CN103199565A - Multi-zone automatic generation control coordination method based on differential game theory - Google Patents

Abstract

The invention discloses a multi-zone automatic generation control coordination method based on the differential game theory. The method comprises the following steps: step 1, a dynamic model of zone interconnected network automatic generation control (AGC) is established; step 2, traditional AGC amount based on a proportion integration link is replaced by AGC amount based on the differential game theory and a coordination control model, based on the differential game theory, of zone interconnected network automatic generation is established; step 3, the coordination control model of the zone interconnected network automatic generation is solved through the linear quadratic type differential game theory and the obtained Nash equilibrium strategy serves as automatic generation control amount of multiple zones; and step 4, compared with other existing control methods, the multi-zone automatic generation control coordination method based on the differential game theory enables distribution of frequency modulation among the zones to be fair and convictive. The multi-zone automatic generation control coordination method based on the differential game theory has the advantages of being strong in robustness and the like.

Description

Multizone automatic generation control coordination approach based on the differential theory of games

Technical field

The present invention relates to a kind of electric power system controls automatically, be particularly related to a kind of multizone automatic generation control coordination approach based on the differential theory of games, this control coordination approach is applicable at fitful powers such as wind-powered electricity generations and is incorporated into the power networks on a large scale, interconnection will occur under the increasing interregional power support situation, the field of how to formulate fair and just coordinated operation scheme.

Background technology

Automatic generation control (AGC) has obtained long-term deep research as guaranteeing the stable important means of mains frequency.These researchs have improved the ability of aspects such as the variation of AGC follow load, the change of answering system parameter based on methods such as optimal control, adaptive control, robust control, artificial intelligence, but less relatively at multizone AGC coordinated operation Study on Mechanism.At present, the regional interconnected network moves in order wire frequency Deviation Control (TBC) mode, and each provincial controlled area to be keeping local area power in-situ balancing, and the zone of regulating scarcity of resources is supported, and this process is comprising game.Because along with the propelling of power market reform, each provincial controlled area is developed into independently interests main body gradually, all is reluctant to pay too high control cost in externally supporting.Performance assessment criteria such as A1/A2, CPS has retrained interregional power support amount, makes this game show also not obviously in present stage.But along with fitful powers such as wind-powered electricity generation are incorporated into the power networks, go out fluctuation to the impact of mains frequency for reducing it, must give full play to each zone and regulate resource, power support amount will significantly increase.At this moment, if the fair and just game coordination system of neither one, each zone lacks wish and the guidance method of working in coordination, and may cause power less stress or overshoot, system frequency and interconnection power fluctuation.

The differential theory of games is to find the solution the brand-new thinking of coordinating control problem.This theory originates from the research of both sides' pursuit evasion problem in the military confrontation that the 1950's, USAF was carried out, and is optimal control and game theoretic combination.Perfect along with the expansion of game kind and solution, it has been applied to growing field such as economics, management, environmental science.The differential game refers in time continuous system, the game that a plurality of participants continue, try hard to the optimization target of independent, conflict separately, the strategy that final each participant of acquisition develops in time also reaches Nash Equilibrium, be the wish that any participant does not have to change separately strategy, because can not benefit more.The differential game becomes the instrument mistake of the most natural research multiagent dynamic coordinate decision problem because the energy consideration time is dynamic! Do not find Reference source.。Though the differential game has obtained using widely in every field, in electric power system, the application of this theory remains blank out.

Existing AGC coordination approach is controlled according to practical operating experiences mostly, do not pass through strict mathematical proof, the distribution of interregional frequency modulation task can't embody justice and convincingness, may cause each regional AGC unit to fail to carry out the frequency modulation task that the control centre distributes, or change the generating regulated quantity without authorization, thereby cause the stable harmful effect of system frequency.For example, in correlative study, literary composition [1] is regulated power on the basis of PI control for each zone and is added a component that is inversely proportional to frequency departure, supports to instruct power, but does not explain how to specify this component liberally for each zone.Literary composition [2] utilizes the multi-objective optimization method based on linear weighted function, try to achieve the optimum frequency departure coefficient of target setting, thereby distribute each zone to regulate power, but the artificial weight coefficient of setting can't guarantee interregional justice.Literary composition [3] is pointed out to need badly behind the wind-electricity integration game in the frequency-modulating process is coordinated, and propose with classification coordinate to be controlled to be transition, the whole network centralized control is the AGC coodination modes development course of target, regulates power distribution method but provide concrete zone.And the controlled quentity controlled variable that the present invention calculates in strict accordance with the differential theory of games has absolute fairness and convincingness, need not artificially set chirp parameter qualitatively, has guaranteed that the strict frequency modulation of carrying out in each zone instructs.

Literary composition [1], high ancestor and, Teng Xianliang, Zhang Xiaobai, the substandard automatic generation control strategy of interconnected network CPS,

Automation of Electric Systems, 2005,29 (19): 40-44.

Literary composition [2], Liu Le, Liu harasses, Li Weidong, Lin Wei, Xu Xingwei, the controlled leading frequency departure coefficient of target is true

Decide the method design, Automation of Electric Systems, 2007,31 (5): 40-45.

Literary composition [3], high ancestor and, Teng Xianliang, Zhang Xiaobai adapts to the meritorious scheduling of interconnected network that large-scale wind power inserts

With control scheme, Automation of Electric Systems, 2010,34 (17): 37-41.

Summary of the invention

The objective of the invention is to overcome the shortcoming of prior art with not enough, a kind of multizone automatic generation control coordination approach based on the differential theory of games is provided, this multizone automatic generation control coordination approach reaches Nash Equilibrium by self-organizing competition therebetween, and overall process need not artificially to set weight coefficient.

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

Multizone automatic generation control coordination approach based on the differential theory of games may further comprise the steps:

Step 1, set up the dynamic model of regional interconnected network automatic generation control (AGC);

Step 2, with traditional automatic generation control amount based on the proportional integral link, be replaced by the automatic generation control amount based on the differential theory of games, set up based on the regional interconnected network of the differential theory of games coordination control model of generating automatically;

Step 3, use linear quadratic type differential theory of games, find the solution the regional interconnected network coordination control model of generating automatically, with the Nash Equilibrium strategy of the trying to achieve automatic generation control amount as a plurality of (n) zone;

Step 4, based on the multizone of the differential theory of games coordinated control system of generating electricity automatically, the distribution of interregional frequency modulation amount has fairness and is rich in convincingness, and other existing control methods do not have this feature.

In the described step 1, the dynamic model of the regional interconnected network automatic generation control of described foundation (AGC), its step is specially:

1) selecting the AGC parameter as system state variables, is example with two regional interconnected systemss, that is:

x(t)=[Δf ₁ΔP _g1ΔX _g1Δf ₂ΔP _g2ΔX _g2ΔP _tie] ^T，

Wherein, for regional i, Δ f _iBe the deviation of instantaneous frequency and rated value, Δ P _GiBe prime mover variable quantity of exerting oneself, Δ X _GiBe speed regulator valve location change amount, Δ P _TieBe the Tie line Power deviation;

2) obtain describing the dynamic equation of frequency modulation system by analytical calculation

$\stackrel{\·}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+B_1{u}_1\left(t\right)+B_2{u}_2\left(t\right)+\mathrm{\Γ\Δ}{P}_L,$

Wherein, u _iBe the AGC controlled quentity controlled variable of regional i, Δ P _L=[Δ P _L1Δ P _L2] ^TPoor for load disturbance amount and wind-powered electricity generation undulate quantity.A is the system mode matrix, B _iBe input matrix, Γ is the disturbance transfer matrix, and its value can obtain according to system's dynamic calculation;

3) pay off function J that each is regional _iBe defined as linear quadratic type form

i=(1,2)

$\min J_i={\∫}_{t_0}^{\∞}\frac{1}{2}[x^T\left(t\right)Q_{i}x\left(t\right)+{u_i}^T\left(t\right)R_i{u}_i\left(t\right)]\mathrm{dt},$

Wherein, to regional i, Q _iBe the state variable weight coefficient matrix, embody this zone to frequency and the interconnection power pursuit degree near the rated value target, R _iBe the input variable weight coefficient matrix, embody this zone to the degree of concern of AGC unit loss in the one's respective area in the frequency adjustment process, Q _i, R _iWeight coefficient only reflects that each zone, can be according to the actual demand adjustment to the preference of control target.

In the described step 2, described with traditional automatic generation control amount based on the proportional integral link, be replaced by the automatic generation control amount based on the differential theory of games, described foundation based on the step of the coordination control model of the automatic generating of regional interconnected network of differential theory of games is:

In A, the traditional two regional interconnected systems FREQUENCY CONTROL models, the automatic generation control amount of regional i adopts the proportional integral link to obtain, that is:

ΔP _ci=-K _1i×∫ACE _idt-K _ti×ACE _i，

Wherein, Δ f _iDeparture for actual frequency and rated value; K _LiAnd K _TiBe storage gain and proportional gain, get on the occasion of; ACE _iBe the Region control deviation, computing formula is Δ P _Tie-10B _iΔ f _i, Δ P _TieBe interregional Tie line Power deviation, B _iFor the frequency response coefficient, get negative value;

Set up based on differential theory of games control model in, this proportional integral link is removed, replacement be the coordination control strategy u that differential game controller provides _i, i.e. AGC power of the assembling unit adjusting command Δ P _Ci

The difference Γ Δ P of B, elimination load disturbance amount and wind-powered electricity generation undulate quantity _LThis supposes to replace actual change at random amount with ultra-short term value and ultrashort phase wind power predicted value in control procedure, and as redefining each variable with reference to point, subscript ss represents steady-state value with the steady-state value after the disturbance:

x _N(t)=x(t)-x _ss(t)，

u _iN(t)=u _i(t)-u _iss(t)，

ΔP _LN(t)=ΔP _L(t)-ΔP _Lss(t)=0，

Thereby obtain general type:

${\stackrel{\·}{x}}_N\left(t\right)=A{x}_N\left(t\right)+B_1{u}_{1N}\left(t\right)+B_2{u}_{2N}\left(t\right),$

The final form of pay off function is:

i=(1,2)

$\min J_i={\∫}_{t_0}^{\∞}\frac{1}{2}[{x_N}^T\left(t\right)Q_i{x}_N\left(t\right)+{u_{\mathrm{iN}}}^T\left(t\right)R_i{u}_{\mathrm{iN}}\left(t\right)]\mathrm{dt}.$

In the described step 3, described utilization linear quadratic type differential theory of games is found the solution the automatically coordination control model of generating of regional interconnected network, and with the Nash Equilibrium strategy of the trying to achieve automatic generation control amount as a plurality of zones, its computational process is:

Utilize the differential theory of games of existing maturation, find the solution linear quadratic type differential betting model, obtain the Nash Equilibrium strategy, as each regional automatic generation control amount,

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

(P wherein ₁, P ₂, L, P _n) be the solution of algebraic riccati equation group,

Described algebraic riccati equation group refers to:

$\∃i\∈(\mathrm{1,2},\·\·\·,n)$

$Q_i+P_{i}A+A^T{P}_i-\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{P}_{i}B{R_k}^{-1}{B_k}^T{P}_k-\underset{j=1j\≠i}{\overset{n}{\mathrm{\Σ}}}{\left(B_j{R_j}^{-1}{B_j}^T{P}_j\right)}^T{P}_i=0.$

In the described step 4, described interregional frequency modulation amount is carried out fair allocat, and its fair allocat has fairness and be rich in the proof procedure of convincingness as follows:

A, the frequency modulation control amount of establishing regional i are:

u _iNNEW=k _i*u _iNORIGNAL，

Controlled quentity controlled variable to one of them regional s is carried out the fairness analysis, i.e. fixed area i=1, and 2 ..., s-1, s+1 ..., the feedback factor k of n _i=1;

B, make k _sValue near 1 neighborhood, change, make regional s payment J _sWith k _sThe curve chart that changes; General, curve is at k _sReached extreme value at=1 o'clock.

C, when Nash Equilibrium strategies are adopted in other zones, the one's respective area optimal strategy also is the Nash Equilibrium strategy.Thereby guaranteed that each zone does not have to change separately the intention of strategy, has guaranteed tactful fairness.

Other existing control methods are carried out fairness when analyzing, and each zone changes the target function that can both more optimize after controlled quentity controlled variable separately separately, so both sides are reluctant to accept named policer, prove that additive method does not have fairness and the convincingness of strictness.Interconnected network is weaker than the electrical link of intra-zone by interconnection in interregional generation, thereby has consistent steady frequency.When certain regional frequency modulation pressure is excessive, can obtain other regional power and support to accelerate frequency retrieval, as the zone 2 that contains wind energy turbine set among Fig. 1, this is one of electrical network purpose of interconnecting just.But it should be noted that being incorporated into the power networks of the high permeability batch (-type) energy will increase frequency and the amplitude that power is supported, highlight game in the support process problem of playing a game.

Among Fig. 1, zone 1,2,3 is as interests main body independently, support each other stable as early as possible in the hope of system frequency in, also all want to minimize the power adjustments amount of self having jurisdiction over the AGC unit, game produces thus.The regulated quantity that existing TBC operational mode is distributed each regional AGC with fixing frequency departure coefficient, the injustice that the game simple process is caused may cause the passive execution command in some zone.Coordinate this game, set up fair frequency regulating duty distribution mechanism, be to transfer each zone to play an active part in the prerequisite that wind-powered electricity generation is dissolved, but be a very difficult problem simultaneously, consider that especially each regional fm capacity difference, interregional intensity difference, fitful power geographical distribution inequality and the fitful power of being electrically connected benefit to distribute unequal factor.

In view of existing technical scheme, the differential theory of games is the ideal tools of multizone AGC being carried out mathematical modeling, can directly, relevantly reflect game relation therebetween.The differential betting model that invention is used is:

N people's nonzero sum, non-cooperation, determine, the linear quadratic type do not have in the game of limit differential, every participant i tries hard to minimize pay off function J separately _i:

$\∃i,i=\mathrm{1,2},\·\·\·,n$

$\min J_i={\∫}_{t_0}^{\∞}\frac{1}{2}[x^T\left(t\right)Q_{i}x\left(t\right)+{u_i}^T\left(t\right)R_i{u}_i\left(t\right)]\mathrm{dt},$

Wherein, t ₀Be the game time started, Q _iBe symmetrical weight coefficient matrix, R _iBe the weight coefficient greater than zero, u _i(t) be the control strategy of participant i, x (t) is state vector, depends on following m rank linear system:

$\begin{array}{c}\stackrel{\·}{x}\left(t\right)=f[x\left(t\right),u_1\left(t\right),\·\·\·u_n\left(t\right),t]=\mathrm{Ax}\left(t\right)+B_1{u}_1\left(t\right)+\·\·\·+B_n{u}_n\left(t\right)\\ =\mathrm{Ax}\left(t\right)+\mathrm{BU}\left(t\right),x\left(t_0\right)=x_0\end{array},$

A is m rank square formations, B _iBe the m dimensional vector, B is m * n matrix [B ₁B ₂B _n], U (t) is u _i(t) the n dimensional vector of Zu Chenging, x ₀It is initial state vector.

Consider the reality of electric power system frequency modulation, i.e. AGC control is the reality of the data that current data collection center SCADA collects being carried out FEEDBACK CONTROL, and the feedback Nash Equilibrium strategy of the interconnected frequency modulation model in zoning of the present invention is as each regional AGC regulated quantity.When the differential game is the linear quadratic type at target function, its feedback Nash Equilibrium solution is the linear feedback form of system state amount, be easy to Project Realization and can guarantee that problem has solution, so the present invention earlier is incorporated into the feedback differential game of linear quadratic type in the coordination control problem between the regional interconnected systems AGC.The solution procedure of feedback Nash Equilibrium is as follows:

If the Hamilton function of every participant i is

H _i[x(t),u ₁(t),…u _n(t),λ _i(t)]，

$=\frac{1}{2}{x}^T\left(t\right)Q_{i}x\left(t\right)+\frac{1}{2}{u_i}^T\left(t\right)R_i{u}_i\left(t\right)+{{\mathrm{\λ}}_i}^T\left(t\right)f[x\left(t\right),u_1\left(t\right),\·\·\·u_n\left(t\right)],$

[u then ₁* (t), u ₂* (t) ..., u _n* (t)] be that the necessary and sufficient condition of differential game feedback Nash Equilibrium solution is to satisfy following equation group

$\∃i\∈(\mathrm{1,2},\·\·\·,n)$

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{\mathrm{\&lambda;}}}_i\left(t\right)=-\&PartialD;H_i/\&PartialD;x\left(t\right)=-\mathrm{Qx}\left(t\right)-A^T\mathrm{\&lambda;}\left(t\right)\\ \stackrel{\&CenterDot;}{x}\left(t\right)=f[x\left(t\right),u_1\left(t\right),\&CenterDot;\&CenterDot;\&CenterDot;u_n\left(t\right),t]\\ =\mathrm{Ax}\left(t\right)+\mathrm{BU}\left(t\right)\\ \&PartialD;H_i[x\left(t\right),{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">u</figure-callout>}}_1*\left(t\right),\&CenterDot;\&CenterDot;\&CenterDot;u_n*\left(t\right),{\mathrm{\&lambda;}}_i\left(t\right),t_i]/\&PartialD;u_i\left(t\right){|}_{u_i\left(t\right)=u_i*\left(t\right)}\\ =R_i{u}_i\left(t\right)+{B_i}^T{\mathrm{\&lambda;}}_i\left(t\right)=0\end{array}\right.,$

Can get $u_i*\left(t\right)=-R^{-1}{B_i}^T{P}_{i}x\left(t\right),i=1,\&CenterDot;\&CenterDot;\&CenterDot;,n,$

(P wherein ₁, P ₂..., P _n) be the solution of algebraic riccati equation group,

$\&Exists;i\&Element;(\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n),$

$Q_i+P_{i}A+A^T{P}_i-\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{P}_{i}B{R_k}^{-1}{B_k}^T{P}_k-\underset{j=1j\&NotEqual;i}{\overset{n}{\mathrm{\&Sigma;}}}{\left(B_j{R_j}^{-1}{B_j}^T{P}_j\right)}^T{P}_i=0,$

For realizing that the differential theory of games is applied to multizone frequency modulation reality, the technical solution used in the present invention is

A. set up regional interconnected network AGC frequency modulation model;

B. utilize the differential theory of games to find the solution to the model of setting up;

C. with the Nash Equilibrium strategy of trying to achieve as each regional FM signal.

Be compared with the prior art, the present invention makes the income of multizone reach optimum point simultaneously under named policer, changes the tactful income that only can cut down separately separately, thereby has coordinated the game between two regional AGC better, reached stable situation, i.e. the Nash Equilibrium point.

Operation principle of the present invention: the multizone automatic generation control coordination approach based on the differential theory of games that the present invention proposes, at first set up regional interconnected AGC frequency modulation model according to the dynamic behaviour of AGC unit, speed regulator, interconnection power delivery etc.; With traditional automatic generation control amount based on the proportional integral link, be replaced by the automatic generation control amount based on the differential theory of games simultaneously, set up the frequency modulation model based on the regional interconnected network AGC of differential theory of games; Utilize linear quadratic type differential theory of games, to the regional interconnected network AGC model solution of setting up, with the Nash Equilibrium strategy of trying to achieve as n regional automatic generation control amount.By to finding the solution based on the frequency modulation model of the regional interconnected network AGC of differential theory of games, obtain fair, convictive each regional frequency modulation sendout, guarantee that each zone is strict and carry out frequency modulation instruction, reach the fast and stable power system frequency, the purpose of the intermittent energy source of dissolving and load change.

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

(1) the present invention sets up the differential betting model of multizone AGC coordination problem, each zone is considered as the independent decision-making main body, self-organizing competition by therebetween reaches Nash Equilibrium, and gained Nash Equilibrium strategy has strict mathematical meaning overall process and need not artificially to set weight coefficient.

(2) the coordination control scheme of the present invention's formulation has embodied fair and just principle, if the benefit damage that the frequency modulation instruction that distributes will make one's own side is run counter in each zone separately, guaranteed the strict institute's distribution instruction of carrying out in each zone, help to transfer the enthusiasm that each zone participates in frequency modulation, the batch (-type) energy of dissolving jointly.

(3) control strategy that proposes of the present invention can carry out off-line operation and draws, and applies to actual electric power system again, has stronger robustness, and the present invention is suitable for solving the more complicated decentralized coordinating control of following electrical network.

Description of drawings

Fig. 1 has the multizone interconnected network schematic diagram that the batch (-type) energy inserts, " i " expression " i " individual zone among the figure, and " W " represents wind energy turbine set, the direction of arrow is supported direction for interconnection active power.

Fig. 2 is based on two regional interconnected systems illustratons of model of differential game control, and square frame C represents differential game controller among the figure.

Fig. 3 is zone 1 payment J ₁With k ₁Change curve.

Fig. 4 is zone 2 payment J ₂With k ₂Change curve.

Fig. 5 be the differential solution of game with different weight coefficients under the comparison diagram of optimal control solution, F point expression feedback Nash Equilibrium point among the figure.

Fig. 6 is the details enlarged drawing of Fig. 5 centre circle D, F point expression feedback Nash Equilibrium point among the figure, and X, Y, Z point are the Pareto optimum points, part is the point set of domination point F on the Pareto forward position between X and the Z.

Embodiment

The present invention is described in further detail below in conjunction with embodiment and accompanying drawing, but embodiments of the present invention are not limited thereto.

Embodiment

For ease of understanding the present invention, set forth below in conjunction with accompanying drawing.

Be example with two regional interconnected networks, its based on the control procedure of differential theory of games as shown in Figure 2, Fig. 2 is based on two regional interconnected systems illustratons of model of differential game control, square frame C represents differential game controller among the figure.Each meaning of parameters is among the figure: u ₁And u ₂The coordination control strategy that provides for the game controller, i.e. AGC power of the assembling unit adjusting command Δ P _C1With Δ P _C2, r ₁And r ₂Be primary frequency modulation difference coefficient, T _G1And T _G2Be the speed regulator time constant, Δ X _G1With Δ X _G2Be speed regulator valve location change amount, T _T1And T _T2For vapour holds time constant, Δ P _G1With Δ P _G2Be prime mover variable quantity of exerting oneself, Δ P _L1With Δ P _L2Be the power disturbance amount, namely load disturbance amount and wind power undulate quantity is poor, K _P1And K _P2For LOAD FREQUENCY is regulated effect coefficient, T _P1And T _P2Be inertia time constant, Δ P _TieBe Tie line Power deviation, T ₁₂Be the interconnection synchronous coefficient, Δ f ₁With Δ f ₂Deviation for instantaneous frequency and rated value.It is as follows to set up two regional AGC differential betting models in the game controller:

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

Wherein, $x\left(t\right)={\left[\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">f</figure-callout>}}_1\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="P\; g"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">P</figure-callout>}}_g\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="X\; g"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">X</figure-callout>}}_g\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">f</figure-callout>}}_2\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="P\; g"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">P</figure-callout>}}_g\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="X\; g"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">X</figure-callout>}}_g\mathrm{\&Delta;}{P}_{\mathrm{tie}}\right]}^T,$

$\mathrm{\&Gamma;}={\left[\begin{array}{cccccccc}-\frac{K_{p1}}{{\mathrm{<figure-callout\; id="1"\; label="T\; p"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">T</figure-callout>}}_p}& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& -\frac{K_{p2}}{{\mathrm{<figure-callout\; id="2"\; label="T\; p"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">T</figure-callout>}}_p}& 0& 0& 0& 0\end{array}\right]}^T\mathrm{\&Delta;}{P}_L={\left[\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="P\; L"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">P</figure-callout>}}_L\mathrm{\&Delta;}{P}_{L2}\right]}^T,$

$A=\left[\begin{array}{ccccccc}\frac{-1}{T_{p1}}& \frac{K_{p1}}{{\mathrm{<figure-callout\; id="1"\; label="T\; p"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">T</figure-callout>}}_p}& 0& 0& 0& 0& \frac{-K_{p1}}{{\mathrm{<figure-callout\; id="1"\; label="T\; p"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">T</figure-callout>}}_p}\\ 0& \frac{-1}{{\mathrm{<figure-callout\; id="1"\; label="T\; T"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">T</figure-callout>}}_T}& \frac{1}{{\mathrm{<figure-callout\; id="1"\; label="T\; T"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">T</figure-callout>}}_T}& 0& 0& 0& 0\\ \frac{-1}{r_1{\mathrm{<figure-callout\; id="1"\; label="T\; G"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">T</figure-callout>}}_G}& 0& \frac{-1}{{\mathrm{<figure-callout\; id="1"\; label="T\; G"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">T</figure-callout>}}_G}& 0& 0& 0& 0\\ 0& 0& 0& \frac{-1}{T_{p2}}& \frac{K_{p2}}{{\mathrm{<figure-callout\; id="2"\; label="T\; p"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">T</figure-callout>}}_p}& 0& \frac{K_{p2}}{{\mathrm{<figure-callout\; id="2"\; label="T\; p"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">T</figure-callout>}}_p}\\ 0& 0& 0& 0& \frac{-1}{{\mathrm{<figure-callout\; id="2"\; label="T\; T"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">T</figure-callout>}}_T}& \frac{1}{{\mathrm{<figure-callout\; id="2"\; label="T\; T"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">T</figure-callout>}}_T}& 0\\ 0& 0& 0& \frac{-1}{r_2{\mathrm{<figure-callout\; id="2"\; label="T\; G"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">T</figure-callout>}}_G}& 0& \frac{-1}{{\mathrm{<figure-callout\; id="2"\; label="T\; G"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">T</figure-callout>}}_G}& 0\\ {\mathrm{<figure-callout\; id="12"\; label="T"\; filenames="HDA00002987882500022.png"\; state="\{\{state\}\}">T</figure-callout>}}_{12}& 0& 0& -{\mathrm{<figure-callout\; id="12"\; label="T"\; filenames="HDA00002987882500022.png"\; state="\{\{state\}\}">T</figure-callout>}}_{12}& 0& 0& 0\end{array}\right],$

Target function is:

$\begin{array}{c}i=\left(\mathrm{1,2}\right)\\ \min J_i={\&Integral;}_{t_0}^{\&infin;}\frac{1}{2}[\mathrm{\&Delta;}{f}_i{\left(t\right)}^2+\mathrm{\&Delta;}{P}_{\mathrm{tie}}{\left(t\right)}^2+10u_i{\left(t\right)}^2]\mathrm{dt}\end{array},$

Target function represents, frequency and interconnection power are all pursued near rated value in two zones, all wish the control cost minimum of paying simultaneously.Weight coefficient unification in each regional aim is made as [1,1,10], and this weight coefficient only reflects that each zone to the preference of control target, can not influence the fairness of payoff according to the actual demand adjustment.

Suppose to replace real change at random amount with ultra-short term value and ultrashort phase wind power predicted value in control procedure, as redefining each variable with reference to putting, subscript ss represents steady-state value with the steady-state value after the disturbance:

x _N(t)=x(t)-x _ss(t)，

u _iN(t)=u _i(t)-u _iss(t)，

ΔP _LN(t)=ΔP _L(t)-ΔP _Lss(t)=0，

Because of Δ f _1ss=Δ f _2ss=Δ P _Tiess=0, model finally turns to canonical form shown in the formula (9):

i=(1,2)

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

${\stackrel{\&CenterDot;}{x}}_N\left(t\right)=A{x}_N\left(t\right)+B_1{u}_{1N}\left(t\right)+B_2{u}_{2N}\left(t\right)$

Wherein, A, B ₁, B ₂Remain unchanged Q _iWith R _iValue is as follows:

${\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">Q</figure-callout>}}_1=\left[\begin{array}{ccccccc}1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 1\end{array}\right]{\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">Q</figure-callout>}}_2=\left[\begin{array}{ccccccc}0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 1\end{array}\right],$

R ₁=R ₂=10，

Control flow of the present invention utilizes the differential theory of games to find the solution above-mentioned AGC frequency modulation model with reference to figure 2, with the Nash Equilibrium strategy of trying to achieve as each regional frequency modulation strategy.If the control strategy of appointment all is willing to accept in each zone, do not deviate from the wish of scheme separately, can think that then this scheme coordinated the income in two zones.Establish for this reason:

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">u</figure-callout>}}_{1\mathrm{NNEW}}={\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">k</figure-callout>}}_1*{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">u</figure-callout>}}_{1\mathrm{<figure-callout\; id="2"\; label="NORIGNAL\; u"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">NORIGNAL</figure-callout>}}& \\ u_{}{}_{2\mathrm{NNEW}}={\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">u</figure-callout>}}_{2\mathrm{NORIGNAL}}\end{array}\right.,$

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">u</figure-callout>}}_{1\mathrm{NNEW}}={\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA00002987882500011.png,HDA00002987882500012.png"\; state="\{\{state\}\}">u</figure-callout>}}_{1\mathrm{<figure-callout\; id="2"\; label="NORIGNAL\; u"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">NORIGNAL</figure-callout>}}& \\ u_{}{}_{2\mathrm{NNEW}}={\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">k</figure-callout>}}_2*{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA00002987882500011.png,HDA00002987882500013.png"\; state="\{\{state\}\}">u</figure-callout>}}_{2\mathrm{NORIGNAL}}\end{array}\right.,$

Make k ₁With k ₂Change in [0,2], the results are shown in Figure 3 and Fig. 4, Fig. 3 is zone 1 payment J ₁With k ₁Change curve, Fig. 4 be the zone 2 the payment J ₂With k ₂Change curve.Can see J ₁With J ₂Value is respectively at k ₁=1 and k ₂Reached extreme value at=1 o'clock, namely the income in two zones has reached optimum point simultaneously under named policer, changes the tactful income that only can cut down separately separately, thereby has guaranteed tactful fairness.

To other existing control strategies, as traditional PI control strategy with based on the coordination control strategy of weighting Multiple Criteria Optimum Control Problem Via theory, carry out identical simulation analysis, simulation result proves, when adopting these control strategies, the payment in each zone still has the space of improvement, so each zone might change the control strategy of one's respective area separately, because this change is blindly, thereby may cause the unstability of power system frequency.Other existing control strategies do not have fairness and convincingness.

Fig. 5 be the differential solution of game with different weight coefficients under the comparison diagram of optimal control solution, F point expression feedback Nash Equilibrium point among the figure, Fig. 6 is the amplification of Fig. 5 centre circle D part details, the Nash Equilibrium point is fed back in the expression of F point among the figure, X, Y, Z point are the Pareto optimum points.Part is the point set of domination point F on the Pareto forward position between X and the Z, and these two figure have illustrated the difference of the present invention and optimal control.Coordination control based on weighting Multiple Criteria Optimum Control Problem Via theory can obtain the optimum forward position of Pareto shown in Figure 5, but it is theoretical for choosing suitable operating point therein to lack a cover, makes the result reach equalization stable.The non-cooperation feedback Nash Equilibrium solution (FBNE) of gained of the present invention is very near optimum forward position, and only by the domination of the Pareto optimal solution of X, Z point-to-point transmission among Fig. 6, this part solution is called as Pareto and improves disaggregation.Though by the domination of certain Pareto optimal solution, equilibrium solution has guaranteed interregional justice, thereby the frequency modulation instruction that each zone is strictly carried out distribute has guaranteed the stable of system.

Above-described embodiment is preferred implementation 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 spiritual essence of the present invention and the principle, substitutes, combination, simplify; all should be the substitute mode of equivalence, be included within protection scope of the present invention.

Claims (5)

1. based on the multizone automatic generation control coordination approach of differential theory of games, it is characterized in that, may further comprise the steps:

Step 1, set up the dynamic model of regional interconnected network automatic generation control (AGC);

Step 2, with traditional automatic generation control amount based on the proportional integral link, be replaced by the automatic generation control amount based on the differential theory of games, set up based on the regional interconnected network of the differential theory of games coordination control model of generating automatically;

Step 3, use linear quadratic type differential theory of games, find the solution the regional interconnected network coordination control model of generating automatically, with the Nash Equilibrium strategy of the trying to achieve automatic generation control amount as a plurality of zones;

Step 4, based on the multizone of the differential theory of games coordinated control system of generating electricity automatically, the distribution of interregional frequency modulation amount has fairness and is rich in convincingness, and other existing control methods do not have this feature.

2. the multizone automatic generation control coordination approach based on the differential theory of games according to claim 1 is characterized in that:

In the described step 1, the dynamic model of the regional interconnected network automatic generation control of described foundation (AGC), its step is specially:

1) selecting the AGC parameter as system state variables, is example with two regional interconnected systemss, that is:

x(t)=[Δf ₁ΔP _g1ΔX _g1Δf ₂ΔP _g2ΔX _g2ΔP _tie] ^T，

Wherein, for regional i, Δ f _iBe the deviation of instantaneous frequency and rated value, Δ P _GiBe prime mover variable quantity of exerting oneself, Δ X _GiBe speed regulator valve location change amount, Δ P _TieBe the Tie line Power deviation;

2) obtain describing the dynamic equation of frequency modulation system by analytical calculation

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

Wherein, u _iBe the AGC controlled quentity controlled variable of regional i, Δ P _L=[Δ P _L1Δ P _L2] ^TPoor for load disturbance amount and wind-powered electricity generation undulate quantity.A is the system mode matrix, B _iBe input matrix, Γ is the disturbance transfer matrix, and its value can obtain according to system's dynamic calculation;

3) pay off function J that each is regional _iBe defined as linear quadratic type form

$\begin{array}{c}i=\left(\mathrm{1,2}\right)\\ \min J_i={\&Integral;}_{t_0}^{\&infin;}\frac{1}{2}[x^T\left(t\right)Q_{i}x\left(t\right)+{u_i}^T\left(t\right)R_i{u}_i\left(t\right)]\mathrm{dt}\end{array},$

Wherein, to regional i, Q _iBe the state variable weight coefficient matrix, embody this zone to frequency and the interconnection power pursuit degree near the rated value target, R _iBe the input variable weight coefficient matrix, embody this zone to the degree of concern of AGC unit loss in the one's respective area in the frequency adjustment process, Q _i, R _iWeight coefficient only reflects that each zone is to the preference of control target.

3. the multizone automatic generation control coordination approach based on the differential theory of games according to claim 1 is characterized in that:

In the described step 2, described with traditional automatic generation control amount based on the proportional integral link, be replaced by the automatic generation control amount based on the differential theory of games, described foundation based on the step of the coordination control model of the automatic generating of regional interconnected network of differential theory of games is:

In A, the traditional two regional interconnected systems FREQUENCY CONTROL models, the automatic generation control amount of regional i adopts the proportional integral link to obtain, that is:

ΔP _ci=-K _1i×∫ACE _idt-K _ti×ACE _i，

Wherein, Δ f _iDeparture for actual frequency and rated value; K _LiAnd K _TiBe storage gain and proportional gain, get on the occasion of; ACE _iBe the Region control deviation, computing formula is Δ P _Tie-10B _iΔ f _i, Δ P _TieBe interregional Tie line Power deviation, B _iFor the frequency response coefficient, get negative value;

The difference Γ Δ P of B, elimination load disturbance amount and wind-powered electricity generation undulate quantity _L, suppose in control procedure, to replace actual change at random amount with ultra-short term value and ultrashort phase wind power predicted value, as redefining each variable with reference to point, subscript ss represents steady-state value with the steady-state value after the disturbance:

x _N(t)=x(t)-x _ss(t)，

u _iN(t)=u _i(t)-u _iss(t)，

ΔP _LN(t)=ΔP _L(t)-ΔP _Lss(t)=0，

Thereby obtain:

${\stackrel{\&CenterDot;}{x}}_N\left(t\right)={\mathrm{Ax}}_N\left(t\right)+B_1{u}_{1N}\left(t\right)+B_2{u}_{2N}\left(t\right),$

The form of pay off function is:

$\begin{array}{c}i=\left(\mathrm{1,2}\right)\\ \min J_i={\&Integral;}_{t_0}^{\&infin;}\frac{1}{2}[{x_N}^T\left(t\right)Q_i{x}_N\left(t\right)+{u_{\mathrm{iN}}}^T\left(t\right)R_i{u}_{\mathrm{iN}}\left(t\right)]\mathrm{dt}\end{array}.$

4. the multizone automatic generation control coordination approach based on the differential theory of games according to claim 1 is characterized in that:

In the described step 3, described utilization linear quadratic type differential theory of games is found the solution the automatically coordination control model of generating of regional interconnected network, and with the Nash Equilibrium strategy of the trying to achieve automatic generation control amount as a plurality of zones, its computational process is:

Utilize the differential theory of games, find the solution linear quadratic type differential betting model, obtain the Nash Equilibrium strategy, as each regional automatic generation control amount,

$u_i*\left(t\right)=-R^{-1}{B_i}^T{P}_{i}x\left(t\right),i=1,\&CenterDot;\&CenterDot;\&CenterDot;,n,$

(P wherein ₁, P ₂..., P _n) be the solution of algebraic riccati equation group,

Described algebraic riccati equation group refers to:

$\&Exists;i\&Element;(\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n)$

$Q_i+P_{i}A+A^T{P}_i-\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{P}_{i}B{R_k}^{-1}{B_k}^T{P}_k-\underset{j=1j\&NotEqual;i}{\overset{n}{\mathrm{\&Sigma;}}}{\left(B_j{R_j}^{-1}{B_j}^T{P}_j\right)}^T{P}_i=0.$

5. the multizone automatic generation control coordination approach based on the differential theory of games according to claim 1 is characterized in that:

In the described step 4, the process that described interregional frequency modulation amount is carried out fair allocat is as follows:

A, the frequency modulation control amount of establishing regional i are:

u _iNNEW=k _i*u _iNORIGNAL，

Controlled quentity controlled variable to one of them regional s is carried out the fairness analysis, i.e. fixed area i=1, and 2 ..., s-1, s+1 ..., the feedback factor k of n _i=1;

B, make k _sValue near 1 neighborhood, change, make regional s payment J _sWith k _sThe curve chart that changes;

C, when Nash Equilibrium strategies are adopted in other zones, the one's respective area optimal strategy also is the Nash Equilibrium strategy.

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