CN105787650A - Simulation calculation method for Nash equilibrium point of electricity market including multiple load agents - Google Patents

Abstract

The invention discloses a simulation calculation method for a Nash equilibrium point of an electricity market including multiple load agents. The electricity market is simulated based on a conjectured supply function equilibrium (CSFE) model, and profit of a load agent company comes from a result formed by subtracting the cost used by the load agents for scheduling electricity price type and excitation type load resources from a subsidy given by an electricity company after bid success. Based on features of electricity price type and excitation type loads, the cost of the load agents is a secondary function of output of the load agents, a bidding strategy limit compensation price is a primary function of the output, a bidding coefficient is determined by response conjecture variables of the agents for the market, the agents dynamically adjust their own bidding strategies through learning, after full competition, finally, the market reaches the Nash equilibrium point, an algorithm performs analog simulation on a bidding process of each time, the market gaming process when the multiple load agents appear in a specific market is fully represented, a clearing price of a market final balance state is obtained, and guidance is provided for construction of the electricity market and evaluation of resource utilization efficiency.

Description

A kind of emulated computation method acting on behalf of electricity market Nash equilibrium point containing many loads

Technical field

The invention belongs to intelligent power grid technology field, specifically a kind of emulated computation method acting on behalf of electricity market Nash equilibrium point containing many loads.

Background technology

Along with becoming increasingly conspicuous of Structure of national economy contradiction, electrical network peak load constantly rises, and electrical network peak-valley difference presents and progressively expands trend, and the power supply and demand imbalance contradiction of some areas is very serious, has a strong impact on the safe and stable operation of power system.For meeting ever-increasing workload demand, country to put into every year exceeds 100 billion for variable load plant's construction, but towards peak regulation demand send out, transmission facility annual utilization hours low, average unit cost is higher, simple dependence is continuously increased installed capacity to meet of short duration Peak power use, can cause that sending out power supply cost constantly rises, and is unfavorable for the Appropriate application of social resources.Meanwhile, the Demand-side resource become increasingly abundant brings new challenge to electrical network, and as the important component part of electrical network, Demand-side can pass through to optimize self electricity consumption, participates in electrical network interactive, reaches the target of peak load shifting, energy-saving and emission-reduction.

Load agency, as the intermediary agency coordinating a large amount of middle and small scale demand response resources and grid control centre, has played important function in demand response is put into practice.Load agency participates in the unified regulation and control of control centre with bidding fashion, and its power that content is power adjustment and correspondence of bidding adjusts making up price；Be in the bid information that the control centre of scheduling controlling layer submits to according to each load agency, carry out hair electricity unified optimize calculate after by integrated scheduling goal decomposition and be handed down to successfully each load agency that bids；The load adjustment capacity that control centre is distributed by successful load of bidding agency distributes to its each internal load by the mode of electricity price and excitation, carries out being conducive to the disperse policy decision of number one.

Load agency is responsible for the distributed power generation in region and load, by dissimilar generated output and load being integrated and complementary, there is provided the service of exerting oneself possessing certain controllability being similar to conventional power plants to electrical network, the central control unit of load Acting Center only need to be regulated and controled by control centre.Load Acting Center is the application of distributed power generation and dsm provides new thinking, but is no matter that Demonstration Application or theoretical research are at present all in the exploratory stage.

Summary of the invention

The present invention is directed to the present situation that in current electricity market, the construction of load agency and numerous power distribution companies is at the early-stage, what provide a kind of electricity market acting on behalf of sufficient competition containing many loads acts on behalf of Nash equilibrium point emulation mode, Market Games process when fully occurring that multiple load is acted on behalf of in performance particular market by calculating, obtaining the cleaing price of the final equilibrium state in market, construction and level of resources utilization assessment for electricity market provide and instruct.

In order to solve the problems referred to above, the technical solution used in the present invention is:

A kind of emulated computation method acting on behalf of electricity market Nash equilibrium point containing many loads, it is characterized in that: electricity market adopts and is simulated based on conjecture supply function equilibrium model, assume that load agency pursues the maximization of self profit all reasoningly, the profit optimization that target is the current generation of load agency n, simultaneously need to valency needs to meet the restriction of exerting oneself of system power Constraints of Equilibrium and agency, and the profit of load agency comes from the subsidy that after successfully, Utilities Electric Co. gives of bidding and deducts the cost of load proxy call electricity price type and stimulable type burdened resource,

Based on the feature of electricity price type and stimulable type load, the cost of load agency is that load acts on behalf of the quadratic function exerted oneself, and quotation strategy limit making up price is the linear function exerted oneself, it may be assumed that q_n(t)=A_n(t)+B_n(t)·p_n(t), p in formula_nT () acts on behalf of the n marginal making up price reported, A for period t load_n(t) and B_nT () is quotation coefficient, q_nT () is exerting oneself that load is acted on behalf of, definition load is acted on behalf of the n sum of exerting oneself to its all rivals and relative to the response guessed variable of the micro-increasing of the market price isThen quotation coefficient A_n(t) and B_n(t) be $\left\{\begin{array}{c}{A}_n\left(t\right)=\frac{-b_n\·V_n}{1+c_n\·V_n}\\ B_n\left(t\right)=\frac{V_n}{1+c_n\·V_n}\end{array}\right.;$

In CSFE electricity market, each quotation terminates rear market and reaches $\left\{\begin{array}{c}{p}^{*}\left(t\right)=\frac{D\left(t\right)-\underset{i=1}{\overset{N_{Ag}}{\mathrm{\Σ}}}{A}_i\left(t\right)}{\underset{i=1}{\overset{N_{Ag}}{\Σ}}{B}_i\left(t\right)}\\ q_n^{*}=A_n\left(t\right)+B_n\left(t\right)\·p^{*}\left(t\right)\end{array}\right.$ The poised state retrained, wherein p^*T () is market clearing price, D (t) is total capacity requirement, N_AgQuantity, q is acted on behalf of for total load^* _nFor exerting oneself of each agency.

Aforesaid a kind of emulated computation method acting on behalf of electricity market Nash equilibrium point containing many loads, it is characterized in that: the profit optimization that target is the current generation of load agency n, simultaneously need to valency needs to meet the restriction of exerting oneself of system power Constraints of Equilibrium and agency, it is considered to the cost curve of the known agency of the cost model (Agent) of electricity price type load and stimulable type load is represented by following form:

W_n(t)=a_n+b_n·q(t)+0.5c_n·q²(t)

W in formula_nT () is the cost of agency, a_n, b_n, c_nFor cost coefficient,

Correspondingly the unit power of load agency adjusts and there is linear relationship between making up price and power adjustment, and quotation strategy is represented by:

q_n(t)=A_n(t)+B_n(t)·p_n(t)

In formula: p_nT () is acted on behalf of the n unit power reported for period t load and is adjusted price, for simplicity, the power adjustment that load is acted on behalf of be called " load agency exerts oneself " later, be regarded as a kind of energy source corresponding with generator output；

Based on conjecture supply function equilibrium model, load agency pursues the maximization of self profit all reasoningly, and as the profit optimization that target is the current generation of the agency n of, then the object function of proxy bid is

maxπ_n=p (t) q_n(t)-W_n(t) (1), π in formula_nFor agency profit,

Proxy bid needs to meet system power Constraints of Equilibrium, namely

$D\left(t\right)=\underset{j\≠n}{\overset{N_{Ag}}{\underset{j=1}{\mathrm{\Σ}}}}{q}_j\left(t\right)+\underset{j=1}{\overset{N_G}{\mathrm{\Σ}}}{P}_j^G\left(t\right)+q_n\left(t\right)$

Also should meet the restriction of exerting oneself of agency simultaneously:

$q_n^{\min }\≤q_n\≤q_n^{\max }$

In formula, D (t) is the workload demand of t period,Here represent the history of generating set j to estimate and exert oneself, N_GFor the sum of conventional power generation usage unit, N in system_AgLoad for participating in management and running acts on behalf of number,For exerting oneself of period t generating set j, q_nT load that () is period t acts on behalf of exerting oneself of n.

Aforesaid a kind of emulated computation method acting on behalf of electricity market Nash equilibrium point containing many loads, it is characterized in that: the profit of load agency comes from the subsidy that after successfully, Utilities Electric Co. gives of bidding and deducts the cost of load proxy call electricity price type and stimulable type burdened resource

(1) marginal cost of electricity price type load is called,

Call electricity price type cost can be calculated as $Q_i^P=l_i^0\·P_i^0-(P_i^0-{\mathrm{\ΔP}}_i)(l_i^0+{\mathrm{\Δl}}_i)$

Q in formula_i ^PFor electricity price cost, l_i ⁰For initial electricity price, P_i ⁰For initial power consumption, Δ P_iFor power consumption variable quantity, Δ l_iFor electricity price variable quantity,

Compensate electricity price Δ l_iWith electricity consumption variation delta P_iRelation as follows:

ε in formula_iiFor electricity price autocorrelation coefficient,

The marginal cost calling electricity price type load can be expressed as

(2) marginal cost of stimulable type load is called,

The marginal cost calling stimulable type load can be expressed asWherein k is stimulable type load cost parameter, reflects the situation that its marginal cost increases when the stimulable type load called increases.

Aforesaid a kind of emulated computation method acting on behalf of electricity market Nash equilibrium point containing many loads, it is characterised in that: when adopting conjecture supply function equilibrium model Simulated Power Market, optimization problem formula (1) should meet single order optimal conditions:

$\frac{\∂{\mathrm{\π}}_n}{\∂p}=0$

Act on behalf of the optimization price of n and exert oneself such that it is able to derive load and must be fulfilled for:

$q_n\left(t\right)+(p\left(t\right)-\left(b_n+c_n{q}_n\left(t\right)\right)\·\[-\frac{\∂\[\underset{j=1,j\≠n}{\overset{N_{Ag}}{\mathrm{\Σ}}}{q}_j\left(t\right)+\underset{j=1}{\overset{N_G}{\mathrm{\Σ}}}{P}_j^G\left(t\right)\]}{\∂p\left(t\right)}\]=0$

Assume that load is acted on behalf of n and the sum of exerting oneself of (other loads agency) is defined as relative to the response guessed variable of the micro-increasing of the market price by its all competitions:In formula:Act on behalf of exerting oneself of all rivals of n for load, coefficient A can be derived_n(t) and B_nT () is respectively as follows:

$\left\{\begin{array}{c}{A}_n\left(t\right)=\frac{-b_n\·V_n}{1+c_n\·V_n}\\ B_n\left(t\right)=\frac{V_n}{1+c_n\·V_n}\end{array}\right.$

Aforesaid a kind of emulated computation method acting on behalf of electricity market Nash equilibrium point containing many loads, it is characterized in that: simulating each load agency in simulation process can learn according to the quotation strategy of other loads agency in market, adjusting self strategy thus obtaining more profit, its learning process isIt is about in t-1 on last stage to act on behalf of that market guidance change is ready to make by all rivals of n exerts oneself and change the conjecture as the current t stage.

Aforesaid a kind of emulated computation method acting on behalf of electricity market Nash equilibrium point containing many loads, it is characterised in that: according to formulaObtain this conjecture to be load and act on behalf of the sum of coefficient of first order that all rivals of n have the linear bidding function of non-zero intercept in upper together workload demand curve bidding period $\underset{j=1,j\≠n}{\overset{N_{Ag}}{\mathrm{\Σ}}}{B}_n\left(t-1\right)\mathrm{..}$

The beneficial effect that the present invention reaches: the present invention is directed to the present situation that in current electricity market, the construction of load agency and numerous power distribution companies is at the early-stage, propose a kind of many loads act on behalf of sufficient competition electricity market act on behalf of Nash equilibrium point emulation mode, Market Games process when fully occurring that multiple load is acted on behalf of in performance particular market by calculating, obtaining the cleaing price of the final equilibrium state in market, construction and level of resources utilization assessment for electricity market provide and instruct.

Accompanying drawing explanation

Tu1Shi Utilities Electric Co.-load agency-load three layers Power Market Structure figure.

Fig. 2 is the electricity market bid process schematic diagram containing many agencies.

Fig. 3 is market clearing price iterative process schematic diagram.

Fig. 4 is the market conjectural variation situation of change of each load agency.

Detailed description of the invention

Below in conjunction with accompanying drawing, the invention will be further described.Following example are only for clearly illustrating technical scheme, and can not limit the scope of the invention with this.

A kind of emulated computation method acting on behalf of electricity market Nash equilibrium point containing many loads, comprises the steps:

1, electricity market adopts and is simulated based on balanced (CSFE) model of conjecture supply function, it is assumed that load agency pursues the maximization of self profit all reasoningly.The profit optimization that target is the current generation of load agency n, simultaneously need to valency needs to meet the restriction of exerting oneself of system power Constraints of Equilibrium and agency.

Consider that the cost curve of the known agency of the cost model (Agent) of electricity price type load and stimulable type load is represented by following form

W_n(t)=a_n+b_n·q(t)+0.5c_n·q²(t)

W in formula_nT () is the cost of agency, a_n, b_n, c_nFor cost coefficient,

Correspondingly the unit power of load agency adjusts and there is linear relationship between making up price and power adjustment, and quotation strategy is represented by

q_n(t)=A_n(t)+B_n(t)·p_n(t)

In formula: p_nT () is acted on behalf of the n unit power reported for period t load and is adjusted price, for simplicity, the power adjustment that load is acted on behalf of be called " load agency exerts oneself " later, be regarded as a kind of energy source corresponding with generator output.

Based on balanced (CSFE) model of conjecture supply function, load agency pursues the maximization of self profit all reasoningly.As the profit optimization that target is the current generation of the agency n of an Agent, then the object function of proxy bid is

maxπ_n=p (t) q_n(t)-W_n(t)(1)

π in formula_nFor agency profit,

Proxy bid needs to meet system power Constraints of Equilibrium, namely

$D\left(t\right)=\underset{j\≠n}{\overset{N_{Ag}}{\underset{j=1}{\mathrm{\Σ}}}}{q}_j\left(t\right)+\underset{j=1}{\overset{N_G}{\mathrm{\Σ}}}{P}_j^G\left(t\right)+q_n\left(t\right)$

Also should meet the restriction of exerting oneself of agency simultaneously:

$q_n^{\min }\≤q_n\≤q_n^{\max }$

In formula, D (t) is the workload demand of t period,Here represent the history of generating set j to estimate and exert oneself, N_GFor the sum of conventional power generation usage unit, N in system_AgLoad for participating in management and running acts on behalf of number,For exerting oneself of period t generating set j, q_nT load that () is period t acts on behalf of exert oneself (power adjustment, lower same) of n.

2, the profit of load agency comes from the subsidy that after successfully, Utilities Electric Co. gives of bidding and deducts the cost of load proxy call electricity price type and stimulable type burdened resource.

(1) marginal cost of electricity price type load is called

Call electricity price type cost can be calculated as $Q_i^P=l_i^0\·P_i^0-(P_i^0-{\mathrm{\ΔP}}_i)(l_i^0+{\mathrm{\Δl}}_i)$

Q in formula_i ^PFor electricity price cost, l_i ⁰For initial electricity price, P_i ⁰For initial power consumption, Δ P_iFor power consumption variable quantity, Δ l_iFor electricity price variable quantity,

Compensate electricity price Δ l_iWith electricity consumption variation delta P_iRelation as follows:

ε in formula_iiFor electricity price autocorrelation coefficient,

The marginal cost calling electricity price type load can be expressed as

(2) marginal cost of stimulable type load is called

The marginal cost calling stimulable type load can be expressed asWherein k is stimulable type load cost parameter, reflects the situation that its marginal cost increases when the stimulable type load called increases.

When 3, adopting CSFE modeling electricity market, optimization problem formula (1) should meet single order optimal conditions:

$\frac{\∂{\mathrm{\π}}_n}{\∂p}=0$

Such that it is able to derive load act on behalf of n optimization price-exerting oneself must is fulfilled for:

$q_n\left(t\right)+(p\left(t\right)-\left(b_n+c_n{q}_n\left(t\right)\right)\·\[-\frac{\∂\[\underset{j=1,j\≠n}{\overset{N_{Ag}}{\mathrm{\Σ}}}{q}_j\left(t\right)+\underset{j=1}{\overset{N_G}{\mathrm{\Σ}}}{P}_j^G\left(t\right)\]}{\∂p\left(t\right)}\]=0$

Assume that load is acted on behalf of n and the sum of exerting oneself of (other loads agency) is defined as relative to the response guessed variable of the micro-increasing of the market price by its all competitions:In formula:Exerting oneself of all rivals of n is acted on behalf of for load.Coefficient A can be derived_n(t) and B_nT () is respectively as follows:

$\left\{\begin{array}{c}{A}_n\left(t\right)=\frac{-b_n\·V_n}{1+c_n\·V_n}\\ B_n\left(t\right)=\frac{V_n}{1+c_n\·V_n}\end{array}\right.$

4, market clearing mechanism

Think that market goes out clear system according to uniform price, when all of load agency offers, it is easy to prove that market is up to following balance:

$\left\{\begin{array}{c}{p}^{*}\left(t\right)=\frac{D\left(t\right)-\underset{i=1}{\overset{N_{Ag}}{\mathrm{\Σ}}}{A}_i\left(t\right)}{\underset{i=1}{\overset{N_{Ag}}{\Σ}}{B}_i\left(t\right)}\\ q_n^{*}=A_n\left(t\right)+B_n\left(t\right)\·p^{*}\left(t\right)\end{array}\right.$

Visible, if load acts on behalf of the conjectural variation V adopted in this period_nThe parameter A of Bidding Price Functions shape is then determined for constant_n(t) and B_nT () is unrelated with the market price.Market clearing price p can be uniquely determined according to above formula^*And corresponding each agency exerts oneself q^* _n。

5, act on behalf of learning rules to describe

Owing to the available market information of electricity market Zhong Ge genco is incomplete, the q (t) that exerts oneself of total load D (t) in only each stage, market clearing price p (t) and each load agency, it is assumed that the quote data entire disclosure of history.In this case, each agency can both obtain knowledge thus learning from the market operation environment being continually changing, so that self profit maximization, learning rules are as follows:

$V_n\left(t\right)=\frac{\∂q_{-n}(t-1)}{\∂p(t-1)}$

It is about in t-1 on last stage to act on behalf of that market guidance change is ready to make by all rivals of n exerts oneself and change the conjecture as the current t stage.This conjecture can be load and act on behalf of the sum of coefficient of first order that all rivals of n have the linear bidding function of non-zero intercept in upper together workload demand curve bidding period according to above formula

Simulation example

For IEEE6 machine 30 node system, this system comprises 6 electromotors, now increases by two load agencies, and the parameter of electromotor and agency is as shown in the table, it is assumed that the power shortage in system is 700MW.

Electromotor and load proxy parameter table

The initial conjectural variation of 3 loads agency is respectively 100,40,80 according to market clearing price situation of change after iteration under the model 30 times as shown in Figure 3, after the emulation of visible emulation mode obtains carrying out about 10 iteration in electricity market, market reaches equilibrium state, and the response conjecture function iteration track of each load agency and market reach shown in equilibrium operating state outcome such as accompanying drawing 4 and following table

Market equilibrium result table

	Load agency 1	Load agency 2	Load agency 3
				Response conjecture V	84.14	76.42	70.45
Act on behalf of/the MW that exerts oneself	212.18	237.06	250.75
				Profit ($/h)	535.09	735.42	892.55

In market, according to conventional market operation information, each load agency estimates that the conjectural variation value of its rival is different owing to pursuing respective maximum profit, and each agency will make the decision-making most beneficial for them according to the conjectural variation estimating gained.Emulation mode described in this patent has fully demonstrated containing the situation of change acting on behalf of each load in electricity market more and acting on behalf of track of bidding in sufficient competition process, emulation presents the forming process of electricity power market equilibrium state from multi-angle, can provide useful guidance for the construction of electricity market.

The ultimate principle of the present invention, principal character and advantage have more than been shown and described.Skilled person will appreciate that of the industry; the present invention is not restricted to the described embodiments; described in above-described embodiment and description is that principles of the invention is described; without departing from the spirit and scope of the present invention; the present invention also has various changes and modifications, and these changes and improvements both fall within the claimed scope of the invention.Claimed scope is defined by appending claims and equivalent thereof.

Claims (6)

1. the emulated computation method acting on behalf of electricity market Nash equilibrium point containing many loads, it is characterized in that: electricity market adopts and is simulated based on conjecture supply function equilibrium model, assume that load agency pursues the maximization of self profit all reasoningly, the profit optimization that target is the current generation of load agency n, simultaneously need to valency needs to meet the restriction of exerting oneself of system power Constraints of Equilibrium and agency, and the profit of load agency comes from the subsidy that after successfully, Utilities Electric Co. gives of bidding and deducts the cost of load proxy call electricity price type and stimulable type burdened resource,

Based on the feature of electricity price type and stimulable type load, the cost of load agency is that load acts on behalf of the quadratic function exerted oneself, and quotation strategy limit making up price is the linear function exerted oneself, it may be assumed that q_n(t)=A_n(t)+B_n(t)·p_n(t), p in formula_nT () acts on behalf of the n marginal making up price reported, A for period t load_n(t) and B_nT () is quotation coefficient, q_nT () is exerting oneself that load is acted on behalf of, definition load is acted on behalf of the n sum of exerting oneself to its all rivals and relative to the response guessed variable of the micro-increasing of the market price isThen quotation coefficient A_n(t) and B_n(t) be $\left\{\begin{array}{c}{A}_n\left(t\right)=\frac{-b_n\·V_n}{1+c_n\·V_n}\\ B_n\left(t\right)=\frac{V_n}{1+c_n\·V_n}\end{array}\right.;$

In CSFE electricity market, each quotation terminates rear market and reaches $\left\{\begin{array}{c}{p}^{*}\left(t\right)=\frac{D\left(t\right)-\underset{i=1}{\overset{N_{Ag}}{\mathrm{\Σ}}}{A}_i\left(t\right)}{\underset{i=1}{\overset{N_{Ag}}{\Σ}}{B}_i\left(t\right)}\\ q_n^{*}=A_n\left(t\right)+B_n\left(t\right)\·p^{*}\left(t\right)\end{array}\right.$ The poised state retrained, wherein p^*T () is market clearing price, D (t) is total capacity requirement, N_AgQuantity, q is acted on behalf of for total load^* _nFor exerting oneself of each agency.

2. a kind of emulated computation method acting on behalf of electricity market Nash equilibrium point containing many loads according to claim 1, it is characterized in that: the profit optimization that target is the current generation of load agency n, simultaneously need to valency needs to meet the restriction of exerting oneself of system power Constraints of Equilibrium and agency, it is considered to the cost curve of the known agency of the cost model (Agent) of electricity price type load and stimulable type load is represented by following form:

W_n(t)=a_n+b_n·q(t)+0.5c_n·q²(t)

W in formula_nT () is the cost of agency, a_n, b_n, c_nFor cost coefficient,

Correspondingly the unit power of load agency adjusts and there is linear relationship between making up price and power adjustment, and quotation strategy is represented by:

q_n(t)=A_n(t)+B_n(t)·p_n(t)

In formula: p_nT () is acted on behalf of the n unit power reported for period t load and is adjusted price, for simplicity, the power adjustment that load is acted on behalf of be called " load agency exerts oneself " later, be regarded as a kind of energy source corresponding with generator output；

Based on conjecture supply function equilibrium model, load agency pursues the maximization of self profit all reasoningly, and as the profit optimization that target is the current generation of the agency n of, then the object function of proxy bid is

maxπ_n=p (t) q_n(t)-W_n(t) (1), π in formula_nFor agency profit,

Proxy bid needs to meet system power Constraints of Equilibrium, namely

$D\left(t\right)=\underset{j\≠n}{\overset{N_{Ag}}{\underset{j=1}{\mathrm{\Σ}}}}{q}_j\left(t\right)+\underset{j=1}{\overset{N_G}{\mathrm{\Σ}}}{P}_j^G\left(t\right)+q_n\left(t\right)$

Also should meet the restriction of exerting oneself of agency simultaneously:

$q_n^{\min }\≤q_n\≤q_n^{\max }$

In formula, D (t) is the workload demand of t period,Here represent the history of generating set j to estimate and exert oneself, N_GFor the sum of conventional power generation usage unit, N in system_AgLoad for participating in management and running acts on behalf of number,For exerting oneself of period t generating set j, q_nT load that () is period t acts on behalf of exerting oneself of n.

3. a kind of emulated computation method acting on behalf of electricity market Nash equilibrium point containing many loads according to claim 2, it is characterized in that: the profit of load agency comes from the subsidy that after successfully, Utilities Electric Co. gives of bidding and deducts the cost of load proxy call electricity price type and stimulable type burdened resource

(1) marginal cost of electricity price type load is called,

Call electricity price type cost can be calculated as $Q_i^P=l_i^0\·P_i^0-(P_i^0-{\mathrm{\ΔP}}_i)(l_i^0+{\mathrm{\Δl}}_i)$

In formulaFor electricity price cost,For initial electricity price,For initial power consumption, Δ P_iFor power consumption variable quantity, Δ l_iFor electricity price variable quantity,

Compensate electricity price Δ l_iWith electricity consumption variation delta P_iRelation as follows:

ε in formula_iiFor electricity price autocorrelation coefficient,

The marginal cost calling electricity price type load can be expressed as $C_{iP}=\frac{\∂Q_i^P}{\∂{\mathrm{\ΔP}}_i}=\frac{l_i^0\[({\mathrm{\ϵ}}_{ii}-1)P_i^0+2{\mathrm{\ΔP}}_i\]}{P_i^0\·{\mathrm{\ϵ}}_{ii}}$

(2) marginal cost of stimulable type load is called,

The marginal cost calling stimulable type load can be expressed asWherein l₀Representing stimulable type load responding basic cost, k is stimulable type load cost parameter, reflects the situation that its marginal cost increases when the stimulable type load called increases.

4. a kind of emulated computation method acting on behalf of electricity market Nash equilibrium point containing many loads according to claim 3, it is characterized in that: when adopting conjecture supply function equilibrium model Simulated Power Market, optimization problem formula (1) should meet single order optimal conditions:

$\frac{\∂{\mathrm{\π}}_n}{\∂p}=0$

Act on behalf of the optimization price of n and exert oneself such that it is able to derive load and must be fulfilled for:

$q_n\left(t\right)+(p\left(t\right)-\left(b_n+c_n{q}_n\left(t\right)\right)\·\[-\frac{\∂\[\underset{j=1,j\≠n}{\overset{N_{Ag}}{\mathrm{\Σ}}}{q}_j\left(t\right)+\underset{j=1}{\overset{N_G}{\mathrm{\Σ}}}{P}_j^G\left(t\right)\]}{\∂p\left(t\right)}\]=0$

Assume that load is acted on behalf of n and the sum of exerting oneself of (other loads agency) is defined as relative to the response guessed variable of the micro-increasing of the market price by its all competitions:In formula:Act on behalf of exerting oneself of all rivals of n for load, coefficient A can be derived_n(t) and B_nT () is respectively as follows:

$\left\{\begin{array}{c}{A}_n\left(t\right)=\frac{-b_n\·V_n}{1+c_n\·V_n}\\ B_n\left(t\right)=\frac{V_n}{1+c_n\·V_n}\end{array}\right..$

5. a kind of emulated computation method acting on behalf of electricity market Nash equilibrium point containing many loads according to claim 4, it is characterized in that: simulating each load agency in simulation process can learn according to the quotation strategy of other loads agency in market, adjusting self strategy thus obtaining more profit, its learning process isIt is about in t-1 on last stage to act on behalf of that market guidance change is ready to make by all rivals of n exerts oneself and change the conjecture as the current t stage.

6. a kind of emulated computation method acting on behalf of electricity market Nash equilibrium point containing many loads according to claim 5, it is characterised in that: according to formulaObtain this conjecture to be load and act on behalf of the sum of coefficient of first order that all rivals of n have the linear bidding function of non-zero intercept in upper together workload demand curve bidding period $\underset{j=1,j\≠n}{\overset{N_{Ag}}{\Σ}}{B}_n(t-1).$