CN105956799B - Method for evaluating rotating standby benefit and risk of wind power-containing power system - Google Patents
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Abstract
The invention relates to a method for evaluating the benefit and risk of a rotating reserve of a power system containing wind power. The method for evaluating the benefit and risk of the rotating reserve of the power system containing the wind power can describe the relationship between the benefit and risk of the rotating reserve more intuitively and provide reference for a rotating reserve decision maker to make a rotating reserve plan and expect the evaluation of the benefit and risk of the rotating reserve.
Description
Technical Field
The invention relates to the field of electric power market analysis, in particular to a method for evaluating rotating standby benefit and risk of a wind power-containing electric power system.
Background
Large-scale wind power integration has great influence on the reliability and economy of a power system; because the randomness of the load power and the wind power causes great difficulty in the formulation of a system rotation standby plan, the related documents also carry out a great deal of research and obtain a lot of research results. However, currently, evaluation research on standby benefits and risks of large-scale wind power grid-connected rotation is few. The system purchases the rotary standby to ensure the reliability of the system, and simultaneously strives for the rotary standby to generate the maximum benefit and reduce the risk of the system. Therefore, how to balance the benefit and risk of spinning reserve to make spinning reserve capacity is a significant issue.
With large-scale wind power integration, the difficulty of making a system rotation standby plan is increased, and the evaluation of the rotation standby benefit and risk of a wind power-containing power system has important significance on the development of renewable energy sources and the guarantee of the reliability and the economy of the system. Due to the randomness and uncertainty factors of load power and wind power output, the rotating reserve benefit of the wind power-containing power system becomes an uncertain factor and is difficult to accurately estimate, and therefore the risk of the rotating reserve benefit needs to be evaluated.
Disclosure of Invention
In view of the above, the present invention provides a method for evaluating the benefit and risk of a rotating reserve of a power system including wind power, which can describe the relationship between the benefit and risk of the rotating reserve more intuitively, and provide a reference for a rotating reserve decider to make a rotating reserve plan and evaluate the benefit and risk of an expected rotating reserve.
The invention is realized by adopting the following scheme: a method for evaluating the benefits and risks of a rotating standby power system containing wind power specifically comprises the following steps:
step S1: extracting capacity price, energy price, unit load loss price and wind abandoning price of the system rotation standby;
step S2: establishing a maximum system rotation standby benefit expected value model; and due to the prediction deviation of the load power and the wind power output, the rotating reserve benefit is not a determined value, and therefore the expected rotating reserve benefit is used as an estimated value of the rotating reserve benefit. Defining the model: the difference between the expected value of the loss reduction due to purchase of spinning reserve and the expected value of the cost required for spinning reserve within the system 24h is maximized as follows using a mathematical function:
wherein, E (V)t)、E(Wt) Respectively, an expectation value for reducing loss of load due to rotation of the reserve at the time of purchase and an expectation value for reducing loss of wind curtailment due to rotation of the reserve at the time of purchase; e (B)u·t)、E(Bd·t) Expected values for spinning reserve and spinning reserve energy costs over a period of t, respectively; cu·t、Cd·tCapacity costs for spinning reserve and spinning reserve down over a period of t, respectively;
step S3: establishing a minimum system rotation standby benefit risk model: measuring the risk of the rotary reserve benefit by adopting a weighted half-variance method, and describing the relationship between the income degree and the loss degree;
step S4: and solving the expected rotary standby benefit and risk value.
Further, the step S2 specifically includes the following steps:
step S21: loss of load V during period t due to reduced spin reserve on purchaset：
Vt＝qLloss·tQLloss·t；
Wherein q isLloss·t、QLloss·tRespectively, unit lost load loss during the t period and reduced lost load power due to spinning reserve on purchase;
wherein Q isLloss·tTaking the spare capacity R of the rotary spare in the t periodu·tAnd actually rotating reserve capacity demand Mu·tMinimum of (2):
QLloss·t＝min[Mu·t,Ru·t]；
step S22: wind curtailment loss W reduced by purchasing spinning reserve at time tt：
Wt＝qWloss·tQWloss·t；
Wherein q isWloss·t、QWloss·tRespectively the unit wind abandon loss in the time period t and the wind abandon power reduced by purchasing the rotary standby;
wherein Q isWloss·tSpare capacity R for rotating spare at t time intervald·tAnd actual rotational reserve capacity demand Md·tMinimum of (2):
QWloss·t＝min[Md·t,Rd·t]；
step S23: capacity cost and energy cost due to purchase of up-down spinning reserve for period t:
Cu·t＝ru·tRu·t；Cd·t＝rd·tRd·t；
Bu·t＝hu·tHu·t；Bd·t＝hd·tHd·t；
E(Bu·t)＝hu·tE(Hu·t)；E(Bd·t)＝hd·tE(Hd·t)；
wherein the content of the first and second substances,ru·t、hu·t、rd·t、hd·trespectively the capacity price and the energy price of the spinning reserve and the capacity price and the energy price of the lower spinning reserve in the t period; hu·t、Hd·tRespectively, the call volume of the actual up-down rotation reserve capacity, which is respectively equal to QLloss·tAnd QWloss·t；E(Hu·t)、E(Hd·t) Respectively expected values of the spinning reserve and the spinning reserve call amount in the t time period;
step S24: approximately considering the load prediction deviation as normal distribution with the mean value of zero, and adopting Laplace normal mixed distribution for the wind power output prediction deviation; simulating the prediction deviation of the actual load power and the wind power output by adopting a Monte Carlo method, wherein each possible prediction deviation corresponds to an actual equivalent load random state; obtaining expected value (E (V)) of corresponding part by Monte Carlo method simulated datat)、E(Wt)、E(Bu·t)、E(Bd·t)。
Further, the step S3 is specifically: the weighted difference of the two half-variances for the rotational reserve benefit above and below the rotational reserve benefit expected value is expressed as a mathematical function as follows:
wherein, II and E (II) respectively represent the rotating reserve benefit and the expected value of the rotating reserve benefit of the system within 24 h; i is a set of actual equivalent load random states; lambda [ alpha ]iIs the probability of occurrence of the ith state; alpha is a risk preference coefficient and is a sign of the degree of risk aversion;
wherein the content of the first and second substances,
further, the step S4 includes the following constraints: standby opportunity constraint and wind power plant active output constraint;
the alternate opportunity constraint is: in order to ensure the reliability requirement of the system, the rotary standby is required to meet certain probability of load power fluctuation and wind power output fluctuation. Defined from a single time period, the probability of ensuring that the rotating standby meets the system equivalent load prediction deviation within the single time period is not less than a given value and is expressed by a mathematical function as follows:
Pr{Ru·t≥Pt-Pf·t}≥γ；
Pr{Rd·t≥Pf·t-Pt}≥δ；
wherein, Pf·t、PtRespectively predicting the equivalent load and the actual equivalent load for the system in the period t; the reliability levels gamma and delta are respectively the upper limit values allowed by the loss load probability and the wind abandoning probability of the market at the day before;
the system predicted equivalent load is the difference between the day-ahead load power predicted value and the wind power output predicted value, the system actual equivalent load is the difference between the actual load power and the actual wind power output, and the system predicted equivalent load is expressed by a mathematical function as follows:
Pf·t＝PLf·t-PWf·t；
Pt＝PL·t-PW·t＝PLf·t+ΔPL·t-(PWf·t+ΔPW·t)；
wherein, PLf·t、PWf·tRespectively a day-ahead load power predicted value and a wind power output predicted value in a t period; pL·t、PW·tActual load power and wind power output are respectively in a time period t; delta PL·t、ΔPW·tRespectively predicting deviation of load power and wind power output in a time period t, and obtaining random variables which obey certain probability distribution;
the wind power plant active power output constraint is expressed by a mathematical function as follows:
wherein the content of the first and second substances,
the maximum active output of the wind farm.
Further, in step S4, the maximum expected rotational reserve benefit and the minimum risk are used as a multi-target model, and a multi-target particle swarm algorithm based on an extreme value comprehensive strategy is used to perform optimization calculation to solve the expected rotational reserve benefit and the risk value:
wherein the global optimum particle GiThe selection strategy of best is: using different GiSelecting the optimal particles in the population by the combination of best selection strategies, wherein the global optimal of the particles is obtained by three strategies:
strategy 1: randomly selecting a non-dominant solution from the non-inferior solution set of the external archive as a global optimum, and recording the global optimum as the gbest1；
Strategy 2: according to the dense distance of the non-inferior solution of the external archive, performing descending order arrangement on the non-dominant solution, and randomly selecting one particle from the top 10% of the dense distance as a global optimum which is recorded as gbest2(ii) a Wherein the dense distance does not include a dense distance of two endpoints;
strategy 3: randomly selecting one particle from two extreme values in the non-inferior solution set as global optimum, and recording the global optimum as the gbest3(ii) a Strategy 3 is an extreme value selection strategy;
let the number of particles be m, and in each iteration, select a of the particles to be gbest1For global optimization, select b particles among them to be gbest2For global optimization, (m-a-b) of the particles are selected to be gbest3The global optimization is achieved, and a and b meet the condition that a + b is less than m;
wherein the particle velocity and position are updated as:
vi(n+1)＝ωvi(n)+c1r1(pibest-xi(n))
+c2r2[Gibest·Zi-xi(n)]；
xi(n+1)＝xi(n)+vi(n+1)；
wherein G isibest is the global optimal vector of the ith particle; ziIs a coefficient vector; p is a radical ofibest is the individual optimal particle; omega is an inertia weight; r is1And r2Is [0,1 ]]A random number in between; n is the current iteration number; c. C1And c2Is a constant; v is the particle velocity; x is the particle position;
wherein G isibest＝[gbest1,gbest2,gbest3]，Zi＝[z1,z2,z3]T(ii) a From the above analysis, it can be seen that: if i is less than or equal to a, Zi＝[1,0,0]T(ii) a If a<i≤b，Zi＝[0,1,0]T(ii) a Otherwise, Zi＝[0,0,1]T。
Compared with the prior art, the invention has the following beneficial effects: the invention considers the capacity cost and the energy cost of the vertical rotation reserve of the system, the system loss reduced by purchasing the rotation reserve and the discrete degree of the rotation reserve benefit to establish a multi-objective model, and the model comprehensively reflects the influence of the rotation reserve on the system rotation reserve benefit and risk after wind power integration and describes the relationship between the rotation reserve benefit and the risk. And simulating the actual load power and the wind power output by adopting a Monte Carlo method, and solving by adopting a multi-target particle swarm algorithm based on an extreme value comprehensive strategy to obtain the expected rotary standby benefit-risk effective front and day-ahead rotary standby plans, as well as the risk preference coefficient, the reliability level, the prediction deviation and the influence on the expected rotary standby benefit and risk. And providing reference for the reserve decision maker to make a rotary reserve plan and estimate the expected rotary reserve benefit and risk, and realizing the balance of the rotary reserve benefit and the risk.
Drawings
FIG. 1 is a schematic flow chart of the principle of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
As shown in fig. 1, the present embodiment provides a method for evaluating the benefit and risk of a rotating backup of a wind power system, which specifically includes the following steps:
step S1: extracting capacity price, energy price, unit load loss price and wind abandoning price of the system rotation standby;
step S2: establishing a maximum system rotation standby benefit expected value model; and due to the prediction deviation of the load power and the wind power output, the rotating reserve benefit is not a determined value, and therefore the expected rotating reserve benefit is used as an estimated value of the rotating reserve benefit. Defining the model: the difference between the expected value of the loss reduction due to purchase of spinning reserve and the expected value of the cost required for spinning reserve within the system 24h is maximized as follows using a mathematical function:
wherein, E (V)t)、E(Wt) Respectively, an expectation value for reducing loss of load due to rotation of the reserve at the time of purchase and an expectation value for reducing loss of wind curtailment due to rotation of the reserve at the time of purchase; e (B)u·t)、E(Bd·t) Expected values for spinning reserve and spinning reserve energy costs over a period of t, respectively; cu·t、Cd·tCapacity costs for spinning reserve and spinning reserve down over a period of t, respectively;
step S3: establishing a minimum system rotation standby benefit risk model: measuring the risk of the rotary reserve benefit by adopting a weighted half-variance method, and describing the relationship between the income degree and the loss degree;
step S4: and solving the expected rotary standby benefit and risk value.
In this embodiment, the step S2 specifically includes the following steps:
step S21: loss of load V during period t due to reduced spin reserve on purchaset：
Vt＝qLloss·tQLloss·t；
Wherein q isLloss·t、QLloss·tThe unit load loss and purchase loss in the period t are respectivelyReduced power loss from spinning reserve;
wherein Q isLloss·tTaking the spare capacity R of the rotary spare in the t periodu·tAnd actually rotating reserve capacity demand Mu·tMinimum of (2):
QLloss·t＝min[Mu·t,Ru·t]；
step S22: wind curtailment loss W reduced by purchasing spinning reserve at time tt：
Wt＝qWloss·tQWloss·t；
Wherein q isWloss·t、QWloss·tRespectively the unit wind abandon loss in the time period t and the wind abandon power reduced by purchasing the rotary standby;
wherein Q isWloss·tSpare capacity R for rotating spare at t time intervald·tAnd actual rotational reserve capacity demand Md·tMinimum of (2):
QWloss·t＝min[Md·t,Rd·t]；
step S23: capacity cost and energy cost due to purchase of up-down spinning reserve for period t:
Cu·t＝ru·tRu·t；Cd·t＝rd·tRd·t；
Bu·t＝hu·tHu·t；Bd·t＝hd·tHd·t；
E(Bu·t)＝hu·tE(Hu·t)；E(Bd·t)＝hd·tE(Hd·t)；
wherein r isu·t、hu·t、rd·t、hd·tRespectively the capacity price and the energy price of the spinning reserve and the capacity price and the energy price of the lower spinning reserve in the t period; hu·t、Hd·tRespectively, the call volume of the actual up-down rotation reserve capacity, which is respectively equal to QLloss·tAnd QWloss·t；E(Hu·t)、E(Hd·t) Respectively rotating over a period of tExpected values of the amount of reserve calls for use and for down-rotation;
step S24: approximately considering the load prediction deviation as normal distribution with the mean value of zero, and adopting Laplace normal mixed distribution for the wind power output prediction deviation; simulating the prediction deviation of the actual load power and the wind power output by adopting a Monte Carlo method, wherein each possible prediction deviation corresponds to an actual equivalent load random state; obtaining expected value (E (V)) of corresponding part by Monte Carlo method simulated datat)、E(Wt)、E(Bu·t)、E(Bd·t)。
In this embodiment, the step S3 specifically includes: the weighted difference of the two half-variances for the rotational reserve benefit above and below the rotational reserve benefit expected value is expressed as a mathematical function as follows:
wherein, II and E (II) respectively represent the rotating reserve benefit and the expected value of the rotating reserve benefit of the system within 24 h; i is a set of actual equivalent load random states; lambda [ alpha ]iIs the probability of occurrence of the ith state; alpha is a risk preference coefficient and is a sign of the degree of risk aversion;
wherein the content of the first and second substances,
in this embodiment, the step S4 includes the following constraints: standby opportunity constraint and wind power plant active output constraint;
the alternate opportunity constraint is: in order to ensure the reliability requirement of the system, the rotary standby is required to meet certain probability of load power fluctuation and wind power output fluctuation. Defined from a single time period, the probability of ensuring that the rotating standby meets the system equivalent load prediction deviation within the single time period is not less than a given value and is expressed by a mathematical function as follows:
Pr{Ru·t≥Pt-Pf·t}≥γ；
Pr{Rd·t≥Pf·t-Pt}≥δ；
wherein, Pf·t、PtRespectively predicting the equivalent load and the actual equivalent load for the system in the period t; the reliability levels gamma and delta are respectively the upper limit values allowed by the loss load probability and the wind abandoning probability of the market at the day before;
the system predicted equivalent load is the difference between the day-ahead load power predicted value and the wind power output predicted value, the system actual equivalent load is the difference between the actual load power and the actual wind power output, and the system predicted equivalent load is expressed by a mathematical function as follows:
Pf·t＝PLf·t-PWf·t；
Pt＝PL·t-PW·t＝PLf·t+ΔPL·t-(PWf·t+ΔPW·t)；
wherein, PLf·t、PWf·tRespectively a day-ahead load power predicted value and a wind power output predicted value in a t period; pL·t、PW·tActual load power and wind power output are respectively in a time period t; delta PL·t、ΔPW·tRespectively predicting deviation of load power and wind power output in a time period t, and obtaining random variables which obey certain probability distribution;
the wind power plant active power output constraint is expressed by a mathematical function as follows:
wherein the content of the first and second substances,
the maximum active output of the wind farm.
Preferably, in this embodiment, the expected rotary standby benefit and the expected rotary standby risk are taken as a multi-target model, and a multi-target particle swarm algorithm based on an extreme value comprehensive strategy is adopted to perform optimization calculation to solve the expected rotary standby benefit and the expected rotary standby risk.
Wherein the global optimum particle GiSelection strategy of best:
this example uses different GiSelecting the optimal particles in the population by the combination of best selection strategies, wherein the global optimal of the particles is obtained by three strategies:
strategy 1: randomly selecting a non-dominant solution from the non-inferior solution set of the external archive as a global optimum, and recording the global optimum as the gbest1。
Strategy 2: according to the dense distance of the non-inferior solution of the external archive, performing descending order arrangement on the non-dominant solution (excluding the dense distance of two end points), and arbitrarily selecting one particle from the top 10% of the dense distance as a global optimum, which is recorded as gbest2。
Strategy 3 (extreme selection strategy): randomly selecting one particle from two extreme values in the non-inferior solution set as global optimum, and recording the global optimum as the gbest3。
Strategy 1 is simple to operate, but each non-dominant solution has the same probability of being selected, so that the probability of selecting a region with dense particles is high, and global search is not facilitated. Strategy 2 improves the probability of dense and distant particles being selected, but the global search capability is not sufficient. Strategy 3 improves the searching capability of the particle edge, expands the range of the non-dominant solution set, but is not beneficial to the distribution of Pareto optimal boundaries. Therefore, the invention combines the three selection strategies for the selection of the globally optimal particles.
Let the number of particles be m, and in each iteration, select a of the particles to be gbest1For global optimization, select b particles among them to be gbest2For global optimization, (m-a-b) of the particles are selected to be gbest3The global optimum is achieved, and a and b satisfy a + b < m.
Wherein the particle velocity and position are updated as:
vi(n+1)＝ωvi(n)+c1r1(pibest-xi(n))
+c2r2[Gibest·Zi-xi(n)]；
xi(n+1)＝xi(n)+vi(n+1)；
wherein G isibest is the global optimal vector of the ith particle; ziIs a coefficient vector; p is a radical ofibest is the individual optimal particle; omega is an inertia weight; r is1And r2Is [0,1 ]]A random number in between; n is the current iteration number; c. C1And c2Is a constant; v is the particle velocity; x is the particle position.
Wherein G isibest＝[gbest1,gbest2,gbest3]，Zi＝[z1,z2,z3]T. From the above analysis, it can be seen that: if i is less than or equal to a, Zi＝[1,0,0]T(ii) a If a<i≤b，Zi＝[0,1,0]T(ii) a Otherwise, Zi＝[0,0,1]T。
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 (1)
1. A method for evaluating the benefit and risk of a rotating standby power system containing wind power is characterized by comprising the following steps: the method comprises the following steps:
step S1: extracting capacity price, energy price, unit load loss price and wind abandoning price of the system rotation standby;
step S2: establishing a maximum system rotation standby benefit expected value model; defining the model: the system has the greatest difference between the expected value for loss reduction due to purchase of spinning reserve and the expected value for the cost required for spinning reserve in 24 hours, expressed as a mathematical function:
wherein, E (V)t)、E(Wt) Reducing lost load loss due to spinning reserve on purchase during time t, respectivelyAnd an expectation of reducing wind curtailment losses due to purchase of spinning reserve; e (B)u·t)、E(Bd·t) Expected values for spinning reserve and spinning reserve energy costs over a period of t, respectively; cu·t、Cd·tCapacity costs for spinning reserve and spinning reserve down over a period of t, respectively;
step S3: establishing a minimum system rotation standby benefit risk model: measuring the risk of the rotary reserve benefit by adopting a weighted half-variance method, and describing the relationship between the income degree and the loss degree;
step S4: obtaining expected rotary reserve benefit by solving through the maximum system rotary reserve benefit expected value model established in the step S2, and obtaining expected risk value by solving through the minimum system rotary reserve benefit risk model established in the step S3, so as to describe the relation between the rotary reserve benefit and the risk of the wind power-containing power system;
wherein, the step S2 specifically includes the following steps:
step S21: loss of load V during period t due to reduced spin reserve on purchaset：
Vt＝qLloss·tQLloss·t；
Wherein q isLloss·t、QLloss·tRespectively, unit lost load loss during the t period and reduced lost load power due to spinning reserve on purchase;
wherein Q isLloss·tTaking the spare capacity R of the rotary spare in the t periodu·tAnd actually rotating reserve capacity demand Mu·tMinimum of (2):
QLloss·t＝min[Mu·t，Ru·t]；
step S22: wind curtailment loss W reduced by purchasing spinning reserve at time tt：
Wt＝qWloss·tQWloss·t；
Wherein q isWloss·t、QWloss·tRespectively the unit wind abandon loss in the time period t and the wind abandon power reduced by purchasing the rotary standby;
wherein Q isWloss·tSpare capacity R for rotating spare at t time intervald·tAnd actual rotational reserve capacity demand Md·tMinimum of (2):
QWloss·t＝min[Md·t，Rd·t]；
step S23: capacity cost and energy cost due to purchase of up-down spinning reserve for period t:
Cu·t＝ru·tRu·t；Cd·t＝rd·tRd·t；
Bu·t＝hu·tHu·t；Bd·t＝hd·tHd·t；
E(Bu·t)＝hu·tE(Hu·t)；E(Bd·t)＝hd·tE(Hd·t)；
wherein r isu·t、hu·t、rd·t、hd·tRespectively the capacity price and the energy price of the spinning reserve and the capacity price and the energy price of the lower spinning reserve in the t period; hu·t、Hd·tRespectively, the call volume of the actual up-down rotation reserve capacity, which is respectively equal to QLloss·tAnd QWloss·t；E(Hu·t)、E(Hd·t) Respectively expected values of the spinning reserve and the spinning reserve call amount in the t time period;
step S24: approximately considering the load prediction deviation as normal distribution with the mean value of zero, and adopting Laplace normal mixed distribution for the wind power output prediction deviation; simulating the prediction deviation of the actual load power and the wind power output by adopting a Monte Carlo method, wherein each possible prediction deviation corresponds to an actual equivalent load random state; obtaining expected value (E (V)) of corresponding part by Monte Carlo method simulated datat)、E(Wt)、E(Bu·t)、E(Bd·t)；
Wherein, the step S3 specifically includes: the weighted difference of the two half-variances for the rotational reserve benefit above and below the rotational reserve benefit expected value is expressed as a mathematical function as follows:
wherein the content of the first and second substances,
respectively representing the expected values of the spinning reserve benefit and the spinning reserve benefit of the system within 24 hours; i is a set of actual equivalent load random states; lambda [ alpha ]iIs the probability of occurrence of the ith state; alpha is a risk preference coefficient and is a sign of the degree of risk aversion;
wherein the content of the first and second substances,
wherein, the constraint conditions included in the step S4 include: standby opportunity constraint and wind farm active power output constraint;
the alternate opportunity constraint is: defined from a single time period, the probability of ensuring that the rotating standby meets the system equivalent load prediction deviation within the single time period is not less than a given value and is expressed by a mathematical function as follows:
Pr{Ru·t≥Pt-Pf·t}≥γ；
Pr{Rd·t≥Pf·t-Pt}≥δ；
wherein, Pf·t、PtRespectively predicting the equivalent load and the actual equivalent load for the system in the period t; the reliability levels gamma and delta are respectively the upper limit values allowed by the loss load probability and the wind abandoning probability of the market at the day before;
the system predicted equivalent load is the difference between the day-ahead load power predicted value and the wind power output predicted value, the system actual equivalent load is the difference between the actual load power and the actual wind power output, and the system predicted equivalent load is expressed by a mathematical function as follows:
Pf·t＝PLf·t-PWf·t；
Pt＝PL·t-PW·t＝PLf·t+ΔPL·t-(PWf·t+ΔPW·t)；
wherein, PLf·t、PWf·tRespectively a day-ahead load power predicted value and a wind power output predicted value in a t period; pL·t、PW·tActual load power and wind power output are respectively in a time period t; delta PL·t、ΔPW·tRespectively predicting deviation of load power and wind power output in a time period t, and obtaining random variables which obey certain probability distribution;
the wind power plant active power output constraint is expressed by a mathematical function as follows:
wherein the content of the first and second substances,
the maximum active output of the wind farm.
In step S4, the method uses the maximum expected rotary reserve benefit and the minimum risk as a multi-target model, and adopts a multi-target particle swarm algorithm based on an extreme value comprehensive strategy to perform optimization calculation, so as to solve the expected rotary reserve benefit and the risk value:
wherein the global optimum particle GiThe selection strategy of best is: using different GiSelecting the optimal particles in the population by the combination of best selection strategies, wherein the global optimal of the particles is obtained by three strategies:
strategy 1: randomly selecting a non-dominant solution from the non-inferior solution set of the external archive as a global optimum, and recording the global optimum as the gbest1；
Strategy 2: according to the dense distance of the non-inferior solution of the external archive, performing descending order arrangement on the non-dominant solution, and randomly selecting one particle from the top 10% of the dense distance as a global optimum which is recorded as gbest2(ii) a Wherein the denseThe distance does not include the dense distance of the two endpoints;
strategy 3: randomly selecting one particle from two extreme values in the non-inferior solution set as global optimum, and recording the global optimum as the gbest3(ii) a Strategy 3 is an extreme value selection strategy;
let the number of particles be m, and in each iteration, select a of the particles to be gbest1For global optimization, select b particles among them to be gbest2For global optimization, (m-a-b) of the particles are selected to be gbest3The global optimization is achieved, and a and b meet the condition that a + b is less than m;
wherein the particle velocity and position are updated as:
xi(n+1)＝xi(n)+vi(n+1)；
wherein G isibest is the global optimal vector of the ith particle; ziIs a coefficient vector; p is a radical ofibest is the individual optimal particle; omega is an inertia weight; r is1And r2Is [0,1 ]]A random number in between; n is the current iteration number; c. C1And c2Is a constant; v is the particle velocity; x is the particle position;
wherein G isibest＝[gbest1，gbest2，gbest3]，Zi＝[z1，z2，z3]T(ii) a From the above analysis, it can be seen that: if i is less than or equal to a, Zi＝[1，0，0]T(ii) a If a is more than i and less than or equal to b, Zi＝[0，1，0]T(ii) a Otherwise, Zi＝[0，0，1]T。
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