CN103413182A - Monthly electricity generation and transmission integrated maintenance optimization method based on induced function - Google Patents

Abstract

The invention discloses a monthly electricity generation and transmission integrated maintenance optimization method based on an induced function, and belongs to the field of electric power system optimized operation. The method comprises the steps that a grid company obtains relevant basic data from a database; the grid company builds a mathematical model for monthly electricity generation and transmission integrated maintenance optimization; a monthly electricity generation and transmission integrated maintenance optimization relaxation model is built and solved; a monthly electricity generation and transmission integrated maintenance optimization model based on the induced function is built and solved; maintenance plan optimization is completed; the grid company feeds back generator set maintenance plans to a power plant, and the power plant and the grid company respectively arrange generator set maintenance and electric transmission line maintenance. The method can be used for solving the large-scale monthly electricity generation and transmission integrated maintenance plan optimization problem, greatly accelerate computation speed on the basis that optimality is guaranteed, and have good application prospect in actual engineering.

Description

Monthly the integrated maintenance optimization method of transmission of electricity based on induced function

Technical field

The invention belongs to electric power system optimization operation field, particularly the integrated maintenance optimization of transmission of electricity is sent out in electric system.

Background technology

Maintenance Schedule Optimization refers in the certain hour interval, guarantees that the equipment of declaring maintenance is arranged, under the prerequisite of overhauling, to reduce the impact of overhaul of the equipments on power system security and economy smoothly as far as possible.The maintenance of genset has a significant impact the establishment of generation schedule, and the maintenance of transmission line of electricity has a significant impact system power supply reliability and ability to transmit electricity.Along with the expansion of electric system scale and the raising of complicacy, how the turnaround plan of arranged rational genset and transmission line of electricity, distribute the power equipment resource rationally, become important action of electrical production.

M.K.C.Marwali and S.M.Shahidehpour propose first the concept that medium-term and long-term the integrated maintenance of transmission of electricity optimize (Integrated generation and transmission maintenance scheduling with network constraints[J] .IEEE Transactions on Power Systems, 1998,13 (3): 1063-1068), realized the coordination optimization of medium-term and long-term transmission of electricity turnaround plan and Short Term Generation Schedules.In actual turnaround plan is arranged work, owing in annual scope, having many uncertain factors, the a lot of regional turnaround plan arrangements of China be take monthly as main, side is old have been proposed method that monthly the integrated maintenance of transmission of electricity optimize (side is old, Xia Qing, Hu Zhaoyang etc. monthly transmission of electricity maintenance one optimization method [J]. Automation of Electric Systems, 2011,35(11): 50-54), the method comprises optimized algorithm two parts of setting up monthly the integrated maintenance Optimized model of transmission of electricity and solving this model:

1) set up monthly the integrated maintenance Optimized model of transmission of electricity formed by objective function and constraint condition:

1-1) objective function

In actual turnaround plan was arranged work, each repair apparatus can be declared a maintenance wish interval, namely wishes most to be arranged maintenance in this interval, and grid company is understood the reasonable arrangement turnaround plan, as far as possible farthest meets the maintenance wish of each equipment.

$\min \{\underset{i=1}{\overset{N_g}{\mathrm{\Σ}}}\underset{t=1}{\overset{T+1}{\mathrm{\Σ}}}{W}_{i,t}g{X}_{i,t}+\underset{j=1}{\overset{N_l}{\mathrm{\Σ}}}\underset{t=1}{\overset{T+1}{\mathrm{\Σ}}}{W}_{j,t}g{Y}_{j,t}\}---\left(1\right)$

In formula (1), N _gFor declaring the genset quantity of lower monthly repair, N _lFor declaring the transmission line of electricity quantity of lower monthly repair, T is total number of days next month, U _iFor maintenance unit i inspection and repair shop takes time; X _i,tCharacterize unit i and constantly start from t the 0-1 variable overhauled, if maintenance unit i is starting maintenance lasting U the α day of next month _iTime, X _{I, α}=1, all the other periods are 0; W _i,tFor the maintenance wish function of maintenance unit i, mean that maintenance unit i is in the maintenance wish that t day starts to overhaul; U _jFor maintenance circuit j inspection and repair shop takes time; Y _j,tCharacterize circuit j and constantly start from t the 0-1 variable overhauled, if maintenance circuit j is starting maintenance lasting U the β day of next month _jTime, Y _{J, β}=1, all the other periods are 0; W _j,tFor the maintenance wish function of maintenance circuit j, mean that maintenance circuit j is in the maintenance wish that t day starts to overhaul;

The maintenance wish function W of unit i _i,tExpression as follows:

$W_{i,t}=\left\{\begin{array}{cc}L& e_i\&le;t\&le;l_i\\ H& 1\&le;t<e_i{l}_i<t\&le;T\\ M& t=T+1\end{array}\right.---\left(2\right)$

In formula (2), [e _i, l _i] be the maintenance wish interval of unit i; Maintenance wish function W _i,tFor piecewise function: at the interval [e of inferior monthly repair wish _i, l _i] interior value L, L is a very little constant (for example 1), value H outside inferior monthly repair wish interval, H are a great constant (for example 10000000), finally at inferior month have virtually increased by one day, corresponding maintenance wish function W _{I, T+1}Value M, M are a larger constant (for example 10000); When genset starts maintenance from virtual sky, be considered as this genset and at inferior month, can't arrange maintenance, need to extend to following month and arrange maintenance; Wherein, H>>M>>L, As soon as possible Promising Policy maintenance wish while having guaranteed genset arrangement maintenance, extend to following month and arrange maintenance if can't meet;

In like manner, the maintenance wish function W of transmission line of electricity j _j,tExpression formula as follows:

$W_{j,t}=\left\{\begin{array}{cc}L& e_j\&le;t\&le;l_j\\ H& 1\&le;t<e_j{l}_j<t\&le;T\\ M& t=T+1\end{array}\right.---\left(3\right)$

In formula (3), [e _j, l _j] be the maintenance wish interval of circuit j; Maintenance wish function W _j,tFor piecewise function: at the interval [e of maintenance wish _j, l _j] interior value L, L is a very little constant (for example 1), value H outside inferior monthly repair wish interval, H are a great constant (for example 10000000), finally at inferior month have virtually increased by one day, corresponding maintenance wish function W _{J, T+1}Value M, M are a larger constant (for example 10000); When transmission line of electricity starts maintenance from virtual sky, be considered as this transmission line of electricity and at inferior month, can't arrange maintenance, need to extend to following month and arrange maintenance; Wherein, H>>M>>L, As soon as possible Promising Policy maintenance wish while having guaranteed transmission line of electricity arrangement maintenance, extend to following month and arrange maintenance if can't meet;

1-2) constraint condition, comprise overhauling and declare constraint condition, unit output bound constraint condition, node power equilibrium constraint, system reserve constraint condition, branch road DC power flow constraint condition, circuit transmission limit constraint condition and start inspecting state integer constraint condition, be respectively described below:

1-2-1) constraint condition is declared in maintenance:

To all units of declaring maintenance, need to meet:

$\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{X}_{i,t}=1,i=1,K,N_g$

To all circuits of declaring maintenance, need to meet:

$\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{Y}_{j,t}=1,j=1,K,N_l$

1-2-2) unit output bound constraint condition:

$0\&le;P_{i,t}\&le;(1-\underset{\mathrm{\&tau;}=t-U_i+1}{\overset{t}{\mathrm{\&Sigma;}}}{X}_{i,\mathrm{\&tau;}})G_{i,\max },i=1,K,N_1;t=1,K,T$

In following formula, N ₁For genset sum, G _{I, max}For genset i max cap.;

1-2-3) node power equilibrium constraint:

K*F=A*P-B*L

K is node branch road incidence matrix, and F is the meritorious trend vector of circuit, and A is node unit incidence matrix, and P is the meritorious vector of unit output, and B is the node load incidence matrix, and L is the meritorious vector of node load;

1-2-4) system reserve constraint condition:

$\underset{i=1}{\overset{N_1}{\mathrm{\&Sigma;}}}(1-\underset{\mathrm{\&tau;}=t-U_i+1}{\overset{t}{\mathrm{\&Sigma;}}}{X}_{i,\mathrm{\&tau;}})G_{i,\max }\&GreaterEqual;D_t(1+R),t=1,K,T$

D _tFor t load constantly, R is positive percentage reserve;

1-2-5) branch road DC power flow constraint condition:

$|F_{j,t}-({\mathrm{\&theta;}}_{a,t}-{\mathrm{\&theta;}}_{b,t})/x_{\mathrm{ab}}|\&le;C\underset{\mathrm{\&tau;}=t-U_j+1}{\overset{t}{\mathrm{\&Sigma;}}}{Y}_{j,\mathrm{\&tau;}},j=1,K,N_2,t=1,K,T$

Wherein, N ₂For transmission line of electricity sum, F _j,tFor circuit j at t meritorious trend constantly, θ _a,tFor the phase angle of node a, x _AbFor the branch road reactance, C is a very large number;

1-2-6) circuit transmission limit constraint condition:

$\left|F_{j,t}\right|\&le;F_{j,\max }(1-\underset{\mathrm{\&tau;}=t-U_j+1}{\overset{t}{\mathrm{\&Sigma;}}}{Y}_{j,\mathrm{\&tau;}})j=1,K,N_2,t=1,K,T$

F _{J, max}Transmission capacity limits for circuit j;

1-2-7) start inspecting state integer constraint condition:

X _i,t∈{0,1},i＝1,2,...,N _g;t＝1,...,T+1

Y _j,t∈{0,1},j＝1,K,N _l;t＝1,K,T+1

2) solve the optimized algorithm of this model

Feature for genset maintenance variable and power transmission lines overhauling Coupled Variable a little less than, proposed to overhaul the composition decomposition algorithm based on the transmission of electricity of sending out of the decision variable identification of working, monthly the integrated maintenance optimization problem of transmission of electricity resolved into to two subproblems such as monthly generating maintenance optimization problem and monthly transmission of electricity maintenance optimization problem and solve respectively, by the progressively convergence optimum solution that iterates.

The method has been accelerated computing velocity to a certain extent, but can't guarantee optimality while facing extensive example, and speed also has room for promotion.

Comprehensive current achievement in research can be found, sending out the integrated maintenance Optimized model of transmission of electricity is a large-scale mixed integer programming problem, its constrain set is in large scale, not only comprise the repair time constraint, the maintenance continuous constraint, the maintenance related constraints such as maintenance resource constraint, also comprise the node power balance, the Branch Power Flow equation, the unit output bound, the Operation of Electric Systems related constraints such as circuit transmission limit, relate to maintenance variable and unit output, the dual coupling of the variablees such as Line Flow on the time and space, therefore sending out the integrated maintenance optimization of transmission of electricity is np hard problem.Aspect algorithm, method commonly used comprises Benders decomposition method, Lagrangian Relaxation and intelligent algorithm etc. at present.The Benders decomposition method is that primal problem and subproblem solve by former PROBLEM DECOMPOSITION.The Benders decomposition method can comprise the integer of turnaround plan, the characteristics such as non-linear and simultaneously without simplification; Yet the calculation process more complicated of Benders decomposition method, for large-scale practical power systems, may occur that iterations is more, cause long situation computing time.The core of Lagrangian Relaxation is that destroyed constraint condition is added to objective function by the form of punishment amount.The method has overcome the problem of " dimension calamity " to a certain extent, and numerous Lagrange multipliers of still introducing are easily vibrated in iteration, is difficult for convergence.Intelligent algorithm such as particle cluster algorithm, genetic algorithm etc. have the advantage that can process nonlinear problem, but easily are absorbed in locally optimal solution, affected greatly by calculating parameter.

Continuous increase along with the electrical network scale, grid company in the urgent need to efficiently a kind of and do not lose optimality send out the integrated maintenance optimization method of transmission of electricity, make grid company can arrange accordingly the turnaround plan of genset and transmission line of electricity, on the basis that guarantees electric power netting safe running, maximize the maintenance wish that meets repair apparatus, reach the target of most optimum distribution of resources.

Summary of the invention

The objective of the invention is for overcoming the weak point of prior art, monthly the integrated maintenance optimization method of transmission of electricity based on induced function of proposition, for extensive monthly the integrated maintenance of transmission of electricity provides a kind of fast Optimization.Method provided by the invention takes full advantage of lax monthly the information that the integrated maintenance Optimized model solution of transmission of electricity provides, and the objective function of model is optimized.Model that the present invention carries be take and at utmost met the overhaul of the equipments wish and be objective function, and the constraint conditions such as constraint, maintenance mutual exclusive restrict, system reserve constraint, the constraint of unit output bound, node power Constraints of Equilibrium, the constraint of branch road DC power flow, the constraint of circuit transmission limit are declared in satisfied maintenance.

Monthly the integrated maintenance optimization method of transmission of electricity based on induced function of this method, is characterized in that, comprises the following steps:

1) set up monthly the integrated maintenance Optimized model of transmission of electricity formed by objective function and constraint condition:

1-1) from database, obtaining the relevant rudimentary data;

Required basic data comprises repair apparatus related data, monthly load prediction data, grid topology data and Optimal Parameters data etc.;

1-2) according to the basic data of obtaining, build monthly the integrated maintenance Optimized model of transmission of electricity, this model is comprised of objective function and constraint condition, specifically comprises:

1-2-1) objective function of monthly the integrated maintenance Optimized model of transmission of electricity of structure is as follows:

$\min \{\underset{i=1}{\overset{N_g}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{W}_{i,t}g{X}_{i,t}+\underset{j=1}{\overset{N_l}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{W}_{j,t}g{Y}_{j,t}\}---\left(1\right)$

In formula (1), N _gFor declaring the genset quantity of lower monthly repair, N _lFor declaring the transmission line of electricity quantity of lower monthly repair, T is total number of days next month, U _iFor maintenance unit i inspection and repair shop takes time; X _i,tCharacterize unit i and constantly start from t the 0-1 variable overhauled, if maintenance unit i is starting maintenance lasting U the α day of next month _iTime, X _{I, α}=1, all the other periods are 0; W _i,tFor the maintenance wish function of maintenance unit i, mean that maintenance unit i is in the maintenance wish that t day starts to overhaul; U _jFor maintenance circuit j inspection and repair shop takes time; Y _j,tCharacterize circuit j and constantly start from t the 0-1 variable overhauled, if maintenance circuit j is starting maintenance lasting U the β day of next month _jTime, Y _{J, β}=1, all the other periods are 0; W _j,tFor the maintenance wish function of maintenance circuit j, mean that maintenance circuit j is in the maintenance wish that t day starts to overhaul;

The maintenance wish function W of unit i _i,tExpression as follows:

$W_{i,t}=\left\{\begin{array}{cc}L& e_i\&le;t\&le;l_i\\ H& 1\&le;t<e_i{l}_i<t\&le;T\\ M& t=T+1\end{array}\right.---\left(2\right)$

In formula (2), [e _i, l _i] be the maintenance wish interval of unit i; Maintenance wish function W _i,tFor piecewise function: at the interval [e of inferior monthly repair wish _i, l _i] interior value L, L is a very little constant (for example 1), value H outside inferior monthly repair wish interval, H are a great constant (for example 10000000), finally at inferior month have virtually increased by one day, corresponding maintenance wish function W _{I, T+1}Value M, M are a larger constant (for example 10000); When genset starts maintenance from virtual sky, be considered as this genset and at inferior month, can't arrange maintenance, need to extend to following month and arrange maintenance; Wherein, H>>M>>L, As soon as possible Promising Policy maintenance wish while having guaranteed genset arrangement maintenance, extend to following month and arrange maintenance if can't meet;

In like manner, the maintenance wish function W of transmission line of electricity j _j,tExpression as follows:

$W_{j,t}=\left\{\begin{array}{cc}L& e_j\&le;t\&le;l_j\\ H& 1\&le;t<e_j{l}_j<t\&le;T\\ M& t=T+1\end{array}\right.---\left(3\right)$

In formula (3), [e _j, l _j] be the maintenance wish interval of circuit j; Maintenance wish function W _j,tFor piecewise function: at the interval [e of maintenance wish _j, l _j] interior value L, L is a very little constant (for example 1), value H outside inferior monthly repair wish interval, H are a great constant (for example 10000000), have virtually increased by one day, corresponding maintenance wish function W inferior month last day _{J, T+1}Value M, M are a larger constant (for example 10000); When transmission line of electricity starts maintenance from virtual sky, be considered as this transmission line of electricity and at inferior month, can't arrange maintenance, need to extend to following month and arrange maintenance; Wherein, H>>M>>L, As soon as possible Promising Policy maintenance wish while having guaranteed transmission line of electricity arrangement maintenance, extend to following month and arrange maintenance if can't meet;

1-2-2) build the constraint condition of monthly the integrated maintenance Optimized model of transmission of electricity, comprise overhauling and declare constraint condition, unit output bound constraint condition, node power equilibrium constraint, system reserve constraint condition, branch road DC power flow constraint condition, circuit transmission limit constraint condition and start inspecting state integer constraint condition, be respectively described below:

1-2-2-1) constraint condition is declared in maintenance:

To all units of declaring maintenance, need to meet:

$\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{X}_{i,t}=1,i=1,K,N_g$

To all circuits of declaring maintenance, need to meet:

$\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{Y}_{i,t}=1,j=1,K,N_l$

1-2-2-2) unit output bound constraint condition:

$0\&le;P_{i,t}\&le;(1-\underset{\mathrm{\&tau;}=t-U_i+1}{\overset{t}{\mathrm{\&Sigma;}}}{X}_{i,\mathrm{\&tau;}})G_{i,\max },i=1,K,N_1;t=1,K,T$

In following formula, N ₁For genset sum, G _{I, max}For genset i max cap.;

1-2-2-3) node power equilibrium constraint:

K*F=A*P-B*L

K is node branch road incidence matrix, and F is the meritorious trend vector of circuit, and A is node unit incidence matrix, and P is the meritorious vector of unit output, and B is the node load incidence matrix, and L is the meritorious vector of node load;

1-2-2-4) system reserve constraint condition:

$\underset{i=1}{\overset{N_1}{\mathrm{\&Sigma;}}}(1-\underset{\mathrm{\&tau;}=t-U_i+1}{\overset{t}{\mathrm{\&Sigma;}}}{X}_{i,\mathrm{\&tau;}})G_{i,\max }\&GreaterEqual;D_t(1+R),t=1,K,T$

D _tFor t load constantly, R is positive percentage reserve;

1-2-2-5) branch road DC power flow constraint condition:

$|F_{j,t}-({\mathrm{\&theta;}}_{a,t}-{\mathrm{\&theta;}}_{b,t})/x_{\mathrm{ab}}|\&le;C\underset{\mathrm{\&tau;}=t-U_j+1}{\overset{t}{\mathrm{\&Sigma;}}}{Y}_{j,\mathrm{\&tau;}},j=1,K,N_2,t=1,K,T$

Wherein, N ₂For transmission line of electricity sum, F _j,tFor circuit j at t meritorious trend constantly, θ _a,tFor the phase angle of node a, x _AbFor the branch road reactance, C is a very large constant (for example 100000);

1-2-2-6) circuit transmission limit constraint condition:

$\left|F_{j,t}\right|\&le;F_{j,\max }(1-\underset{\mathrm{\&tau;}=t-U_j+1}{\overset{t}{\mathrm{\&Sigma;}}}{Y}_{j,\mathrm{\&tau;}})j=1,K,N_2,t=1,K,T$

F _{J, max}Transmission capacity limits for circuit j;

1-2-2-7) start inspecting state integer constraint condition:

X _i,t∈{0,1},i＝1,2,...,N _g;t＝1,...,T+1

Y _j,t∈{0,1},j＝1,K,N _l;t＝1,K,T+1

2) solve the optimized algorithm of this model;

2-1) by the integer variable X in monthly the integrated maintenance Optimized model of transmission of electricity _i,tAnd Y _j,tRelax, even X _i,tAnd Y _j,tCan get any value in [0,1], build lax monthly the integrated maintenance Optimized model of transmission of electricity;

2-2) adopt linear programming for solution device solution procedure 2-1) middle lax monthly the integrated maintenance Optimized model of transmission of electricity built, the optimum solution that obtains relaxation model is With

2-3) according to the optimum solution of the relaxation model that obtains

With

The structure induced function;

Definition means that unit i is at t inspecting state variable constantly

$\stackrel{\&OverBar;}{X_{i,t}}=\underset{\mathrm{\&tau;}=t-U_i+1}{\overset{t}{\mathrm{\&Sigma;}}}{X}_{i,\mathrm{\&tau;}}^{\&prime;}$

If

Be 1, mean that this unit is in inspecting state; If

Be 0, mean that this unit is in the state do not overhauled;

Definition means that unit i at the variable that t starts to overhaul the wish size constantly is

$\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{X_{i,t}}}=\frac{\underset{\mathrm{\&tau;}=t}{\overset{t+U_i-1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{X_{i,\mathrm{\&tau;}}}}{U_i}$

Larger, mean that unit i more tends to constantly start maintenance at t; Therefore, the induced function of unit i

Be defined as follows:

$\stackrel{\&OverBar;}{W_{i,t}}=\left\{\begin{array}{cc}L-\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{X_{i,t}}}& e_i\&le;t\&le;l_i\\ H& 1\&le;t<e_i{l}_i<t\&le;T\\ M& t=T+1\end{array}\right.$

The induced function of unit i

At the interval [e of maintenance wish _i, l _i] interior value is relevant with the solution of lax monthly the integrated maintenance Optimized model of transmission of electricity, for

Value H outside inferior monthly repair wish interval, finally also virtually at inferior month increased by one day, corresponding induced function

Value M;

In like manner, for the maintenance circuit, introduce variable

Mean that circuit j is at t inspecting state constantly; ,

$\stackrel{\&OverBar;}{Y_{j,t}}=\underset{\mathrm{\&tau;}=t-U_j+1}{\overset{t}{\mathrm{\&Sigma;}}}{Y}_{j,\mathrm{\&tau;}}^{\&prime;}$

If

Be 1, mean that this circuit is in inspecting state, if

Be 0, mean that this circuit is in the state do not overhauled; Variable

Mean that circuit j starts to overhaul the wish size constantly at t:

$\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{Y_{j,t}}}=\frac{\underset{\mathrm{\&tau;}=t}{\overset{t+U_j-1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{Y_{j,\mathrm{\&tau;}}}}{U_j}$

Larger, circuit j more tends to constantly start maintenance at t; Therefore, the induced function of circuit j

Be defined as follows:

$\stackrel{\&OverBar;}{W_{j,t}}=\left\{\begin{array}{cc}L-\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{Y_{j,t}}}& e_j\&le;t\&le;l_j\\ H& 1\&le;t<e_j{l}_j<t\&le;T\\ M& t=T+1\end{array}\right.$

The induced function of circuit j

At the interval [e of maintenance wish _j, l _j] interior value is Should be relevant with the solution of lax monthly the integrated maintenance Optimized model of transmission of electricity; Value H outside inferior monthly repair wish interval, be a great constant (for example 10000000), and last virtual increase was one day at inferior month, corresponding induced function

Value M, be larger constant (for example 10000);

2-4) according to step 2-3) induced function of structure, build monthly the integrated maintenance Optimized model of transmission of electricity based on induced function;

This model is comprised of objective function and constraint condition:

Wherein, objective function is:

$\min \{\underset{i=1}{\overset{N_g}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{W_{i,t}}g{X}_{i,t}+\underset{j=1}{\overset{N_l}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{W_{j,t}}g{Y}_{j,t}\}$

The constraint condition of model and step 1-2) in monthly the integrated maintenance Optimized model of transmission of electricity building in full accord;

2-5) solve monthly the integrated maintenance Optimized model of transmission of electricity based on induced function;

Adopt the mixed integer programming solver to solve monthly the integrated maintenance Optimized model of transmission of electricity based on induced function, obtain the turnaround plan of monthly genset and transmission line of electricity;

2-6) according to step 2-5) turnaround plan that obtains overhauls repair apparatus; So far, institute of the present invention extracting method is implemented complete.

The present invention is owing to taking above technical scheme, and it has the following advantages:

Aspect counting yield, while directly calculating, because minute number is more, reduce the upper bound of optimum solution and expend long time, cause computing velocity slower.The present invention is directed to extensive mixed integer programming problem, adopt branch's cutting-plane method to solve, and introduce induced function according to the lax solution of former problem.The method based on induced function that the present invention proposes promptly reduces the upper bound of primal problem optimum solution, thereby the calculating of a large amount of branch problems has been avoided in the quick location of having realized Optimum Solution, has greatly accelerated computing velocity.Simultaneously, the method for the present invention's proposition has also guaranteed optimality.

The accompanying drawing explanation

Fig. 1 is monthly the integrated maintenance optimization method process flow diagram of transmission of electricity of the present invention;

Fig. 2 is genset maintenance wish function curve in institute of the present invention extracting method;

Fig. 3 is power transmission lines overhauling wish function curve in institute of the present invention extracting method.

Embodiment

Below the present invention is further detailed explanation.Should be appreciated that embodiment described herein can be in order to explain the present invention, but do not limit the present invention.

The invention provides monthly the integrated Maintenance Schedule Optimization method of transmission of electricity based on induced function, as shown in Figure 1, the method comprises according to the basic data of obtaining sets up monthly the integrated maintenance Optimized model of transmission of electricity and the optimized algorithm two parts that solve this model.Embodiment is as follows:

1) set up monthly the integrated maintenance Optimized model of transmission of electricity formed by objective function and constraint condition:

1-1) from database, obtaining the relevant rudimentary data;

Required basic data comprises repair apparatus related data, monthly load prediction data, grid topology data and Optimal Parameters data etc.;

The repair apparatus related data comprises repair apparatus ID, the maintenance wish is interval, inspection and repair shop takes time etc.;

Monthly load prediction data comprise the peak load data of each day of next month electrical network, the node load data of each node of peak load period;

Grid topology data comprises the node of electric power networks and annexation, circuit ID, node ID, unit ID, unit correlation parameter (comprising unit capacity etc.), the circuit correlation parameter (comprising line reactance etc.) of transmission line of electricity;

1-2) according to the basic data of obtaining, build monthly the integrated maintenance Optimized model of transmission of electricity, this model is comprised of objective function and constraint condition, specifically comprises:

1-2-1) objective function of monthly the integrated maintenance Optimized model of transmission of electricity of structure is as follows:

$\min \{\underset{i=1}{\overset{N_g}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{W}_{i,t}g{X}_{i,t}+\underset{j=1}{\overset{N_l}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{W}_{j,t}g{Y}_{j,t}\}---\left(1\right)$

In formula (1), N _gFor declaring the genset quantity of lower monthly repair, N _lFor declaring the transmission line of electricity quantity of lower monthly repair, T is total number of days next month, U _iFor maintenance unit i inspection and repair shop takes time; X _i,tCharacterize unit i and constantly start from t the 0-1 variable overhauled, if maintenance unit i is starting maintenance lasting U the α day of next month _iTime, X _{I, α}=1, all the other periods are 0; W _i,tFor the maintenance wish function of maintenance unit i, mean that maintenance unit i is in the maintenance wish that t day starts to overhaul; U _jFor maintenance circuit j inspection and repair shop takes time; Y _j,tCharacterize circuit j and constantly start from t the 0-1 variable overhauled, if maintenance circuit j is starting maintenance lasting U the β day of next month _jTime, Y _{J, β}=1, all the other periods are 0; W _j,tFor the maintenance wish function of maintenance circuit j, mean that maintenance circuit j is in the maintenance wish that t day starts to overhaul;

The maintenance wish function W of unit i _i,tAs shown in Figure 2, expression is as follows:

$W_{i,t}=\left\{\begin{array}{cc}L& e_i\&le;t\&le;l_i\\ H& 1\&le;t<e_i{l}_i<t\&le;T\\ M& t=T+1\end{array}\right.---\left(2\right)$

In formula (2), [e _i, l _i] be the maintenance wish interval of unit i; Maintenance wish function W _i,tFor piecewise function: at the interval [e of inferior monthly repair wish _i, l _i] interior value L, L is a very little constant (for example 1), value H outside inferior monthly repair wish interval, H are a great constant (for example 10000000), have virtually increased by one day, corresponding maintenance wish function W inferior month last day _{I, T+1}Value M, M are a larger constant (for example 10000); When genset starts maintenance from virtual sky, be considered as this genset and at inferior month, can't arrange maintenance, need to extend to following month and arrange maintenance; Wherein, H>>M>>L, As soon as possible Promising Policy maintenance wish while having guaranteed genset arrangement maintenance, extend to following month and arrange maintenance if can't meet;

In like manner, the maintenance wish function W of transmission line of electricity j _j,tAs shown in Figure 3, expression is as follows:

$W_{j,t}=\left\{\begin{array}{cc}L& e_j\&le;t\&le;l_j\\ H& 1\&le;t<e_j{l}_j<t\&le;T\\ M& t=T+1\end{array}\right.---\left(3\right)$

In formula (3), [e _j, l _j] be the maintenance wish interval of circuit j; Maintenance wish function W _j,tFor piecewise function: at the interval [e of maintenance wish _j, l _j] interior value L, L is a very little constant (for example 1), value H outside inferior monthly repair wish interval, H are a great constant (for example 10000000), have virtually increased by one day, corresponding maintenance wish function W inferior month last day _{J, T+1}Value M, M are a larger constant (for example 10000); When transmission line of electricity starts maintenance from virtual sky, be considered as this transmission line of electricity and at inferior month, can't arrange maintenance, need to extend to following month and arrange maintenance; Wherein, H>>M>>L, As soon as possible Promising Policy maintenance wish while having guaranteed transmission line of electricity arrangement maintenance, extend to following month and arrange maintenance if can't meet;

1-2-2) build the constraint condition of monthly the integrated maintenance Optimized model of transmission of electricity, comprise overhauling and declare constraint condition, unit output bound constraint condition, node power equilibrium constraint, system reserve constraint condition, branch road DC power flow constraint condition, circuit transmission limit constraint condition and start inspecting state integer constraint condition, be respectively described below:

1-2-2-1) constraint condition is declared in maintenance:

To all units of declaring maintenance, need to meet:

$\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{X}_{i,t}=1,i=1,K,N_g$

To all circuits of declaring maintenance, need to meet:

$\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{Y}_{j,t}=1,j=1,K,N_l$

1-2-2-2) unit output bound constraint condition:

$0\&le;P_{i,t}\&le;(1-\underset{\mathrm{\&tau;}=t-U_i+1}{\overset{t}{\mathrm{\&Sigma;}}}{X}_{i,\mathrm{\&tau;}})G_{i,\max },i=1,K,N_1;t=1,K,T$

In following formula, N ₁For genset sum, G _{I, max}For genset i max cap.;

1-2-2-3) node power equilibrium constraint:

K*F=A*P-B*L

K is node branch road incidence matrix, and F is the meritorious trend vector of circuit, and A is node unit incidence matrix, and P is the meritorious vector of unit output, and B is the node load incidence matrix, and L is the meritorious vector of node load;

1-2-2-4) system reserve constraint condition:

$\underset{i=1}{\overset{N_1}{\mathrm{\&Sigma;}}}(1-\underset{\mathrm{\&tau;}=t-U_i+1}{\overset{t}{\mathrm{\&Sigma;}}}{X}_{i,\mathrm{\&tau;}})G_{i,\max }\&GreaterEqual;D_t(1+R),t=1,K,T$

D _tFor t load constantly, R is positive percentage reserve;

1-2-2-5) branch road DC power flow constraint condition:

$|F_{j,t}-({\mathrm{\&theta;}}_{a,t}-{\mathrm{\&theta;}}_{b,t})/x_{\mathrm{ab}}|\&le;C\underset{\mathrm{\&tau;}=t-U_j+1}{\overset{t}{\mathrm{\&Sigma;}}}{Y}_{j,\mathrm{\&tau;}},j=1,K,N_2,t=1,K,T$

Wherein, N ₂For transmission line of electricity sum, F _j,tFor circuit j at t meritorious trend constantly, θ _a,tFor the phase angle of node a, x _AbFor the branch road reactance, C is a very large constant (for example 100000);

1-2-2-6) circuit transmission limit constraint condition:

$\left|F_{j,t}\right|\&le;F_{j,\max }(1-\underset{\mathrm{\&tau;}=t-U_j+1}{\overset{t}{\mathrm{\&Sigma;}}}{Y}_{j,\mathrm{\&tau;}})j=1,K,N_2,t=1,K,T$

F _{J, max}Transmission capacity limits for circuit j;

1-2-2-7) start inspecting state integer constraint condition:

X _i,t∈{0,1},i＝1,2,...,N _g;t＝1,...,T+1

Y _j,t∈{0,1},j＝1,K,N _l;t＝1,K,T+1

2) solve the optimized algorithm of this model;

2-1) by the integer variable X in monthly the integrated maintenance Optimized model of transmission of electricity _i,tAnd Y _j,tRelax, even X _i,tAnd Y _j,tCan get any value in [0,1], build lax monthly the integrated maintenance Optimized model of transmission of electricity;

2-2) adopt linear programming for solution device solution procedure 2-1) middle lax monthly the integrated maintenance Optimized model of transmission of electricity built, the optimum solution that obtains relaxation model is

With

2-3) according to the optimum solution of the relaxation model that obtains

With

The structure induced function;

Definition means that unit i is at t inspecting state variable constantly

$\stackrel{\&OverBar;}{X_{i,t}}=\underset{\mathrm{\&tau;}=t-U_i+1}{\overset{t}{\mathrm{\&Sigma;}}}{X}_{i,\mathrm{\&tau;}}^{\&prime;}$

If Be 1, mean that this unit is in inspecting state; If

Be 0, mean that this unit is in the state do not overhauled;

Definition means that unit i at the variable that t starts to overhaul the wish size constantly is

$\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{X_{i,t}}}=\frac{\underset{\mathrm{\&tau;}=t}{\overset{t+U_i-1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{X_{i,\mathrm{\&tau;}}}}{U_i}$

Larger, mean that unit i more tends to constantly start maintenance at t; Therefore, the induced function of unit i

Be defined as follows:

$\stackrel{\&OverBar;}{W_{i,t}}=\left\{\begin{array}{cc}L-\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{X_{i,t}}}& e_i\&le;t\&le;l_i\\ H& 1\&le;t<e_i{l}_i<t\&le;T\\ M& t=T+1\end{array}\right.$

Maintenance wish function W with unit i _i,tDifferent is: the induced function of unit i

At the interval [e of maintenance wish _i, l _i] interior value is relevant with the solution of lax monthly the integrated maintenance Optimized model of transmission of electricity, for

Value H outside inferior monthly repair wish interval, finally also virtually at inferior month increased by one day, corresponding induced function

Value M;

In like manner, for the maintenance circuit, introduce variable

Mean that circuit j is at t inspecting state constantly; ,

$\stackrel{\&OverBar;}{Y_{j,t}}=\underset{\mathrm{\&tau;}=t-U_j+1}{\overset{t}{\mathrm{\&Sigma;}}}{Y}_{j,\mathrm{\&tau;}}^{\&prime;}$

If Be 1, mean that this circuit is in inspecting state, if

Be 0, mean that this circuit is in the state do not overhauled; Variable

Mean that circuit j starts to overhaul the wish size constantly at t:

$\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{Y_{j,t}}}=\frac{\underset{\mathrm{\&tau;}=t}{\overset{t+U_j-1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{Y_{j,\mathrm{\&tau;}}}}{U_j}$

Larger, circuit j more tends to constantly start maintenance at t; Therefore, the induced function of circuit j

Be defined as follows:

$\stackrel{\&OverBar;}{W_{j,t}}=\left\{\begin{array}{cc}L-\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{Y_{j,t}}}& e_j\&le;t\&le;l_j\\ H& 1\&le;t<e_j{l}_j<t\&le;T\\ M& t=T+1\end{array}\right.$

Induced function Maintenance wish function W with circuit j _j,tDifferent is: the induced function of circuit j

At the interval [e of maintenance wish _j, l _j] interior value is Should be relevant with the solution of lax monthly the integrated maintenance Optimized model of transmission of electricity; Value H outside inferior monthly repair wish interval, be a great constant (for example 10000000), and last virtual increase was one day at inferior month, corresponding induced function

Value M, be larger constant (for example 10000);

2-4) according to step 2-3) induced function of structure, build monthly the integrated maintenance Optimized model of transmission of electricity based on induced function;

Be about to monthly the integrated maintenance Optimized model of transmission of electricity and be revised as monthly the integrated maintenance Optimized model of transmission of electricity based on induced function, this model is comprised of objective function and constraint condition:

Wherein, objective function is:

$\min \{\underset{i=1}{\overset{N_g}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{W_{i,t}}g{X}_{i,t}+\underset{j=1}{\overset{N_l}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{W_{j,t}}g{Y}_{j,t}\}$

The constraint condition of model and step 1-2) in monthly the integrated maintenance Optimized model of transmission of electricity building in full accord;

2-5) solve monthly the integrated maintenance Optimized model of transmission of electricity based on induced function;

Adopt the mixed integer programming solver to solve monthly the integrated maintenance Optimized model of transmission of electricity based on induced function, obtain the turnaround plan of monthly genset and transmission line of electricity;

2-6) according to step 2-5) turnaround plan that obtains overhauls repair apparatus; So far, institute of the present invention extracting method is implemented complete.

Take certain provincial power network is embodiment, and the effect that the inventive method realizes illustrates as follows:

1) monthly the integrated maintenance Optimized model of transmission of electricity consists of objective function and constraint condition:

1-1) from database, obtaining the relevant rudimentary data;

Required basic data comprises repair apparatus related data, monthly load prediction data, grid topology data and Optimal Parameters data etc.;

The repair apparatus related data comprises repair apparatus ID, the maintenance wish is interval, inspection and repair shop takes time etc.;

Monthly load prediction data comprise the peak load data of each day of next month electrical network, the node load data of each node of peak load period;

Grid topology data comprises the node of electric power networks and annexation, circuit ID, node ID, unit ID, unit correlation parameter (comprising unit capacity etc.), the circuit correlation parameter (comprising line reactance etc.) of transmission line of electricity;

This provincial power network has 168 bus nodes, 41 genset, 333 transmission lines of electricity; Wherein, 4 units, 66 circuits are declared maintenance in next month; Overhauling concrete data does not repeat them here;

1-2) according to the basic data of obtaining, build monthly transmission of electricity one maintenance Optimized model, this model is comprised of objective function and constraint condition, specifically comprises:

1-2-1) objective function of monthly transmission of electricity one maintenance Optimized model of structure is as follows:

$\min \{\underset{i=1}{\overset{N_g}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{W}_{i,t}g{X}_{i,t}+\underset{j=1}{\overset{N_l}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{W}_{j,t}g{Y}_{j,t}\}---\left(1\right)$

In formula (1), N _gFor declaring the genset quantity of lower monthly repair, N _lFor declaring the transmission line of electricity quantity of lower monthly repair, T is total number of days next month, U _iFor maintenance unit i inspection and repair shop takes time; X _i,tCharacterize unit i and constantly start from t the 0-1 variable overhauled, if maintenance unit i is starting maintenance lasting U the α day of next month _iTime, X _{I, α}=1, all the other periods are 0; W _i,tFor the maintenance wish function of maintenance unit i, mean that maintenance unit i is in the maintenance wish that t day starts to overhaul; U _jFor maintenance circuit j inspection and repair shop takes time; Y _j,tCharacterize circuit j and constantly start from t the 0-1 variable overhauled, if maintenance circuit j is starting maintenance lasting U the β day of next month _jTime, Y _{J, β}=1, all the other periods are 0; W _j,tFor the maintenance wish function of maintenance circuit j, mean that maintenance circuit j is in the maintenance wish that t day starts to overhaul;

The maintenance wish function W of unit i _i,tExpression is as follows:

$W_{i,t}=\left\{\begin{array}{cc}1& e_i\&le;t\&le;l_i\\ 10000000& 1\&le;t<e_i{l}_i<t\&le;T\\ 10000& t=T+1\end{array}\right.---\left(2\right)$

In formula (2), [e _i, l _i] be the maintenance wish interval of unit i; Maintenance wish function W _i,tFor piecewise function: at the interval [e of inferior monthly repair wish _i, l _i] interior value 1, value 10000000 outside inferior monthly repair wish interval, virtual increase was one day at inferior month, corresponding maintenance wish function W _{I, T+1}Value 10000; When genset starts maintenance from virtual sky, be considered as this genset and at inferior month, can't arrange maintenance, need to extend to following month and arrange maintenance;

In like manner, the maintenance wish function W of transmission line of electricity j _j,tExpression is as follows:

$W_{j,t}=\left\{\begin{array}{cc}1& e_j\&le;t\&le;l_j\\ 10000000& 1\&le;t<e_j{l}_j<t\&le;T\\ 10000& t=T+1\end{array}\right.---\left(3\right)$

In formula (3), [e _j, l _j] be the maintenance wish interval of circuit j; Maintenance wish function W _j,tFor piecewise function: at the interval [e of maintenance wish _j, l _j] interior value 1, value 10000000 outside inferior monthly repair wish interval, virtual increase was one day at inferior month, corresponding maintenance wish function W _{J, T+1}Value 10000; When transmission line of electricity starts maintenance from virtual sky, be considered as this transmission line of electricity and at inferior month, can't arrange maintenance, need to extend to following month and arrange maintenance;

1-2-2) build the constraint condition of monthly transmission of electricity one maintenance Optimized model, comprise overhauling and declare constraint condition, unit output bound constraint condition, node power equilibrium constraint, system reserve constraint condition, branch road DC power flow constraint condition, circuit transmission limit constraint condition and start inspecting state integer constraint condition, be respectively described below:

1-2-2-1) constraint condition is declared in maintenance:

To all units of declaring maintenance, need to meet:

$\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{X}_{i,t}=1,i=1,K,N_g$

To all circuits of declaring maintenance, need to meet:

$\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{Y}_{j,t}=1,j=1,K,N_l$

1-2-2-2) unit output bound constraint condition:

$0\&le;P_{i,t}\&le;(1-\underset{\mathrm{\&tau;}=t-U_i+1}{\overset{t}{\mathrm{\&Sigma;}}}{X}_{i,\mathrm{\&tau;}})G_{i,\max },i=1,K,N_1;t=1,K,T$

In following formula, N ₁For genset sum, G _{I, max}For genset i max cap.;

1-2-2-3) node power equilibrium constraint:

K*F=A*P-B*L

K is node branch road incidence matrix, and F is the meritorious trend vector of circuit, and A is node unit incidence matrix, and P is the meritorious vector of unit output, and B is the node load incidence matrix, and L is the meritorious vector of node load;

1-2-2-4) system reserve constraint condition:

$\underset{i=1}{\overset{N_1}{\mathrm{\&Sigma;}}}(1-\underset{\mathrm{\&tau;}=t-U_i+1}{\overset{t}{\mathrm{\&Sigma;}}}{X}_{i,\mathrm{\&tau;}})G_{i,\max }\&GreaterEqual;D_t(1+R),t=1,K,T$

D _tFor t load constantly, R is positive percentage reserve;

1-2-2-5) branch road DC power flow constraint condition:

$|F_{j,t}-({\mathrm{\&theta;}}_{a,t}-{\mathrm{\&theta;}}_{b,t})/x_{\mathrm{ab}}|\&le;C\underset{\mathrm{\&tau;}=t-U_j+1}{\overset{t}{\mathrm{\&Sigma;}}}{Y}_{j,\mathrm{\&tau;}},j=1,K,N_2,t=1,K,T$

Wherein, N ₂For transmission line of electricity sum, F _j,tFor circuit j at t meritorious trend constantly, θ _a,tFor the phase angle of node a, x _AbFor the branch road reactance, C is a very large constant (for example 100000);

1-2-2-6) circuit transmission limit constraint condition:

$\left|F_{j,t}\right|\&le;F_{j,\max }(1-\underset{\mathrm{\&tau;}=t-U_j+1}{\overset{t}{\mathrm{\&Sigma;}}}{Y}_{j,\mathrm{\&tau;}})j=1,K,N_2,t=1,K,T$

F _{J, max}Transmission capacity limits for circuit j;

1-2-2-7) start inspecting state integer constraint condition:

X _i,t∈{0,1},i＝1,2,...,N _g;t＝1,...,T+1

Y _j,t∈{0,1},j＝1,K,N _l;t＝1,K,T+1

2) solve the optimized algorithm of this model;

2-1) by the integer variable X in monthly the integrated maintenance Optimized model of transmission of electricity _i,tAnd Y _j,tRelax, even X _i,tAnd Y _j,tCan get any value in [0,1], build lax monthly the integrated maintenance Optimized model of transmission of electricity;

2-2) adopt linear programming for solution device solution procedure 2-1) middle lax monthly the integrated maintenance Optimized model of transmission of electricity built, the optimum solution that obtains relaxation model is

With

2-3) according to the optimum solution of the relaxation model that obtains

With

The structure induced function;

Definition means that unit i is at t inspecting state variable constantly

$\stackrel{\&OverBar;}{X_{i,t}}=\underset{\mathrm{\&tau;}=t-U_i+1}{\overset{t}{\mathrm{\&Sigma;}}}{X}_{i,\mathrm{\&tau;}}^{\&prime;}$

If

Be 1, mean that this unit is in inspecting state; If

Be 0, mean that this unit is in the state do not overhauled;

Definition means that unit i at the variable that t starts to overhaul the wish size constantly is

$\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{X_{i,t}}}=\frac{\underset{\mathrm{\&tau;}=t}{\overset{t+U_i-1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{X_{i,\mathrm{\&tau;}}}}{U_i}$

Larger, mean that unit i more tends to constantly start maintenance at t; Therefore, the induced function of unit i

Be defined as follows:

$\stackrel{\&OverBar;}{W_{i,t}}=\left\{\begin{array}{cc}L-\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{X_{i,t}}}& e_i\&le;t\&le;l_i\\ H& 1\&le;t<e_i{l}_i<t\&le;T\\ M& t=T+1\end{array}\right.$

Maintenance wish function W with unit i _i,tDifferent is: the induced function of unit i

At the interval [e of maintenance wish _i, l _i] interior value is relevant with the solution of lax monthly the integrated maintenance Optimized model of transmission of electricity, for

Value H outside inferior monthly repair wish interval, finally also virtually at inferior month increased by one day, corresponding induced function Value M;

In like manner, for the maintenance circuit, introduce variable

Mean that circuit j is at t inspecting state constantly; ,

$\stackrel{\&OverBar;}{Y_{j,t}}=\underset{\mathrm{\&tau;}=t-U_j+1}{\overset{t}{\mathrm{\&Sigma;}}}{Y}_{j,\mathrm{\&tau;}}^{\&prime;}$

If

Be 1, mean that this circuit is in inspecting state, if

Be 0, mean that this circuit is in the state do not overhauled; Variable

Mean that circuit j starts to overhaul the wish size constantly at t:

$\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{Y_{j,t}}}=\frac{\underset{\mathrm{\&tau;}=t}{\overset{t+U_j-1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{Y_{j,\mathrm{\&tau;}}}}{U_j}$

Larger, circuit j more tends to constantly start maintenance at t; Therefore, the induced function of circuit j Be defined as follows:

$\stackrel{\&OverBar;}{W_{j,t}}=\left\{\begin{array}{cc}L-\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{Y_{j,t}}}& e_j\&le;t\&le;l_j\\ H& 1\&le;t<e_j{l}_j<t\&le;T\\ M& t=T+1\end{array}\right.$

Induced function

Maintenance wish function W with circuit j _j,tDifferent is: the induced function of circuit j

At the interval [e of maintenance wish _j, l _j] interior value is

Should be relevant with the solution of lax monthly the integrated maintenance Optimized model of transmission of electricity; Value H outside inferior monthly repair wish interval, be a great constant (for example 10000000), and last virtual increase was one day at inferior month, corresponding induced function

Value M, be larger constant (for example 10000);

2-4) according to step 2-3) induced function of structure, build monthly the integrated maintenance Optimized model of transmission of electricity based on induced function;

Monthly the integrated maintenance Optimized model of transmission of electricity is revised as to monthly the integrated maintenance Optimized model of transmission of electricity based on induced function, and this model is comprised of objective function and constraint condition:

Wherein, objective function is:

$\min \{\underset{i=1}{\overset{N_g}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{W_{i,t}}g{X}_{i,t}+\underset{j=1}{\overset{N_l}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{W_{j,t}}g{Y}_{j,t}\}$

The constraint condition of model and step 1-2) in monthly the integrated maintenance Optimized model of transmission of electricity building in full accord;

2-5) solve monthly the integrated maintenance Optimized model of transmission of electricity based on induced function;

Adopt the mixed integer programming solver to solve monthly the integrated maintenance Optimized model of transmission of electricity based on induced function, obtain the turnaround plan of monthly genset and transmission line of electricity;

2-6) according to step 2-5) turnaround plan that obtains overhauls repair apparatus; So far, institute of the present invention extracting method is implemented complete.

More directly calculate respectively the counting yield of the method (first calculate induced function, then call CPLEX software) of (directly calling CPLEX software) and the present invention's proposition, result of calculation is as shown in table 1.As shown in Table 1, the method based on induced function that adopts the present invention to propose has improved 14 times by computing velocity.Therefore, the method that the present invention proposes can effectively reduce the computing time of turnaround plan, improves the efficiency of turnaround plan establishment.

Table 1 CPLEX directly calculates with the efficiency based on the induced function method and compares

By calculating, can find, the direct result of calculation of CPLEX with the result of calculation that adopts institute of the present invention extracting method is all: the 8th line arrangements is to lower monthly repair, and other all circuits and all units are routed to maintenance in maintenance wish interval.Can verify thus, the method that the present invention proposes has guaranteed optimality.

Further, the effect based on induced function method the present invention proposed is analyzed.Table 2 has provided the method based on induced function that the present invention proposes and the integrated branch's cutting plane method of CPLEX in computation process, situation of change between the optimum solution upper bound of primal problem and branch node Optimum Solution lower bound.

Table 2 CPLEX directly calculate with based on induced function method optimum solution bound situation of change

As can be seen from Table 2, while adopting CPLEX directly to calculate, because minute number is more, reduce the upper bound of optimum solution and expend long time, cause computing velocity slower.The method based on induced function that the present invention proposes promptly reduces the upper bound of primal problem optimum solution, thereby the calculating of a large amount of branch problems has been avoided in the quick location of having realized Optimum Solution.

Obviously, the constraint condition in institute of the present invention extracting method implementation step can be added according to the actual requirements and delete, extensibility is strong.Therefore, the above implementation step unrestricted technical scheme of the present invention in order to explanation only.Any modification or partial replacement that does not break away from spirit and scope of the invention, all should be encompassed in the middle of claim scope of the present invention.

Claims (1)

1. monthly the integrated maintenance optimization method of transmission of electricity based on induced function, is characterized in that, comprises the following steps:

1) set up monthly the integrated maintenance Optimized model of transmission of electricity formed by objective function and constraint condition:

1-1) from database, obtaining the relevant rudimentary data;

Required basic data comprises repair apparatus related data, monthly load prediction data, grid topology data and Optimal Parameters data;

1-2) according to the basic data of obtaining, build monthly the integrated maintenance Optimized model of transmission of electricity, this model is comprised of objective function and constraint condition, specifically comprises:

1-2-1) objective function of monthly the integrated maintenance Optimized model of transmission of electricity of structure is as follows:

$\min \{\underset{i=1}{\overset{N_g}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{W}_{i,t}g{X}_{i,t}+\underset{j=1}{\overset{N_l}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{W}_{j,t}g{Y}_{j,t}\}---\left(1\right)$

In formula (1), N _gFor declaring the genset quantity of lower monthly repair, N _lFor declaring the transmission line of electricity quantity of lower monthly repair, T is total number of days next month, U _iFor maintenance unit i inspection and repair shop takes time; X _i,tCharacterize unit i and constantly start from t the 0-1 variable overhauled, if maintenance unit i is starting maintenance lasting U the α day of next month _iTime, X _{I, α}=1, all the other periods are 0; W _i,tFor the maintenance wish function of maintenance unit i, mean that maintenance unit i is in the maintenance wish that t day starts to overhaul; U _jFor maintenance circuit j inspection and repair shop takes time; Y _j,tCharacterize circuit j and constantly start from t the 0-1 variable overhauled, if maintenance circuit j is starting maintenance lasting U the β day of next month _jTime, Y _{J, β}=1, all the other periods are 0; W _j,tFor the maintenance wish function of maintenance circuit j, mean that maintenance circuit j is in the maintenance wish that t day starts to overhaul;

The maintenance wish function W of unit i _i,tExpression as follows:

$W_{i,t}=\left\{\begin{array}{cc}L& e_i\&le;t\&le;l_i\\ H& 1\&le;t<e_i{l}_i<t\&le;T\\ M& t=T+1\end{array}\right.---\left(2\right)$

In formula (2), [e _i, l _i] be the maintenance wish interval of unit i; Maintenance wish function W _i,tFor piecewise function: at the interval [e of inferior monthly repair wish _i, l _i] interior value L, L is a very little constant, value H outside inferior monthly repair wish interval, H are a great constant, finally at inferior month have virtually increased by one day, corresponding maintenance wish function W _{I, T+1}Value M, M are a larger constant; When genset starts maintenance from virtual sky, be considered as this genset and at inferior month, can't arrange maintenance, need to extend to following month and arrange maintenance; Wherein, H>>M>>L, As soon as possible Promising Policy maintenance wish while having guaranteed genset arrangement maintenance, extend to following month and arrange maintenance if can't meet;

In like manner, the maintenance wish function W of transmission line of electricity j _j,tExpression as follows:

$W_{j,t}=\left\{\begin{array}{cc}L& e_j\&le;t\&le;l_j\\ H& 1\&le;t<e_j{l}_j<t\&le;T\\ M& t=T+1\end{array}\right.---\left(3\right)$

In formula (3), [e _j, l _j] be the maintenance wish interval of circuit j; Maintenance wish function W _j,tFor piecewise function: at the interval [e of maintenance wish _j, l _j] interior value L, L is a very little constant, value H outside inferior monthly repair wish interval, H are a great constant, finally at inferior month have virtually increased by one day, corresponding maintenance wish function W _{J, T+1}Value M, M are a larger constant; When transmission line of electricity starts maintenance from virtual sky, be considered as this transmission line of electricity and at inferior month, can't arrange maintenance, need to extend to following month and arrange maintenance; Wherein, H>>M>>L, As soon as possible Promising Policy maintenance wish while having guaranteed transmission line of electricity arrangement maintenance, extend to following month and arrange maintenance if can't meet;

1-2-2) build the constraint condition of monthly the integrated maintenance Optimized model of transmission of electricity, comprise overhauling and declare constraint condition, unit output bound constraint condition, node power equilibrium constraint, system reserve constraint condition, branch road DC power flow constraint condition, circuit transmission limit constraint condition and start inspecting state integer constraint condition, be respectively described below:

1-2-2-1) constraint condition is declared in maintenance:

To all units of declaring maintenance, need to meet:

$\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{X}_{i,t}=1,i=1,K,N_g$

To all circuits of declaring maintenance, need to meet:

$\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}{Y}_{j,t}=1,j=1,K,N_l$

1-2-2-2) unit output bound constraint condition:

$0\&le;P_{i,t}\&le;(1-\underset{\mathrm{\&tau;}=t-U_i+1}{\overset{t}{\mathrm{\&Sigma;}}}{X}_{i,\mathrm{\&tau;}})G_{i,\max },i=1,K,N_1;t=1,K,T$

In following formula, N ₁For genset sum, G _{I, max}For genset i max cap.;

1-2-2-3) node power equilibrium constraint:

K*F=A*P-B*L

K is node branch road incidence matrix, and F is the meritorious trend vector of circuit, and A is node unit incidence matrix, and P is the meritorious vector of unit output, and B is the node load incidence matrix, and L is the meritorious vector of node load;

1-2-2-4) system reserve constraint condition:

$\underset{i=1}{\overset{N_1}{\mathrm{\&Sigma;}}}(1-\underset{\mathrm{\&tau;}=t-U_i+1}{\overset{t}{\mathrm{\&Sigma;}}}{X}_{i,\mathrm{\&tau;}})G_{i,\max }\&GreaterEqual;D_t(1+R),t=1,K,T$

D _tFor t load constantly, R is positive percentage reserve;

1-2-2-5) branch road DC power flow constraint condition:

$|F_{j,t}-({\mathrm{\&theta;}}_{a,t}-{\mathrm{\&theta;}}_{b,t})/x_{\mathrm{ab}}|\&le;C\underset{\mathrm{\&tau;}=t-U_j+1}{\overset{t}{\mathrm{\&Sigma;}}}{Y}_{j,\mathrm{\&tau;}},j=1,K,N_2,t=1,K,T$

Wherein, N ₂For transmission line of electricity sum, F _j,tFor circuit j at t meritorious trend constantly, θ _a,tFor the phase angle of node a period t, x _AbFor the branch road reactance, C is a very large constant;

1-2-2-6) circuit transmission limit constraint condition:

$\left|F_{j,t}\right|\&le;F_{j,\max }(1-\underset{\mathrm{\&tau;}=t-U_j+1}{\overset{t}{\mathrm{\&Sigma;}}}{Y}_{j,\mathrm{\&tau;}})j=1,K,N_2,t=1,K,T$

F _{J, max}Transmission capacity limits for circuit j;

1-2-2-7) start inspecting state integer constraint condition:

X _i,t∈{0,1},i＝1,2,...,N _g;t＝1,...,T+1

Y _j,t∈{0,1},j＝1,K,N _l;t＝1,K,T+1

2) solve the optimized algorithm of this model;

2-1) by the integer variable X in monthly the integrated maintenance Optimized model of transmission of electricity _i,tAnd Y _j,tRelax, even X _i,tAnd Y _j,tCan get any value in [0,1], build lax monthly the integrated maintenance Optimized model of transmission of electricity;

2-2) adopt linear programming for solution device solution procedure 2-1) middle lax monthly the integrated maintenance Optimized model of transmission of electricity built, the optimum solution that obtains relaxation model is

With

2-3) according to step 2-2) optimum solution of the relaxation model that obtains

With

The structure induced function;

Definition means that unit i is at t inspecting state variable constantly

$\stackrel{\&OverBar;}{X_{i,t}}=\underset{\mathrm{\&tau;}=t-U_i+1}{\overset{t}{\mathrm{\&Sigma;}}}{X}_{i,\mathrm{\&tau;}}^{\&prime;}$

If

Be 1, mean that this unit is in inspecting state; If

Be 0, mean that this unit is in the state do not overhauled;

Definition means that unit i at the variable that t starts to overhaul the wish size constantly is

$\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{X_{i,t}}}=\frac{\underset{\mathrm{\&tau;}=t}{\overset{t+U_i-1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{X_{i,\mathrm{\&tau;}}}}{U_i}$

Larger, mean that unit i more tends to constantly start maintenance at t; Therefore, the induced function of unit i

Be defined as follows:

$\stackrel{\&OverBar;}{W_{i,t}}=\left\{\begin{array}{cc}L-\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{X_{i,t}}}& e_i\&le;t\&le;l_i\\ H& 1\&le;t<e_i{l}_i<t\&le;T\\ M& t=T+1\end{array}\right.$

The induced function of unit i At the interval [e of maintenance wish _i, l _i] interior value is

Value H outside inferior monthly repair wish interval, finally also virtually at inferior month increased by one day, corresponding induced function

Value M;

In like manner, for the maintenance circuit, introduce variable

Mean that circuit j is at t inspecting state constantly; ,

$\stackrel{\&OverBar;}{Y_{j,t}}=\underset{\mathrm{\&tau;}=t-U_j+1}{\overset{t}{\mathrm{\&Sigma;}}}{Y}_{j,\mathrm{\&tau;}}^{\&prime;}$

If

Be 1, mean that this circuit is in inspecting state, if

Be 0, mean that this circuit is in the state do not overhauled; Variable

Mean that circuit j starts to overhaul the wish size constantly at t:

$\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{Y_{j,t}}}=\frac{\underset{\mathrm{\&tau;}=t}{\overset{t+U_j-1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{Y_{j,\mathrm{\&tau;}}}}{U_j}$

Larger, circuit j more tends to constantly start maintenance at t; Therefore, the induced function of circuit j

Be defined as follows:

$\stackrel{\&OverBar;}{W_{j,t}}=\left\{\begin{array}{cc}L-\stackrel{\&OverBar;}{\stackrel{\&OverBar;}{Y_{j,t}}}& e_j\&le;t\&le;l_j\\ H& 1\&le;t<e_j{l}_j<t\&le;T\\ M& t=T+1\end{array}\right.$

The induced function of circuit j

At the interval [e of maintenance wish _j, l _j] interior value is Value H outside inferior monthly repair wish interval, be a great constant, and last virtual increase was one day at inferior month, corresponding induced function

Value M, be larger constant;

2-4) according to step 2-3) induced function of structure, build monthly the integrated maintenance Optimized model of transmission of electricity based on induced function;

This model is comprised of objective function and constraint condition:

Wherein, objective function is:

$\min \{\underset{i=1}{\overset{N_g}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{W_{i,t}}g{X}_{i,t}+\underset{j=1}{\overset{N_l}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T+1}{\mathrm{\&Sigma;}}}\stackrel{\&OverBar;}{W_{j,t}}g{Y}_{j,t}\}$

The constraint condition of model and step 1-2) in monthly the integrated maintenance Optimized model of transmission of electricity building in full accord;

2-5) solve monthly the integrated maintenance Optimized model of transmission of electricity based on induced function;

Adopt the mixed integer programming solver to solve monthly the integrated maintenance Optimized model of transmission of electricity based on induced function, obtain the turnaround plan of monthly genset and transmission line of electricity;

2-6) according to step 2-5) turnaround plan that obtains overhauls repair apparatus; So far, institute of the present invention extracting method is implemented complete.

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