CN103441492A - Frequency modulation feedback Nash equilibrium control method based on coevolution algorithm - Google Patents

Abstract

The invention discloses a frequency modulation feedback Nash equilibrium control method based on a coevolution algorithm. The control method includes the steps that step1, in consideration of a speed controller dead zone, control action amplitude limit, unit creep speed constraint and other engineering practice factors, a differential game model between a primary frequency modulation and a secondary frequency modulation in an IEEE two-area interconnection system is built; step2, the coevolution algorithm is adopted for solving the differential game model, with kinds of complex constraint, between the primary frequency modulation and the secondary frequency modulation in the IEEE two-area interconnection system, and a feedback Nash equilibrium solution of the differential game model is obtained; step3, the obtained feedback Nash equilibrium strategy serves as a primary frequency modulation control quantity and a secondary frequency modulation control quantity of an area, the conflict anti-tune problem between the primary frequency modulation and the secondary frequency modulation is effectively solved, and therefore coordination control between the primary frequency modulation and the secondary frequency modulation of an electric system is achieved. The frequency modulation feedback Nash equilibrium control method has the advantages of reducing unit wastage and achieving a good control effect.

Description

Frequency modulation feedback Nash Equilibrium control method based on Cooperative Evolutionary Algorithm

Technical field

The present invention relates to a kind of automatic control technology of power system, particularly a kind of frequency modulation feedback Nash Equilibrium control method based on Cooperative Evolutionary Algorithm.

Background technology

In electric power system, (automatic generation control, AGC) be the real-time tracking load variations, adjusts generated output and realize active balance, the Main Means that sustain pulse frequency is stable for primary frequency modulation and frequency modulation frequency modulation.

The working method of primary frequency modulation and frequency modulation frequency modulation, response cycle, control signal, control target all have larger difference, it is signal that primary frequency modulation be take equipment location frequency departure, through DEH system or meritorious the exerting oneself of mechanical governor Ji Xietiaoxie change unit, it is local Frequency servo; It is signal that frequency modulation frequency modulation be take frequency departure and regional Tie line Power deviation, provides the active power adjustment amount of each AGC unit after total station control calculates, finally by each Coordinated Control Systems, realized, and be whole district's power closed-loop control.Both sides' real-time adjustment direction may be contrary, and they act on simultaneously, unit is meritorious exerts oneself, any time, power of the assembling unit exporting change amount was the meritorious adjustment amount summation of exerting oneself of first and second frequency modulation unit, therefore may clash anti-tune phenomenon, cause the waste with adjustment amount that increases of adjusting action frequency.In the extensive grid-connected situation of the batch (-type) energy, the new forms of energy power fluctuation will cause system frequency and the larger fluctuation of regional Tie line Power, greatly increase the anti-phenomenon probability of happening of adjusting of conflict.

The present invention uses the differential theory of games to solve the anti-problem of adjusting of conflict between primary frequency modulation and frequency modulation frequency modulation.Because primary frequency modulation is made response according to current frequency departure, frequency modulation frequency modulation is made response according to current region control deviation (ACE), therefore be a feedback betting model, after considering all kinds of Complex Constraints, the frequency control system model should be nonlinear, and control variables and state variable are subject to inequality constraints.

The feedback betting model of non-linear, control variables and state variable Constrained model solves very difficult, is difficult to find theoretic equilibrium solution.In order to make up the deficiency of traditional mathematics method, the present invention adopts Cooperative Evolutionary Algorithm to be solved (because Cooperative Evolutionary Algorithm is the evolution of a plurality of populations this complex model, each population realizes separately evolving by genetic algorithm, and the evolutionary process of Cooperative Evolutionary Algorithm comprises genetic algorithm).Cooperative Evolutionary Algorithm is used for reference coevolution (Coevolution also claims common the evolution or the coevolution) mechanism of occurring in nature.Application can be traced back to the species coevolution model of the Job Shop Scheduling of the host of Hillis and parasitic animal and plant model and Husbands the earliest.Cooperative Evolutionary Algorithm can be processed the multiagent problem, and, owing to having considered intersubjective mutual conflict and effect, meets well the natural evolvement process of game, is effective ways that solve problem of game.In existing research, this field of Linear-Quadratic Problem differential game solved with Complex Constraints by Cooperative Evolutionary Algorithm is still a blank, and the present invention attempts proving the application prospect of Cooperative Evolutionary Algorithm in this field.

The present invention is under National 863 planning item fund assistance, set up a frequency modulation frequency modulation and coordinate the Linear-Quadratic Problem feedback differential game of controlling, and consider the engineering factors such as controller dead band, control action amplitude limitation, unit ramping rate constraints, try to achieve its feedback Nash Equilibrium Solution (FNES) by Cooperative Evolutionary Algorithm, the controlled quentity controlled variable of trying to achieve can meet under various engineering factors the anti-problem of adjusting of conflict between a frequency modulation frequency modulation that effectively solves.The present invention is applied to provide strong computational tool in the actual frequency modulation system of electric power system for the differential theory of games.

Summary of the invention

The object of the invention is to overcome the shortcoming of prior art with not enough, a kind of frequency modulation feedback Nash Equilibrium control method based on Cooperative Evolutionary Algorithm is provided, the method is in complicated electric power system, coordinate primary frequency modulation and frequency modulation frequency modulation controlled quentity controlled variable, effectively reduce the unit waste, obtained good control effect.

Purpose of the present invention is achieved through the following technical solutions:

The present invention is Linear-Quadratic Problem by target function, information set is that feedback game memoryless, complete state information is introduced in power system frequency control, n people's nonzero sum, non-cooperation, certainty are without in the game of limit Linear-Quadratic Problem differential, and every participant i tries hard to minimize pay off function J separately _i:

$J_i={\&Integral;}_{{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">t</figure-callout>}}_0}^{\&infin;}\frac{1}{2}[x^T\left(t\right)Q_{i}x\left(t\right)+u_i^T\left(t\right)R_i{u}_i\left(t\right)]\mathrm{dt},---\left(1\right)$

Wherein, t ₀the game time started, Q _ithe weight coefficient matrix corresponding to state variable, R _ifor the weight coefficient matrix corresponding to control variables, Q _i, R _ifor symmetric positive definite matrix, u _i(t) control strategy of corresponding participant i, x (t) is state variable.System state equation is:

， (2)

A is m scalariform state matrix, B _ifor the m dimensional vector, the input matrix [B that B is m * n rank ₁b ₂b _n].

If the information set of feedback game process is memoryless, complete state information, the balance policy of game each side is:

${u_i}^{*}\left(t\right)=-R_i^{-1}{B_i}^T{P}_{i}x\left(t\right),$ i=1,…,n，

Wherein, (P ₁, P ₂..., P _n) be the solution of algebraic riccati equation group, P _i, i=1 ... n is all symmetrical matrix

$-P_{i}A-A^T{P}_i-Q_i-\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}(-P_i{B}_i{R}_i^{-1}{B}_i^T{P}_i-P_i{B}_j{R}_j^{-1}{B}_j^T{P}_j,$

$-P_j{B}_j{R}_j^{-1}{B}_j^T{P}_i)=0$

Each participant's pay off function size is:

$J_i^{*}=\frac{1}{2}{x}^T{P}_{i}x,$

The Linear-Quadratic Problem optimal control is linear at state equation, and control variables and state variable are without under restraint condition, the linear feedback that the optimal control rate obtained is state variable.Yet, in engineering reality, control variables and state variable be Constrained often, and the real system model is also non-linear.In electric power system, primary frequency modulation and frequency modulation frequency modulation controlled quentity controlled variable have amplitude limitation, and the AGC unit has the creep speed restriction, and the governor dead time restriction makes frequency modulation system become non linear system.Optimal control rate in this case is difficult to try to achieve.

The nonlinear feedback that the optimal control rate of Constrained Nonlinear system is quantity of state, but solving of this control rate is very complicated, and be not easy to Project Realization.The present invention asks for the saturated linear feedback of the optimum met under Complex Constraints, when control rate arrives restrained boundary, will keep this maximum constant.

For making algorithm can consider more practical factor, the present invention adopts Cooperative Evolutionary Algorithm to solve the feedback Nash Equilibrium of Constrained Nonlinear system.The frame clsss of Cooperative Evolutionary Algorithm is similar to multi agent simulation, meets game evolution framework.Each optimal control subproblem adopts genetic algorithm independently to evolve and solve, and takes elite's retention strategy.Algorithmic procedure is described below:

It is variable that step 1:n participant be take the linear feedback coefficient k of state variable, even the strategy of participant i is u _i=k _ix, for each participant arranges independent population pop _i;

Step 2: establish current system and be evolved to L generation, each population is evolved under synergistic mechanism, and the system state equation that formula (2) is described is the hinge of each population of contact, the 1J reciprocal of the pay off function that formula (1) is expressed _ievaluation function as chromosome fitness in population.Take population i as example, adopt the c-best strategy, select the corresponding strategy of the chromosome that other population-i are the highest for fitness at L-1 as representative, form and represent set of strategies be expressed as

by each chromosome relative strategy in population i

the set of strategies that represents with other populations

substitution formula (2) is obtained the system mode track, by the pay off function of participant i 1/J reciprocal _ibe set to this individual fitness;

Step 3: by the highest individuality of fitness in population i

be made as the representative strategy of this population, separately population i selected, intersects, makes a variation;

Step 4: repeating step 2 and 3 makes n represent that tactful population all realizes evolving;

Step 5: repeating step 2 to 4, end condition is the convergence of representative strategy.

In iteration, the selection of strategy likely makes system restrain, as frequency finally can't converge to set point.Adopt Means of Penalty Function Methods to process this situation,, when system does not restrain, fitness is set to 1/ (J _i+ M), penalty factor M is a constant, and value is much larger than the J in the convergence situation _i.

The controlled quentity controlled variable u2 of primary frequency modulation u1 and frequency modulation frequency modulation be all ui=ki*x (t) thus pattern be all just the linear feedback of quantity of state.

Population pop1 and population pop2 all are comprised of a plurality of chromosome, if for population pop1, the value of chromosome representative is exactly the linear feedback coefficient k 1 that represents the primary frequency modulation in zone 1, if for population pop2, the value of chromosome representative is exactly the linear feedback coefficient k 2 that represents regional 1 frequency modulation frequency modulation, each chromosome all has a fitness value, described fitness value is as the foundation of the selection operation of genetic algorithm, pay off function 1/Ji reciprocal is set as fitness value, select the representative strategy of that chromosome of fitness value maximum in pop1 as population pop1, select the representative strategy of that chromosome of fitness value maximum in pop2 as population pop2.

Operation principle of the present invention: the frequency modulation feedback Nash Equilibrium control method based on Cooperative Evolutionary Algorithm that the present invention proposes, at first according to the dynamic behaviour of AGC unit, speed regulator, interconnection power delivery etc., and consider the engineering practical factors such as governor dead time, control action amplitude limitation, unit ramping rate constraints, set up the differential game model between first and second frequency modulation in the regional interconnected systems of IEEE two; Keep adopting traditional proportional plus integral control mode with seasonal zone 2, and be the control signal u asked for differential game controller by a frequency modulation frequency modulation signal in zone 1 ₁and u ₂; Adopt Cooperative Evolutionary Algorithm to solve to set up with the differential game model between first and second frequency modulation of Complex Constraints, try to achieve its feedback Nash Equilibrium Solution; The first and second frequency modulation control amount using the feedback Nash Equilibrium strategy of trying to achieve as zone, efficiently solve the anti-problem of adjusting of conflict between first and second frequency modulation, thereby realized that the coordination between electric power system first and second frequency modulation controls.

The present invention has following advantage and effect with respect to prior art:

1, the present invention can coordinate primary frequency modulation and frequency modulation frequency modulation controlled quentity controlled variable in the electric power system of considering various Complex Constraints, has effectively reduced the unit waste, has obtained good control effect; The present invention efficiently solves the anti-problem of adjusting of conflict between first and second frequency modulation, has realized that the coordination between electric power system first and second frequency modulation is controlled.

2, the present invention has used Cooperative Evolutionary Algorithm, feedback betting model to non-linear, control variables and state variable Constrained model is solved, and successfully obtain approximate Nash Equilibrium strategy, solved the problem that this model utilizes the traditional mathematics method to be difficult to solve.

3, in the present invention, first and second frequency modulation in zone 1 has reached the feedback Nash Equilibrium, and first and second frequency modulation changes separately the income decline that strategy will cause one's own side, thereby game between the two reaches a stable situation, shows " harmony " of balance policy.

The accompanying drawing explanation

Fig. 1 is the two regional frequency modulation differential game model figure that consider Complex Constraints.

Fig. 2 is the curve chart of the primary frequency modulation differential game controlled quentity controlled variable of trying to achieve by Cooperative Evolutionary Algorithm, Δ P in figure _r1represent regional 1 primary frequency modulation controlled quentity controlled variable.

Fig. 3 is the curve chart of the frequency modulation frequency modulation differential game controlled quentity controlled variable of trying to achieve by Cooperative Evolutionary Algorithm, Δ P in figure _c1represent regional 1 frequency modulation frequency modulation controlled quentity controlled variable.

Fig. 4 is that the primary frequency modulation pay off function is with feedback factor k ₁change curve.

Fig. 5 is that the frequency modulation frequency modulation pay off function is with feedback factor k ₂change curve.

Embodiment

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited to this.

Embodiment

The two regional interconnected systemss of take are example, and two regional interconnected systemss are that two FREQUENCY CONTROL zones are to realize taking full advantage of of frequency modulation machine pool-size, through regional interconnection, realize interconnected and system Power Exchange.After adding governor dead time, control action amplitude limitation, unit ramping rate constraints factor, betting model as shown in Figure 1.

The control signal u of the one frequency modulation frequency modulation signal in zone 1 for asking for feedback differential theory of games ₁and u ₂, zone 2 adopts traditional control mode, and one, the meritorious conditioning signal of frequency modulation frequency modulation are respectively:

ΔP _r2=-1/R ₂×Δf ₂，

ΔP _c2=-K ₁₂×∫ACE ₂dt-K _t2×ACE ₂，

Wherein, Δ f ₂for the frequency departure amount in zone 2, R ₂for regional 2 primary frequency modulation difference coefficients, K ₁₂, K _t2be respectively integral coefficient and the proportionality coefficient of regional 2 frequency modulation frequency modulations, ACE ₂for regional 2 control deviations, computing formula is Δ P _tie-10B ₂Δ f ₂, Δ P _tiefor interregional Tie line Power deviation, B ₂for the frequency response coefficient, get negative value.

System state variables:

x(t)=[Δf ₁ ΔP _g1 ΔX _g1 Δf ₂ ΔP _g2 ΔX _g2 ΔP _c2 ΔP _tie] ^T，

The load disturbance item is Δ P _l=[Δ P _l1Δ P _l2].Δ X _g1with Δ X _g2speed regulator valve position change amount, Δ P _g1with Δ P _g2it is the unit output variable quantity.System state equation is

State matrix A form is:

$A=\left[\begin{array}{cccccccc}\frac{-1}{T_{p1}}& \frac{K_{p1}}{{\mathrm{<figure-callout\; id="1"\; label="T\; p"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_p}& 0& 0& 0& 0& 0& \frac{{-K}_{p1}}{{\mathrm{<figure-callout\; id="1"\; label="T\; p"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_p}\\ 0& \frac{-1}{{\mathrm{<figure-callout\; id="1"\; label="T\; T"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_T}& \frac{1}{{\mathrm{<figure-callout\; id="1"\; label="T\; T"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_T}& 0& 0& 0& 0& 0\\ 0& 0& \frac{-1}{{\mathrm{<figure-callout\; id="1"\; label="T\; G"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_G}& 0& 0& 0& 0& 0\\ 0& 0& 0& \frac{-1}{T_{p2}}& \frac{K_{p2}}{{\mathrm{<figure-callout\; id="2"\; label="T\; p"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_p}& 0& 0& \frac{K_{p2}}{{\mathrm{<figure-callout\; id="2"\; label="T\; p"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_p}\\ 0& 0& 0& 0& \frac{-1}{{\mathrm{<figure-callout\; id="2"\; label="T\; T"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_T}& \frac{1}{{\mathrm{<figure-callout\; id="2"\; label="T\; T"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_T}& 0& 0\\ 0& 0& 0& \frac{-1}{R_2{\mathrm{<figure-callout\; id="2"\; label="T\; G"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_G}& 0& \frac{-1}{T_{T2}}& \frac{-1}{{\mathrm{<figure-callout\; id="2"\; label="T\; G"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_G}& 0\\ A_{71}& 0& 0& A_{74}& A_{75}& 0& 0& A_{78}\\ {2\mathrm{\&pi;T}}_{12}& 0& 0& -2\mathrm{\&pi;}{T}_{12}& 0& 0& 0& 0\end{array}\right],$

A ₇₁=-2πT ₁₂K _t2， $A_{74}=\frac{K_{i2}}{R_2}-\frac{K_{t2}}{R_2{\mathrm{<figure-callout\; id="2"\; label="T\; p"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_p}+2\mathrm{\&pi;}{T}_{12}{\mathrm{<figure-callout\; id="2"\; label="K\; t"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">K</figure-callout>}}_t,$

$A_{75}=\frac{K_{t2}{K}_{p2}}{R_2{\mathrm{<figure-callout\; id="2"\; label="T\; p"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_p},$ $A_{78}=\frac{K_{t2}{K}_{p2}}{R_2{T}_{p2}}-K_{i2},$

Input matrix B ₁, B ₂form be:

${\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">B</figure-callout>}}_1={\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">B</figure-callout>}}_2={\left[\begin{array}{cccccccc}0& 0& \frac{1}{{\mathrm{<figure-callout\; id="1"\; label="T\; G"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_G}& \frac{1}{{\mathrm{<figure-callout\; id="1"\; label="T\; G"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_G}& 0& 0& 0& 0\end{array}\right]}^T,$

Load disturbance item coefficient matrix is:

$\mathrm{\&Gamma;}={\left[\begin{array}{cccccccc}-\frac{K_{p1}}{{\mathrm{<figure-callout\; id="1"\; label="T\; p"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_p}& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& -\frac{K_{p2}}{{\mathrm{<figure-callout\; id="2"\; label="T\; p"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">T</figure-callout>}}_p}& 0& 0& 0& 0\end{array}\right]}^T,$

First and second frequency modulation control action Filters with Magnitude Constraints is:

${\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_{1\max },{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_1>{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_{1\mathrm{<figure-callout\; id="1"\; label="max\; u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">max</figure-callout>}}& \\ u_{}{}_1,{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_{1\min }\&le;{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_1\&le;{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_{1\mathrm{<figure-callout\; id="1"\; label="max\; u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">max</figure-callout>}}& \\ u_{}{}_{1\min },{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_1<{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_{1\min }\end{array}\right.,$ ${\mathrm{\&Delta;P}}_{r2}=\left\{\begin{array}{c}{\mathrm{\&Delta;P}}_{r2\max },{\mathrm{\&Delta;P}}_{r2}>{\mathrm{\&Delta;P}}_{r2\max }\\ {\mathrm{\&Delta;P}}_{r2},{\mathrm{\&Delta;P}}_{r2\min }\&le;{\mathrm{\&Delta;P}}_{r2}\&le;{\mathrm{\&Delta;P}}_{r2\max }\\ {\mathrm{\&Delta;P}}_{r2\min },{\mathrm{\&Delta;P}}_{r2}<{\mathrm{\&Delta;P}}_{r2\min }\end{array}\right.,$

${\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_{2\max },{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_2>{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_{2\mathrm{<figure-callout\; id="2"\; label="max\; u"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">max</figure-callout>}}& \\ u_{}{}_2,{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_{2\min }\&le;{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_2\&le;{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_{2\mathrm{<figure-callout\; id="2"\; label="max\; u"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">max</figure-callout>}}& \\ u_{}{}_{2\min },{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_2<{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_{2\min }\end{array}\right.,$ ${\mathrm{\&Delta;P}}_{c2}=\left\{\begin{array}{c}{\mathrm{\&Delta;P}}_{c2\max },{\mathrm{\&Delta;P}}_{c2}>{\mathrm{\&Delta;P}}_{c2\max }\\ {\mathrm{\&Delta;P}}_{c2},{\mathrm{\&Delta;P}}_{c2\min }\&le;{\mathrm{\&Delta;P}}_{c2}\&le;{\mathrm{\&Delta;P}}_{c2\max }\\ {\mathrm{\&Delta;P}}_{c2\min },{\mathrm{\&Delta;P}}_{c2}<{\mathrm{\&Delta;P}}_{c2\min }\end{array}\right.,$

After primary frequency modulation is considered governor dead time, controlled quentity controlled variable is:

${\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=\left\{\begin{array}{c}0,\left|{\mathrm{\&Delta;<figure-callout\; id="1"\; label="f"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">f</figure-callout>}}_1\right|<{\mathrm{\&Delta;f}}_{1\mathrm{<figure-callout\; id="1"\; label="min\; u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">min</figure-callout>}}& \\ u_{}{}_1,\left|{\mathrm{\&Delta;<figure-callout\; id="1"\; label="f"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">f</figure-callout>}}_1\right|{\&GreaterEqual;\mathrm{\&Delta;<figure-callout\; id="1"\; label="f"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">f</figure-callout>}}_{1\min }\end{array}\right.,$ ${\mathrm{\&Delta;P}}_{r2}=\left\{\begin{array}{c}0,\left|{\mathrm{\&Delta;<figure-callout\; id="2"\; label="f"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">f</figure-callout>}}_2\right|<{\mathrm{\&Delta;f}}_{2\min }\\ {\mathrm{\&Delta;P}}_{r2},\left|{\mathrm{\&Delta;<figure-callout\; id="2"\; label="f"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">f</figure-callout>}}_2\right|\&GreaterEqual;\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">f</figure-callout>}}_{2\min }\end{array}\right.,$

The unit creep speed is similar to the derivative of unit output, is constrained to:

Suppose that load makes the certainty step and change, with the define system state as a reference point of steady-state value after disturbance:

x ¹(t)=x(t)-x _ss(t)，

u _i ¹(t)=u _i(t)-u _iss(t)，

ΔP _L ¹(t)=ΔP _L(t)-ΔP _Lss(t)=0，

Q _iwith R _iget:

${\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">Q</figure-callout>}}_1=\left[\begin{array}{cccccccc}1& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0\end{array}\right],$ ${\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">Q</figure-callout>}}_2=\left[\begin{array}{cccccccc}1& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 2\end{array}\right],$

R ₁=10 R ₂=1，

，

Obtain u ₁and u ₂between the canonical form of differential game model, be expressed as follows:

i=(1,2)

$J_i={\&Integral;}_{{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">t</figure-callout>}}_0}^{\&infin;}\frac{1}{2}[x^{1T}\left(t\right)Q_i{x}^1\left(t\right)+{u_i}^{1T}\left(t\right)R_i{u_i}^1\left(t\right)]\mathrm{dt}$

，

${\stackrel{\&CenterDot;}{x}}^1\left(t\right)={\mathrm{Ax}}^1\left(t\right)+B_1{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}^1}_1\left(t\right)+B_2{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}^1}_2\left(t\right)$

Game both sides' pay off function means: u ₁pursue f ₁press close to rated value and speed regulator valve actuating quantity is as far as possible little; u ₂pursue f ₁and P _tiepress close to rated value, the active power fiducial value is set accurate tracking load variations as far as possible, and suitably supports zone 2.

Utilize the Cooperative Evolutionary Algorithm step to solve two regional interconnect models of top consideration Complex Constraints, obtain regional 1 primary frequency modulation, the frequency modulation frequency modulation controlled quentity controlled variable, concrete steps are as follows:

1) to take the linear feedback coefficient k of state variable be variable for zone 1 primary frequency modulation and frequency modulation frequency modulation; Primary frequency modulation and the frequency modulation frequency modulation in zone 1 all adopt genetic algorithm to solve, and the computational methods of described genetic algorithm are: give the primary frequency modulation in zone 1 and the population pop that frequency modulation frequency modulation is provided for genetic algorithm ₁and pop ₂, each population is comprised of a plurality of chromosome, the random sample that each chromosome is regional 1 primary frequency modulation or frequency modulation frequency modulation variable k;

2) suppose that current algorithm is evolved to L generation, population pop ₁and pop ₂under synergistic mechanism, evolve, the hinge using the described system state equation of step c as contact two populations, by the 1/J reciprocal of regional 1 primary frequency modulation and frequency modulation frequency modulation pay off function _ias chromosomal fitness in population.Population pop ₁and pop ₂all carry out following operation: with population pop ₁for example, select another population pop ₂the chromosome corresponding strategy the highest for fitness at L-1

as representative, form and represent set of strategies

be expressed as

by population pop ₁in each chromosome relative strategy

the set of strategies that represents with another population

the substitution system state equation is obtained the system mode track, by the pay off function of regional 1 primary frequency modulation 1/J reciprocal ₁be set to this chromosomal fitness, set up population pop ₁in after all chromosomal fitness, selected population pop ₁the highest individuality of middle fitness

for the representative strategy of this population, separately to population pop ₁carry out selection, intersection, the mutation operation of genetic algorithm;

3) repeating step 2), make two to represent that tactful population all realizes evolving;

4) repeating step 2) to 3), end condition is algorithmic statement.

The optimum linear feedback factor of 5) step 1) to 4) trying to achieve

the feedback Nash Equilibrium strategy that forms the differential game,

this strategy is as the first and second frequency modulation control amount u in zone 1 ₁, u ₂.

Tried to achieve the primary frequency modulation in zone 1, after the frequency modulation frequency modulation controlled quentity controlled variable, controlled quentity controlled variable is acted in interconnected systems, obtain the control effect shown in Fig. 2, Fig. 3, visible first and second FM signal keeps jack per line in whole transient process, thereby is considering under various Complex Constraints effectively to have avoided the anti-tune problem of conflict.

By simulating, verifying one frequency modulation frequency modulation at strategy

reached the feedback Nash Equilibrium.Order:

${\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_1^{\&prime;}=k_1{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_1^{*},$ ${\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_2^{\&prime;}=k_2{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="DEST\_PATH\_HDA00003601114000012.png,HDA00003065493400022.png"\; state="\{\{state\}\}">u</figure-callout>}}_2^{*},$

Make k ₁in [10,10], change, with for control signal emulation, pay off function J ₁at k ₁=1 reaches extreme value, as Fig. 4.Make k ₂in [10,10], change, with

for control signal is carried out emulation, pay off function J ₂at k ₂=1 reaches extreme value, as Fig. 5.More generally, fixing

constant, make k ₁in 8 elements [10,10] interior random value 1000 times, emulation obtains pay off function J ₁the value always than

the time large, fixing

constant, make k ₂in 8 elements [10,10] interior random value 1000 times, emulation obtains pay off function J ₂the value always than

the time large.Proved that thus Cooperative Evolutionary Algorithm successfully seeks out the feedback Nash Equilibrium of problem.

The present invention will feed back the differential game applications in solving conflict between electric power system first and second frequency modulation instead in the tune problem, meet the reality that first and second FM signal is fed back the current system quantity of state.When considering the affecting of the engineering factors such as governor dead time, control signal amplitude limitation, unit ramping rate constraints, frequency modulation system be non-linear and controlled quentity controlled variable and quantity of state constrained, traditional algorithm is difficult to solve.The present invention has successfully solved this problem by Cooperative Evolutionary Algorithm, and the control strategy of gained has reached the feedback Nash Equilibrium, has realized that the coordination between first and second frequency modulation is controlled.

Above-described embodiment is preferably execution mode of the present invention; but embodiments of the present invention are not restricted to the described embodiments; other any do not deviate from change, the modification done under Spirit Essence of the present invention and principle, substitutes, combination, simplify; all should be equivalent substitute mode, within being included in protection scope of the present invention.

Claims (5)

1. the feedback of the frequency modulation based on Cooperative Evolutionary Algorithm Nash Equilibrium control method, is characterized in that, comprises that step comprises:

Step 1, set up the differential game model between first and second frequency modulation in two regional interconnected systemss, described two regional interconnected systemss comprise zone 1 and zone 2;

The state of the described two regional interconnected systemss after step 2, the saltus step of definition load;

Step 3, employing Cooperative Evolutionary Algorithm solve the differential game model between described first and second frequency modulation, try to achieve the feedback Nash Equilibrium Solution of the differential game model between described first and second frequency modulation;

Step 4, described feedback Nash Equilibrium Solution that step 3 is tried to achieve are as the first and second frequency modulation control amount in zone.

2. the frequency modulation based on Cooperative Evolutionary Algorithm according to claim 1 feeds back the Nash Equilibrium control method, it is characterized in that:

In described step 1, the step of setting up the differential game model between first and second frequency modulation in two regional interconnected systemss is:

A. adopt differential game controller to ask for described regional 1 primary frequency modulation controlled quentity controlled variable and the size of frequency modulation frequency modulation controlled quentity controlled variable, equal use, to described regional 2 adoption rate integral control modes;

B. the state variable of selective system is:

x(t)=[Δf ₁ ΔP _g1 ΔX _g1 Δf ₂ ΔP _g2 ΔX _g2 ΔP _c2 ΔP _tie] ^T，

Wherein, for regional i, Δ f _ifor the deviation of instantaneous frequency and rated value, Δ P _gifor prime mover variable quantity of exerting oneself, Δ X _gifor speed regulator valve position change amount, Δ P _tiefor the Tie line Power deviation; Δ P _c2frequency modulation frequency modulation controlled quentity controlled variable for zone 2;

C. obtain system state equation by analytical calculation:

$\stackrel{\&CenterDot;}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+B_1{u}_1\left(t\right)+B_2{u}_2\left(t\right)+\mathrm{\&Gamma;}{\mathrm{\&Delta;P}}_L,$

Wherein, u ₁, u ₂be respectively primary frequency modulation controlled quentity controlled variable and the frequency modulation frequency modulation controlled quentity controlled variable in zone 1, they are solved and are obtained by differential game controller; Δ P _l=[Δ P _l1Δ P _l2] ^tfor the load disturbance amount; A is the system mode matrix, B _ifor input matrix, Γ is the disturbance transfer matrix, A, B _i, Γ value can obtain according to the system dynamic calculation.

3. the frequency modulation based on Cooperative Evolutionary Algorithm according to claim 1 feeds back the Nash Equilibrium control method, it is characterized in that:

Described step 1, described differential game model has the Practical Project of adding constraint, and described Practical Project constraint comprises governor dead time constraint, controlled quentity controlled variable Filters with Magnitude Constraints and unit ramping rate constraints;

The expression formula of described governor dead time constraint is:

$u_1=\left\{\begin{array}{c}0,\left|{\mathrm{\&Delta;f}}_1\right|<{\mathrm{\&Delta;f}}_{1\min }\\ u_1,\left|{\mathrm{\&Delta;f}}_1\right|{\&GreaterEqual;\mathrm{\&Delta;f}}_{1\min }\end{array}\right.,$ ${\mathrm{\&Delta;P}}_{r2}=\left\{\begin{array}{c}0,\left|{\mathrm{\&Delta;f}}_2\right|<{\mathrm{\&Delta;f}}_{2\min }\\ {\mathrm{\&Delta;P}}_{r2},\left|{\mathrm{\&Delta;f}}_2\right|\&GreaterEqual;\mathrm{\&Delta;}{f}_{2\min }\end{array}\right.,$

Δ f _1min, Δ f _2minbe respectively the governor dead time threshold values in zone 1 and zone 2, Δ P _r2primary frequency modulation controlled quentity controlled variable for zone 2;

The expression formula of described controlled quentity controlled variable Filters with Magnitude Constraints is:

$u_1=\left\{\begin{array}{c}{u}_{1\max },u_1>u_{1\max }\\ u_1,u_{1\min }\&le;u_1\&le;u_{1\max }\\ u_{1\min },u_1<u_{1\min }\end{array}\right.,$ ${\mathrm{\&Delta;P}}_{r2}=\left\{\begin{array}{c}{\mathrm{\&Delta;P}}_{r2\max },{\mathrm{\&Delta;P}}_{r2}>{\mathrm{\&Delta;P}}_{r2\max }\\ {\mathrm{\&Delta;P}}_{r2},{\mathrm{\&Delta;P}}_{r2\min }\&le;{\mathrm{\&Delta;P}}_{r2}\&le;{\mathrm{\&Delta;P}}_{r2\max }\\ {\mathrm{\&Delta;P}}_{r2\min },{\mathrm{\&Delta;P}}_{r2}<{\mathrm{\&Delta;P}}_{r2\min }\end{array}\right.,$

$u_2=\left\{\begin{array}{c}{u}_{2\max },u_2>u_{2\max }\\ u_2,u_{2\min }\&le;u_2\&le;u_{2\max }\\ u_{2\min },u_2<u_{2\min }\end{array}\right.,$ ${\mathrm{\&Delta;P}}_{c2}=\left\{\begin{array}{c}{\mathrm{\&Delta;P}}_{c2\max },{\mathrm{\&Delta;P}}_{c2}>{\mathrm{\&Delta;P}}_{c2\max }\\ {\mathrm{\&Delta;P}}_{c2},{\mathrm{\&Delta;P}}_{c2\min }\&le;{\mathrm{\&Delta;P}}_{c2}\&le;{\mathrm{\&Delta;P}}_{c2\max }\\ {\mathrm{\&Delta;P}}_{c2\min },{\mathrm{\&Delta;P}}_{c2}<{\mathrm{\&Delta;P}}_{c2\min }\end{array}\right.,$

Wherein, u _1max, u _1minbe respectively maximum and the minimum value of regional 1 primary frequency modulation amount, u _2max, u _2minbe respectively maximum and the minimum value of regional 1 frequency modulation frequency modulation amount, Δ P _r2max, Δ P _r2minbe respectively maximum and the minimum value of regional 2 primary frequency modulations, Δ P _c2for the frequency modulation frequency modulation controlled quentity controlled variable in zone 2, Δ P _c2max, Δ P _c2minbe respectively maximum and the minimum value of regional 2 frequency modulation frequency modulations;

The expression formula of described unit ramping rate constraints is:

Wherein,

be respectively maximum and the minimum value of regional 1 generating set regulated quantity derivative, be respectively maximum and the minimum value of regional 2 generating set regulated quantity derivatives.

4. the frequency modulation based on Cooperative Evolutionary Algorithm according to claim 1 feeds back the Nash Equilibrium control method, it is characterized in that:

In described step 1, described differential game model is reduced to canonical form, the step that described differential game model is reduced to canonical form is:

A. hypothesis load is made the certainty step and is changed, with the define system state as a reference point of steady-state value after disturbance:

x ¹(t)=x(t)-x _ss(t),

u _i ¹(t)=u _i(t)-u _iss(t),

ΔP _L ¹(t)=ΔP _L(t)-ΔP _Lss(t)=0,

Under be designated as ss scale show steady-state value, x ¹(t), u _i ¹(t), Δ P _l ¹(t) be respectively system state amount, input variable and the load disturbance amount after definition;

B. the first and second frequency modulation both sides' in zone 1 pay off function is set to Linear-Quadratic Problem:

i=(1,2)

$J_i={\&Integral;}_{t_0}^{\&infin;}\frac{1}{2}[x^{1T}\left(t\right)Q_i{x}^1\left(t\right)+{u_i}^{1T}\left(t\right)R_i{u_i}^1\left(t\right)]\mathrm{dt},$

${\stackrel{\&CenterDot;}{x}}^1\left(t\right)={\mathrm{Ax}}^1\left(t\right)+B_1{u^1}_1\left(t\right)+B_2{u^1}_2\left(t\right)$

Pay off function J _ibe defined as the Linear-Quadratic Problem form, Q _i, R _ibe respectively the weight coefficient matrix of quantity of state and input variable.

5. the frequency modulation based on Cooperative Evolutionary Algorithm according to claim 1 feeds back the Nash Equilibrium control method, it is characterized in that:

Described step 3 comprises the following steps:

1) to take the linear feedback coefficient k of state variable be variable for described regional 1 primary frequency modulation and frequency modulation frequency modulation; Primary frequency modulation and the frequency modulation frequency modulation in zone 1 all adopt genetic algorithm to solve, and the computational methods of described genetic algorithm are: give the primary frequency modulation in zone 1 and two populations that frequency modulation frequency modulation is provided for genetic algorithm, described two populations are population pop ₁with population pop ₂, described population pop ₁with population pop ₂form a random sample of the linear feedback coefficient k of the primary frequency modulation that each described chromosome is zone 1 and the state variable of frequency modulation frequency modulation by several chromosomes;

2) suppose that current algorithm is evolved to L generation, described pop ₁and pop ₂under synergistic mechanism, evolve, using the described system state equation of step c as contact population pop ₁with population pop ₂hinge, by the 1/J reciprocal of described regional 1 primary frequency modulation and frequency modulation frequency modulation pay off function _ias chromosomal fitness value;

To population pop ₁carry out following operation: select population pop ₂at L-1 for the corresponding strategy of the chromosome of fitness value maximum

as representing strategy; To population pop ₁in each chromosome relative strategy

with population pop ₂the representative strategy

order

and by u ₁, u ₂the substitution system state equation is obtained the system mode track, by the pay off function of the primary frequency modulation in zone 1 1/J reciprocal ₁be set to chromosomal fitness value, each chromosome in population pop1 all has a fitness value, and described fitness value, as the foundation of the selection operation of genetic algorithm, is chosen the chromosome of chromosomal fitness value maximum in population pop1

as the representative strategy of population pop1, the representative strategy of described population pop1 is separately to population pop ₁carry out selection operation, interlace operation and the mutation operation of genetic algorithm;

To population pop ₂do following operation: select population pop ₁at L-1 for the corresponding strategy of the chromosome of fitness value maximum as representing strategy; To population pop ₂in each chromosome relative strategy

with population pop ₁the representative strategy

order

and by u ₁, u ₂the substitution system state equation is obtained the system mode track, by the pay off function of the frequency modulation frequency modulation in zone 1 1/J reciprocal ₂be set to this chromosomal fitness, in population pop2, each chromosome all has a fitness value, and described fitness value, as the foundation of the selection operation of genetic algorithm, is chosen the chromosome of chromosomal fitness value maximum in population pop2

as the representative strategy of population pop2, the representative strategy of described population pop2 is separately to population pop ₂carry out selection operation, interlace operation and the mutation operation of genetic algorithm;

3) repeating step 2), make population pop ₁with population pop ₂all realize evolving;

4) repeating step 2) to 3), until the convergence of described Cooperative Evolutionary Algorithm;

5) step 1) to 4) the population pop that tries to achieve ₁with population pop ₂the representative strategy

with

form the feedback Nash Equilibrium strategy of differential game, the expression formula of described feedback Nash Equilibrium strategy is:

$u_1^{*}=k_1^{\mathrm{best}}x\left(t\right),u_2^{*}=k_2^{\mathrm{best}}x\left(t\right),$

Wherein,

the feedback Nash Equilibrium strategy of the primary frequency modulation for regional 1,

the feedback Nash Equilibrium strategy of the frequency modulation frequency modulation in zone 1;

Primary frequency modulation controlled quentity controlled variable u using described feedback Nash Equilibrium strategy as zone 1 ₁with frequency modulation frequency modulation controlled quentity controlled variable u ₂.

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