CN106875049A - A kind of Electrical Power System Dynamic economic load dispatching method of meter and valve point effect - Google Patents

Abstract

The invention discloses a kind of meter and the Electrical Power System Dynamic economic load dispatching method of valve point effect, comprise the following steps：(1) the dynamic economic dispatch model of meter and valve point effect, is set up, the dynamic economic dispatch object function for considering valve point effect is given；(2) the Electrical Power System Dynamic economic load dispatching constraints of meter and valve point effect, is set up；(3), dynamic economic dispatch object function is simplified by the method for piece-wise linearization, the problem of MILP is converted into, then is solved with the MILP solvers in CPLEX, so as to obtain initial approximation solution；(4), by resetting exerting oneself bound and realizing the decoupling between adjacent moment for each period unit, dynamic economic dispatch problem is converted into static economy scheduling problem；(5) rapid solving, is carried out to the unit output of each period using improved dimension prompt drop method, final optimization solution is obtained.

Description

A kind of Electrical Power System Dynamic economic load dispatching method of meter and valve point effect

Technical field

The present invention relates to electrical engineering field, more particularly, to a kind of meter and valve point of power-system short-term traffic control The dynamic economic dispatch method of effect.

Background technology

Electrical Power System Dynamic economic load dispatching is in the case where system operation constraints is met, by each generating set of Optimized Operation Exert oneself, make system all operation periods overall running costs it is minimum, be one of key issue for facing in Operation of Electric Systems. In systems in practice, the hot candied phenomenon occurred when being opened suddenly due to steam turbine intake valve can make unit consumption characteristic produce valve point Effect, can be superimposed a pulsation effect on the consumption characteristic curve of unit, that is, produce valve point effect.Practical operating experiences table Bright, ignoring valve point effect can be significantly affected the operation result of economic load dispatching.

Mathematically, it is considered to the Electrical Power System Dynamic economic load dispatching of valve point effect be a typical higher-dimension, dynamic it is non- Convex, nonlinear optimal problem, solves more difficult.Analysis current research, mainly has two class methods to can be used to solve this problem. The first kind is meta-heuristic optimized algorithm, and meta-heuristic algorithm and its hybrid algorithm are required for setting the parameter related to algorithm, The setting of these parameters can produce influence to the performance of algorithm.Equations of The Second Kind is optimization algorithm, due to considering valve point effect The non-linear and non-convex characteristic of dynamic economic dispatch problem, classical optimization algorithm is not appropriate for solving this problem.

The content of the invention

It is an object of the invention to provide a kind of meter and the Electrical Power System Dynamic economic load dispatching method of valve point effect, valve is being considered On the basis of the static economy scheduling optimum result characteristic of point effect, by the way that constraint will be coupled between the dynamic economic dispatch period (Climing constant) is decoupled, and introduces the concept of class singular point, finally using improved dimension prompt drop method (Modified Dimensional Steepest Decline Method, MDSD) and MILP (Mixed Integer Linear Programming, MILP) method solves to the problem.

To achieve the above object, the present invention uses following technical proposals：

A kind of Electrical Power System Dynamic economic load dispatching method of meter and valve point effect, comprises the following steps：

(1) the dynamic economic dispatch model of meter and valve point effect, is set up, the dynamic economic dispatch for considering valve point effect is given Object function；

(2) power balance of, the Electrical Power System Dynamic economic load dispatching constraints of foundation meter and valve point effect, including system Constraint and the constraint of system spinning reserve；

(3), dynamic economic dispatch object function is simplified by the method for piece-wise linearization, MIXED INTEGER is converted into linear The problem of planning, then solved with the MILP solvers in CPLEX, so as to obtain initial approximation solution；

(4), on the basis of the initial approximation solution obtained in step (3), by resetting exerting oneself for each period unit Bound realizes the decoupling between adjacent moment, and dynamic economic dispatch problem is converted into static economy scheduling problem；

(5), for the static economy scheduling problem after decoupling in step (4), using improved dimension prompt drop method to each The unit output of period carries out rapid solving, obtains final optimization solution.

Further, in step (1) foundation meter and the dynamic economic dispatch model of valve point effect, it is considered to valve point effect Dynamic economic dispatch object function is：

In formula：TC is total generation cost；C_iIt is i-th group of cost function of t periods of generator；N_GIt is generating set number； N_TIt is the period sum of dispatching cycle；a_i, b_i, c_iIt is fuel cost coefficient；P_{I, t}It is to export i-th group of t period of generator Active power；P_i ^minIt is the minimum load of generating set i；e_i, f_iIt is valve point effect coefficient.

Further, in step (2), the power balance of system is constrained to：

In formula：P_t ^lossIt is the system losses of t periods, is tried to achieve by B Y-factor method Ys；D_tIt is the system loading of t periods, B_ij It is the coefficient of B matrixes,

The power output constraint of generator：

In formula, P_i ^maxIt is the EIAJ of i-th group of generator；

Generator Climing constant：

In formula, UR_i,DR_iIt is the upper and lower climbing rate of fired power generating unit；

2) system spinning reserve constraint：

In formula, SR_i,tIt is spinning reserve that the generating set i t periods provide；SSR_t ^reqBe t period systems rotation it is standby Use demand.

Further, in step (3), the dynamic economic dispatch object function of generating set i t periods is segmented linearisation For：

Will generating set dynamic economic dispatch object function C_i(P_{I, t}) it is expressed as being segmented the summation of line segment：Parameter K_iRepresent Generating set i from minimum unit output to the segments of maximum unit output, if each sinusoidal cycles is averagely divided into M Section, then K_iFor：

In formula, b_{M, i}And c_{M, i}The slope and intercept of each segmentation line segment are represented respectively：

Wherein, the bound of each segmentationWithThe corresponding function representation of point on abscissa：

Setting parameter U_{M, i, t}It is 0,1 variable, represents in the t periods, whether generating set i's exerts oneself at m sections of linear segmented On；The then power output P of unit_{I, t}With exert oneself P of the generating set i ts in the m sections of linear segmented_{M, i, t}Should meet with Lower constraints：

3) each sinusoidal cycles is averaged and is divided into two sections (M=2), and the Optimized model for finally obtaining directly passes through MILP Solved, obtained an initial approximation solution, convergence during solution can be set to the convergence gap of MILP less than one to Fixed value.

Further, the bound equation of exerting oneself of unit is as follows in step (4)：

In formula,WithRespectively new units limits of generating set i t periods；

It is determined that a certain unit of period t exert oneself new bound when, it is necessary to the period of using t-1 and period t+1 this Unit is exerted oneself, and the unit output of t-1 periods needs the new power generating value that is obtained with dimension prompt drop method, and the unit of t+1 periods Exert oneself, with the initial power generating value obtained in the first step.

Further, solving static economy scheduling problem using improved dimension prompt drop method can be divided into two steps：

1) first step needs to obtain unit output initial solution；

Improved dimension prompt drop method needs to use the singular point of unit, with P_SP 0_{I, j}To represent that i-th unit operation exists On its j-th singular point：

P_SP is used herein_{I, t, j}Represent that generating set i is the P_SP on its j-th singular point in exerting oneself for period t_{I, t, j}Bag IncludeAnd in P_SP 0 between the two_{I, j}, N_{Sp, t}Represent the sum of t period singular points；With D_{I, t, j}Carry out table Show the rate of descent of improved dimension prompt drop method, it is the t periods, and generating set i is by+1 singular point output drop of jth to Every megawatt of cost when being exerted oneself at j singular point；Use Lenght_{I, t, j}Represent+1 singular point of jth of t periods, generating set i Exert oneself and the difference exerted oneself at j-th singular point at place；

Length_{I, t, j}=P_SP_{I, t, j+1}-P_SP_{I, t, j} (20)

Initial solution need not strictly observe power-balance constraint, can be using bubbling method to D_{I, t, j}It is ascending to be ranked up,Represent the D after sequence_{I, t, j}Order is order,AsSorted accordingly, In first time iteration, every unit operation is exerted oneself on lower limit at it, per iteration once, according to the order of order in each unit Exert oneself lower limit and on the basis of plus one sectionThe difference EER of power-balance_tCalculated by following formula：

In iterative process, in EER_tIn the case of zero, when it is closest to zero, iteration stopping；Then will be in iteration During useThe exerting oneself on lower limit of every unit is added to respectively according to machine group # i, is obtained just Every power generating value of unit in beginning solution, wherein parameter I0+1 are set to the value of final iterations；

2) second step is to adjust the initial solution that obtains in the first step, records the result after all adjustment, so as to remake into One successive step：It is variableness to select I0 iteration and its state of first three vertical motion and the state of rear four vertical motions, Further adjustment is done for each case, exactly selects wherein one unit as lax unit to meet power-balance constraint, it is right All in the t periods meet the constraint of unit output boundSituation sum up the costs, choosing Take the feasible solution that totle drilling cost can be made minimum.

The beneficial effects of the invention are as follows,

The present invention is adjusted on the basis of the static economy scheduling optimum result characteristic for considering valve point effect by by dynamic economy Climing constant decoupling between spending the period, and the concept of class singular point is introduced, finally utilize improved dimension prompt drop method and mix Integral linear programming method is solved to the problem, with obtain globally optimal solution in terms of feasibility and validity, preferably Solve the problems, such as non-linear and non-convex characteristic dynamic economic dispatch.

Brief description of the drawings

Fig. 1 is flow chart of the present invention.

Specific embodiment

As shown in figure 1, a kind of Electrical Power System Dynamic economic load dispatching method of meter and valve point effect, comprises the following steps：

(1) the dynamic economic dispatch model of meter and valve point effect, is set up, the dynamic economic dispatch for considering valve point effect is given Object function, it is considered to which the dynamic economic dispatch object function of valve point effect is：

In formula：TC is total generation cost；C_iIt is i-th group of cost function of t periods of generator；N_GIt is generating set number； N_TIt is the period sum of dispatching cycle；a_i, b_i, c_iIt is fuel cost coefficient；P_{I, t}It is to export i-th group of t period of generator Active power；P_i ^minIt is the minimum load of generating set i；e_i, f_iIt is valve point effect coefficient.

(2) the Electrical Power System Dynamic economic load dispatching constraints of meter and valve point effect, the power balance constraint of system, are set up For：

In formula：P_t ^lossIt is the system losses of t periods, is tried to achieve by B Y-factor method Ys；D_tIt is the system loading of t periods, B_ij It is the coefficient of B matrixes,

The power output constraint of generator：

In formula, P_i ^maxIt is the EIAJ of i-th group of generator；

Generator Climing constant：

In formula, UR_i,DR_iIt is the upper and lower climbing rate of fired power generating unit；

System spinning reserve is constrained：

In formula, SR_i,tIt is spinning reserve that the generating set i t periods provide；SSR_t ^reqBe t period systems rotation it is standby Use demand.

(3), dynamic economic dispatch object function is simplified by the method for piece-wise linearization, MIXED INTEGER is converted into linear The problem of planning, then solved with the MILP solvers in CPLEX, so as to obtain initial approximation solution.

The dynamic economic dispatch object function of generating set i t periods is segmented and linearly turns to：

Will generating set dynamic economic dispatch object function C_i(R_{I, t}) it is expressed as being segmented the summation of line segment：Parameter K_iRepresent Generating set i from minimum unit output to the segments of maximum unit output, if each sinusoidal cycles is averagely divided into M Section, then K_iFor：

In formula, b_{M, i}And c_{M, i}The slope and intercept of each segmentation line segment are represented respectively：

Wherein, the bound of each segmentationWithThe corresponding function representation of point on abscissa：

Setting parameter U_{M, i, t}It is 0,1 variable, represents in the t periods, whether generating set i's exerts oneself at m sections of linear segmented On；P_{M, i, t}Expression generating set i exerting oneself in the m sections of linear segmented in t, sometime, generates electricity to certain Machine, in all of linear segmented, the generator output value in only one segmentation is greater than 0, in remaining all segmentation Generator output is all 0, but the power generating value of the generator in which segmentation is determined by optimization more than 0.Then unit is defeated Go out power P_{I, t}With exert oneself P of the generating set i ts in the m sections of linear segmented_{M, i, t}Following constraints should be met：

Each sinusoidal cycles is averaged and is divided into two sections (M=2), and the Optimized model for finally obtaining directly is entered by MILP Row is solved, and obtains an initial approximation solution, and the convergence gap that convergence during solution can be set to MILP gives less than one Value.

(4), on the basis of the initial approximation solution obtained in step (3), by resetting exerting oneself for each period unit Bound realizes the decoupling between adjacent moment, and dynamic economic dispatch problem is converted into static economy scheduling problem；Step (4) The bound equation of exerting oneself of middle unit is as follows：

In formula,WithRespectively new units limits of generating set i t periods；

It is determined that a certain unit of period t exert oneself new bound when, it is necessary to the period of using t-1 and period t+1 this Unit is exerted oneself, and the unit output of t-1 periods needs the new power generating value that is obtained with dimension prompt drop method, and the unit of t+1 periods Exert oneself, with the initial power generating value obtained in the first step.

(5), for the static economy scheduling problem after decoupling in step (4), using improved dimension prompt drop method to each The unit output of period carries out rapid solving, obtains final optimization solution.Static warp is solved using improved dimension prompt drop method Ji scheduling problem can be divided into two steps：

1) first step needs to obtain unit output initial solution；

Improved dimension prompt drop method needs to use the singular point of unit, with P_SP 0_{I, j}To represent that i-th unit operation exists On its j-th singular point：

P_SP is used herein_{I, t, j}Represent that generating set i is the P_SP on its j-th singular point in exerting oneself for period t_{I, t, j}Bag IncludeAnd in P_SP 0 between the two_{I, j}, N_{Sp, t}Represent the sum of t period singular points；With D_{I, t, j}Carry out table Show the rate of descent of improved dimension prompt drop method, it is the t periods, and generating set i is by+1 singular point output drop of jth to Every megawatt of cost when being exerted oneself at j singular point；Use Length_{I, t, j}Represent+1 singular point of jth of t periods, generating set i Exert oneself and the difference exerted oneself at j-th singular point at place；

Length_{I, t, j}=P_SP_{I, t, j+1}-P_SP_{I, t, j} (20)

Initial solution need not strictly observe power-balance constraint, can be using bubbling method to D_{I, t, j}It is ascending to be ranked up,Represent the D after sequence_{I, t, j}Order is order,AsSorted accordingly, In first time iteration, every unit operation is exerted oneself on lower limit at it, per iteration once, according to the order of order in each unit Exert oneself lower limit and on the basis of plus one sectionThe difference EER of power-balance_tCalculated by following formula：

In iterative process, in EER_tIn the case of zero, when it is closest to zero, iteration stopping；Then will be in iteration During useThe exerting oneself on lower limit of every unit is added to respectively according to machine group # i, obtains initial Every power generating value of unit in solution, wherein parameter I0+1 are set to the value of final iterations, obtain the value of parameter I0；

2) second step is to adjust the initial solution that obtains in the first step, records the result after all adjustment, so as to remake into One successive step, makes it strictly observe power-balance constraint.Finally, the feasible solution that totle drilling cost can be made minimum is chosen.By the first small step In iterative process be referred to as initial rise process, occur in that uphill process, then vertical motion be exactly open state, if I≤ I0, vertical motion is the state opened in the I times iteration during initial rise, if conversely, I ＞ I0, are to close State.On the basis of ensureing that every unit is all operated on singular point, adjust the I0 times during initial rise and change The instead of state of the several uphill process after preceding several uphill process to the I0 times iteration.In general, state is changed The quantity of vertical motion is more, and totle drilling cost increase is also more.Therefore, it is same by the quantity set of state change in uphill process When change state no more than 4.Select I0 iteration and its state and the shape of rear four vertical motions of first three vertical motion State is variableness, it will have 163 kinds of situations.For each case do further adjustment, exactly select wherein one unit by for Lax unit meets power-balance constraint.All for the t periods meet the constraint of unit output boundSituation sum up the costs, selection can make the minimum feasible solution of totle drilling cost.

Although above-mentioned be described with reference to accompanying drawing to specific embodiment of the invention, not to present invention protection model The limitation enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme those skilled in the art are not Need the various modifications made by paying creative work or deformation still within protection scope of the present invention.

Claims (6)

1. it is a kind of count and valve point effect Electrical Power System Dynamic economic load dispatching method, it is characterised in that comprise the following steps：

(1) the dynamic economic dispatch model of meter and valve point effect, is set up, the dynamic economic dispatch target for considering valve point effect is given Function；

(2) the Electrical Power System Dynamic economic load dispatching constraints of meter and valve point effect, is set up, including the power balance of system is constrained And the constraint of system spinning reserve；

(3), dynamic economic dispatch object function is simplified by the method for piece-wise linearization, MILP is converted into Problem, then solved with the MILP solvers in CPLEX, so as to obtain initial approximation solution；

(4), on the basis of the initial approximation solution obtained in step (3), by resetting exerting oneself up and down for each period unit Limit to realize the decoupling between adjacent moment, dynamic economic dispatch problem is converted into static economy scheduling problem；

(5), for the static economy scheduling problem after decoupling in step (4), using improved dimension prompt drop method to each period Unit output carry out rapid solving, obtain final optimization solution.

2. it is as claimed in claim 1 it is a kind of count and valve point effect Electrical Power System Dynamic economic load dispatching method, it is characterised in that The dynamic economic dispatch model of foundation meter and valve point effect in step (1), it is considered to the dynamic economic dispatch target of valve point effect Function is：

$\min TC=\underset{t=1}{\overset{N_T}{\Σ}}\underset{i=1}{\overset{N_G}{\Σ}}{C}_i\left(P_{i,t}\right)---\left(1\right)$

$C_i\left(P_{i,t}\right)=a_i{P}_{i,t}^2+b_i{P}_{i,t}+c_i+e_i\left|\sin f_i(P_{i,t}-P_i^{\min })\right|---\left(2\right)$

In formula：TC is total generation cost；C_iIt is i-th group of cost function of t periods of generator；N_GIt is generating set number；N_TIt is One period sum of dispatching cycle；a_i, b_i, c_iIt is fuel cost coefficient；P_{I, t}It is having of exporting i-th group of t period of generator Work(power；It is the minimum load of generating set i；e_i, f_iIt is valve point effect coefficient.

3. it is as claimed in claim 1 it is a kind of count and valve point effect Electrical Power System Dynamic economic load dispatching method, it is characterised in that In step (2), the power balance of system is constrained to：

$\underset{i=1}{\overset{N_G}{\Σ}}{P}_{i,t}=D_t+P_t^{loss},t=1,2,...N_T---\left(3\right)$

$P_t^{loss}=\underset{i=1}{\overset{N_G}{\Σ}}\underset{j=1}{\overset{N_G}{\Σ}}{P}_{i,t}{B}_{i,j}{P}_{j,t},t=1,2,...N_T---\left(4\right)$

In formula：P_t ^lossIt is the system losses of t periods, is tried to achieve by B Y-factor method Ys；D_tIt is the system loading of t periods, B_ijIt is B The coefficient of matrix,

The power output constraint of generator：

$P_i^{min}\≤P_{i,t}\≤P_i^{max},\∀i,t---\left(5\right)$

In formula, P_i ^maxIt is the EIAJ of i-th group of generator；

Generator Climing constant：

In formula, UR_i,DR_iIt is the upper and lower climbing rate of fired power generating unit；

2) system spinning reserve constraint：

$\left\{\begin{array}{c}{\mathrm{SR}}_{i,t}\≤P_i^{\max }-P_{i,t}\\ {\mathrm{SR}}_{i,t}\≤{\mathrm{UR}}_i\end{array}\right.---\left(7\right)$

$\underset{i=1}{\overset{N_G}{\Σ}}{\mathrm{SR}}_{i,t}\≥{\mathrm{SSR}}_t^{req}---\left(8\right)$

In formula, SR_i,tIt is spinning reserve that the generating set i t periods provide；SSR_t ^reqThe spinning reserve for being t period systems need to Ask.

4. it is as claimed in claim 1 it is a kind of count and valve point effect Electrical Power System Dynamic economic load dispatching method, it is characterised in that In step (3), the dynamic economic dispatch object function of generating set i t periods is segmented and linearly turns to：

$C_i\left(P_{i,t}\right)={\mathrm{\Σ}}_{i=1}^{K_i}(b_{m,i}\·P_{m,i,t}+c_{m,i}\·U_{m,i,t})---\left(9\right)$

Will generating set dynamic economic dispatch object function C_i(P_{I, t}) it is expressed as being segmented the summation of line segment：Parameter K_iRepresent and generate electricity Unit i from minimum unit output to the segments of maximum unit output, if each sinusoidal cycles is averagely divided into M sections, Then K_iFor：

$K_i=ceil\left(M\frac{f_i(P_i^{\max }-P_i^{\min })}{\mathrm{\π}}\right)---\left(10\right)$

In formula, b_{M, i}And c_{M, i}The slope and intercept of each segmentation line segment are represented respectively：

$b_{m,i}=\frac{C_i\left(P_{m,i}^{\max }\right)-C_i\left(P_{m,i}^{\min }\right)}{P_{m,i}^{\max }-P_{m,i}^{\min }}---\left(11\right)$

$c_{m,i}=C_i\left(P_{m,i}^{\min }\right)-b_{m,i}\·P_{m,i}^{\min }---\left(12\right)$

Wherein, the bound of each segmentationWithThe corresponding function representation of point on abscissa：

$P_{m,i}^{\min }=P_i^{\min }+(m-1)\frac{\mathrm{\π}}{M\·f_i},m=1,2,...,K_i;---\left(13\right)$

$P_{m,i}^{max}=\left\{\begin{array}{cc}{P}_i^{\min }+m\frac{\mathrm{\π}}{M\·f_i}& m=1,2,...,K_i-1;\\ P_i^{\max }& m=K_i;\end{array}\right.---\left(14\right)$

Setting parameter U_{M, i, t}It is 0,1 variable, represents in the t periods, whether generating set i's exerts oneself in the m sections of linear segmented；Then The power output P of unit_{I, t}With exert oneself P of the generating set i ts in the m sections of linear segmented_{M, i, t}Should meet it is following about Beam condition：

$\left\{\begin{array}{c}{P}_{i,t}=\underset{m=1}{\overset{K_i}{\Σ}}{P}_{m,i,t}\\ P_{m,i}^{\min }{U}_{m,i,t}\≤P_{m,i,t}\≤P_{m,i}^{\max }{U}_{m,i,t}\\ \underset{m=1}{\overset{K_i}{\Σ}}{U}_{m,i,t}=1\end{array}\right.---\left(15\right)$

3) each sinusoidal cycles is averaged and is divided into two sections (M=2), and the Optimized model for finally obtaining directly is carried out by MILP Solve, obtain an initial approximation solution, the convergence gap that convergence during solution can be set to MILP is given less than one Value.

5. it is as claimed in claim 1 it is a kind of count and valve point effect Electrical Power System Dynamic economic load dispatching method, it is characterised in that The bound equation of exerting oneself of unit is as follows in step (4)：

$P_{i,t}^{{\min }^{*}}=\left\{\begin{array}{c}\max \{P_i^{\min },P_{i,t+1}-{\mathrm{UR}}_t\},t=1;\\ \max \{P_i^{\min },P_{i,t+1}-{\mathrm{UR}}_t,P_{i,t-1}-{\mathrm{DR}}_t\},t=2,3,\mathrm{...},23;\\ \max \{P_i^{\min },P_{i,t+1}-{\mathrm{UR}}_t\},t=24;\end{array}\right.---\left(16\right)$

$P_{i,t}^{{\max }^{*}}=\left\{\begin{array}{c}\min \{P_i^{\max },P_{i,t+1}+{\mathrm{DR}}_t\},t=1;\\ \min \{P_i^{\max },P_{i,t+1}+{\mathrm{DR}}_t,P_{i,t-1}+{\mathrm{UR}}_t\},t=2,3,\mathrm{...},23;\\ \min \{P_i^{\max },P_{i,t+1}+{\mathrm{UR}}_t\},t=24;\end{array}\right.---\left(17\right)$

In formula,WithRespectively new units limits of generating set i t periods；

It is determined that a certain unit of period t exert oneself new bound when, it is necessary to the period of using t-1 and period t+1 this unit Exert oneself, the unit output of t-1 periods needs the new power generating value obtained with dimension prompt drop method, and the unit output of t+1 periods Then with the initial power generating value obtained in the first step.

6. it is as claimed in claim 5 it is a kind of count and valve point effect Electrical Power System Dynamic economic load dispatching method, it is characterised in that Solving static economy scheduling problem using improved dimension prompt drop method can be divided into two steps：

1) first step needs to obtain unit output initial solution；

Improved dimension prompt drop method needs to use the singular point of unit, with P_SP0_{I, j}To represent i-th unit operation in its On j singular point：

$P\_SP{0}_{i,j}=\left\{\begin{array}{cc}{P}_i^{\min }+j\·\frac{\mathrm{\π}}{f_i}& j=0,1,...,K_i;\\ P_i^{\max }& j=K_i+1;\end{array}\right.---\left(18\right)$

P_SP is used herein_{I, t, j}Represent that generating set i is the P_SP on its j-th singular point in exerting oneself for period t_{I, t, j}Including And in P_SP0 between the two_{I, j}, N_{Sp, t}Represent the sum of t period singular points；With D_{I, t, j}To represent improvement Dimension prompt drop method rate of descent, it is the t periods, and generating set i is strange to j-th by+1 singular point output drop of jth Every megawatt of cost when being exerted oneself at dissimilarity；Use Length_{I, t, j}Go out at+1 singular point of jth for representing t periods, generating set i The difference exerted oneself at power and j-th singular point；

$D_{i,t,j}=\frac{C_i(P\_{\mathrm{SP}}_{i,t,j+1})-C_i(P\_{\mathrm{SP}}_{i,t,j})}{{\mathrm{Length}}_{i,t,j}}---\left(19\right)$

Length_{I, t, j}=P_SP_{I, t, j+1}-P_SP_{I, t, j} (20)

Initial solution need not strictly observe power-balance constraint, can be using bubbling method to D_{I, t, j}It is ascending to be ranked up, Represent the D after sequence_{I, t, j}Order is order,AsSorted accordingly, for the first time In iteration, every unit operation is exerted oneself on lower limit at it, per iteration once, according to order the exerting oneself in each unit of order Lower limit adds one section with the basis ofThe difference EER of power-balance_tCalculated by following formula：

${\mathrm{EER}}_t=\underset{i=1}{\overset{N_G}{\Σ}}{P}_{i,t}^{\min *}+\underset{order=1}{\overset{N_{sp,t}-1}{\Σ}}{\mathrm{Length}}_{i,t,j}^{order}-D_t---\left(21\right)$

In iterative process, in EER_tIn the case of zero, when it is closest to zero, iteration stopping；Then will in an iterative process UseThe exerting oneself on lower limit of every unit is added to respectively according to machine group # i, in obtaining initial solution Every power generating value of unit, wherein parameter I0+1 are set to the value of final iterations；

2) second step is to adjust the initial solution obtained in the first step, records the result after all adjustment, so as to remake further Adjustment：It is variableness to select I0 iteration and its state of first three vertical motion and the state of rear four vertical motions, for Each case does further adjustment, exactly selects wherein one unit as lax unit to meet power-balance constraint, during for t The all of section meet the constraint of unit output boundSituation sum up the costs, selection can make The minimum feasible solution of totle drilling cost.