CN105939017A - Engineering practical solution to reactive power optimization considering coupling among period - Google Patents

Abstract

The invention provides an engineering practical solution to reactive power optimization considering coupling among a period, and belongs to the field of electric power system dispatching and optimizing operation. The method comprises the following specific steps: firstly reading system operation basic information and technical parameters required by reactive power optimization considering coupling among the period and unit operation basic information and technical parameters; then, constructing a nonlinear programming model taking system operation power loss minimization as a goal, and calculating a continuous solution to control variable of reactive power regulation equipment; constructing a mixed integer programming model taking system power loss increment minimization as the goal, and calculating a discrete solution to control variable of the reactive power regulation equipment; then, substituting the obtained discrete solution into the nonlinear programming model constructed before, and calculating reactive power output level for regulating a generator set again; and obtaining the engineering practical solution to reactive power optimization considering coupling among the period on the basis of meeting security constraint conditions of electric power system operation. The solution is low in development difficulty and high in efficiency, and has extremely high practicability.

Description

The practical application method for solving of the idle work optimization of intersegmental coupling during consideration

Technical field

The present invention relates to electric power system dispatching and optimize operation field, specifically providing a kind of nothing of intersegmental coupling when considering The practical application method for solving that merit optimizes.

Background technology

Currently, China's electrical network alternating current-direct current series-parallel connection degree is constantly deepened, and system voltage control problem highlights day by day.In order to enter one Step promotes the management level of operation of power networks and the effect of optimization of management and running, when needing to further investigate consideration in Operation of Electric Systems The Reactive Power Optimazation Problem of intersegmental coupling.When considering in power system, the idle work optimization of intersegmental coupling refers to that the load according to next day is pre- Survey situation, after Unit Combination and meritorious economic load dispatching complete, on the basis of meeting every operation constraints, by adjusting The joint reactive power of unit, the group number of switched capacitors and the first-class idle control device of tap of ULTC, The reactive power distribution of zones of different and node in optimization system, to improve node voltage quality, to reduce system losses, it is ensured that electricity The safe and economical operation of Force system.

But, it is considered to time intersegmental coupling idle work optimization model in, the height non-thread of its AC power flow reactive balance equation Property, can switching reactive compensator and the discreteness of on-load transformer tap changer gear control variable and device action Number limit caused by time intersegmental coupling so that this Reactive Power Optimazation Problem become one extensive, multi-period, close coupling Nonlinear Mixed Integer Programming Problem, direct solution is the most difficult.

The existing method solving Reactive Power Optimazation Problem mainly has regular method and heuritic approach two class.But, simply with " rounding up " is the regular processing method of the principle optimality that is difficult to ensure that solution, and optimum results is the most infeasible；And open The computational efficiency of hairdo algorithm is relatively low, optimum results exists randomness, limits its answering in extensive practical power systems With.

Summary of the invention

It is an object of the invention to can be used for, with optimizing to run to provide, the technological means that engineering is actual for electric power system dispatching With solution, run and the Back ground Information of unit operation, technical parameter and constraints based on system, it is proposed that a kind of consideration Time intersegmental coupling the practical application method for solving of idle work optimization, it is possible to greatly reduce the scale that solves of former problem and solve Difficulty, improves the solution efficiency of former problem, ensures the safe and economical operation of power system.

A kind of practical application method for solving of the idle work optimization of intersegmental coupling when considering that the present invention proposes, specifically includes Following steps:

1) Back ground Information and technical parameter that the system needed for idle work optimization is run are read；

The Back ground Information of system operation and technical parameter, including: the interstitial content of system, number of lines, machine set type, machine Group number, unit access node information, node load information, network topology structure, Line technology parameter, number of capacitors, electricity Container access node information, capacitor technology parameter, transformator number, transformator connecting joint dot information and transformer technology ginseng Number；

2) Back ground Information and the technical parameter of unit operation needed for idle work optimization are read；

The Back ground Information of unit operation and technical parameter, including: the meritorious minimum of machine set type, unit rated capacity, unit Climbing capacity that minimum technology that technology is exerted oneself, unit is idle is exerted oneself and unit is gained merit；

3) structure runs loss minimization with system and turns to the Nonlinear programming Model of target, and model is by object function and constraint Condition is constituted；

The system that 3-1) sets has N number of node, U platform ULTC, M platform is adjustable electromotor, has R node installing to throw Cutting Capacitor banks, the whole day period is T, if object function is:

$\begin{array}{c}\min P_{loss}=\underset{t=1}{\overset{T}{\Σ}}{p}_{loss}\left(t\right)\\ =\underset{t=1}{\overset{T}{\Σ}}\[\underset{i=1}{\overset{N}{\Σ}}\underset{j=1}{\overset{N}{\Σ}}{V}_i\left(t\right)V_j\left(t\right)Y_{ij}{\mathrm{cos\δ}}_{ij}\left(t\right)\]\end{array}---\left(1\right)$

Formula (1) is the calculation expression that system whole day active power loss minimizes；In formula, P_lossGain merit net for system whole day Damage, p_lossT () is the system active power loss of day part；Y_ijElement for bus admittance matrix the i-th row jth row；V_iT () is the period The voltage of t node i, δ_ijT () is the phase angle difference of period t circuit ij head and end；

3-2) constraints includes:

Node is meritorious/constraint of reactive balance equation, as shown in formula (2):

$\left\{\begin{array}{c}{P}_{Gi}\left(t\right)-P_{Di}\left(t\right)-V_i\left(t\right)\underset{j=1}{\overset{N}{\Σ}}{Y}_{ij}{V}_j\left(t\right){\mathrm{cos\δ}}_{ij}\left(t\right)=0\\ Q_{Gi}\left(t\right)-Q_{Di}\left(t\right)-V_i\left(t\right)\underset{j=1}{\overset{N}{\Σ}}{Y}_{ij}{V}_j\left(t\right){\mathrm{sin\δ}}_{ij}\left(t\right)+Q_{Ci}\left(t\right)=0\end{array}\right.---\left(2\right)$

In formula, P_Gi(t)、Q_GiT () is respectively the meritorious, idle of period t node i unit and exerts oneself, P_Di(t)、Q_Di(t) difference Meritorious, the load or burden without work for period t node i；Q_CiT () is the reactive power that period t node i capacitor injects, calculation expression is Q_Ci(t)=k_Ci(t)Q_cN, k_CiT () is the group number that period t puts into capacitor, Q_cNCapacity for single group capacitor；

The bound constraint of state variable, as shown in formula (3):

x_SVmin(t)≤x_SV(t)≤x_SVmax(t) (3)

In formula, the expression formula of state variable is x_SV(t)=[V₁(t),V₂(t),...,V_N(t),P_Gslack(t)]^T, V₁(t), V₂(t) ..., V_NT () is respectively node 1,2 ..., the node voltage of N, P_GslackT () is that the meritorious of slack bus is exerted oneself；T is square Battle array transposition symbol；x_SVminT () is the lower limit value of period t state variable, x_SVmaxT () is that the period t upper limit of state variable takes Value；

The bound constraint of control variable, as shown in formula (4):

x_CVmin(t)≤x_CV(t)≤x_CVmax(t) (4)

In formula, the expression formula of control variable is x_CV(t)=[Q_G(t),k_C(t),k_T(t)]^T, Q_G(t), k_C(t) and k_T(t) point Wei not exerted oneself Q by the generator reactive of control variable_Gi(t), reactive-load compensation capacitor switching group number k_CiT () becomes with on-load voltage regulation Transformer voltage ratio k_TiT row vector that () is formed；x_CVminT () is the lower limit value of period t control variable, x_CVmaxT () is period t The upper limit value of control variable；

4) continuous solution of Reactive-power control equipment control variable is calculated；By step 1) and step 2) the middle system operation read Back ground Information and technical parameter and the Back ground Information of unit operation and technical parameter, substitute into step 3) constructed by idle work optimization mould In type, it is calculated the continuous solution of Reactive-power control equipment control variable, including: the idle of each generating set is exerted oneself, capacitor The continuous solution of switching group number and the continuous solution of transformer voltage ratio；

5) structure is minimised as the mixed-integer programming model of target with system losses increment, and model is by object function peace treaty Bundle condition is constituted；

5-1) this model optimization target is the action time of discrete control variable and the whole day effectively processing idle control equipment Number constraint, if object function is:

${\mathrm{min\ΔP}}_{losssum}=\min \underset{t=1}{\overset{T}{\Σ}}\ΣS_{{\mathrm{Px}}_{CV}}\left(t\right)\[x_{CV}^{\′}\left(t\right)-x_{CV}^{\′0}\left(t\right)\]{\mathrm{\Ω}}_{step}---\left(5\right)$

Formula (5) is the calculation expression that system losses increment is minimum；In formula, x '_CV(t)=[k '_Ci(t),k′_Ti(t)] for optimize from Dissipate capacitor switching group number and the regulation stall of load tap changer of control variable, i.e. period t； For step 3) optimize the lax solution obtaining control variable, the initial value of adjustment it is optimized as this step control variable；For the t period system losses sensitivity matrix to control variable, Ω_step=[Q_Cstep,T_step] Action step-length for idle control equipment；

5-2) constraints includes:

The bound constraint of state variable adjusting range, as shown in formula (6):

$U_{min}\left(t\right)\≤S_{{\mathrm{Ux}}_{CV}}\left(t\right)\[x_{CV}^{\′}\left(t\right)-x_{CV}^{\′0}\left(t\right)\]{\mathrm{\Ω}}_{step}+U_i\left(t\right)\≤U_{max}\left(t\right)---\left(6\right)$

In formula,For the node voltage sensitivity matrix to control variable；U_i(t) be time The voltage magnitude of section t node i, U_minT () is the lower limit value of period t node voltage, U_maxT () is the upper of period t node voltage Limit value；

The bound constraint of control variable, as shown in formula (7):

$\mathrm{int}\left(x_{CV}^{\′0}\right(t\left)\right)\≤x_{CV}^{\′}\left(t\right)\≤\mathrm{int}\left(x_{CV}^{\′0}\right(t)+1)---\left(7\right)$

In formula, int is for rounding mark；

The switching number constraint of control equipment whole day, as shown in formula (8):

$\underset{t=1}{\overset{T-1}{\Σ}}|x_{CV}^{\′}\left(t\right)-x_{CV}^{\′}(t+1)|\≤K---\left(8\right)$

In formula, reactive apparatus action frequency limits K=[k_Cmax,k_Tmax]^T, wherein k_Cmax,k_TmaxIt is respectively k_C(t), k_T(t) Maximum；

Formula (8) transfers following shape to and shows expression:

$\left\{\begin{array}{c}0\≤Z\left(t\right)-\[x_{CV}^{\′}\left(t\right)-x_{CV}^{\′}(t+1)\]\≤M_C\·{\mathrm{\δ}}_1\left(t\right)\\ 0\≤Z\left(t\right)-\[x_{CV}^{\′}(t+1)-x_{CV}^{\′}\left(t\right)\]\≤M_C\·{\mathrm{\δ}}_2\left(t\right)\\ {\mathrm{\δ}}_1\left(t\right)+{\mathrm{\δ}}_2\left(t\right)=1\\ \underset{t=1}{\overset{T-1}{\Σ}}Z\left(t\right)\≤K\end{array}\right.---\left(9\right)$

In formula, Z (t) is discrete variable, represents the action frequency of idle control equipment period t；δ₁(t),δ₂T () is that 0-1 is whole Number variable, M_CIt it is a big positive number；

6) discrete solution of Reactive-power control equipment control variable is calculated；By step 4) in calculated Reactive-power control equipment control The continuous solution of variable processed, is updated to step 5) in the mixed-integer programming model that builds, it is calculated capacitor switching group number Discrete solution and the discrete solution of transformer voltage ratio；

7) by step 6) in result of calculation substitute into step 3) in the Nonlinear programming Model that builds, again calculate to adjust and send out Group of motors idle go out force level；

8) on the basis of meeting all kinds of security constraints of Operation of Electric Systems, when obtaining considering, intersegmental coupling is idle The Practical solution optimized.

The feature of the present invention and having the beneficial effect that:

The present invention is based on the deep assurance to Operation of Electric Systems physical essence with intension, it is proposed that intersegmental coupling during consideration The practical application method for solving of idle work optimization, thus for solve this type of extensive, multi-period, non-linear mixing of close coupling Integer programming problem provides and can be used for the solution that engineering is actual, improves the business water ensureing power grid security economical operation Flat.The method has taken into full account all kinds of constraintss that Operation of Electric Systems is run with generating set, by dividing different attribute The processing mode of subproblem, it may be difficult to during the consideration of direct solution, the Reactive Power Optimazation Problem of intersegmental coupling is converted into non-thread dexterously Property planning and two subproblems of mixed integer programming, significantly reduce the scale that solves of former problem and solve difficulty, improve The solution efficiency of former problem.The method and electric power system dispatching contact closely with optimizing operation, possess the strongest suitability, permissible Be embedded into current power system planning formulation as a functional module, mode arrange with the links such as management and running among, it is opened Degree of raising difficult questions is little, development efficiency is high, has the strongest practicality.

Accompanying drawing explanation

Fig. 1 is the implementing procedure block diagram of the inventive method.

Detailed description of the invention

A kind of practical application method for solving of the idle work optimization of intersegmental coupling when considering that the present invention proposes, below in conjunction with The drawings and specific embodiments further describe as follows.

A kind of practical application method for solving of the idle work optimization of intersegmental coupling, FB(flow block) when considering that the present invention proposes As it is shown in figure 1, specifically include following steps:

1) Back ground Information and technical parameter that the system needed for idle work optimization is run are read；

The Back ground Information of system operation and technical parameter, including: the interstitial content of system, number of lines, machine set type, machine Group number, unit access node information, node load information, network topology structure, Line technology parameter, number of capacitors, electricity Container access node information, capacitor technology parameter, transformator number, transformator connecting joint dot information and transformer technology ginseng Number；

2) Back ground Information and the technical parameter of unit operation needed for idle work optimization are read；

The Back ground Information of unit operation and technical parameter, including: the meritorious minimum of machine set type, unit rated capacity, unit Climbing capacity that minimum technology that technology is exerted oneself, unit is idle is exerted oneself and unit is gained merit；

3) structure runs loss minimization with system and turns to the Nonlinear programming Model of target, and model is by object function and constraint Condition is constituted；

The system that 3-1) sets has N number of node, U platform ULTC, M platform is adjustable electromotor, has R node installing to throw Cutting Capacitor banks, the whole day period is T, if object function is:

$\begin{array}{c}\min P_{loss}=\underset{t=1}{\overset{T}{\Σ}}{p}_{loss}\left(t\right)\\ =\underset{t=1}{\overset{T}{\Σ}}\[\underset{i=1}{\overset{N}{\Σ}}\underset{j=1}{\overset{N}{\Σ}}{V}_i\left(t\right)V_j\left(t\right)Y_{ij}{\mathrm{cos\δ}}_{ij}\left(t\right)\]\end{array}---\left(1\right)$

Formula (1) is the calculation expression that system whole day active power loss minimizes；In formula, P_lossGain merit net for system whole day Damage, p_lossT () is the system active power loss of day part；Y_ijElement for bus admittance matrix the i-th row jth row；V_iT () is the period The voltage of t node i, δ_ijT () is the phase angle difference of period t circuit ij head and end；

3-2) constraints includes:

Node is meritorious/constraint of reactive balance equation, as shown in formula (2):

$\left\{\begin{array}{c}{P}_{Gi}\left(t\right)-P_{Di}\left(t\right)-V_i\left(t\right)\underset{j=1}{\overset{N}{\Σ}}{Y}_{ij}{V}_j\left(t\right){\mathrm{cos\δ}}_{ij}\left(t\right)=0\\ Q_{Gi}\left(t\right)-Q_{Di}\left(t\right)-V_i\left(t\right)\underset{j=1}{\overset{N}{\Σ}}{Y}_{ij}{V}_j\left(t\right){\mathrm{sin\δ}}_{ij}\left(t\right)+Q_{Ci}\left(t\right)=0\end{array}\right.---\left(2\right)$

In formula, P_Gi(t)、Q_GiT () is respectively the meritorious, idle of period t node i unit and exerts oneself, P_Di(t)、Q_Di(t) difference Meritorious, the load or burden without work for period t node i；Q_CiT () is the reactive power that period t node i capacitor injects, calculation expression is Q_Ci(t)=k_Ci(t)Q_cN, k_CiT () is the group number that period t puts into capacitor, Q_cNCapacity for single group capacitor；

The bound constraint of state variable (including that node voltage, slack bus are meritorious to exert oneself), as shown in formula (3):

x_SVmin(t)≤x_SV(t)≤x_SVmax(t) (3)

In formula, the expression formula of state variable is x_SV(t)=[V₁(t),V₂(t),...,V_N(t),P_Gslack(t)]^T, V₁(t), V₂(t) ..., V_NT () is respectively node 1,2 ..., the node voltage of N, P_GslackT () is that the meritorious of slack bus is exerted oneself；T is square Battle array transposition symbol；x_SVminT () is the lower limit value of period t state variable, x_SVmaxT () is that the period t upper limit of state variable takes Value；

Control variable (includes that generator reactive is exerted oneself, reactive-load compensation capacitor switching group number and ULTC become Than) bound constraint, as shown in formula (4):

x_CVmin(t)≤x_CV(t)≤x_CVmax(t) (4)

In formula, the expression formula of control variable is x_CV(t)=[Q_G(t),k_C(t),k_T(t)]^T, Q_G(t), k_C(t) and k_T(t) point Wei not exerted oneself Q by the generator reactive of control variable_Gi(t), reactive-load compensation capacitor switching group number k_CiT () becomes with on-load voltage regulation Transformer voltage ratio k_TiT row vector that () is formed；x_CVminT () is the lower limit value of period t control variable, x_CVmaxT () is period t The upper limit value of control variable, span is determined by device parameter.

4) continuous solution of Reactive-power control equipment control variable is calculated；By step 1) and step 2) the middle system operation read Back ground Information and technical parameter and the Back ground Information of unit operation and technical parameter, substitute into step 3) constructed by idle work optimization mould In type, it is calculated the continuous solution of Reactive-power control equipment control variable, including: the idle of each generating set is exerted oneself, capacitor The continuous solution of switching group number and the continuous solution of transformer voltage ratio；

5) structure is minimised as the mixed-integer programming model of target with system losses increment, and model is by object function peace treaty Bundle condition is constituted；

5-1) this model optimization target is the action time of discrete control variable and the whole day effectively processing idle control equipment Number constraint, if object function is:

${\mathrm{min\ΔP}}_{losssum}=\min \underset{t=1}{\overset{T}{\Σ}}\ΣS_{{\mathrm{Px}}_{CV}}\left(t\right)\[x_{CV}^{\′}\left(t\right)-x_{CV}^{\′0}\left(t\right)\]{\mathrm{\Ω}}_{step}---\left(5\right)$

Formula (5) is the calculation expression that system losses increment is minimum；In formula, x '_CV(t)=[k '_Ci(t),k′_Ti(t)] be The discrete control variable optimized, i.e. the capacitor switching group number of period t and the regulation stall of load tap changer；For step 3) optimize the lax solution obtaining control variable, enter as this step control variable The initial value that row is optimized and revised；For the t period system losses sensitivity square to control variable Battle array, Ω_step=[Q_Cstep,T_step] it is the action step-length of idle control equipment；

5-2) constraints includes:

The bound constraint of state variable adjusting range, as shown in formula (6):

$U_{min}\left(t\right)\≤S_{{\mathrm{Ux}}_{CV}}\left(t\right)\[x_{CV}^{\′}\left(t\right)-x_{CV}^{\′0}\left(t\right)\]{\mathrm{\Ω}}_{step}+U_i\left(t\right)\≤U_{max}\left(t\right)---\left(6\right)$

In formula,For the node voltage sensitivity matrix to control variable；U_i(t) be time The voltage magnitude of section t node i, U_minT () is the lower limit value of period t node voltage, U_maxT () is the upper of period t node voltage Limit value；

Control variable, i.e. the bound constraint of reactive-load compensation capacitor switching group number, ULTC no-load voltage ratio, such as formula (7) shown in:

$\mathrm{int}\left(x_{CV}^{\′0}\right(t\left)\right)\≤x_{CV}^{\′}\left(t\right)\≤\mathrm{int}\left(x_{CV}^{\′0}\right(t)+1)---\left(7\right)$

In formula, int is for rounding mark；

The switching number constraint of control equipment whole day, as shown in formula (8):

$\underset{t=1}{\overset{T-1}{\Σ}}|x_{CV}^{\′}\left(t\right)-x_{CV}^{\′}(t+1)|\≤K---\left(8\right)$

In formula, reactive apparatus action frequency limits K=[k_Cmax,k_Tmax]^T, wherein k_Cmax,k_TmaxIt is respectively k_C(t), k_T(t) Maximum, to reflect the whole day action frequency upper limit of idle control equipment；

Due to the existence of switching number constraint, substantially increase this step model solves difficulty.To this end, the present invention carries Going out a kind of method that absolute value inequality constraints equivalence is converted into general inequality constraints, formula (8) transfers following shape to and shows expression:

$\left\{\begin{array}{c}0\≤Z\left(t\right)-\[x_{CV}^{\′}\left(t\right)-x_{CV}^{\′}(t+1)\]\≤M_C\·{\mathrm{\δ}}_1\left(t\right)\\ 0\≤Z\left(t\right)-\[x_{CV}^{\′}(t+1)-x_{CV}^{\′}\left(t\right)\]\≤M_C\·{\mathrm{\δ}}_2\left(t\right)\\ {\mathrm{\δ}}_1\left(t\right)+{\mathrm{\δ}}_2\left(t\right)=1\\ \underset{t=1}{\overset{T-1}{\Σ}}Z\left(t\right)\≤K\end{array}\right.---\left(9\right)$

In formula, Z (t) is discrete variable, represents the action frequency of idle control equipment period t, if period t inner capacitor Switching group number changes, then Z (t) is equal to corresponding switching frequency situation of change, otherwise Z (t)=0；δ₁(t),δ₂T () is 0-1 Integer variable, the value different by it represents x '_CV(t) and x '_CV(t+1) numerical value relative size situation, as x '_CV(t) ≤x′_CV(t+1) time, then δ₁(t)=1, δ₂(t)=0, M_CIt it is a big positive number；

6) discrete solution of Reactive-power control equipment control variable is calculated；By step 4) in calculated Reactive-power control equipment control The continuous solution of variable processed, is updated to step 5) in the mixed-integer programming model that builds, it is calculated capacitor switching group number Discrete solution and the discrete solution of transformer voltage ratio；

7) by step 6) in result of calculation substitute into step 3) in the Nonlinear programming Model that builds, again calculate to adjust and send out Group of motors idle go out force level；

By step 6) the calculated discrete solution of capacitor switching group number fixes with the discrete solution of transformer voltage ratio, as Constant inflow is to step 3) constructed by Nonlinear programming Model in, use interior point method solve this Nonlinear programming Model, calculate Obtain the idle numerical value of exerting oneself considering capacitor switching group number with each generating set under transformer voltage ratio discrete solution；

8) on the basis of meeting all kinds of security constraints of Operation of Electric Systems, when obtaining considering, intersegmental coupling is idle The Practical solution optimized.

It is emphasized that this method to implement in step to ask with the practical application of the intersegmental idle work optimization coupled when considering The model that solution method is relevant can run the most customized with optimization demand etc. according to actual electric power system dispatching with computing formula, can Autgmentability is strong.Therefore, above enforcement step is only in order to illustrative not limiting technical scheme.Without departing from present invention spirit With any modification or partial replacement of scope, all should contain in the middle of scope of the presently claimed invention.

Claims (1)

1. the practical application method for solving of the idle work optimization of intersegmental coupling when considering, it is characterised in that the method is concrete Comprise the following steps:

1) Back ground Information and technical parameter that the system needed for idle work optimization is run are read；

The Back ground Information of system operation and technical parameter, including: the interstitial content of system, number of lines, machine set type, unit number Mesh, unit access node information, node load information, network topology structure, Line technology parameter, number of capacitors, capacitor Access node information, capacitor technology parameter, transformator number, transformator connecting joint dot information and transformer technology parameter；

2) Back ground Information and the technical parameter of unit operation needed for idle work optimization are read；

The Back ground Information of unit operation and technical parameter, including: machine set type, unit rated capacity, unit are gained merit minimum technology Exert oneself, unit is idle minimum technology exerts oneself and unit is gained merit climbing capacity；

3) structure runs loss minimization with system and turns to the Nonlinear programming Model of target, and model is by object function and constraints Constitute；

The system that 3-1) sets has N number of node, U platform ULTC, M platform is adjustable electromotor, has R the node installing can switching electricity Container group, the whole day period is T, if object function is:

$\begin{array}{c}\min P_{loss}=\underset{t=1}{\overset{T}{\mathrm{\Σ}}}{p}_{loss}\left(t\right)\\ =\underset{t=1}{\overset{T}{\mathrm{\Σ}}}\[\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{V}_i\left(t\right)V_j\left(t\right)Y_{ij}{\mathrm{cos\δ}}_{ij}\left(t\right)\]\end{array}---\left(1\right)$

Formula (1) is the calculation expression that system whole day active power loss minimizes；In formula, P_lossFor system whole day active power loss, p_loss T () is the system active power loss of day part；Y_ijElement for bus admittance matrix the i-th row jth row；V_iT () is period t node i Voltage, δ_ijT () is the phase angle difference of period t circuit ij head and end；

3-2) constraints includes:

Node is meritorious/constraint of reactive balance equation, as shown in formula (2):

$\left\{\begin{array}{c}{P}_{Gi}\left(t\right)-P_{Di}\left(t\right)-V_i\left(t\right)\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{Y}_{ij}{V}_j\left(t\right){\mathrm{cos\δ}}_{ij}\left(t\right)=0\\ Q_{Gi}\left(t\right)-Q_{Di}\left(t\right)-V_i\left(t\right)\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{Y}_{ij}{V}_j\left(t\right){\mathrm{sin\δ}}_{ij}\left(t\right)+Q_{Ci}\left(t\right)=0\end{array}\right.---\left(2\right)$

In formula, P_Gi(t)、Q_GiT () is respectively the meritorious, idle of period t node i unit and exerts oneself, P_Di(t)、Q_DiWhen () is respectively t Section t node i is meritorious, load or burden without work；Q_CiT () is the reactive power that period t node i capacitor injects, calculation expression is Q_Ci (t)=k_Ci(t)Q_cN, k_CiT () is the group number that period t puts into capacitor, Q_cNCapacity for single group capacitor；

The bound constraint of state variable, as shown in formula (3):

x_SVmin(t)≤x_SV(t)≤x_SVmax(t) (3)

In formula, the expression formula of state variable is x_SV(t)=[V₁(t),V₂(t),...,V_N(t),P_Gslack(t)]^T, V₁(t), V₂ (t) ..., V_NT () is respectively node 1,2 ..., the node voltage of N, P_GslackT () is that the meritorious of slack bus is exerted oneself；T is matrix Transposition symbol；x_SVminT () is the lower limit value of period t state variable, x_SVmaxT () is the upper limit value of period t state variable；

The bound constraint of control variable, as shown in formula (4):

x_CVmin(t)≤x_CV(t)≤x_CVmax(t) (4)

In formula, the expression formula of control variable is x_CV(t)=[Q_G(t),k_C(t),k_T(t)]^T, Q_G(t), k_C(t) and k_TT () is respectively Exerted oneself Q by the generator reactive of control variable_Gi(t), reactive-load compensation capacitor switching group number k_Ci(t) and ULTC No-load voltage ratio k_TiT row vector that () is formed；x_CVminT () is the lower limit value of period t control variable, x_CVmaxT () is that period t controls The upper limit value of variable；

4) continuous solution of Reactive-power control equipment control variable is calculated；By step 1) and step 2) in read system run basis Information and technical parameter and the Back ground Information of unit operation and technical parameter, substitute into step 3) constructed by idle work optimization model In, it is calculated the continuous solution of Reactive-power control equipment control variable, including: the idle of each generating set is exerted oneself, and capacitor is thrown Cut continuous solution and the continuous solution of transformer voltage ratio of group number；

5) structure is minimised as the mixed-integer programming model of target with system losses increment, and model is by object function and constraint bar Part is constituted；

5-1) this model optimization target is effectively to process the action frequency of the discrete control variable of idle control equipment and whole day about Bundle, if object function is:

${\mathrm{min\ΔP}}_{losssum}=min\underset{t=1}{\overset{T}{\Σ}}{\mathrm{\ΣS}}_{{\mathrm{Px}}_{CV}}\left(t\right)\[x_{CV}^{\′}\left(t\right)-x_{CV}^{\′0}\left(t\right)\]{\mathrm{\Ω}}_{step}---\left(5\right)$

Formula (5) is the calculation expression that system losses increment is minimum；In formula, x '_CV(t)=[k '_Ci(t),k′_Ti(t)] discrete for optimize The capacitor switching group number of control variable, i.e. period t and the regulation stall of load tap changer； For step 3) optimize the lax solution obtaining control variable, the initial value of adjustment it is optimized as this step control variable；For the t period system losses sensitivity matrix to control variable, Ω_step=[Q_Cstep,T_step] Action step-length for idle control equipment；

5-2) constraints includes:

The bound constraint of state variable adjusting range, as shown in formula (6):

$U_{min}\left(t\right)\≤S_{{\mathrm{Ux}}_{CV}}\left(t\right)\[x_{CV}^{\′}\left(t\right)-x_{CV}^{\′0}\left(t\right)\]{\mathrm{\Ω}}_{step}+U_i\left(t\right)\≤U_{max}\left(t\right)---\left(6\right)$

In formula, S_UxCV(t)=[S_UQC(t),S_UT(t)] it is the node voltage sensitivity matrix to control variable；U_iT () is period t The voltage magnitude of node i, U_minT () is the lower limit value of period t node voltage, U_maxT () is that the period t upper limit of node voltage takes Value；

The bound constraint of control variable, as shown in formula (7):

$\mathrm{int}\left(x_{CV}^{\′0}\right(t\left)\right)\≤x_{CV}^{\′}\left(t\right)\≤\mathrm{int}\left(x_{CV}^{\′0}\right(t)+1)---\left(7\right)$

In formula, int is for rounding mark；

The switching number constraint of control equipment whole day, as shown in formula (8):

$\underset{t=1}{\overset{T-1}{\Σ}}|x_{CV}^{\′}\left(t\right)-x_{CV}^{\′}(t+1)|\≤K---\left(8\right)$

In formula, reactive apparatus action frequency limits K=[k_Cmax,k_Tmax]^T, wherein k_Cmax,k_TmaxIt is respectively k_C(t), k_TT () Big value；

Formula (8) transfers following shape to and shows expression:

$\left\{\begin{array}{c}0\≤Z\left(t\right)-\[x_{CV}^{\′}\left(t\right)-x_{CV}^{\′}(t+1)\]\≤M_C\·{\mathrm{\δ}}_1\left(t\right)\\ 0\≤Z\left(t\right)-\[x_{CV}^{\′}(t+1)-x_{CV}^{\′}\left(t\right)\]\≤M_C\·{\mathrm{\δ}}_2\left(t\right)\\ {\mathrm{\δ}}_1\left(t\right)+{\mathrm{\δ}}_2\left(t\right)=1\\ \underset{t=1}{\overset{T-1}{\Σ}}Z\left(t\right)\≤K\end{array}\right.---\left(9\right)$

In formula, Z (t) is discrete variable, represents the action frequency of idle control equipment period t；δ₁(t),δ₂T () is that 0-1 integer becomes Amount, M_CIt it is a big positive number；

6) discrete solution of Reactive-power control equipment control variable is calculated；By step 4) in calculated Reactive-power control equipment control become The continuous solution of amount, is updated to step 5) in the mixed-integer programming model that builds, it is calculated the discrete of capacitor switching group number Solve the discrete solution with transformer voltage ratio；

7) by step 6) in result of calculation substitute into step 3) in the Nonlinear programming Model that builds, again calculate and adjust electromotor Group idle go out force level；

8) on the basis of meeting all kinds of security constraints of Operation of Electric Systems, the idle work optimization of intersegmental coupling when obtaining considering Practical solution.