CN102931689A - Online rolling scheduling method taking power generation adjusting number constraint into account - Google Patents

Abstract

The invention relates to an exponential-function-based online rolling scheduling method taking power generation adjusting number constraint into account, belonging to the field of power system operation and control technologies. The method comprises the following steps of: setting the number of time periods, and adjusting threshold coefficients of generators, the number of sub time periods contained by each generator, the tail time period of each sub time period, barrier parameters and iteration accuracy; setting the original power generation plan values of all the generators in an electric power system; calculating the unit power generation adjusting price of all the generators; establishing and solving an online rolling scheduling model; and carrying out online rolling scheduling on the active power generated by all the adjusted generators in each time period. The online rolling scheduling method taking the power generation adjusting number constraint into account has the advantages that the difficulty of problem solving is reduced, calculated results strictly meet the power generation adjusting number constraint and time interval constraint, and obtained rolling scheduling plans have strong practicability.

Description

Consider the online rolling scheduling method of generating adjusting number of times constraint

Technical field

The invention belongs to power system operation and control technology field, particularly a kind of online rolling scheduling method of regulating the number of times constraint based on the consideration generating of exponential function.

Background technology

The power generation dispatching plan is the core basic module of MODERN ENERGY management system.The power generation dispatching plan, refer under the condition of load prediction data, interconnection exchange plan, electric equipment maintenance scheduling, generator start and stop state and the initial active power of generator of giving fixed system the active power that each generator will send within following a period of time.Because the randomness of load and the existence of various external interference, the running status of electric power system has uncertainty.The dispatching method of Multiple Time Scales can be tackled the uncertainty of operation states of electric power system effectively, and online rolling scheduling is an important link of this dispatching method.Online rolling scheduling is according to situation and the load prediction data in the following moment of the current operation of electric power system, the power generation dispatching plan is carried out the correction of rolling type, with the deviation between elimination power generation dispatching plan and the actual load, thus economy and the fail safe of assurance power system operation.

What traditional online rolling scheduling method adopted is classical dynamic economic dispatch.Classical dynamic economic dispatch is in the situation of the constraints such as creep speed of the output power limit of considering electric power system generation load balance, generator and generator output, being in the load power that distribution is born separately between the generator of open state, to reach the target of cost of electricity-generating minimum.In the dynamic economic dispatch model of classics, under the condition that satisfies maximum, minimum output power restriction and ramping rate constraints, the active power that generator sends can be regulated arbitrarily.Yet in the actual motion of electric power system, owing to regulate the life-span that the generating meeting brings loss to generator and affects generator, the generating adjusting number of times of therefore tackling generator is limited.In addition, be subject to the impact of network communication condition, the time interval that generator is regulated generated output also should be restricted.Traditional rolling scheduling method can't be considered above constraint, if the rolling power generation dispatching plan that the method is generated directly is issued to the power plant execution, the situation that generator can't generate electricity in strict accordance with generation schedule might appear so, also may regulate the consequence that generated output causes generator minimizing in useful life owing to frequent, thereby affect the normal operation of electric power system.The actual demand of using in order to satisfy engineering considers that the online rolling scheduling method of generating adjusting number of times constraint has very important meaning for the practicality that improves the plan of online rolling power generation dispatching.

Summary of the invention

The objective of the invention is for overcoming the weak point of prior art, propose a kind of consider to generate electricity regulate the online rolling scheduling method of number of times constraint, the method that adopts the present invention to propose generates the online rolling scheduling plan that number of times constraint and generating adjusting time interval constraint are regulated in the consideration generating, can guarantee the operability of online rolling scheduling, the practicality of raising method.

The present invention proposes a kind of consider to generate electricity regulate the online rolling scheduling method of number of times constraint, it is characterized in that the method may further comprise the steps:

1) time span that rolling scheduling is set is T _Span, T _SpanSpan be generally 1～4 hour; The time interval length that the time period of rolling scheduling adjacent in the time span of rolling scheduling is set is T _Space, T _SpaceSpan be generally 5～15 minutes; The period number T of rolling scheduling is as the formula (1):

$T=\frac{T_{\mathrm{span}}}{T_{\mathrm{space}}}---\left(1\right)$

The adjustment threshold value coefficient r of generator is set, and the span of r is generally 1 ~ 10(according to artificial experience, determines according to computational efficiency, and typical value is 1.39);

The sub-period number S that each generator comprised within T period in the electric power system is set _iAnd the end period of each sub-period

S wherein _iBe the sub-period number that i platform generator comprised within T period, S _iTypical value be 4, its span is generally 1 ~ 4,

Be that i platform generator is in the end period of j sub-period; The parameter of placing obstacles σ, its span is generally 0 ~ 1; Iteration precision ε is set, and its span is generally 1e-5 to 1e-3;

The original generation schedule value of all generators in the electric power system is set

N wherein _gNumber of units for generator;

The original scheme value of the active power that to be i platform generator send t period;

2) calculate the unit generation adjustment price of all generators

Wherein

Be the generation adjustment price of i platform generator t period;

The point place does Taylor expansion to i platform generator at the cost of electricity-generating function of t period, Value is the Monomial coefficient of Taylor expansion;

3) foundation is as follows based on the online rolling scheduling model that number of times retrains and the time interval retrains of the consideration generating adjusting of exponential function:

$\underset{x}{\min }f\left(x\right)$

s.t.h(x)=0 （2）

$g\left(x\right)\≤\stackrel{\‾}{g}$

In formula (2) model, x is decision variable, comprising: i platform generator is in the upwards generation adjustment amount of t period I platform generator is in the downward generation adjustment amount of t period I platform generator accounts for the ratio of creep speed at the adjustment amount of t period Wherein:

i＝1,2,...,N _g,t＝1,2,...,T；

F (x) be all generators at the target function of the generation adjustment price sum of all periods, suc as formula (3) be:

$f\left(x\right)=\underset{i=1}{\overset{N_g}{\mathrm{\Σ}}}\underset{t=1}{\overset{T}{\mathrm{\Σ}}}{a}_i^t({\mathrm{pu}}_i^t+{\mathrm{pd}}_i^t)---\left(3\right)$

Equality constraint h (x)=0 comprises: the generation load Constraints of Equilibrium of each period, as the formula (4):

$\underset{i=1}{\overset{N_g}{\mathrm{\Σ}}}{p}_i^t-d_t=0,\∀t=\mathrm{1,2},...,T---\left(4\right)$

In the formula (4), d _tBe the system loading predicted value t period;

The active power constraint that each generator sent in each time period after adjusting, as the formula (5):

${p_{0,}}_i^t+{\mathrm{pu}}_i^t-{\mathrm{pd}}_i^t-p_i^t=0,\∀t=\mathrm{1,2},...,T,i=\mathrm{1,2},...,N_g---\left(5\right)$

In the formula (5),

The active power of sending t period for adjusting rear i platform generator;

In formula (2) model, inequality constraints

Comprise:

The generation adjustment total degree constraint of each generator:

$\underset{t=1}{\overset{T}{\mathrm{\Σ}}}(1-e^{-{\mathrm{ru}}_i^t})\≤C_i,\∀i=\mathrm{1,2},...,N_g---\left(6\right)$

In the formula (6), C _iIt is i platform generator is regulated the generating number of times within T period maximum;

Each generator is in the generation adjustment number of times constraint of each sub-period, as the formula (7):

$\underset{t=s_i^{j-1}+1}{\overset{s_i^j}{\mathrm{\Σ}}}\left(\text{1-}{e}^{-{\mathrm{ru}}_i^t}\right)\≤n_i^j,\∀i=\mathrm{1,2},...,N_g,j=\mathrm{1,2},...,S_i---\left(7\right)$

In the formula (7), It is i platform generator is regulated the generating number of times in j sub-period maximum;

Each generator is at the ramping rate constraints of each period, as the formula (8):

$\left\{\begin{array}{c}{-p}_i^t+p_i^{t-1}-u_i^{t}R{D}_i^{t-1}\≤0\\ p_i^t-p_i^{t-1}-u_i^t{\mathrm{RU}}_i^{t-1}\≤0\end{array}\right.,\∀t=\mathrm{1,2},...,T,i=\mathrm{1,2},...,N_g$

In the formula (8),

Be i platform generator in the maximum regulated quantity downwards of t period,

Be i platform generator in the maximum of t the period regulated quantity that makes progress;

The active power constraint that each generator sent in each period, as the formula (9):

$\left\{\begin{array}{c}-p_i^t\≤-P_{\min ,i}^t\\ p_i^t\≤P_{\max ,i}^t\end{array}\right.,\∀t=\mathrm{1,2},...,T,i=\mathrm{1,2},...,N_g---\left(9\right)$

In the formula (9),

The minimum value of the active power that to be i platform generator send t period, The maximum of the active power that to be i platform generator send t period;

4) find the solution the online rolling scheduling model that number of times retrains and the time interval retrains of considering that generating is regulated, detailed process is as follows:

4-1) the Augmented Lagrangian Functions of the described online rolling scheduling model of structure, as the formula (10)

$L(x,y,w,\mathrm{\μ},u)=f\left(x\right)-y^{T}h\left(x\right)-w^T[g\left(x\right)+u-\stackrel{\‾}{g}]-\mathrm{\μ}\underset{j=1}{\overset{r_g}{\mathrm{\Σ}}}\ln \left(u_j\right)---\left(10\right)$

In the formula (10), x, u are the original variable of Optimized model, and y, w are the dual variable of Optimized model; Wherein, u is the slack variable of inequality constraints, and y is the dual variable corresponding with equality constraint, and w is the dual variable corresponding with inequality constraints, r _gBe the dimension of vector w, μ is the barrier coefficient; Each variable satisfies constraints u 〉=0, w≤0;

4-2) original variable x is set, u, dual variable y, the initial value of w and barrier coefficient μ is designated as respectively x ⁽⁰⁾, u ⁽⁰⁾, y ⁽⁰⁾, w ⁽⁰⁾And μ ⁽⁰⁾, x ⁽⁰⁾, y ⁽⁰⁾, u ⁽⁰⁾, w ⁽⁰⁾, μ ⁽⁰⁾Generally be taken as 0; Iterations k=0 is set;

4-3) calculate Lagrangian augmentation function to the single order partial derivative of each original variable and dual variable, as the formula (11):

$\left\{\begin{array}{c}{\▿}_{x}L={\▿}_{x}f\left(x^{\left(k\right)}\right)-{\▿}_{x}h\left(x^{\left(k\right)}\right)y^{\left(k\right)}-{\▿}_{x}g\left(x^{\left(k\right)}\right)w^{\left(k\right)}\\ {\▿}_{y}L=h\left(x^{\left(k\right)}\right)\\ {\▿}_{w}L=g\left(x^{\left(k\right)}\right)+u^{\left(k\right)}-\stackrel{\‾}{g}\\ {\▿}_{u}L=-w^{\left(k\right)}-{\mathrm{\μ}}^{\left(k\right)}{U}^{\left(k\right)-1}e\end{array}\right.---\left(11\right)$

In the formula (11), $U^{\left(k\right)}=\mathrm{diag}(u_1^{\left(k\right)},u_2^{\left(k\right)},...,u_{r_g}^{\left(k\right)}),e={(\mathrm{1,1},...,1)}_{r_g}^T;$

4-4) foundation is found the solution the correction amount x that obtains the k time iteration original variable x suc as formula the update equation of (12) ^(k)Correction amount y with dual variable y ^(k):

$\left[\begin{array}{cc}{H}^{\′\left(k\right)}& {\▿}_{x}h\left(x^{\left(k\right)}\right)\\ {\▿}_x^{T}h\left(x^{\left(k\right)}\right)& 0\end{array}\right]\left[\begin{array}{c}{\mathrm{\Δx}}^{\left(k\right)}\\ {\mathrm{\Δy}}^{\left(k\right)}\end{array}\right]=\left[\begin{array}{c}{\▿}_{x}L\\ -{\▿}_{y}L\end{array}\right]---\left(12\right)$

In the formula (12), $H^{\′\left(k\right)}=-[{\▿}_x^{2}f\left(x^{\left(k\right)}\right)-{\▿}_x^{2}h\left(x^{\left(k\right)}\right)y^{\left(k\right)}-{\▿}_x^{2}g\left(x^{\left(k\right)}\right)w^{\left(k\right)}]+{\▿}_{x}g\left(x^{\left(k\right)}\right)U^{\left(k\right)-1}{W}^{\left(k\right)}{\▿}_x^{T}g\left(x^{\left(k\right)}\right),$

$W^{\left(k\right)}=\mathrm{diag}(w_1^{\left(k\right)},w_2^{\left(k\right)},...,w_{r_g}^{\left(k\right)});$

4-5) calculate the k time iteration variable u, the correction amount u of w according to formula (13) ^(k), Δ w ^(k):

${\mathrm{\Δu}}^{\left(k\right)}=-{\▿}_{x}g{\left(x^{\left(k\right)}\right)}^T{\mathrm{\Δx}}^{\left(k\right)}-[g\left(x^{\left(k\right)}\right)+u^{\left(k\right)}-\stackrel{\‾}{g}]$

${\mathrm{\Δw}}^{\left(k\right)}=U^{\left(k\right)-1}{W}^{\left(k\right)}{\▿}_{x}g{\left(x^{\left(k\right)}\right)}^T{\mathrm{\Δx}}^{\left(k\right)}---\left(13\right)$

${-U}^{\left(k\right)-1}\left\{\right[U^{\left(k\right)}{W}^{\left(k\right)}e+{\mathrm{\μ}}^{\left(k\right)}e]-W^{\left(k\right)}[g\left(x^{\left(k\right)}\right)+u^{\left(k\right)}-\stackrel{\‾}{g}\left]\right\}$

4-6) calculate the correction step-length of the k time iteration original variable according to formula (14)

Correction step-length with dual variable For:

${\mathrm{step}}_P^{\left(k\right)}=0.9995\min \{\underset{i=\mathrm{1,2},...,r_g}{\min }(\frac{-u_i^{\left(k\right)}}{{\mathrm{\&Delta;u}}_i^{\left(k\right)}}:\mathrm{\&Delta;}{u}_i^{\left(k\right)}<0),1\}$ （14）

${\mathrm{step}}_D^{\left(k\right)}=0.9995\min \{\underset{i=\mathrm{1,2},...,r_g}{\min }(\frac{-w_i^{\left(k\right)}}{{\mathrm{\&Delta;w}}_i^{\left(k\right)}}:\mathrm{\&Delta;}{w}_i^{\left(k\right)}>0),1\}$

4-7) according to formula (15) original variable and the dual variable of the k time iteration are revised:

$\left[\begin{array}{c}{x}^{(k+1)}\\ u^{(k+1)}\end{array}\right]=\left[\begin{array}{c}{x}^{\left(k\right)}\\ u^{\left(k\right)}\end{array}\right]+{\mathrm{step}}_P^{\left(k\right)}\left[\begin{array}{c}{\mathrm{\&Delta;x}}^{\left(k\right)}\\ {\mathrm{\&Delta;u}}^{\left(k\right)}\end{array}\right]$ （15）

$\left[\begin{array}{c}{y}^{(k+1)}\\ w^{(k+1)}\end{array}\right]=\left[\begin{array}{c}{y}^{\left(k\right)}\\ w^{\left(k\right)}\end{array}\right]+{\mathrm{step}}_D^{\left(k\right)}\left[\begin{array}{c}{\mathrm{\&Delta;y}}^{\left(k\right)}\\ {\mathrm{\&Delta;w}}^{\left(k\right)}\end{array}\right]$

4-8) according to formula (16) calculate the k time iteration original-antithesis complementation gap ρ ^(k)With barrier coefficient μ ^(k):

ρ ^(k)=-u ^(k)Tw

${\mathrm{\&mu;}}^{\left(k\right)}=\mathrm{\&sigma;}\frac{{\mathrm{\&rho;}}^{\left(k\right)}}{{2r}_g}---\left(16\right)$

4-9) to the complementary gap ρ of original-antithesis ^(k)Judge, if ρ ^(k)＜ε then carries out step 5); If ρ ^(k)〉=ε then arranges k=k+1, and carries out step 4-3);

5) be adjusted the active power that rear each generator sent in each period according to formula (17), shown in (17):

$p_i^t={p_{0,}}_i^t+{\mathrm{pu}}_i^t-{\mathrm{pd}}_i^t,\&ForAll;t=\mathrm{1,2},...,T,i=\mathrm{1,2},...,N_g---\left(17\right);$

6) will adjust after the active power sent in each period of each generator be issued to each power plant and carry out, carry out online rolling scheduling.

The online rolling scheduling method that the present invention proposes, its advantage is:

1, regulates the number of times constraint by the generating of describing generator with exponential function, avoided in the rolling scheduling planning model, introducing discrete variable, thereby the rolling scheduling planning model that will consider the constraint of generating adjusting number of times is reduced to nonlinear programming problem, has reduced the difficulty of problem solving.

2, adopt the interior point method of high robust to find the solution online rolling scheduling planning model, result of calculation strictly satisfies number of times constraint and the time interval constraint that generating is regulated, and can guarantee the operability of online rolling scheduling, improves the practicality of dispatching method.

Embodiment

The present invention proposes a kind of online rolling scheduling method of regulating the number of times constraint of considering to generate electricity and is described in detail as follows in conjunction with the embodiments:,

Present embodiment a kind of considers to generate electricity and regulates the online rolling scheduling method of number of times constraint, it is characterized in that the method may further comprise the steps:

1) time span that rolling scheduling considers being set is T _Span, T _SpanTypical value be 4 hours; The time interval length that the adjacent time period is set is T _Space, T _SpaceTypical value be 15 minutes; The period number T of rolling scheduling is as the formula (1):

$T=\frac{T_{\mathrm{span}}}{T_{\mathrm{space}}}---\left(1\right)$

The adjustment threshold value coefficient r of generator is set, and the typical value of r is 1.39;

The sub-period number S that each generator comprised within T period in the electric power system is set _iAnd the end period of each sub-period

S wherein _iBe the sub-period number that i platform generator comprised within T period, S _iTypical value be 4,

Be that i platform generator is in the end period of j sub-period; The parameter of placing obstacles σ, its typical value is 1; Iteration precision ε is set, and its typical value is 1e-3;

The original generation schedule value of all generators in the electric power system is set

N wherein _gNumber of units for generator;

The original scheme value of the active power that to be i platform generator send t period;

2) calculate the unit generation adjustment price of all generators

Wherein

Be the generation adjustment price of i platform generator t period;

The point place does Taylor expansion to i platform generator at the cost of electricity-generating function of t period,

Value is the Monomial coefficient of Taylor expansion;

3) foundation is as follows based on the online rolling scheduling model that number of times retrains and the time interval retrains of the consideration generating adjusting of exponential function:

$\underset{x}{\min }f\left(x\right)$

s.t.h(x)=0 （2）

$g\left(x\right)\&le;\stackrel{\&OverBar;}{g}$

In formula (2) model, x is decision variable, comprising: i platform generator is in the upwards generation adjustment amount of t period

I platform generator is in the downward generation adjustment amount of t period

I platform generator accounts for the ratio of creep speed at the adjustment amount of t period

Wherein:

i＝1,2，...,N _g,t＝1,2，...,T；

F (x) be all generators at the target function of the generation adjustment price sum of all periods, suc as formula (3) be:

$f\left(x\right)=\underset{i=1}{\overset{N_g}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T}{\mathrm{\&Sigma;}}}{a}_i^t({\mathrm{pu}}_i^t+{\mathrm{pd}}_i^t)---\left(3\right)$

Equality constraint h (x)=0 comprises: the generation load Constraints of Equilibrium of each period, as the formula (4):

$\underset{i=1}{\overset{N_g}{\mathrm{\&Sigma;}}}{p}_i^t-d_t=0,\&ForAll;t=\mathrm{1,2},...,T---\left(4\right)$

In the formula (4), d _tBe the system loading predicted value t period;

The active power constraint that each generator sent in each time period after adjusting, as the formula (5):

${p_{0,}}_i^t+{\mathrm{pu}}_i^t-{\mathrm{pd}}_i^t-p_i^t=0,\&ForAll;t=\mathrm{1,2},...,T,i=\mathrm{1,2},...,N_g---\left(5\right)$

In the formula (5),

The active power of sending t period for adjusting rear i platform generator;

In formula (2) model, inequality constraints

Comprise: the generation adjustment total degree constraint of each generator:

$\underset{t=1}{\overset{T}{\mathrm{\&Sigma;}}}(1-e^{-{\mathrm{ru}}_i^t})\&le;C_i,\&ForAll;i=\mathrm{1,2},...,N_g---\left(6\right)$

In the formula (6), C _iIt is i platform generator is regulated the generating number of times within T period maximum;

Each generator is in the generation adjustment number of times constraint of each sub-period, as the formula (7):

$\underset{t=s_i^{j-1}+1}{\overset{s_i^j}{\mathrm{\&Sigma;}}}\left(\text{1-}{e}^{-{\mathrm{ru}}_i^t}\right)\&le;n_i^j,\&ForAll;i=\mathrm{1,2},...,N_g,j=\mathrm{1,2},...,S_i---\left(7\right)$

In the formula (7),

It is i platform generator is regulated the generating number of times in j sub-period maximum;

Each generator is at the ramping rate constraints of each period, as the formula (8):

$\left\{\begin{array}{c}{-p}_i^t+p_i^{t-1}-u_i^{t}R{D}_i^{t-1}\&le;0\\ p_i^t-p_i^{t-1}-u_i^t{\mathrm{RU}}_i^{t-1}\&le;0\end{array}\right.,\&ForAll;t=\mathrm{1,2},...,T,i=\mathrm{1,2},...,N_g$

In the formula (8),

Be i platform generator in the maximum regulated quantity downwards of t period,

Be i platform generator in the maximum of t the period regulated quantity that makes progress;

The active power constraint that each generator sent in each period, as the formula (9):

$\left\{\begin{array}{c}-p_i^t\&le;-P_{\min ,i}^t\\ p_i^t\&le;P_{\max ,i}^t\end{array}\right.,\&ForAll;t=\mathrm{1,2},...,T,i=\mathrm{1,2},...,N_g---\left(9\right)$

In the formula (9),

The minimum value of the active power that to be i platform generator send t period,

The maximum of the active power that to be i platform generator send t period;

4) find the solution the online rolling scheduling model that number of times retrains and the time interval retrains of considering that generating is regulated, detailed process is as follows:

4-1) the Augmented Lagrangian Functions of the described online rolling scheduling model of structure, as the formula (10)

$L(x,y,w,\mathrm{\&mu;},u)=f\left(x\right)-y^{T}h\left(x\right)-w^T[g\left(x\right)+u-\stackrel{\&OverBar;}{g}]-\mathrm{\&mu;}\underset{j=1}{\overset{r_g}{\mathrm{\&Sigma;}}}\ln \left(u_j\right)---\left(10\right)$

In the formula (10), x, u are the original variable of Optimized model, and y, w are the dual variable of Optimized model; Wherein, u is the slack variable of inequality constraints, and y is the dual variable corresponding with equality constraint, and w is the dual variable corresponding with inequality constraints, r _gBe the dimension of vector w, μ is the barrier coefficient; Each variable satisfies constraints u 〉=0, w≤0;

4-2) original variable x is set, u, dual variable y, the initial value of w and barrier coefficient μ is designated as respectively x ⁽⁰⁾, u ⁽⁰⁾, y ⁽⁰⁾, w ⁽⁰⁾And μ ⁽⁰⁾, x ⁽⁰⁾, y ⁽⁰⁾, u ⁽⁰⁾, w ⁽⁰⁾, μ ⁽⁰⁾Generally be taken as 0; Iterations k=0 is set;

4-3) calculate Lagrangian augmentation function to the single order partial derivative of each original variable and dual variable, as the formula (11):

$\left\{\begin{array}{c}{\&dtri;}_{x}L={\&dtri;}_{x}f\left(x^{\left(k\right)}\right)-{\&dtri;}_{x}h\left(x^{\left(k\right)}\right)y^{\left(k\right)}-{\&dtri;}_{x}g\left(x^{\left(k\right)}\right)w^{\left(k\right)}\\ {\&dtri;}_{y}L=h\left(x^{\left(k\right)}\right)\\ {\&dtri;}_{w}L=g\left(x^{\left(k\right)}\right)+u^{\left(k\right)}-\stackrel{\&OverBar;}{g}\\ {\&dtri;}_{u}L=-w^{\left(k\right)}-{\mathrm{\&mu;}}^{\left(k\right)}{U}^{\left(k\right)-1}e\end{array}\right.---\left(11\right)$

In the formula (11), $U^{\left(k\right)}=\mathrm{diag}(u_1^{\left(k\right)},u_2^{\left(k\right)},...,u_{r_g}^{\left(k\right)}),e={(\mathrm{1,1},...,1)}_{r_g}^T;$

4-4) foundation is found the solution the correction amount x that obtains the k time iteration original variable x suc as formula the update equation of (12) ^(k)Correction amount y with dual variable y ^(k):

$\left[\begin{array}{cc}{H}^{\&prime;\left(k\right)}& {\&dtri;}_{x}h\left(x^{\left(k\right)}\right)\\ {\&dtri;}_x^{T}h\left(x^{\left(k\right)}\right)& 0\end{array}\right]\left[\begin{array}{c}{\mathrm{\&Delta;x}}^{\left(k\right)}\\ {\mathrm{\&Delta;y}}^{\left(k\right)}\end{array}\right]=\left[\begin{array}{c}{\&dtri;}_{x}L\\ -{\&dtri;}_{y}L\end{array}\right]---\left(12\right)$

In the formula (12), $H^{\&prime;\left(k\right)}=-[{\&dtri;}_x^{2}f\left(x^{\left(k\right)}\right)-{\&dtri;}_x^{2}h\left(x^{\left(k\right)}\right)y^{\left(k\right)}-{\&dtri;}_x^{2}g\left(x^{\left(k\right)}\right)w^{\left(k\right)}]+{\&dtri;}_{x}g\left(x^{\left(k\right)}\right)U^{\left(k\right)-1}{W}^{\left(k\right)}{\&dtri;}_x^{T}g\left(x^{\left(k\right)}\right),$

$W^{\left(k\right)}=\mathrm{diag}(w_1^{\left(k\right)},w_2^{\left(k\right)},...,w_{r_g}^{\left(k\right)});$

4-5) calculate the k time iteration variable u, the correction amount u of w according to formula (13) ^(k), Δ w ^(k):

${\mathrm{\&Delta;u}}^{\left(k\right)}=-{\&dtri;}_{x}g{\left(x^{\left(k\right)}\right)}^T{\mathrm{\&Delta;x}}^{\left(k\right)}-[g\left(x^{\left(k\right)}\right)+u^{\left(k\right)}-\stackrel{\&OverBar;}{g}]$

${\mathrm{\&Delta;w}}^{\left(k\right)}=U^{\left(k\right)-1}{W}^{\left(k\right)}{\&dtri;}_{x}g{\left(x^{\left(k\right)}\right)}^T{\mathrm{\&Delta;x}}^{\left(k\right)}---\left(13\right)$

${-U}^{\left(k\right)-1}\left\{\right[U^{\left(k\right)}{W}^{\left(k\right)}e+{\mathrm{\&mu;}}^{\left(k\right)}e]-W^{\left(k\right)}[g\left(x^{\left(k\right)}\right)+u^{\left(k\right)}-\stackrel{\&OverBar;}{g}\left]\right\}$

4-6) calculate the correction step-length of the k time iteration original variable according to formula (14)

Correction step-length with dual variable

For:

${\mathrm{step}}_P^{\left(k\right)}=0.9995\min \{\underset{i=\mathrm{1,2},...,r_g}{\min }(\frac{-u_i^{\left(k\right)}}{{\mathrm{\&Delta;u}}_i^{\left(k\right)}}:\mathrm{\&Delta;}{u}_i^{\left(k\right)}<0),1\}$ （14）

${\mathrm{step}}_D^{\left(k\right)}=0.9995\min \{\underset{i=\mathrm{1,2},...,r_g}{\min }(\frac{-w_i^{\left(k\right)}}{{\mathrm{\&Delta;w}}_i^{\left(k\right)}}:\mathrm{\&Delta;}{w}_i^{\left(k\right)}>0),1\}$

4-7) according to formula (15) original variable and the dual variable of the k time iteration are revised:

$\left[\begin{array}{c}{x}^{(k+1)}\\ u^{(k+1)}\end{array}\right]=\left[\begin{array}{c}{x}^{\left(k\right)}\\ u^{\left(k\right)}\end{array}\right]+{\mathrm{step}}_P^{\left(k\right)}\left[\begin{array}{c}{\mathrm{\&Delta;x}}^{\left(k\right)}\\ {\mathrm{\&Delta;u}}^{\left(k\right)}\end{array}\right]$ （15）

$\left[\begin{array}{c}{y}^{(k+1)}\\ w^{(k+1)}\end{array}\right]=\left[\begin{array}{c}{y}^{\left(k\right)}\\ w^{\left(k\right)}\end{array}\right]+{\mathrm{step}}_D^{\left(k\right)}\left[\begin{array}{c}{\mathrm{\&Delta;y}}^{\left(k\right)}\\ {\mathrm{\&Delta;w}}^{\left(k\right)}\end{array}\right]$

4-8) according to formula (16) calculate the k time iteration original-antithesis complementation gap ρ ^(k)With barrier coefficient μ ^(k):

ρ ^(k)=-u ^(k)Tw

${\mathrm{\&mu;}}^{\left(k\right)}=\mathrm{\&sigma;}\frac{{\mathrm{\&rho;}}^{\left(k\right)}}{{2r}_g}---\left(16\right)$

4-9) to the complementary gap ρ of original-antithesis ^(k)Judge, if ρ ^(k)＜ε then carries out step 5); If ρ ^(k)〉=ε then arranges k=k+1, and carries out step 4-3);

5) be adjusted the active power that rear each generator sent in each period according to formula (17), shown in (17):

$p_i^t={p_{0,}}_i^t+{\mathrm{pu}}_i^t-{\mathrm{pd}}_i^t,\&ForAll;t=\mathrm{1,2},...,T,i=\mathrm{1,2},...,N_g---\left(17\right);$

6) will adjust after the active power sent in each period of each generator be issued to each power plant and carry out, carry out online rolling scheduling.

Claims (1)

1. consider to generate electricity and regulate the online rolling scheduling method of number of times constraint for one kind, it is characterized in that the method may further comprise the steps:

1) time span that rolling scheduling is set is T _Span, T _SpanSpan be 1～4 hour; The time interval length that the time period of rolling scheduling adjacent in the time span of rolling scheduling is set is T _Space, T _SpaceSpan be 5～15 minutes; The period number T of rolling scheduling is as the formula (1):

$T=\frac{T_{\mathrm{span}}}{T_{\mathrm{space}}}---\left(1\right)$

The adjustment threshold value coefficient r of generator is set, and the span of r is generally 1 ~ 10;

The sub-period number S that each generator comprised within T period in the electric power system is set _iAnd the end period of each sub-period S wherein _iBe the sub-period number that i platform generator comprised within T period,

Be that i platform generator is in the end period of j sub-period; The parameter of placing obstacles σ, its span is 0 ~ 1; Iteration precision ε is set, and its span is 1e-5 to 1e-3;

The original generation schedule value of all generators in the electric power system is set N wherein _gNumber of units for generator;

The original scheme value of the active power that to be i platform generator send t period;

2) calculate the unit generation adjustment price of all generators

Wherein

Be the generation adjustment price of i platform generator t period; The point place does Taylor expansion to i platform generator at the cost of electricity-generating function of t period,

Value is the Monomial coefficient of Taylor expansion;

3) foundation is as follows based on the online rolling scheduling model that number of times retrains and the time interval retrains of the consideration generating adjusting of exponential function:

$\underset{x}{\min }f\left(x\right)$

s.t.h(x)=0 （2）

$g\left(x\right)\&le;\stackrel{\&OverBar;}{g}$

In formula (2) model, x is decision variable, comprising: i platform generator is in the upwards generation adjustment amount of t period

I platform generator is in the downward generation adjustment amount of t period

I platform generator accounts for the ratio of creep speed at the adjustment amount of t period

Wherein:

i＝1,2,...,N _g,t＝1,2,...,T；

F (x) be all generators at the target function of the generation adjustment price sum of all periods, suc as formula (3) be:

$f\left(x\right)=\underset{i=1}{\overset{N_g}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T}{\mathrm{\&Sigma;}}}{a}_i^t({\mathrm{pu}}_i^t+{\mathrm{pd}}_i^t)---\left(3\right)$

Equality constraint h (x)=0 comprises: the generation load Constraints of Equilibrium of each period, as the formula (4):

$\underset{i=1}{\overset{N_g}{\mathrm{\&Sigma;}}}{p}_i^t-d_t=0,\&ForAll;t=\mathrm{1,2},...,T---\left(4\right)$

In the formula (4), d _tBe the system loading predicted value t period;

The active power constraint that each generator sent in each time period after adjusting, as the formula (5):

${p_{0,}}_i^t+{\mathrm{pu}}_i^t-{\mathrm{pd}}_i^t-p_i^t=0,\&ForAll;t=\mathrm{1,2},...,T,i=\mathrm{1,2},...,N_g---\left(5\right)$

In the formula (5),

The active power of sending t period for adjusting rear i platform generator;

In formula (2) model, inequality constraints

Comprise:

The generation adjustment total degree constraint of each generator:

$\underset{t=1}{\overset{T}{\mathrm{\&Sigma;}}}(1-e^{-{\mathrm{ru}}_i^t})\&le;C_i,\&ForAll;i=\mathrm{1,2},...,N_g---\left(6\right)$

In the formula (6), C _iIt is i platform generator is regulated the generating number of times within T period maximum;

Each generator is in the generation adjustment number of times constraint of each sub-period, as the formula (7):

$\underset{t=s_i^{j-1}+1}{\overset{s_i^j}{\mathrm{\&Sigma;}}}\left(\text{1-}{e}^{-{\mathrm{ru}}_i^t}\right)\&le;n_i^j,\&ForAll;i=\mathrm{1,2},...,N_g,j=\mathrm{1,2},...,S_i---\left(7\right)$

In the formula (7), It is i platform generator is regulated the generating number of times in j sub-period maximum;

Each generator is at the ramping rate constraints of each period, as the formula (8):

$\left\{\begin{array}{c}{-p}_i^t+p_i^{t-1}-u_i^{t}R{D}_i^{t-1}\&le;0\\ p_i^t-p_i^{t-1}-u_i^t{\mathrm{RU}}_i^{t-1}\&le;0\end{array}\right.,\&ForAll;t=\mathrm{1,2},...,T,i=\mathrm{1,2},...,N_g$

In the formula (8),

Be i platform generator in the maximum regulated quantity downwards of t period,

Be i platform generator in the maximum of t the period regulated quantity that makes progress;

The active power constraint that each generator sent in each period, as the formula (9):

$\left\{\begin{array}{c}-p_i^t\&le;-P_{\min ,i}^t\\ p_i^t\&le;P_{\max ,i}^t\end{array}\right.,\&ForAll;t=\mathrm{1,2},...,T,i=\mathrm{1,2},...,N_g---\left(9\right)$

In the formula (9),

The minimum value of the active power that to be i platform generator send t period,

The maximum of the active power that to be i platform generator send t period;

4) find the solution the online rolling scheduling model that number of times retrains and the time interval retrains of considering that generating is regulated, detailed process is as follows:

4-1) the Augmented Lagrangian Functions of the described online rolling scheduling model of structure, as the formula (10)

$L(x,y,w,\mathrm{\&mu;},u)=f\left(x\right)-y^{T}h\left(x\right)-w^T[g\left(x\right)+u-\stackrel{\&OverBar;}{g}]-\mathrm{\&mu;}\underset{j=1}{\overset{r_g}{\mathrm{\&Sigma;}}}\ln \left(u_j\right)---\left(10\right)$

In the formula (10), x, u are the original variable of Optimized model, and y, w are the dual variable of Optimized model; Wherein, u is the slack variable of inequality constraints, and y is the dual variable corresponding with equality constraint, and w is the dual variable corresponding with inequality constraints, r _gBe the dimension of vector w, μ is the barrier coefficient; Each variable satisfies constraints u 〉=0, w≤0;

4-2) original variable x is set, u, dual variable y, the initial value of w and barrier coefficient μ is designated as respectively x ⁽⁰⁾, u ⁽⁰⁾, y ⁽⁰⁾, w ⁽⁰⁾And μ ⁽⁰⁾, x ⁽⁰⁾, y ⁽⁰⁾, u ⁽⁰⁾, w ⁽⁰⁾, μ ⁽⁰⁾Generally be taken as 0; Iterations k=0 is set;

4-3) calculate Lagrangian augmentation function to the single order partial derivative of each original variable and dual variable, as the formula (11):

$\left\{\begin{array}{c}{\&dtri;}_{x}L={\&dtri;}_{x}f\left(x^{\left(k\right)}\right)-{\&dtri;}_{x}h\left(x^{\left(k\right)}\right)y^{\left(k\right)}-{\&dtri;}_{x}g\left(x^{\left(k\right)}\right)w^{\left(k\right)}\\ {\&dtri;}_{y}L=h\left(x^{\left(k\right)}\right)\\ {\&dtri;}_{w}L=g\left(x^{\left(k\right)}\right)+u^{\left(k\right)}-\stackrel{\&OverBar;}{g}\\ {\&dtri;}_{u}L=-w^{\left(k\right)}-{\mathrm{\&mu;}}^{\left(k\right)}{U}^{\left(k\right)-1}e\end{array}\right.---\left(11\right)$

In the formula (11), $U^{\left(k\right)}=\mathrm{diag}(u_1^{\left(k\right)},u_2^{\left(k\right)},...,u_{r_g}^{\left(k\right)}),e={(\mathrm{1,1},...,1)}_{r_g}^T;$

4-4) foundation is found the solution the correction amount x that obtains the k time iteration original variable x suc as formula the update equation of (12) ^(k)Correction amount y with dual variable y ^(k):

$\left[\begin{array}{cc}{H}^{\&prime;\left(k\right)}& {\&dtri;}_{x}h\left(x^{\left(k\right)}\right)\\ {\&dtri;}_x^{T}h\left(x^{\left(k\right)}\right)& 0\end{array}\right]\left[\begin{array}{c}{\mathrm{\&Delta;x}}^{\left(k\right)}\\ {\mathrm{\&Delta;y}}^{\left(k\right)}\end{array}\right]=\left[\begin{array}{c}{\&dtri;}_{x}L\\ -{\&dtri;}_{y}L\end{array}\right]---\left(12\right)$

In the formula (12), $H^{\&prime;\left(k\right)}=-[{\&dtri;}_x^{2}f\left(x^{\left(k\right)}\right)-{\&dtri;}_x^{2}h\left(x^{\left(k\right)}\right)y^{\left(k\right)}-{\&dtri;}_x^{2}g\left(x^{\left(k\right)}\right)w^{\left(k\right)}]+{\&dtri;}_{x}g\left(x^{\left(k\right)}\right)U^{\left(k\right)-1}{W}^{\left(k\right)}{\&dtri;}_x^{T}g\left(x^{\left(k\right)}\right),$ $W^{\left(k\right)}=\mathrm{diag}(w_1^{\left(k\right)},w_2^{\left(k\right)},...,w_{r_g}^{\left(k\right)});$

4-5) calculate the k time iteration variable u, the correction amount u of w according to formula (13) ^(k), Δ w ^(k):

${\mathrm{\&Delta;u}}^{\left(k\right)}=-{\&dtri;}_{x}g{\left(x^{\left(k\right)}\right)}^T{\mathrm{\&Delta;x}}^{\left(k\right)}-[g\left(x^{\left(k\right)}\right)+u^{\left(k\right)}-\stackrel{\&OverBar;}{g}]$

${\mathrm{\&Delta;w}}^{\left(k\right)}=U^{\left(k\right)-1}{W}^{\left(k\right)}{\&dtri;}_{x}g{\left(x^{\left(k\right)}\right)}^T{\mathrm{\&Delta;x}}^{\left(k\right)}---\left(13\right)$

${-U}^{\left(k\right)-1}\left\{\right[U^{\left(k\right)}{W}^{\left(k\right)}e+{\mathrm{\&mu;}}^{\left(k\right)}e]-W^{\left(k\right)}[g\left(x^{\left(k\right)}\right)+u^{\left(k\right)}-\stackrel{\&OverBar;}{g}\left]\right\}$

4-6) calculate the correction step-length of the k time iteration original variable according to formula (14)

Correction step-length with dual variable

For:

${\mathrm{step}}_P^{\left(k\right)}=0.9995\min \{\underset{i=\mathrm{1,2},...,r_g}{\min }(\frac{-u_i^{\left(k\right)}}{{\mathrm{\&Delta;u}}_i^{\left(k\right)}}:\mathrm{\&Delta;}{u}_i^{\left(k\right)}<0),1\}$ （14）

${\mathrm{step}}_D^{\left(k\right)}=0.9995\min \{\underset{i=\mathrm{1,2},...,r_g}{\min }(\frac{-w_i^{\left(k\right)}}{{\mathrm{\&Delta;w}}_i^{\left(k\right)}}:\mathrm{\&Delta;}{w}_i^{\left(k\right)}>0),1\}$

4-7) according to formula (15) original variable and the dual variable of the k time iteration are revised:

$\left[\begin{array}{c}{x}^{(k+1)}\\ u^{(k+1)}\end{array}\right]=\left[\begin{array}{c}{x}^{\left(k\right)}\\ u^{\left(k\right)}\end{array}\right]+{\mathrm{step}}_P^{\left(k\right)}\left[\begin{array}{c}{\mathrm{\&Delta;x}}^{\left(k\right)}\\ {\mathrm{\&Delta;u}}^{\left(k\right)}\end{array}\right]$ （15）

$\left[\begin{array}{c}{y}^{(k+1)}\\ w^{(k+1)}\end{array}\right]=\left[\begin{array}{c}{y}^{\left(k\right)}\\ w^{\left(k\right)}\end{array}\right]+{\mathrm{step}}_D^{\left(k\right)}\left[\begin{array}{c}{\mathrm{\&Delta;y}}^{\left(k\right)}\\ {\mathrm{\&Delta;w}}^{\left(k\right)}\end{array}\right]$

4-8) according to formula (16) calculate the k time iteration original-antithesis complementation gap ρ ^(k)With barrier coefficient μ ^(k):

ρ ^(k)=-u ^(k)Tw

${\mathrm{\&mu;}}^{\left(k\right)}=\mathrm{\&sigma;}\frac{{\mathrm{\&rho;}}^{\left(k\right)}}{{2r}_g}---\left(16\right)$

4-9) to the complementary gap ρ of original-antithesis ^(k)Judge, if ρ ^(k)＜ε then carries out step 5); If ρ ^(k)〉=ε then arranges k=k+1, and carries out step 4-3);

5) be adjusted the active power that rear each generator sent in each period according to formula (17), shown in (17):

$p_i^t={p_{0,}}_i^t+{\mathrm{pu}}_i^t-{\mathrm{pd}}_i^t,\&ForAll;t=\mathrm{1,2},...,T,i=\mathrm{1,2},...,N_g---\left(17\right);$

6) will adjust after the active power sent in each period of each generator be issued to each power plant and carry out, carry out online rolling scheduling.