltage offset rate as the objective function, fully considers the improvement of the voltage quality and the improvement of the system's reactive power management capability, and also gives the system safety and economy Run provides a better physical basis;

2) Flexibility. According to the characteristics of the feasible domain of the optimization problem under different load modes, the present invention performs PQ-PV node type conversion on load nodes and relaxes the transformer stall constraints, fully considering the uncertainty of the system operation mode, Be able to study the reactive power configuration under different load modes;

3) Intuitive and clear, the present invention converts the load node type from the PQ node to the PV node, and then obtains the additional reactive power configuration capacity required by the node according to the reactive power shortage index, and relaxes the limit of the transformer stall to optimize the current power grid. The network structure can also be obtained through the structure of the optimal solution to determine whether the current power grid operation status needs to be optimized and what measures to take, and the most intuitive, clear and reasonable suggestions can be obtained for the power grid operation dispatching and planning departments;

4) Strong robustness, the present invention is applied in large-scale regional power grids and IEEE standard systems, and can provide reasonable reactive power configuration and network structure optimization suggestions under various load modes, and has wide application and robustness.

Description of drawings

Fig. 1 is a block diagram of the present invention;

Fig. 2 is a 220kV single-station grid structure in an embodiment of the present invention.

Detailed ways

An embodiment of the present invention provides a method for optimizing reactive power of regional power grid based on limit power flow; including the following process:

S1. Collect the power information of the regional power grid to calculate the power flow, and obtain the result of the power flow calculation.

The load mode of the load in the power grid presents a typical daily load curve with certain periodicity. However, under the uncertainty of the system operating environment and the fluctuation of the load, there is a non-negligible gap between the actual load value and the typical predicted value. error. Therefore, before reactive power optimization, it is necessary to extract the characteristics of the feasible region under different load modes, and carry out different processing methods according to the corresponding characteristics.

In typical load mode, the theoretical optimal solution does not exist in the feasible region, but under different load modes, the characteristics of the feasible region are closely related to the corresponding voltage offset rate and gate power factor index, so the above calculation can Indicators characterize the characteristics of the feasible domain.

S2. Obtain the voltage offset rate and the gate power factor according to the calculation result of the power flow.

Therefore, the present invention performs characterization judgment by obtaining the key influencing factors voltage offset rate and gate power factor from the power flow big data.

S3. Determine the weight coefficient of the voltage offset rate and the gate power factor, and obtain a weighted sum of the voltage offset rate and the weight coefficient of the gate power factor. The weighted sum refers to the sum of the products of the voltage offset rate and the gate power factor and their weight coefficients respectively.

After obtaining the relevant parameters of the voltage deviation rate and the gate power factor from the power system, the operation status of the power grid is judged by calculating the weighted sum of the key influencing factors. The weight coefficients referred to in the present invention can be input in parameters in advance or determined by layer analysis method or empirical value method. The weight coefficient refers to the importance of the influencing factor among all factors.

After obtaining the weighted sum, judge whether the weighted sum is greater than the engineering threshold;

S4. When the weighted sum is greater than the engineering threshold, convert the PQ node among the load nodes of the regional power grid into a PV node; and obtain the power deficit load node and the total power deficit. The total amount of power deficit = the required capacity under the PV node type - the capacity issued by the reactive power source + the load demand of the node. The engineering threshold is a preset parameter; it is related to the data of various influencing factors in the power system.

Convert the power deficit load node from PV node to PQ node, and judge whether the voltage deviation rate and gate power factor after the load node conversion are improved.

In the present invention, whether the voltage deviation rate and the gate power factor are improved means that after the adjustment operation is performed, after the relevant influencing factor parameters are obtained from the adjusted power flow data, the voltage deviation rate and the gate power factor are calculated, and the adjusted Whether the data is closer to the rated data or preset parameters, when these parameters are closer to the rated data or preset data than after adjustment, it can be considered to be improved.

S5. When the voltage deviation rate and the gate power factor are not improved, the load node PQ node in the regional power grid is converted into a PV node; when the voltage deviation rate and the gate power factor are not improved, reactive power optimization is performed according to the adjusted power flow parameters ;

S6. When the weighted sum is not greater than the engineering threshold, relax the gear limit of the transformer; and then optimize the reactive power.

The objective function of the reactive power optimal model of the present invention is:

$\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; K</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; \&cup;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; \&Delta;P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$

Among them, ΔP _i is the active power loss of electrical components; λ is the weight coefficient; V _ispec is the expected voltage value of node i; V _imax is the maximum voltage value of node i.

Preferably, the constraints of reactive power optimization include equality constraints and inequality constraints, and the inequality constraints include control variable constraints and state variable constraints.

Preferably, the function of the equality constraint is:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;U</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;U</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>\end{array}\right.$

Among them, P _i and Q _i are the injected power of node i; U _j is the node voltage amplitude; θ _ij is the phase angle difference between nodes i and j.

Preferably, the function of state variable constraints is:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}<span\; class="notranslate">\; \}</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; K</span>}}\end{array}\right.$

Among them, Q _Gmin and Q _Gmax are the upper and lower limits of the reactive output of the generator; U _min and U _max are the upper and lower limits of the node voltage; Q _Timin and Q _Timax are the upper and lower limits of the reactive power of the high voltage side of the gateway transformer.

Preferably, the function to control variable constraints is:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right.$

Among them, parallel capacitor Q _Ci ∈ N _C '; transformer gear T _Ki ∈ N _T ; and represents the upper limit of the slack, and Indicates the lower limit of the amount of relaxation;

and adding constraints as:

$\left\{\begin{array}{c}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\\ {\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}\\ {\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.$

in, and Indicates the upper and lower limits of transformer gear slack; T _Ki ′ is the step size of transformer gear; and Indicates the upper and lower limits of the slack of capacitor capacity; Q _Ci ′ is the capacity of a group of capacitors; s ₁ , s ₂ , y ₁ , y ₂ ∈ Z.

Preferably, the result of reactive power optimization is

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ,</span>\\ {\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; 10</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; 10</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\\ {\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; 10</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; 10</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; .</span>\end{array}$

The relaxation of the transformer stall limit in the present invention means that the existing transformer stalls are limited during operation, and generally the transformer stalls can only be adjusted to one stall; after the transformer stalls are relaxed in the present invention, it can be made Adjust at least 2 gears to expand the range of transformer gear changes.

Capacitor capacity limitation and transformer gear limitation are important factors affecting reactive power optimization, so it is necessary to adjust the relaxation strategy according to different load modes when relaxing it. The following takes a 220kV single station as an example to illustrate the establishment of the limit power flow model.

Under the requirements of coordination, especially in the mode of large load, due to the purpose of economical and safe operation, it is impossible for the 500kV main network to transmit reactive power with a large capacity, and the reactive power compensation must follow the principle of local balance; while in the mode of small load, 500kV The reactive power of the main grid is sufficient, and the regional grid needs sufficient adjustment measures to ensure the safe operation of the grid.

In Figure 2, the total load of the system is 243.0648+j73.05MVA, and the gate power factor in the basic power flow is 0.941. In order to meet the requirements of the gate power factor above 0.95 and the system load demand, a 10kV bus capacitor is put into the system, causing the system 110KV voltage to exceed the limit , and the local power grid must choose between satisfying the voltage qualification and the gate power factor, which directly reflects the irrationality of the reactive power configuration of the system.

Therefore, the introduction of slack variables and represents the upper limit of the slack, and Indicates the lower limit of the slack, and relaxes the control variable; and in the existing reactive power configuration, it is very likely that there is no parallel capacitor in the 10kV bus, so under the framework of the limit power flow, it is necessary to add a corresponding capacitor w and form a set N _CE , then N _C '＝{ _NC , N _CE }, the control variables are constrained in the following form

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, parallel capacitor Q _Ci ∈ N _C '; transformer gear T _Ki ∈ _NT .

and add constraints

$\left\{\begin{array}{c}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}\\ {\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}\\ {\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

in, and Indicates the upper and lower limits of transformer gear slack; T _Ki ′ is the step size of transformer gear; and Indicates the upper and lower limits of the slack of capacitor capacity; Q _Ci ′ is the capacity of a group of capacitors; s ₁ , s ₂ , y ₁ , y ₂ ∈ Z.

Under the framework of limit power flow, the gate power factor and node voltage amplitude in the state variables are more strictly restricted. Therefore, the reactive power optimization model of the regional power grid is changed to the following form:

$\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; K</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; B</span>}}<span\; class="notranslate">\; \&cup;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; \&Delta;P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}\frac{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; |</span>}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Among them, the function of the equality constraint is:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;\; U</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;\; U</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; sin\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; cos\&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>\end{array}\right.$

The function of state variable constraints is:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}\\ {\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}}<span\; class="notranslate">\; \}</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; K</span>}}\end{array}\right.$

Then the optimized results that can be exported are:

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>\\ {\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ,</span>\\ {\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; 10</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; 10</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>\\ {\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; 10</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; Q</span>}}}_{\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; 10</span>}}\mathrm{<span\; class="notranslate">\; ...</span>}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}}_{\mathrm{<span\; class="notranslate">\; K</span>}\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; \&rsqb;</span>\end{array}$

Through the structure of the optimal solution, it can be concluded that under the limit power flow, if the slack of the transformer gear is large, it proves that the reactive power configuration of the grid under this section meets the requirements, and the network structure needs to be optimized; similarly, if the slack of the capacitor is large , it proves the irrationality of the reactive power configuration of the grid, and gives corresponding suggestions to the grid planning department.

In the embodiment of the present invention, the load nodes converted from PQ nodes in the regional power grid to PV nodes include 10KV nodes and 30KV nodes.

In the embodiment of the present invention, the power deficit load node is converted into the PQ node from the PV node and is carried out step by step; Whether the converted voltage offset rate and gate power factor are improved.

Claims (10)

1. A regional power grid reactive power optimization method based on limit power flow comprises the following steps:

collecting power information of a regional power grid to perform load flow calculation, and obtaining a load flow calculation result;

obtaining a voltage deviation rate and a gateway power factor according to the load flow calculation result;

determining the weight coefficients of the voltage offset rate and the gateway power factor, and obtaining the weighted sum of the voltage offset rate and the gateway power factor weight coefficients;

judging whether the weighted sum is greater than an engineering threshold value;

when the weighted sum is larger than an engineering threshold value, converting the load node of the regional power grid from a PQ node to a PV node, and obtaining a power shortage load node and a power shortage total amount;

converting the power shortage load node from a PV node to a PQ node, and judging whether the voltage deviation rate and the gateway power factor after the load node conversion are improved or not;

converting a load node in a regional power grid from a PQ node to a PV node when the voltage offset rate and a gateway power factor are not improved; when the voltage deviation rate and the gateway power factor are not improved, performing reactive power optimization according to the adjusted power flow parameters;

when the weighted sum is not greater than the engineering threshold value, the gear limit of the relaxation transformer is carried out; and finishing reactive power optimization.

2. The method of claim 1, wherein: the load nodes for converting the PQ nodes into the PV nodes in the regional power grid comprise 10KV nodes and 30KV nodes.

3. The method of claim 1, wherein: the transition of the power deficit load node from the PV node to the PQ node is done step by step.

4. The method of claim 3, wherein: the method for gradually switching the power shortage load node from the PV node to the PQ node comprises the following steps: and judging whether the voltage deviation rate and the gateway power factor after the conversion of the load nodes are improved or not every time one load node is recovered.

5. The method of claim 1, wherein: the objective function of the reactive power optimization model is as follows:

<math> <mrow> <mi>min</mi> <mi> </mi> <mi>F</mi> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msup> <msub> <mi>&rho;</mi> <mi>s</mi> </msub> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <munder> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>&Element;</mo> <msub> <mi>N</mi> <mi>B</mi> </msub> <mo>&cup;</mo> <msub> <mi>N</mi> <mi>T</mi> </msub> </mrow> </munder> <msub> <mi>&Delta;P</mi> <mi>i</mi> </msub> <mo>+</mo> <mi>&lambda;</mi> <munder> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>&Element;</mo> <mi>N</mi> </mrow> </munder> <mfrac> <mrow> <mo>|</mo> <msub> <mi>V</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>V</mi> <mrow> <mi>i</mi> <mi>s</mi> <mi>p</mi> <mi>e</mi> <mi>c</mi> </mrow> </msub> <mo>|</mo> </mrow> <msub> <mi>V</mi> <mrow> <mi>i</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mo>;</mo> </mrow> </math>

wherein, Δ P_iIs the active loss of the electrical component; λ is a weight coefficient; v_ispecIs the voltage desired value of node i; v_imaxIs the maximum voltage at node i.

6. The method of claim 1 or 5, wherein: the constraint conditions of the reactive power optimization comprise equality constraints and inequality constraints, and the inequality constraints comprise control variable constraints and state variable constraints.

7. The method of claim 6, wherein: the function of the equality constraint is:

<math> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>U</mi> <mi>i</mi> </msub> <msub> <mi>&Sigma;U</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>G</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>cos&theta;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>sin&theta;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Q</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>U</mi> <mi>i</mi> </msub> <msub> <mi>&Sigma;U</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>G</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>sin&theta;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>cos&theta;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>

wherein, P_i、Q_iInjection power for node i; u shape_jIs the node voltage amplitude; theta_ijIs the phase angle difference of the nodes i, j.

8. The method of claim 6, wherein: the function of the state variable constraint is:

<math> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>Q</mi> <mrow> <mi>G</mi> <mi>i</mi> <mi>min</mi> </mrow> </msub> <mo>&le;</mo> <msub> <mi>Q</mi> <mrow> <mi>G</mi> <mi>i</mi> </mrow> </msub> <mo>&le;</mo> <msub> <mi>Q</mi> <mrow> <mi>G</mi> <mi>i</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <msub> <mi>N</mi> <mi>G</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>U</mi> <mrow> <mi>i</mi> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>&le;</mo> <msub> <mi>U</mi> <mi>i</mi> </msub> <mo>&le;</mo> <msub> <mi>U</mi> <mrow> <mi>i</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <mo>{</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>N</mi> <mi>G</mi> </msub> <mo>}</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Q</mi> <mrow> <mi>T</mi> <mi>i</mi> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>&le;</mo> <msub> <mi>Q</mi> <mrow> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mo>&le;</mo> <msub> <mi>Q</mi> <mrow> <mi>T</mi> <mi>i</mi> <mi>max</mi> </mrow> </msub> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <msub> <mi>N</mi> <mrow> <mi>T</mi> <mi>G</mi> <mi>K</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>

wherein Q is_Gmin、Q_GmaxThe upper limit and the lower limit of the reactive power output of the generator are set; u shape_min、U_maxThe upper and lower limits of the node voltage are set; q_Timin、Q_TimaxThe upper and lower limits of the reactive power of the high-voltage side of the gateway transformer are defined.

9. The method of claim 6, wherein: the function of the control variable constraint is:

<math> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>U</mi> <mrow> <mi>G</mi> <mi>i</mi> <mi>min</mi> </mrow> </msub> <mo>&le;</mo> <msub> <mi>U</mi> <mrow> <mi>G</mi> <mi>i</mi> </mrow> </msub> <mo>&le;</mo> <msub> <mi>U</mi> <mrow> <mi>G</mi> <mi>i</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Q</mi> <mrow> <mi>C</mi> <mi>i</mi> <mi>min</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>Q</mi> <mo>~</mo> </mover> <mrow> <mi>C</mi> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>&le;</mo> <msub> <mi>Q</mi> <mrow> <mi>C</mi> <mi>i</mi> </mrow> </msub> <mo>&le;</mo> <msub> <mi>Q</mi> <mrow> <mi>C</mi> <mi>i</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>Q</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>C</mi> <mi>i</mi> <mn>0</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mrow> <mi>K</mi> <mi>i</mi> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>-</mo> <msub> <mover> <mi>T</mi> <mo>~</mo> </mover> <mrow> <mi>K</mi> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>&le;</mo> <msub> <mi>T</mi> <mrow> <mi>K</mi> <mi>i</mi> </mrow> </msub> <mo>&le;</mo> <msub> <mi>T</mi> <mrow> <mi>K</mi> <mi>i</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>+</mo> <msub> <mover> <mi>T</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>K</mi> <mi>i</mi> <mn>0</mn> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>

wherein the capacitor Q is connected in parallel_Ci∈N_C'; transformer gear T_Ki∈N_T； <math> <msub> <mover> <mi>Q</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>C</mi> <mi>i</mi> <mn>0</mn> </mrow> </msub> </math> And <math> <msub> <mover> <mi>T</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>K</mi> <mi>i</mi> <mn>0</mn> </mrow> </msub> </math> the upper limit of the amount of relaxation is expressed, ${\tilde{Q}}_{Ci0}$ and ${\tilde{T}}_{Ki0}$ represents the lower limit of the amount of relaxation;

and adding the constraint as:

<math> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>T</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>K</mi> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>s</mi> <mn>1</mn> </msub> <msup> <msub> <mi>T</mi> <mrow> <mi>K</mi> <mi>i</mi> </mrow> </msub> <mo>&prime;</mo> </msup> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <msub> <mi>N</mi> <mi>T</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>T</mi> <mo>~</mo> </mover> <mrow> <mi>K</mi> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>s</mi> <mn>2</mn> </msub> <msup> <msub> <mi>T</mi> <mrow> <mi>K</mi> <mi>i</mi> </mrow> </msub> <mo>&prime;</mo> </msup> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>Q</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>C</mi> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>1</mn> </msub> <msup> <msub> <mi>Q</mi> <mrow> <mi>C</mi> <mi>i</mi> </mrow> </msub> <mo>&prime;</mo> </msup> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>i</mi> <mo>&Element;</mo> <msup> <msub> <mi>N</mi> <mi>C</mi> </msub> <mo>&prime;</mo> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>Q</mi> <mo>~</mo> </mover> <mrow> <mi>C</mi> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mn>2</mn> </msub> <msup> <msub> <mi>Q</mi> <mrow> <mi>C</mi> <mi>i</mi> </mrow> </msub> <mo>&prime;</mo> </msup> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>

wherein, <math> <msub> <mover> <mi>T</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>K</mi> <mi>i</mi> <mn>0</mn> </mrow> </msub> </math> and ${\tilde{T}}_{Ki0}$ representing the upper limit and the lower limit of the gear relaxation amount of the transformer; t is_Ki' is the step size of the transformer gear; <math> <msub> <mover> <mi>Q</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>C</mi> <mi>i</mi> <mn>0</mn> </mrow> </msub> </math> and ${\tilde{Q}}_{Ci0}$ representing the capacity of the capacitorUpper and lower limits of the amount of relaxation; q_Ci' is the capacity of a set of capacitors; s₁、s₂、y₁、y₂∈Z。

10. The method of claim 1 or 5, wherein: the result of the reactive power optimization is

<math> <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mo>=</mo> <mo>&lsqb;</mo> <msub> <mi>U</mi> <mn>1</mn> </msub> <mo>...</mo> <msub> <mi>U</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mrow> <mi>G</mi> <mn>1</mn> </mrow> </msub> <mo>...</mo> <msub> <mi>Q</mi> <mrow> <mi>G</mi> <mi>P</mi> </mrow> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Q</mi> <mrow> <mi>C</mi> <mn>1</mn> </mrow> </msub> <mo>...</mo> <msub> <mi>Q</mi> <mrow> <mi>C</mi> <mi>m</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>T</mi> <mrow> <mi>K</mi> <mn>1</mn> </mrow> </msub> <mo>...</mo> <msub> <mi>T</mi> <mrow> <mi>K</mi> <mi>k</mi> </mrow> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>Q</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>C</mi> <mn>10</mn> </mrow> </msub> <mo>...</mo> <msub> <mover> <mi>Q</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>C</mi> <mrow> <mo>(</mo> <mrow> <mi>w</mi> <mo>+</mo> <mi>m</mi> </mrow> <mo>)</mo> </mrow> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>T</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>K</mi> <mn>10</mn> </mrow> </msub> <mo>...</mo> <msub> <mover> <mi>T</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>K</mi> <mi>k</mi> <mn>0</mn> </mrow> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>Q</mi> <mo>~</mo> </mover> <mrow> <mi>C</mi> <mn>10</mn> </mrow> </msub> <mo>...</mo> <msub> <mover> <mi>Q</mi> <mo>~</mo> </mover> <mrow> <mi>C</mi> <mrow> <mo>(</mo> <mrow> <mi>w</mi> <mo>+</mo> <mi>m</mi> </mrow> <mo>)</mo> </mrow> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>T</mi> <mo>~</mo> </mover> <mrow> <mi>K</mi> <mn>10</mn> </mrow> </msub> <mo>...</mo> <msub> <mover> <mi>T</mi> <mo>~</mo> </mover> <mrow> <mi>K</mi> <mi>k</mi> <mn>0</mn> </mrow> </msub> <mo>&rsqb;</mo> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>