CN108491975A - A kind of Day-ahead Electricity Purchase optimization method of electric system containing wind-powered electricity generation based on range optimization - Google Patents

A kind of Day-ahead Electricity Purchase optimization method of electric system containing wind-powered electricity generation based on range optimization Download PDF

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CN108491975A
CN108491975A CN201810266940.3A CN201810266940A CN108491975A CN 108491975 A CN108491975 A CN 108491975A CN 201810266940 A CN201810266940 A CN 201810266940A CN 108491975 A CN108491975 A CN 108491975A
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江岳文
陈梅森
林建新
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Fuzhou University
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Abstract

The present invention relates to a kind of Day-ahead Electricity Purchase optimization method of electric system containing wind-powered electricity generation based on range optimization, consider energy market a few days ago and the spare capacity market combination goes out clear situation, and combine Real-time markets deviation power interval, with total cost minimum and the minimum target in Real-time markets power deviation section, the multi-target non-linear range optimization model containing wind-powered electricity generation is established, and is optimistic solution and pessimistic solution Optimized model by multi-target non-linear range optimization model conversion.The present invention can obtain optimal power purchase section and the spare capacity section of ahead market fired power generating unit, provide reference to power purchase decision, reduce purchases strategies, rationally utilize wind-resources.

Description

Section optimization-based optimization method for power purchase of day-ahead market of wind power-containing power system
Technical Field
The invention relates to the field of electric power markets, in particular to a method for optimizing the electricity purchasing of a day-ahead market of a wind power-containing electric power system based on interval optimization.
Background
In order to reduce the use of fossil fuels, wind power is vigorously developed in China, and with the increase of the wind power grid-connected scale, the influence of wind power uncertainty on power trading and scheduling is larger and larger, and the influence of the wind power uncertainty needs to be considered in the market in the future. At present, in the research of market trading in the future, a probability model is mainly used for representing the uncertainty of wind power, however, the probability model needs a large amount of historical data to be obtained through statistics, and if the data volume is small, the obtained probability distribution may be inaccurate, and the electricity purchasing result is influenced.
In the day-ahead market, the energy market and the reserve capacity market have definite quotes, and if the wind power is controllable, a clear result can be obtained. However, the wind power output has strong randomness, when the actual wind power output is different from the power output purchased in the market at the day before, the real-time market generates large unbalanced power, the reserve capacity needs to be called and balanced through real-time market transaction, and the larger the deviation of the real-time market power is, the larger the reserve capacity needs to be called.
At present, the optimization of the power purchasing in the day-ahead market in consideration of the power deviation of the day-ahead energy market, the reserve capacity market and the real-time market by combining the wind power output change interval is not reported.
Disclosure of Invention
In view of the above, the invention aims to provide a method for optimizing the power purchase of the day-ahead market of a power system containing wind power based on interval optimization.
The invention is realized by adopting the following scheme: a method for optimizing the power purchase of the day-ahead market of a power system containing wind power based on interval optimization specifically comprises the following steps:
step S1: extracting system information: extracting wind power interval prediction information, load prediction information, generator set day-ahead energy market quotation information and generator set reserve capacity market quotation information;
step S2: targeting 1 to minimize the sum of the cost of the energy market and the cost of the reserve capacity market in the day ahead; establishing a multi-target non-linear interval day-ahead market electricity purchasing optimization model containing wind power by taking the minimum real-time market deviation power as a target 2;
step S3: converting the multi-target non-linear interval day-ahead market electricity purchasing optimization model containing the wind power obtained in the step S2 into optimistic solution and pessimistic solution optimization models;
step S4: solving optimistic and pessimistic solution optimization models by using a multi-target quantum particle swarm algorithm to obtain pareto frontiers of the optimistic and pessimistic solutions;
step S5: and (3) solving the pareto frontier compromise between optimistic solution and pessimistic solution by using an ideal point method, and obtaining the optimal power purchasing interval and the optimal spare capacity interval of the thermal power on the market in the day ahead.
In the day-ahead market transaction considering wind power uncertainty, the uncertainty of wind power is represented by an interval, and an interval optimization model containing wind power is established by taking the day-ahead energy market and the reserve capacity market with the minimum cost and the minimum real-time market deviation power as multiple targets. The method can obtain the optimal electricity purchasing interval and the spare capacity interval of the thermal power generating unit in the market at the day before, provide reference for electricity purchasing decision, reduce electricity purchasing cost and reasonably utilize wind resources.
Further, the step S2 specifically includes the following steps:
step S21: aiming at the minimum sum of the cost of the day-ahead energy market and the cost of the reserve capacity market, a combined clearing model of the day-ahead energy market and the reserve capacity market containing wind power is established, and is expressed by a mathematical function as follows:
where ρ isr,i,tClearing price for the ith thermal power generating unit in the t time period; pi,tThe output of the ith thermal power generating unit in the t time period; t is the number of market periods in the day ahead, wherein T is 24; n is a radical ofGThe number of thermal power generating units;the upper standby capacity price and the lower standby capacity price of the ith thermal power generating unit in the market at the time t and before; cu,i,t、Cd,i,tThe upper and lower spare capacities of the ith thermal power generating unit in the market at t time period before day;
step S22: considering real-time market upper and lower deviation power caused by randomness of wind power, establishing a real-time market power deviation model containing the wind power by taking the minimum weighted deviation power as a target, and expressing the real-time market power deviation model as follows by using a mathematical function:
wherein,is the interval [ Pdes,t]Upper bound, [ P ]des,t]＝α[Pde,t]+∪-(1-α)[Pde,t]-Wherein α is a weight coefficient, α ═ p (ρ)r,i,t-ρd,i,t)/(ρr,i,t-ρd,i,t+ρu,i,t) Where ρ isu,i,tThe electricity purchase price rho of the i thermal power generating units in the real-time market at the time td,i,tFor selling electricity prices to the i thermal power generating units in the real-time market at the time t,andpositive power deviation interval and negative power deviation interval of t time interval separately;
specifically, in the electric power trading, in order to reduce the offset power of the real-time market, the real-time market price needs to satisfy ρu,i,t≥ρr,i,t≥ρd,i,tWhere ρ isu,i,tThe electricity purchase price rho of the i thermal power generating units in the real-time market at the time td,i,tAnd selling the electricity price to the i thermal power generating units in the real-time market at the time t. If the real-time deviation power is positive, which is equivalent to excessive power output of thermal power purchased in the market at the day before, the thermal power needs to be called for standby and sold in the real-time market, because rhor,i,t≥ρd,i,tEquivalent to ρ in the day-ahead marketr,i,tCan only buy electricity at the price of rhod,i,tThe price of selling, selling unit electric quantity will lose rhor,i,t－ρd,i,tThe total electricity purchase cost is increased. On the other hand, if the real-time deviation power is negative, which is equivalent to the situation that the power purchasing power of the thermal power in the market before the day is too low, the power is calculated by rhou,i,tThe price of (2) is to purchase electricity in real-time market, and the total electricity purchase cost is also increased. The total electricity purchasing cost of the day-ahead market and the real-time market is increased no matter the deviation power of the real-time market is positive or negative, and an electricity purchasing decision maker needs to find an optimal day-ahead market clearing scheme to reduce the total cost of the day-ahead market and the real-time market. Due to uncertainty of wind power output and unknown energy price of the real-time market, the balance cost of the real-time market cannot be accurately calculated. However, the real-time market deviation power is caused by the wind power prediction error, and the real-time market cost can be reduced by reducing the wind power deviation interval, so that the method aims at minimizing the power deviation interval. The real-time market power deviation interval can be expressed as:
in the formula: n is a radical ofwThe number of wind power plants; pL,tLoad prediction value is t time interval; [ P ]de,t]A power deviation interval of t time period, specifically expressed asWhereinThe lower and upper bounds of the power deviation interval are respectively.
No matter the electricity is purchased or sold in the real-time market, the loss is generated, and in order to reduce the real-time market transaction electric quantity, the wind electricity purchasing output of the day-ahead market is within the actual wind electricity output interval, namelyAt this time, the lower bound of the deviation interval is less than 0, and the upper bound is greater than 0, namely: and when the real-time market deviation power is positive, electricity needs to be purchased in the real-time market, and when the real-time market deviation power is negative, electricity needs to be sold. Loss rho due to unit purchase in real-time marketu,i,tAnd unit power sale loss (p)r,i,t－ρd,i,t) Differently, the power deviation interval can therefore be divided into two parts:
in the formula: [ P ]de,t]+And [ Pde,t]-The power deviation interval is a positive power deviation interval (a power deviation interval with excessive thermal power purchase power) and a negative power deviation interval (a power deviation interval with insufficient thermal power purchase power) in the period t. [ P ]de,t]+And [ Pde,t]-Can be expressed as:
when the electricity is purchased in the market in the day ahead, a power purchase decision maker cannot know whether the actual power deviation is positive or negative in advance, and needs to comprehensively consider an up-down deviation interval according to a certain weight, so that an up-down deviation weighting interval can be obtained:
[Pdes,t]＝α[Pde,t]+∪-(1-α)[Pde,t]-
α is the weight coefficient:
α＝(ρr,i,t-ρd,i,t)/(ρr,i,t-ρd,i,t+ρu,i,t)
since the real-time market price will satisfy rhou,i,t≥ρr,i,t≥ρd,i,tα is [0,0.5 ]]。
Considering the power deviation intervals of each time interval of the market in the future comprehensively, the target 2 can be specifically expressed as:
from the above formula, the target 2 value is one interval number, and the comparison of the interval number is difficult, however [ P ]de,t]+And [ Pde,t]-The lower bound of (2) is 0, and the lower bound of the interval of the target 2 value is also 0, so when comparing the size of the target 2 interval, only the size of the upper bound of the target 2 interval needs to be compared, and therefore the target 2 can be converted into:
in the formula:is the interval [ Pdes,t]And (4) an upper bound.
Step S23: the invention relates to a method for establishing a power purchasing output model of a day-ahead market containing wind power under the condition of considering the wind power output as one interval number, which comprises two sets of constraints: and establishing the daily market clearing plan constraint and the interval constraint when the wind power output is changed in the output interval range.
Further, in step S23, the day-ahead market clearing plan constraint includes:
(1) output restraint of the thermal power generating unit: in the market clearing plan before the day, the output of the thermal power generating unit needs to meet the output constraint of the unit and the upper and lower climbing rate constraints:
max(Pi,min,Ri,down×Δt)≤Pi,t-Cd,i,t≤min(Pi,max,Ri,up×Δt)；
max(Pi,min,Ri,down×Δt)≤Pi,t+Cu,i,t≤min(Pi,max,Ri,up×Δt)；
wherein R isi,down、Ri,upThe up-down climbing speed of the ith thermal power generating unit; pi,min、Pi,maxThe maximum output and the minimum output of the ith thermal power generating unit are respectively; the delta t is two time interval, in the invention, the delta t is one hour;
the market reserve capacity constraint may be expressed as:
in the formula:maximum upper and lower spare capacities declared for the ith unit in the t time period;
(2) and power balance constraint: the power balance constraint for the day-ahead market clearing plan may be expressed as:
wherein,the power output of the wind power purchase of the fresh plan for the market at the day-ahead; pL,tIs the load of the system for the period t; n is a radical ofWThe number of wind power plants;
(3) and (3) alternating current power flow constraint: the ac power flow constraint for a day-ahead market clearing plan may be expressed as:
-Pl,max≤Pl,t≤Pl,max；
wherein, Pl,tIs the power flow of the line l in the time period t; pl,maxIs the maximum power flow of line l;
(4) system spare capacity constraint: when wind power actual output fluctuates in the output interval range, power deviation can be generated, and in order to reduce abandoned wind, enough spare capacity needs to be purchased:
wherein, Cd,t、Cu,tRespectively represent the purchase amount of the upper and lower spare capacities in the period t,the lower bound and the upper bound of the power deviation interval are respectively; the power can change along with the change of the power purchased in the market at the day before;
(5) node voltage constraint: the node voltage constraint for the market clearing program at the day-ahead may be expressed as:
Un,min≤Un,t≤Un,max；
wherein, Un,tRepresents the node voltage of the node n in the period t; u shapen,min、Un,maxNode voltages at which the node n is minimum and maximum are respectively obtained;
(6) and (3) wind power purchase output interval constraint: the wind power purchase output constraint of the market export plan at the day-ahead may be expressed as:
wherein,the power output is purchased for the wind power in the market at the day before,andrespectively representing the lower bound and the upper bound of the actual wind power output;
further, in step S23, the satisfying the section constraint when the wind power output varies within the output section range includes:
(1) output interval constraint of the thermal power generating unit: when the electricity purchasing power of the wind power is outputIn the wind power prediction output intervalDuring internal variation, the optimal output interval consisting of the optimal output of the ith unit in the t periodShould be within the backup adjustment range:
wherein,the ith unit is in the optimal thermal power purchase power output interval at the t time periodAny value within;respectively is the lower bound and the upper bound of the t-time period output interval of the ith unit,maximum upper and lower spare capacities declared for the ith unit in the t time period;
(2) and power balance constraint: when the electricity purchasing power of the wind power is outputIn the wind power prediction output intervalIn internal variation, the day-ahead market power balance constraint may be expressed as:
wherein,the power output of the wind power purchase is possible in the wind power output interval at the t time period of the jth wind power plant;
(3) and (3) power flow constraint: when the power purchasing and outputting of the wind power is changed within the output interval range, the alternating current power flow is within the constraint range:
wherein,when the power purchasing and output of the wind power is changed in the output interval, the line l is in the alternating current power flow interval of the t periodPossible tidal current value, whereinThe lower boundary and the upper boundary of the alternating current power flow interval of the line l in the t period are respectively;
(4) node voltage constraint: when the power purchasing and outputting of the wind power is changed within the output interval range, the node voltage is within the constraint range:
wherein,when the power purchasing and output of the wind power is changed in the output interval, the node n in the t period is in the node voltage intervalInternal possible node voltage values, whereinThe lower bound and the upper bound of the node voltage interval in the t period are respectively;
(5) and (3) wind power purchase output interval constraint: the wind power purchase output constraint of the market export plan at the day-ahead may be expressed as:
further, in step S3, the model of the present invention is a multi-objective nonlinear interval programming model, and an interval solution of the model, that is, the electricity purchasing schemes corresponding to the upper and lower solutions of the objective function, needs to be solved. In order to obtain the interval solution of the model, the invention converts the interval solution into two multi-target nonlinear programming problems, namely an optimistic solution model and a pessimistic solution model. Wherein the pessimistic solution is a solution corresponding to an upper bound of the objective function, and the optimistic solution is a solution corresponding to a lower bound of the objective function
The pessimistic solution optimization model is expressed as:
because the model of the method has two targets, for the convenience of understanding, the meaning of the pessimistic model is explained by taking the electricity purchasing cost target as an example: when the electricity purchasing and output of wind power is the output intervalWhen any value is within the range, an optimal day-ahead market electricity purchasing scheme can be found, so that the total electricity purchasing cost is minimum. For different wind power electricity purchasing outputs, the minimum total electricity purchasing cost is different, wherein the minimum total electricity purchasing cost is the pessimistic solution; otherwise, it is minimumThe solution with the least total cost is an optimistic solution and can be represented by a "minmin" model. The optimistic solution model of the invention is also a multi-objective problem, and because the constraint condition of the optimistic solution model is the same as that of the pessimistic solution model, the optimistic solution model can be expressed as follows:
further, step S5 is specifically: it is first necessary to find an ideal point and then calculate the distance between each solution in the pareto frontier and the ideal point, where the point with the shortest distance from the ideal point is the compromise solution.
The coordinates of the ideal points are typically the optimal values for each target. For the pessimistic solution model of maxmin in this chapter, the ideal point coordinates are as follows, since the outer layer is the "max" model(Maximum value of mth target in optimal solution set); similarly, the ideal point of the 'minmin' optimistic model is(The minimum of the mth target in the optimal solution set). Because the orders of the targets are different, when the distance from each solution to an ideal point in the pareto frontier is calculated, each target needs to be normalized, and then the weighted distance from each solution to the ideal point is calculated, wherein the specific calculation formula is as follows:
in the formula:the value range of the mth target normalization value is [0,1 ]](ii) a m is a target number;a target value for the mth target of the ith solution in the optimal solution set;the target value of the mth target of the normalized ideal point; di,idealIs the distance between the ith solution and the ideal point; lambda [ alpha ]mWeight coefficients representing the m-th object, the sum of the weight coefficients of the objects being 1, i.e. λ1+λ2＝1。
Calculating d to obtain the distance from each solution to the ideal point in the pareto frontieri,idealThen, d can be obtained by comparisoni,idealThe minimum value, the corresponding solution of which is a compromise solution for the pareto frontier.
Compared with the prior art, the invention has the following beneficial effects: the method and the device optimize the utilization interval in the day-ahead transaction of the power market, reasonably optimize the optimal output interval and the reserve capacity interval of thermal power in the day-ahead market, reduce the electricity purchasing cost of the day-ahead market and the power deviation of the real-time market, provide reference for electricity purchasing decision, more effectively utilize wind resources and increase social benefits.
Drawings
FIG. 1 shows a wind power prediction interval and a load prediction value according to the present invention.
Fig. 2 is an optimistic and pessimistic pareto frontier and compromise solution.
Fig. 3 is a genset parameter.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
The embodiment provides a method for optimizing the power purchase of a day-ahead market of a power system containing wind power based on interval optimization, which specifically comprises the following steps:
step S1, extracting system information, namely extracting wind power interval prediction information, load prediction information, generator set day-ahead energy market quotation information and generator set reserve capacity market quotation information, wherein the network data adopts an IEEE-30 node network, a wind power plant is accessed to the system at a node 26, the installed capacity is 100MW, generator set parameters are shown in figure 3, the wind power prediction information and the load prediction information are shown in figure 1, α is 0.3, and lambda is1＝0.7；λ2＝0.3。
Step S2: targeting 1 to minimize the sum of the cost of the energy market and the cost of the reserve capacity market in the day ahead; establishing a multi-target non-linear interval day-ahead market electricity purchasing optimization model containing wind power by taking the minimum real-time market deviation power as a target 2;
step S3: converting the multi-target non-linear interval day-ahead market electricity purchasing optimization model containing the wind power obtained in the step S2 into optimistic solution and pessimistic solution optimization models;
step S4: solving optimistic and pessimistic solution optimization models by using a multi-target quantum particle swarm algorithm to obtain pareto frontiers of the optimistic and pessimistic solutions, as shown in FIG. 2;
step S5: and (3) solving the pareto frontier compromise between optimistic solution and pessimistic solution by using an ideal point method, and obtaining the optimal power purchasing interval and the optimal spare capacity interval of the thermal power on the market in the day ahead.
In the day-ahead market transaction considering wind power uncertainty, the uncertainty of wind power is represented by an interval, and an interval optimization model containing wind power is established by taking the day-ahead energy market and the reserve capacity market with the minimum cost and the minimum real-time market deviation power as multiple targets. The method can obtain the optimal electricity purchasing interval and the spare capacity interval of the thermal power generating unit in the market at the day before, provide reference for electricity purchasing decision, reduce electricity purchasing cost and reasonably utilize wind resources.
In this embodiment, the step S2 specifically includes the following steps:
step S21: aiming at the minimum sum of the cost of the day-ahead energy market and the cost of the reserve capacity market, a combined clearing model of the day-ahead energy market and the reserve capacity market containing wind power is established, and is expressed by a mathematical function as follows:
where ρ isr,i,tClearing price for the ith thermal power generating unit in the t time period; pi,tThe output of the ith thermal power generating unit in the t time period; t is the number of market periods in the day ahead, wherein T is 24; n is a radical ofGThe number of thermal power generating units;the upper standby capacity price and the lower standby capacity price of the ith thermal power generating unit in the market at the time t and before; cu,i,t、Cd,i,tThe upper and lower spare capacities of the ith thermal power generating unit in the market at t time period before day;
step S22: considering real-time market upper and lower deviation power caused by randomness of wind power, establishing a real-time market power deviation model containing the wind power by taking the minimum weighted deviation power as a target, and expressing the real-time market power deviation model as follows by using a mathematical function:
wherein,is a sectionUpper bound, [ P ]des,t]＝α[Pde,t]+∪-(1-α)[Pde,t]-Wherein α is a weight coefficient, α ═ p (ρ)r,i,t-ρd,i,t)/(ρr,i,t-ρd,i,t+ρu,i,t) Where ρ isu,i,tThe electricity purchase price rho of the i thermal power generating units in the real-time market at the time td,i,tFor selling electricity prices to the i thermal power generating units in the real-time market at the time t,andpositive power deviation interval and negative power deviation interval of t time interval separately;
specifically, in the electric power trading, in order to reduce the offset power of the real-time market, the real-time market price needs to satisfy ρu,i,t≥ρr,i,t≥ρd,i,tWhere ρ isu,i,tThe electricity purchase price rho of the i thermal power generating units in the real-time market at the time td,i,tAnd selling the electricity price to the i thermal power generating units in the real-time market at the time t. If the real-time deviation power is positive, which is equivalent to excessive power output of thermal power purchased in the market at the day before, the thermal power needs to be called for standby and sold in the real-time market, because rhor,i,t≥ρd,i,tEquivalent to ρ in the day-ahead marketr,i,tCan only buy electricity at the price of rhod,i,tThe price of selling, selling unit electric quantity will lose rhor,i,t－ρd,i,tThe total electricity purchase cost is increased. On the other hand, if the real-time deviation power is negative, which is equivalent to the situation that the power purchasing power of the thermal power in the market before the day is too low, the power is calculated by rhou,i,tThe price of (2) is to purchase electricity in real-time market, and the total electricity purchase cost is also increased. The total electricity purchasing cost of the day-ahead market and the real-time market is increased no matter the deviation power of the real-time market is positive or negative, and the electricity purchasing decision maker needs to find the optimal day-ahead market clearing scheme to reduce the day-ahead costMarket and real-time market total costs. Due to uncertainty of wind power output and unknown energy price of the real-time market, the balance cost of the real-time market cannot be accurately calculated. However, the real-time market deviation power is caused by the wind power prediction error, and the real-time market cost can be reduced by reducing the wind power deviation interval, so that the method aims at minimizing the power deviation interval. The real-time market power deviation interval can be expressed as:
in the formula: n is a radical ofwThe number of wind power plants; pL,tLoad prediction value is t time interval; [ P ]de,t]A power deviation interval of t time period, specifically expressed asWhereinThe lower and upper bounds of the power deviation interval.
No matter the electricity is purchased or sold in the real-time market, the loss is generated, and in order to reduce the real-time market transaction electric quantity, the wind electricity purchasing output of the day-ahead market is within the actual wind electricity output interval, namelyAt this time, the lower bound of the deviation interval is less than 0, and the upper bound is greater than 0, namely:and when the real-time market deviation power is positive, electricity needs to be purchased in the real-time market, and when the real-time market deviation power is negative, electricity needs to be sold. Loss rho due to unit purchase in real-time marketu,i,tAnd unit power sale loss (p)r,i,t－ρd,i,t) Differently, the power deviation interval can therefore be divided into two parts:
in the formula: [ P ]de,t]+And [ Pde,t]-The power deviation interval is a positive power deviation interval (a power deviation interval with excessive thermal power purchase power) and a negative power deviation interval (a power deviation interval with insufficient thermal power purchase power) in the period t. [ P ]de,t]+And [ Pde,t]-Can be expressed as:
when the electricity is purchased in the market in the day ahead, a power purchase decision maker cannot know whether the actual power deviation is positive or negative in advance, and needs to comprehensively consider an up-down deviation interval according to a certain weight, so that an up-down deviation weighting interval can be obtained:
[Pdes,t]＝α[Pde,t]+∪-(1-α)[Pde,t]-
α is the weight coefficient:
α＝(ρr,i,t-ρd,i,t)/(ρr,i,t-ρd,i,t+ρu,i,t)
since the real-time market price will satisfy rhou,i,t≥ρr,i,t≥ρd,i,tα is [0,0.5 ]]。
Considering the power deviation intervals of each time interval of the market in the future comprehensively, the target 2 can be specifically expressed as:
from the above formula, the target 2 value is one interval number, and the comparison of the interval number is difficult, however [ P ]de,t]+And [ Pde,t]-The lower bound of (2) is 0, and the lower bound of the interval of the target 2 value is also 0, so when comparing the size of the target 2 interval, only the size of the upper bound of the target 2 interval needs to be compared, and therefore the target 2 can be converted into:
in the formula:is the interval [ Pdes,t]And (4) an upper bound.
Step S23: the invention relates to a method for establishing a power purchasing output model of a day-ahead market containing wind power under the condition of considering the wind power output as one interval number, which comprises two sets of constraints: and establishing the daily market clearing plan constraint and the interval constraint when the wind power output is changed in the output interval range.
In this embodiment, in step S23, the day-ahead market clearing plan constraint includes:
(1) output restraint of the thermal power generating unit: in the market clearing plan before the day, the output of the thermal power generating unit needs to meet the output constraint of the unit and the upper and lower climbing rate constraints:
max(Pi,min,Ri,down×Δt)≤Pi,t-Cd,i,t≤min(Pi,max,Ri,up×Δt)；
max(Pi,min,Ri,down×Δt)≤Pi,t+Cu,i,t≤min(Pi,max,Ri,up×Δt)；
wherein R isi,down、Ri,upThe up-down climbing speed of the ith thermal power generating unit; pi,min、Pi,maxMaximum and minimum of the ith thermal power generating unit respectivelyForce is exerted; the delta t is two time interval, in the invention, the delta t is one hour;
the market reserve capacity constraint may be expressed as:
in the formula:maximum upper and lower spare capacities declared for the ith unit in the t time period;
(2) and power balance constraint: the power balance constraint for the day-ahead market clearing plan may be expressed as:
wherein,the power output of the wind power purchase of the fresh plan for the market at the day-ahead; pL,tIs the load of the system for the period t; n is a radical ofWThe number of wind power plants;
(3) and (3) alternating current power flow constraint: the ac power flow constraint for a day-ahead market clearing plan may be expressed as:
-Pl,max≤Pl,t≤Pl,max；
wherein, Pl,tIs the power flow of the line l in the time period t; pl,maxIs the maximum power flow of line l;
(4) system spare capacity constraint: when wind power actual output fluctuates in the output interval range, power deviation can be generated, and in order to reduce abandoned wind, enough spare capacity needs to be purchased:
wherein, Cd,t、Cu,tRespectively represent the purchase amount of the upper and lower spare capacities in the period t,the lower bound and the upper bound of the power deviation interval are respectively; the power can change along with the change of the power purchased in the market at the day before;
(5) node voltage constraint: the node voltage constraint for the market clearing program at the day-ahead may be expressed as:
Un,min≤Un,t≤Un,max；
wherein, Un,tRepresents the node voltage of the node n in the period t; u shapen,min、Un,maxNode voltages at which the node n is minimum and maximum are respectively obtained;
(6) and (3) wind power purchase output interval constraint: the wind power purchase output constraint of the market export plan at the day-ahead may be expressed as:
wherein,the power output is purchased for the wind power in the market at the day before,andrespectively representing the lower bound and the upper bound of the actual wind power output;
in this embodiment, in step S23, the satisfying the section constraint when the wind power output varies within the output section range includes:
(1) output interval constraint of the thermal power generating unit: when the electricity purchasing power of the wind power is outputIn the wind power prediction output intervalDuring internal variation, the optimal output interval consisting of the optimal output of the ith unit in the t periodShould be within the backup adjustment range:
wherein,the ith unit is in the optimal thermal power purchase power output interval at the t time periodAny value within;respectively is the lower bound and the upper bound of the t-time period output interval of the ith unit,maximum upper and lower spare capacities declared for the ith unit in the t time period;
(2) and power balance constraint: when wind powerPower of purchased electricityIn the wind power prediction output intervalIn internal variation, the day-ahead market power balance constraint may be expressed as:
wherein,the power output of the wind power purchase is possible in the wind power output interval at the t time period of the jth wind power plant;
(3) and (3) power flow constraint: when the power purchasing and outputting of the wind power is changed within the output interval range, the alternating current power flow is within the constraint range:
wherein,when the power purchasing and output of the wind power is changed in the output interval, the line l is in the alternating current power flow interval of the t periodPossible tidal current value, whereinThe lower boundary and the upper boundary of the alternating current power flow interval of the line l in the t period are respectively;
(4) node voltage constraint: when the power purchasing and outputting of the wind power is changed within the output interval range, the node voltage is within the constraint range:
wherein,when the power purchasing and output of the wind power is changed in the output interval, the node n in the t period is in the node voltage intervalInternal possible node voltage values, whereinThe lower bound and the upper bound of the node voltage interval in the t period are respectively;
(5) and (3) wind power purchase output interval constraint: the wind power purchase output constraint of the market export plan at the day-ahead may be expressed as:
in this embodiment, in step S3, the model of the present invention is a multi-objective nonlinear interval programming model, and an interval solution of the model, that is, the electricity purchasing schemes corresponding to the upper and lower solutions of the objective function, needs to be solved. In order to obtain the interval solution of the model, the invention converts the interval solution into two multi-target nonlinear programming problems, namely an optimistic solution model and a pessimistic solution model. Wherein the pessimistic solution is a solution corresponding to an upper bound of the objective function, and the optimistic solution is a solution corresponding to a lower bound of the objective function
The pessimistic solution optimization model is expressed as:
since there are two targets in the model of the method, it isFor convenience of understanding, the meaning of the pessimistic understanding model is explained by taking the electricity purchasing cost target as an example: when the electricity purchasing and output of wind power is the output intervalWhen any value is within the range, an optimal day-ahead market electricity purchasing scheme can be found, so that the total electricity purchasing cost is minimum. For different wind power electricity purchasing outputs, the minimum total electricity purchasing cost is different, wherein the minimum total electricity purchasing cost is the pessimistic solution; conversely, the solution with the minimum total cost is an optimistic solution and can be represented by a "minmin" model. The optimistic solution model of the invention is also a multi-objective problem, and because the constraint condition of the optimistic solution model is the same as that of the pessimistic solution model, the optimistic solution model can be expressed as follows:
in this embodiment, step S5 specifically includes: it is first necessary to find an ideal point and then calculate the distance between each solution in the pareto frontier and the ideal point, where the point with the shortest distance from the ideal point is the compromise solution.
The coordinates of the ideal points are typically the optimal values for each target. For the pessimistic solution model of maxmin in this chapter, the ideal point coordinates are as follows, since the outer layer is the "max" model(Maximum value of mth target in optimal solution set); similarly, the ideal point of the 'minmin' optimistic model is(For the mth one in the optimal solution setThe minimum value of the target). Because the orders of the targets are different, when the distance from each solution to an ideal point in the pareto frontier is calculated, each target needs to be normalized, and then the weighted distance from each solution to the ideal point is calculated, wherein the specific calculation formula is as follows:
in the formula:the value range of the mth target normalization value is [0,1 ]](ii) a m is a target number;a target value for the mth target of the ith solution in the optimal solution set;the target value of the mth target of the normalized ideal point; di,idealIs the distance between the ith solution and the ideal point; lambda [ alpha ]mWeight coefficients representing the m-th object, the sum of the weight coefficients of the objects being 1, i.e. λ1+λ2＝1。
Calculating d to obtain the distance from each solution to the ideal point in the pareto frontieri,idealThen, d can be obtained by comparisoni,idealThe minimum value, the corresponding solution of which is a compromise solution for the pareto frontier.
In the embodiment, an optimistic compromise solution S is obtained by using an ideal point methodo(coordinates are (f)1,o,f2,o) Pessimistic solution S) and pessimistic solutionp(coordinates are (f)1,p,f2,p) And as shown in fig. 2), the optimal power purchasing section and the spare capacity section of the thermal power are obtained. Benefit toPessimistic compromise solution S obtained by ideal point methodpTarget function value f of1,pAnd f2,p259.8 ten thousand yuan and 224.53MW respectively, and the deviation interval on the real-time market power is 0,451.05]MW, lower deviation interval [ -142.05,0 [)]MW; optimistic compromise solution SoTarget function value f of1,oAnd f2,o245.9 ten thousand yuan and 315.88MW respectively, wherein the deviation interval on the real-time market power is [0,141.95 ]]MW, lower deviation interval [ -451.15,0 [)]MW。
The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.

Claims (6)

1. A method for optimizing the electricity purchase of the day-ahead market of a wind power-containing power system based on interval optimization is characterized by comprising the following steps of: the method comprises the following steps:
step S1: extracting system information: extracting wind power interval prediction information, load prediction information, generator set day-ahead energy market quotation information and generator set reserve capacity market quotation information;
step S2: targeting 1 to minimize the sum of the cost of the energy market and the cost of the reserve capacity market in the day ahead; establishing a multi-target non-linear interval day-ahead market electricity purchasing optimization model containing wind power by taking the minimum real-time market deviation power as a target 2;
step S3: converting the multi-target non-linear interval day-ahead market electricity purchasing optimization model containing the wind power obtained in the step S2 into optimistic solution and pessimistic solution optimization models;
step S4: solving optimistic and pessimistic solution optimization models by using a multi-target quantum particle swarm algorithm to obtain pareto frontiers of the optimistic and pessimistic solutions;
step S5: and (3) solving the pareto frontier compromise between optimistic solution and pessimistic solution by using an ideal point method, and obtaining the optimal power purchasing interval and the optimal spare capacity interval of the thermal power on the market in the day ahead.
2. The interval optimization-based optimization method for power purchase in the day-ahead market of the wind power-containing power system according to claim 1, wherein the interval optimization-based optimization method comprises the following steps: the step S2 specifically includes the following steps:
step S21: aiming at the minimum sum of the cost of the day-ahead energy market and the cost of the reserve capacity market, a combined clearing model of the day-ahead energy market and the reserve capacity market containing wind power is established, and is expressed by a mathematical function as follows:
where ρ isr,i,tClearing price for the ith thermal power generating unit in the t time period; pi,tThe output of the ith thermal power generating unit in the t time period; t is the number of market periods in the day ahead, wherein T is 24; n is a radical ofGThe number of thermal power generating units;the upper standby capacity price and the lower standby capacity price of the ith thermal power generating unit in the market at the time t and before; cu,i,t、Cd,i,tThe upper and lower spare capacities of the ith thermal power generating unit in the market at t time period before day;
step S22: considering real-time market upper and lower deviation power caused by randomness of wind power, establishing a real-time market power deviation model containing the wind power by taking the minimum weighted deviation power as a target, and expressing the real-time market power deviation model as follows by using a mathematical function:
wherein,is the interval [ Pdes,t]Upper bound, [ P ]des,t]＝α[Pde,t] + ∪-(1-α)[Pde,t]-Wherein α is a weight coefficient, α ═ p (ρ)r,i,t-ρd,i,t)/(ρr,i,t-ρd,i,t+ρu,i,t) Where ρ isu,i,tThe electricity purchase price rho of the i thermal power generating units in the real-time market at the time td,i,tFor the electricity selling price from the i thermal power generating units in the real-time market at the time t, [ P ]de,t]+And [ Pde,t]-Positive power deviation interval and negative power deviation interval of t time interval separately;
step S23: and establishing the daily market clearing plan constraint and the interval constraint when the wind power output is changed in the output interval range.
3. The interval optimization-based optimization method for power purchase in the day-ahead market of the wind power-containing power system according to claim 2, characterized by comprising the following steps: in step S23, the day-ahead market clearing plan constraint includes:
(1) output restraint of the thermal power generating unit: the output of the thermal power generating unit needs to meet the output constraint of the unit and the upper and lower climbing rate constraints:
max(Pi,min,Ri,down×Δt)≤Pi,t-Cd,i,t≤min(Pi,max,Ri,up×Δt)；
max(Pi,min,Ri,down×Δt)≤Pi,t+Cu,i,t≤min(Pi,max,Ri,up×Δt)；
wherein R isi,down、Ri,upThe up-down climbing speed of the ith thermal power generating unit; pi,min、Pi,maxThe maximum output and the minimum output of the ith thermal power generating unit are respectively; Δ t is two time interval;
(2) and power balance constraint:
wherein,the power output of the wind power purchase of the fresh plan for the market at the day-ahead; pL,tIs the load of the system for the period t; n is a radical ofWThe number of wind power plants;
(3) and (3) alternating current power flow constraint:
-Pl,max≤Pl,t≤Pl,max；
wherein, Pl,tIs the power flow of the line l in the time period t; pl,maxIs the maximum power flow of line l;
(4) system spare capacity constraint:
wherein, Cd,t、Cu,tRespectively represent the purchase amount of the upper and lower spare capacities in the period t,the lower bound and the upper bound of the power deviation interval are respectively;
(5) node voltage constraint:
Un,min≤Un,t≤Un,max；
wherein, Un,tRepresents the node voltage of the node n in the period t; u shapen,min、Un,maxNode voltages at which the node n is minimum and maximum are respectively obtained;
(6) and (3) wind power purchase output interval constraint:
wherein,the power output is purchased for the wind power in the market at the day before,andrespectively representing the lower bound and the upper bound of the actual wind power output;
4. the interval optimization-based optimization method for power purchase in the day-ahead market of the wind power-containing power system according to claim 2, characterized by comprising the following steps: in step S23, the satisfying of the section constraint when the wind power output changes within the output section range includes:
(1) output interval constraint of the thermal power generating unit:
wherein,the ith unit is in the optimal thermal power purchase power output interval at the t time periodAny value within;respectively is the lower bound and the upper bound of the t-time period output interval of the ith unit,maximum upper and lower spare capacities declared for the ith unit in the t time period;
(2) and power balance constraint:
wherein,the power output of the wind power purchase is possible in the wind power output interval at the t time period of the jth wind power plant;
(3) and (3) power flow constraint:
wherein,when the power purchasing and output of the wind power is changed in the output interval, the line l is in the alternating current power flow interval of the t periodPossible tidal current value, whereinThe lower boundary and the upper boundary of the alternating current power flow interval of the line l in the t period are respectively;
(4) node voltage constraint:
wherein,when the power purchasing and output of the wind power is changed in the output interval, the node n in the t period is in the node voltage intervalInternal possible node voltage values, whereinThe lower bound and the upper bound of the node voltage interval in the t period are respectively;
(5) and (3) wind power purchase output interval constraint:
5. the interval optimization-based optimization method for power purchase in the day-ahead market of the wind power-containing power system according to claim 1, wherein the interval optimization-based optimization method comprises the following steps: in the step S3, in the step S,
the pessimistic solution optimization model is expressed as:
the optimistic solution optimization model is represented as:
6. the interval optimization-based optimization method for power purchase in the day-ahead market of the wind power-containing power system according to claim 1, wherein the interval optimization-based optimization method comprises the following steps: step S5 specifically includes: it is first necessary to find an ideal point and then calculate the distance between each solution in the pareto frontier and the ideal point, where the point with the shortest distance from the ideal point is the compromise solution.
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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110071504A (en) * 2019-05-15 2019-07-30 长沙理工大学 A kind of distribution optimizing operation method handled based on wind-powered electricity generation and electricity price interval number
CN110516832A (en) * 2019-06-17 2019-11-29 南方电网科学研究院有限责任公司 Standby clearing method and device for cross-regional consumption of renewable energy sources and electronic equipment
CN110829502A (en) * 2019-10-17 2020-02-21 广西电网有限责任公司电力科学研究院 Multi-target interval power generation scheduling method considering new energy
CN113904364A (en) * 2021-09-18 2022-01-07 北京交通大学 Method for making day-ahead power dispatching plan of wind power cluster

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110071504A (en) * 2019-05-15 2019-07-30 长沙理工大学 A kind of distribution optimizing operation method handled based on wind-powered electricity generation and electricity price interval number
CN110516832A (en) * 2019-06-17 2019-11-29 南方电网科学研究院有限责任公司 Standby clearing method and device for cross-regional consumption of renewable energy sources and electronic equipment
CN110516832B (en) * 2019-06-17 2022-04-12 南方电网科学研究院有限责任公司 Standby clearing method and device for cross-regional consumption of renewable energy sources and electronic equipment
CN110829502A (en) * 2019-10-17 2020-02-21 广西电网有限责任公司电力科学研究院 Multi-target interval power generation scheduling method considering new energy
CN110829502B (en) * 2019-10-17 2022-06-21 广西电网有限责任公司电力科学研究院 Multi-target interval power generation scheduling method considering new energy
CN113904364A (en) * 2021-09-18 2022-01-07 北京交通大学 Method for making day-ahead power dispatching plan of wind power cluster
CN113904364B (en) * 2021-09-18 2024-04-09 北京交通大学 Method for making wind power cluster day-ahead power scheduling plan

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