CN116502747A - Power system standby quantification method based on probability prediction and considering uncertainty of multiple time scales of new energy - Google Patents

Power system standby quantification method based on probability prediction and considering uncertainty of multiple time scales of new energy Download PDF

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CN116502747A
CN116502747A CN202310337026.4A CN202310337026A CN116502747A CN 116502747 A CN116502747 A CN 116502747A CN 202310337026 A CN202310337026 A CN 202310337026A CN 116502747 A CN116502747 A CN 116502747A
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万灿
徐钰淇
刘辉
赵长飞
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Abstract

The invention discloses a probability prediction-based standby quantification method for a power system, which takes new energy multi-time scale uncertainty into account. According to the method, a bootstrap extreme learning machine and an Earthway random process theory are combined, probability distribution of the new energy output uncertainty under a minute time scale and a prediction interval thereof are constructed, probability distribution of the new energy output uncertainty under a second time scale and a corresponding prediction interval are obtained through deduction based on Earthway integral and derivative theory, and therefore a new energy output multi-time scale uncertainty model is built, and multidimensional random characteristics of the new energy are accurately quantized. The two-stage robust standby collaborative optimization method solves the problems that the standby climbing response capability of the power system is insufficient and the standby capacity cannot be effectively utilized in real-time scheduling, and realizes the multistage quantification of the standby requirement of the power system which can be delivered in real time; an improved column and constraint generation solving algorithm is provided, and the improved column and constraint generation solving algorithm has good convergence and calculation efficiency when solving a two-stage robust optimization problem.

Description

Power system standby quantification method based on probability prediction and considering uncertainty of multiple time scales of new energy
Technical Field
The invention relates to a probability prediction-based standby quantification method for a power system considering uncertainty of multiple time scales of new energy, and belongs to the field of new energy optimization grid connection.
Background
With the continuous increase of the installed capacity of intermittent new energy, the permeability of wind power and photovoltaic power generation is continuously increased, the randomness and the fluctuation make the power generation of the new energy difficult to be accurately predicted, the prediction error is difficult to eliminate, and great challenges are brought to the operation control and the scheduling management of a power system. In order to ensure the real-time energy balance of the power system, the power generation plan and the operation standby capacity of the system need to be reasonably arranged, and how to optimally configure the power generation system to cope with the operation standby generated by the uncertainty of the new energy output prediction is important to ensure the safe, economic and low-carbon operation of the power system. The existing method for quantifying the reserve of the electric power system considering the uncertainty of the new energy researches a plurality of uncertainties considering a single time scale, defines the upward and downward reserve demands of the system according to a probability prediction interval of 15 minutes/point, ignores the random climbing characteristic of the new energy in a scheduling interval, and has the risk that the reserve capacity reserved by the system is difficult to follow the severe random fluctuation of the new energy in a real-time scheduling link, so that the obtained reserve decision scheme of the system cannot meet the actual running requirement of the system. Therefore, it is necessary to research a power system standby quantification method which is based on probability prediction and accounts for uncertainty of multiple time scales of new energy.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a power system standby quantization method based on probability prediction and considering uncertainty of multiple time scales of new energy.
The technical scheme adopted by the invention is as follows:
a power system standby quantization method based on probability prediction and considering uncertainty of multiple time scales of new energy comprises the following steps:
step 1: a non-parametric probability prediction method for the generated power of the new energy is provided by combining a bootstrap extreme learning machine and a Dirichlet Gaussian mixture model, probability distribution of uncertainty of the output of the new energy is predicted, and an uncertainty model of the output of the new energy under a minute time scale is established. The specific method comprises the following steps:
given a set of observationsInput data x n And output target->Is modeled by an extreme learning machine as
Wherein N is the number of observed data, N is the data number, y (x n ) Is the true regression value of the model, which is related to the input data x n A nonlinear functional relation f (x n The method comprises the steps of carrying out a first treatment on the surface of the w, b, β) are fitted by an extreme learning machine. The extreme learning machine is a single hidden layer feedforward neural network, H is the number of hidden layer neurons, H is the number of neurons, and w h For inputting weight vectors, for connecting input data with hidden layer neurons, b h G (·) is the activation function, β h For the output weight vector, it is used to connect hidden layer neurons and output data. Xi (x) n ) For prediction errors of the model, the tip presented for itThe peak thickness tail distribution characteristics are characterized by adopting a Dirichlet Gaussian mixture model
Wherein p (·) is the prior probability distribution of the prediction error, the prior distribution is composed of infinite gaussian components, m is the number of the gaussian components, infinity is the sign, p m (. Cndot.) is the probability density function of the mth Gaussian component, pi m For the weight of the mth gaussian component,is the variance of the mth gaussian component. The likelihood function of the model given the observed data D is
Wherein, θ= { pi, sigma, beta } represents the parameter set and hidden variable of the dirichlet gaussian mixture modelCharacterizing the association of the nth observation data with the mth gaussian component,/for example>Representing the probability distribution that the nth observation obeys the mth gaussian component, and vice versa, +.>Based on Bayes learning theory, the posterior distribution p (Z, theta|D) of the Dirichlet Gaussian mixture model meets the following conditions
p(Z,θ∣D)∝p(D∣Z,θ)p(Z∣π)p(σ)p(π)p(β)
Wherein,,for the conditional probability distribution of Z over pi, p (sigma), p (pi), p (beta) fractionsOther is the a priori distribution of the parameters pi, sigma, beta. The approximate variation distribution Q (Z, θ) of p (Z, θ|D), expressed as
Wherein,,the posterior approximate variational distribution of Z, sigma, pi and beta is obtained by adopting a variational Bayesian inference algorithm. In order to improve the prediction precision of a prediction model, a bootstrap method is adopted to resample a data set D to construct B training sample sets, B extreme learning machines are respectively added to train to obtain model parameters, and an average value output by the B extreme learning machines is used as an estimate of a true regression value of the prediction model->Represented as
Wherein B is the number of the extreme learning machines, B is the number of the extreme learning machines,is the predicted value output by the b-th extreme learning machine. Model uncertainty variance of predictive model +.>The same bootstrap method is adopted to estimate by the B bootstrap extreme learning machines obtained by training, and the estimation is expressed as
Based on the construction of the bootstrap extreme learning machine and the Dirichlet Gaussian mixture model, the existing 15-minute/point historical power generation data and weather forecast data are madeFor inputting data x t Obtaining probability prediction distribution of new energy output uncertainty at t time
Wherein y is t The new energy output at the time t is represented,zeta is the point prediction result generated by the bootstrap extreme learning machine t The probability distribution p (ζ) is the overall error of the model t ∣x t D) is derived from p (ζ) t ∣x t D, θ) model parameters θ are integrated, and the optimal gaussian mixture model ∈is obtained through variational bayesian inference>N (·) is a standard normal distribution, wherein the mean of the Gaussian components is 0, < >>Is the variance of the mth Gaussian component, +.>Is the weight of the mth gaussian component, +.>Is the number of gaussian components. Based on the prediction error probability distribution of the new energy output, the probability interval of the new energy output under the appointed confidence level can be obtained, so that the uncertainty model of the new energy output under the minute time scale can be obtained
Wherein,,αandlevel of division corresponding to lower and upper end points of interval,/->And->To correspond toαAnd->Quantile estimates of quantile levels.
Step 2: and (3) constructing an illite random process model meeting the probability distribution of the randomness of the new energy output predicted in the step (1), deriving the probability distribution of the illite random process under the second time scale based on the illite integral and derivative theory, and establishing an uncertainty model of the new energy output under the second time scale, thereby establishing a new energy output multi-time scale uncertainty model.
Building an Islamic random process model meeting the uncertainty probability distribution of the new energy output in the step 1 based on the Islamic differential theory, wherein the model is expressed in the form of the following first-order random differential equation
Where τ is continuous time, dτ is time derivative, W (·) is the standard wiener process, ζ [m] (τ) represents the mth Gaussian component, dζ [m] (τ) is ζ [m] Differentiation of (τ), a [m] And b [m] Is a constant term. Wherein a is [m] Expressing a regression target of the illite random process model, and determining the total level of new energy output; b [m] The strength of the new energy output fluctuation is represented; a, a [m] And b [m] Is estimated by the following procedure;
the probability distribution of the uncertainty of the new energy output under the second time scale is obtained by deduction, specifically: firstly, the solution of the first-order random differential equation is obtained based on the Earthway integral theory
Wherein τ 0 Is the initial time;
then, based on the Earthway differential theory, calculating the Gaussian component ζ [m] The first and second moment forms of (tau) are
Wherein E [ xi ] [m] (τ)]And Var [ zeta ] [m] (τ)]Respectively is xi [m] A first moment and a second moment of (τ); the mean value 0 and the variance of each Gaussian component in the Gaussian mixture model obtained in the step 1 are calculatedSubstituting into the following formula to obtain a [m] And b [m] The value of (2) is
Wherein T is the period of the minute-scale time scale;
taking expectations from two sides of the first-order random differential equation to obtain
Wherein E [ dζ ] [m] (τ)]And Var [ dζ ] [m] (τ)]Respectively dζ [m] (τ) a first moment and a second moment. From the above deduction, dζ (τ) is also subjected to the dielcrets process gaussian mixing process, the mean and variance of each gaussian component are known, each weight is consistent with each component weight of ζ (τ), and the probability distribution of dζ (τ) can be obtained through Monte Carlo simulation, so that the new energy output multi-time scale uncertainty model is obtained as follows:
under the specified confidence level, the probability interval of the uncertainty of the new energy output under the minute time scale is
Under the specified confidence level, the probability interval of the uncertainty of the new energy output under the second time scale is
Step 3: and (3) aiming at the new energy output multi-time scale uncertainty model established in the step (2), constructing a two-stage robust standby cooperative optimization model of the electric power system, wherein the two-stage robust standby cooperative optimization model of the electric power system compensates the multi-time scale uncertainty of the new energy output by adjusting the cooperation of standby and climbing standby. Wherein the need to adjust standby is based on ζ estimated in step 2 t Probability intervalIs defined as
Wherein Ru is t And Rd t And respectively adjusting the standby requirement up and down in the period t.
The two-stage robust standby collaborative optimization model of the power system comprises a first-stage model and a second-stage model;
the first stage model makes a power generation and standby plan according to the point prediction result of the new energy output and the probability interval of the prediction error in the step 1, and aims at minimizing the total running cost, and is expressed as
Wherein g is the number of the generator set,for the set of generator sets s is the energy storage device number,/-for>Is a collection of energy storage devices; />For generating power of the unit g in the period t, < >>And->The reserved upper and lower parts of the unit g are adjusted for standby; />And->Charging and discharging power of the energy storage s respectively, +.>And->The reserved upper and lower adjustment for the energy storage s is reserved for standby; />For the unit operating cost factor of the unit g, +.>And->Reserve cost is adjusted up and down for unit capacity of the unit g respectively; />And->The unit charge and discharge cost coefficients of the energy storage device s are respectively +.>And->Reserve costs are adjusted up and down for the unit capacity of the energy storage device s, respectively.
The power system operation constraint conditions to be satisfied by the first stage model include:
a. generating set capacity constraints
Wherein,,and->The minimum and maximum output limits of the generator set are respectively.
b. Climbing constraint of generator set
Wherein,,for the generating power of the unit g in the T-1 period, deltaT is 15 minutes scheduling time interval,/->Andrespectively the limit value of the power climbing rate of the power generator set.
c. Energy storage device operation constraints
Wherein,,andP s S the upper and lower limit values of the charge and discharge power of the energy storage device s.
d. Energy storage device capacity constraints
Wherein,,E s andfor the lower and upper limits of the storage capacity of the energy storage device s, E s,t For storing energy of the energy storage device s in t period, E s,0 For storing energy of the energy storage means s at an initial moment, E s,T For storing energy at the end of a scheduling period, E, of the energy storage means s s,t-1 For storing energy of the energy storage means s during the period t-1 +.>And->Is the charge-discharge efficiency of the energy storage device s.
e. Standby restraint for energy storage device
Where μ is the reserve capacity limit coefficient of the energy storage device.
f. Standby demand constraints
g. Node power balancing constraints
Wherein b is the node number of the power system,for the node set of the power system, w and v are the numbers of the wind farm and the photovoltaic power station respectively,/-for>Predicted force for wind farm w in period t,/->Predicting the power of the photovoltaic power station v in the t period; />For the load power at node b, l is the branch number of the power system, +.>For the power transmitted by branch l fr (l) and to (l) are the start and end of branch l, respectively,/-> b Respectively a generator set, a wind power plant, a photovoltaic power station and an energy storage device set at the node b.
h. Branch tide constraint
Wherein,,andP l F representing upper and lower limits of the line transmission power flow.
The second stage is a rescheduling stage, and the output of the generator set and the energy storage device is adjusted within the standby capacity determined in the first stage according to the possible power generation output scene of the new energy source, so that the real-time balance of the power system is ensured. The power system operation constraint conditions to be met by the second-stage model include:
a. power generator set output adjustment constraint
Wherein,,the regulated generation power for the continuous variation of the unit g during the period t is a function of the time τ.
b. Energy storage device output adjustment constraint
Wherein,,and->Respectively, continuously changing the charging and discharging power of the energy storage device s in the t period.
c. Real-time power balance constraint
Wherein,,for the prediction error of the generated power of the wind power plant w continuously changing according to a certain slope in the period t,for the prediction error delta P of the generated power of the photovoltaic power station v continuously changing according to a certain slope in the t period l F And (τ) is the adjusted transmission power of the leg l that varies continuously over the period t. In this ideal state, the real-time balance constraint condition of the power is always established. Based on the probability interval of dζ (tau) obtained in the step 1, taking into consideration that the generation power of the new energy is +.>In any climbing situation, the power generation unit and the energy storage device are difficult to meet the power real-time balance of the power system by adjusting the output in the adjustment standby range determined in the first stage, so that the uncertainty of the new energy generated power in the dispatching interval is compensated by the additional standby capacity, and the standby capacity is defined as climbing standby. The demand of the climbing reserve of the electric power system is determined by the following process, firstly, two relaxation variables are introduced to ensure the real-time balance of the electric power after the climbing reserve is added, and at the moment, the real-time balance constraint of the electric power becomes
Wherein,,for the possible prediction error of the generated power of the wind farm w in the t period, +.>Prediction error for the possible generation power of the photovoltaic power plant v in the t period, +.>And->Is->And->Probability intervals at 95% confidence level; />Climbing a slope for the possible generation power of the photovoltaic power station v in the t period, +.>Climbing a slope for the possible generation power of the photovoltaic power station v in the t period, +.>And->Is->Andprobability intervals at 95% confidence level; />And->For two slack variables, the physical meaning is to compensate for the upward and downward power needed to maintain the real-time power balance of node b during period t when the regulation is not enough.
Under a two-stage robust standby cooperative optimization framework, the second-stage model finds the worst operation scene in the new energy output multi-time scale uncertain model constructed in the step 2, so that the sum of the rescheduling cost of the system under the scene and the penalty cost of insufficient standby is minimum, and the objective function is that
Wherein C is P,up And C P,dn The cost is punished for upward and downward standby shortage respectively.
Step 4: in view of the isomerism of the two-stage models in the two-stage robust standby collaborative optimization model constructed in the step 3, a model conversion method based on Bernstein polynomials is provided, and continuous time variable of the second stage is changed By discrete time variable V t [i] And Bernstein base function +.>Is expressed mathematically as:
wherein I is the order of Bernstein polynomial, I is an integer less than I, V t [i] Is v t An ith control variable of (τ); thus, in the second stage modelThe trajectory optimization problem of (2) is converted into +.>Is an optimization problem of (a). Similarly, other continuous-time variables in the second-stage model are approximated by Bernstein polynomials, thereby converting the continuous-time model of the second stage into a discrete-time model.
Integrating a two-stage model to obtain a compact mathematical model of the two-stage robust standby collaborative optimization problem as
Ω 0 ＝{E 0 x 0 +F 0 y 0 +G 0 z 0 ≤f}
Ω u ＝{E u x u ≤F u y 0 +Hu+d}
Wherein x is 0 And z 0 Continuous variable and integer variable, y, of the first stage, respectively 0 Is a coupling variable of two phases, x u As a continuous variable of the second stage Ω 0 And omega u For the feasible domain of the first and second stage models, u is the control variable of Bernstein polynomials corresponding to ζ (τ),set of u, b I (τ) is a vector form of the Bernstein basis function of the I order;respectively x 0 ,y 0 ,z 0 ,x u Coefficient of unit cost of E 0 ,F 0 ,G 0 ,E u ,F u H, d are constant coefficients in the inequality constraint.
Step 5: aiming at the two-stage robust standby collaborative optimization model established in the step 3, an improved column and constraint generation algorithm is adopted to decompose the original problem into a main problem and a sub-problem, and an optimal solution of the original problem is found in the iterative calculation process of the main problem and the sub-problem, so that the two-stage robust optimization model is quickly solved to obtain quantization results of adjustment standby and climbing standby.
For the r-th iteration, the mathematical model of the main problem is
(MP):
s.t.E 0 x 0 +F 0 y 0 +G 0 z 0 ≤f
Wherein j is an integer from 1 to r, x u(j) Is the continuous variable optimal solution of the second stage obtained by the j-th iteration, u *(j) Is the value of u corresponding to the worst uncertainty scene obtained by the jth iteration, and eta isIs the maximum value of (a).
The mathematical model of the sub-problem is
(SP):
s.t.E u x u ≤F u y 0 +Hu+d
λ(F u y 0*(r) +Hu+d-E u x u )＝0
Where lambda is the dual variable,and E is uT Respectively->And E is u Transpose of (y) 0*(r) Is y obtained by the r-th iteration 0 Is a solution to the optimization of (3).
Since the model conversion method in step 3 needs to introduce additional decision variables, the standard column and constraint generation algorithm will occupy more solving time when solving the standby quantization problem of the large-scale power system, so an improved column and constraint generation algorithm is provided, and in each iteration process, u obtained by solving the sub-problem is solved by utilizing the ascending property of Bernstein polynomial transformation *(j) Bernstein space mapped to low dimensions is approximatedExpressed mathematically as
Wherein,,b is a positive integer less than I I (tau) and>respectively I and->Compact form of the order Bernstein basis function, M e Is->A dimension mapping matrix; in major questions with->Approximately replace u *(j) Thereby reducing the model complexity of the main problem. The improved column and constraint generation algorithm can quickly solve the problem of two-stage robust standby collaborative optimization of a large-scale power system, and optimal configuration of standby capacity in each adjustment resource is realized through effective collaboration of adjustment standby and climbing standby.
The main advantages and effects of the invention are as follows:
1) The utility model provides a power system reserve quantization method based on probability prediction and accounting for new energy multi-time scale uncertainty, utilizes the effective cooperation of reserve adjustment and climbing reserve to process multi-time scale new energy uncertainty, solves the problem that the reserve climbing response capability is insufficient and the reserve capacity cannot be effectively utilized in the real-time scheduling of the power system, and realizes the multistage quantization of the reserve demand of the power system which is deliverable in real time.
2) The non-parametric probability prediction method for the new energy generated power is provided, a bootstrap extreme learning machine and an Embola random process theory are combined, probability distribution of new energy output uncertainty under a minute time scale and a prediction interval thereof are constructed, probability distribution of new energy output uncertainty under a second time scale and a corresponding prediction interval are obtained through deduction based on Embola integral and derivative theory, and therefore a new energy output multi-time scale uncertainty model is built, and multidimensional random characteristics of new energy are accurately quantized.
3) A model conversion method based on Bernstein polynomials is provided, the standby quantization problem of the power system is converted into a general two-stage robust optimization problem, an improved column and constraint generation solving algorithm is provided, and good convergence and calculation efficiency are shown in solving the large-scale two-stage robust optimization problem.
Drawings
FIG. 1 is a flow chart of a probabilistic prediction based method for quantifying backup for a power system that accounts for multi-time scale uncertainty of new energy.
Detailed Description
Further description is provided below with reference to the accompanying drawings.
Fig. 1 is a flowchart of a power system standby quantization method based on probability prediction and accounting for uncertainty of multiple time scales of new energy, and the main flow is as follows:
1) Predicting probability distribution of the uncertainty of the new energy output under a minute-level time scale according to the known 15 minute/point historical power generation data and weather forecast data;
2) Constructing an Italian grape vine random process meeting the prediction probability distribution;
3) Deriving probability distribution of the uncertainty of the new energy output under a second time scale based on the Earthway integral and derivative theory;
4) Establishing a new energy output multi-time scale uncertainty model;
5) Constructing a two-stage robust standby collaborative optimization model;
6) Converting the second-stage continuous time model by adopting Bernstein polynomials to construct a general two-stage robust optimization model;
7) And solving a two-stage robust standby collaborative optimization problem by adopting an improved column and constraint generation algorithm to obtain quantization results of the adjustment standby and the climbing standby.
The following describes a specific execution flow.
1) 15 minutes/point historical power generation data and weather forecast data are taken as input data x t Obtaining probability prediction distribution of new energy output uncertainty at t time
Wherein y is t The new energy output at the time t is represented,zeta is the point prediction result generated by the bootstrap extreme learning machine t The probability distribution p (ζ) is the overall error of the model t ∣x t D) is represented by the Dirichlet Gaussian mixture modelN (·) is a standard normal distribution, < >>Is the variance of the mth Gaussian component, +.>Is the weight of the mth gaussian component, +.>Is the number of gaussian components.
Based on the prediction error probability distribution of the new energy output, the probability interval of the new energy output under the appointed confidence level can be obtained, so that the uncertainty model of the new energy output under the minute time scale can be obtained
Wherein,,αandlevel of division corresponding to lower and upper end points of interval,/->And->To correspond toαAnd->Quantile estimates of quantile levels.
2) Based on the Embola differential theory, an Embola random process model meeting the predictive error probability distribution of the new energy generated power is constructed, and the model is expressed as a random differential equation
Where τ is continuous time, dτ is time derivative, W (·) is the standard wiener process, ζ [m] (τ) represents the mth Gaussian component, dζ [m] (τ) is ζ [m] Differentiation of (τ), a [m] And b [m] Is a constant term. Wherein a is [m] Expressing a regression target of the illite random process model, and determining the total level of new energy output; b [m] The strength of the fluctuation of the new energy output is indicated.
3) Calculating the solution of the random differential equation according to the Earthway integral theory
Wherein τ 0 Is the initial time;
then, based on the Earthway differential theory, calculating the Gaussian component ζ [m] The first and second moment forms of (tau) are
Wherein E [ dζ ] [m] (τ)]And Var [ dζ ] [m] (τ)]Respectively dζ [m] A first moment and a second moment of (τ);
taking expectations from two sides of the first-order random differential equation to obtain
Wherein E [ dζ ] [m] (τ)]And Var [ dζ ] [m] (τ)]Respectively dζ [m] (τ) a first moment and a second moment. From the above deductions, dζ (τ) is also subjected to the dielcrater process gaussian mixture process, the mean and variance of each gaussian component are known, each weight is consistent with each component weight of ζ (τ), and the probability distribution of dζ (τ) can be obtained through monte carlo simulation. The probability distribution of the uncertainty of the new energy output under the second time scale is obtained by the method that:
under the specified confidence level, the probability interval of the uncertainty of the new energy output under the second time scale is
Wherein,,αandlevel of division corresponding to lower and upper end points of interval,/->And->To correspond toαAnd->A quantile estimate of the quantile level;
4) Establishing a new energy output multi-time scale uncertainty model:
under the specified confidence level, the probability interval of the uncertainty of the new energy output under the minute time scale is
Wherein,,αandlevel of division corresponding to lower and upper end points of interval,/->And->To correspond toαAnd->A quantile estimate of the quantile level;
under the specified confidence level, the probability interval of the uncertainty of the new energy output under the second time scale is
According to xi t Probability interval of (2)Defining the need for adjustment as
Wherein Ru is t And Rd t And respectively adjusting the standby requirement up and down in the period t.
5) And constructing a two-stage robust standby collaborative optimization model, wherein the two-stage robust standby collaborative optimization model comprises a first-stage model and a second-stage model. Wherein the objective function of the first stage model is
Wherein g is the number of the generator set,for the set of generator sets s is the energy storage device number,/-for>Is a collection of energy storage devices; />For generating power of the unit g in the period t, < >>And->The reserved upper and lower parts of the unit g are adjusted for standby; />Andcharging and discharging power of the energy storage s respectively, +.>And->The reserved upper and lower adjustment for the energy storage s is reserved for standby; />For the unit operating cost factor of the unit g, +.>And->Reserve cost is adjusted up and down for unit capacity of the unit g respectively; />Andthe unit charge and discharge cost coefficients of the energy storage device s are respectively +.>And->Reserve costs are adjusted up and down for the unit capacity of the energy storage device s, respectively.
The first stage model contains power system operating constraints including:
a. generating set capacity constraints
Wherein,,and->The minimum and maximum output limits of the generator set are respectively.
b. Climbing constraint of generator set
Wherein,,for the generating power of the unit g in the T-1 period, deltaT is 15 minutes scheduling time interval,/->And->Respectively the limit value of the power climbing rate of the power generator set.
c. Energy storage device operation constraints
Wherein,,andP s S the upper and lower limit values of the charge and discharge power of the energy storage device s.
d. Energy storage device capacity constraints
Wherein E is s Andfor the lower and upper limits of the storage capacity of the energy storage device s, E s,t For storing energy of the energy storage device s in t period, E s,0 For storing energy of the energy storage means s at an initial moment, E s,T For storing energy at the end of a scheduling period, E, of the energy storage means s s,t-1 For storing energy of the energy storage means s during the period t-1 +.>And->Is the charge-discharge efficiency of the energy storage device s.
e. Standby restraint for energy storage device
Where μ is the reserve capacity limit coefficient of the energy storage device.
f. Standby demand constraints
g. Node power balancing constraints
Wherein b is the node number of the power system,for the node set of the power system, w and v are wind power respectivelyNumbering of field and photovoltaic power plants, +.>Predicted force for wind farm w in period t,/->Predicting the power of the photovoltaic power station v in the t period; />For the load power at node b, l is the branch number of the power system, +.>For the power transmitted by branch l fr (l) and to (l) are the start and end of branch l, respectively,/->Respectively a generator set, a wind power plant, a photovoltaic power station and an energy storage device set at the node b.
h. Branch tide constraint
Wherein,,andP l F representing upper and lower limits of the line transmission power flow.
The objective function of the second stage model is
Wherein C is P,up And C P,dn The cost is punished for upward and downward standby deficiency respectively;and->The power balancing method is characterized in that the power balancing method is two relaxation variables, and the physical meaning of the power balancing method is that upward power and downward power which need to be compensated in a t period are needed for maintaining the real-time power balance of a node b when the climbing reserve is insufficient; />The power generation power is adjusted for the continuous change of the unit g in the t period, and is a function of time tau;and->Respectively adjusting charge and discharge power of the energy storage device s continuously changing in the t period;
the power system operation constraint conditions to be met by the second-stage model include:
a. power generator set output adjustment constraint
Wherein,,the regulated generation power for the continuous variation of the unit g during the period t is a function of the time τ.
b. Energy storage device output adjustment constraint
Wherein,,and->Respectively, continuously changing the charging and discharging power of the energy storage device s in the t period.
c. Real-time power balance constraint
Wherein,,for the possible prediction error of the generated power of the wind farm w in the t period, +.>Prediction error for the possible generation power of the photovoltaic power plant v in the t period, +.>And->Is->And->Probability intervals at 95% confidence level; />Climbing a slope for the possible generation power of the photovoltaic power station v in the t period, +.>Climbing a slope for the possible generation power of the photovoltaic power station v in the t period, +.>And->Is->Andprobability intervals at 95% confidence level; />And->For two slack variables, the physical meaning is to compensate for the upward and downward power needed to maintain the real-time power balance of node b during period t when the regulation is not enough.
6) Model conversion method based on Bernstein polynomial, and continuous time variable in second-stage model
By discrete time variable V t [i] And Bernstein basis functionIs expressed mathematically as; />
Wherein I is the order of Bernstein polynomial, I is an integer less than I, V t [i] Is v t The ith control variable of (τ), in turn, converts the continuous time model of the second stage to a discrete time model. The compact mathematical model of the converted general two-stage robust optimization problem is that
Ω 0 ＝{E 0 x 0 +F 0 y 0 +G 0 z 0 ≤f}
Ω u ＝{E u x u ≤F u y 0 +Hu+d}
Wherein x is 0 And z 0 Continuous variable and integer variable, y, of the first stage, respectively 0 Is a coupling variable of two phases, x u As a continuous variable of the second stage Ω 0 And omega u For the feasible domain of the first and second stage models, u is the control variable of Bernstein polynomials corresponding to ζ (τ),set of u, b I (τ) is a vector form of the Bernstein basis function of the I order;respectively x 0 ,y 0 ,z 0 ,x u Coefficient of unit cost of E 0 ,F 0 ,G 0 ,E u ,F u H, d are constant coefficients in the inequality constraint.
7) The original problem is decomposed into a main problem and a sub problem by adopting an improved column and constraint generation algorithm, and the optimal solution of the original problem is found in the iterative calculation process of the main problem and the sub problem. For the r-th iteration, the mathematical model of the main problem is
(MP):
s.t.E 0 x 0 +F 0 y 0 +G 0 z 0 ≤f
Wherein j is an integer from 1 to r, x u(j) Is the continuous variable optimal solution of the second stage obtained by the j-th iteration, u *(j) Is the value of u corresponding to the worst uncertainty scene obtained by the jth iteration, and eta isIs the maximum value of (a). The mathematical model of the sub-problem is
(SP):
s.t.E u x u ≤F u y 0 +Hu+d
λ(F u y 0*(r) +Hu+d-E u x u )＝0
Where lambda is the dual variable,and E is uT Respectively->And E is u Transpose of (y) 0*(r) Is y obtained by the r-th iteration 0 Is a solution to the optimization of (3). In each iteration process, the lifting property of Bernstein polynomial transformation in the step 3 is utilized to solve the sub-problem to obtain u *(j) Bernstein space mapped to low dimension is approximated +.>Expressed mathematically as
/>
Wherein I is a positive integer less than I, b I (τ) andrespectively I < th >>Compact form of the order Bernstein basis function, M e Is->A dimension mapping matrix; in major questions with->Approximately replace u *(j) Thereby reducing the model complexity of the main problem.
The improved column and constraint generation algorithm is adopted to quickly solve the problem of two-stage robust reserve cooperative optimization of a large-scale power system, and the optimal configuration of reserve capacity in each adjustment resource is realized through the effective cooperation of adjustment reserve and climbing reserve.

Claims (6)

1. A power system standby quantization method based on probability prediction and considering new energy multi-time scale uncertainty is characterized in that: the standby quantification method of the power system comprises the following steps:
step 1: combining a bootstrap extreme learning machine and a Dirichlet Gaussian mixture model to provide a non-parametric probability prediction method for the power generated by the new energy, predicting probability distribution of uncertainty of the output of the new energy, and establishing an uncertainty model of the output of the new energy under a minute time scale;
step 2: constructing an illite random process model meeting the probability distribution of the randomness of the new energy output predicted in the step 1, deriving the probability distribution of the illite random process under the second time scale based on the illite integral and derivative theory, and establishing an uncertainty model of the new energy output under the second time scale, thereby establishing a new energy output multi-time scale uncertainty model;
step 3: aiming at the new energy output multi-time scale uncertainty model established in the step 2, a two-stage robust standby cooperative optimization model of the electric power system is established, and the two-stage robust standby cooperative optimization model of the electric power system compensates the new energy output multi-time scale uncertainty by adjusting standby and climbing standby cooperation;
step 4: aiming at the two-stage robust standby collaborative optimization model of the power system constructed in the step 3, a Bernstein polynomial-based model conversion method is provided, a continuous time model of a second stage is converted into a discrete time model and integrated with a first stage model, and the two-stage robust standby collaborative optimization model constructed in the step 3 is converted into a general two-stage robust optimization model;
step 5: aiming at the two-stage robust optimization model obtained in the step 4, an improved column and constraint generation algorithm is provided for rapidly solving the two-stage robust optimization model to obtain quantization results of the adjustment reserve and the climbing reserve.
2. The probability prediction-based standby quantification method for the electric power system considering the uncertainty of multiple time scales of new energy, which is characterized by comprising the following steps of: the non-parameter probability prediction method for the new energy generated power in the step 1 comprises the following steps: given a set of observationsWherein the data x is input n And output target y n Is modeled by an extreme learning machine as
Wherein N is the number of observed data, N is the data number, y (x n ) Is the true regression value of the model, which is related to the input data x n A nonlinear functional relation f (x n The method comprises the steps of carrying out a first treatment on the surface of the w, b, β) is fitted by an extreme learning machine; the extreme learning machine is a single hidden layer feedforward neural network, H is the number of hidden layer neurons, H is the number of neurons, and w h For inputting weight vectors, for connecting input data with hidden layer neurons, b h G (·) is the activation function, β h The hidden layer neurons are used for connecting hidden layer neurons with output data; xi (x) n ) Aiming at the peak thick tail distribution characteristic presented by the prediction error of the model, the model is characterized by adopting a Dirichlet Gaussian mixture model
Wherein p (·) is the prior probability distribution of the prediction error, the prior distribution is composed of infinite Gaussian components, m is the number of the Gaussian components, infinity is an infinite sign, pm (·) is the probability density function of the mth Gaussian component, pi m For the weight of the mth gaussian component,variance for the mth gaussian component;
parameters of a bootstrap extreme learning machine and a Dirichlet Gaussian mixture model are obtained by a bootstrap method and a variational Bayesian inference algorithm respectively, and 15 minutes/point historical power generation data and weather forecast data are used as input data x t Obtaining probability distribution of new energy output uncertainty at t time
Wherein y is t The new energy output at the time t is represented,a point prediction result generated by a bootstrap extreme learning machine; zeta type toy t The probability distribution p (ζ) is the overall error of the model t ∣x t D) is derived from p (ζ) t ∣x t D, θ) is integrated with the model parameter θ, expressed as +.o by Gaussian mixture model>N (·) is a standard normal distribution, wherein the mean of the Gaussian components is 0, < >>Is the variance of the mth Gaussian component, +.>Is the weight of the mth gaussian component, +.>Is the number of gaussian components;
based on the predictive error probability distribution of new energy output, an uncertainty model of the new energy output under a minute time scale is established
Wherein,,αandlevel of division corresponding to lower and upper end points of interval,/->And->For corresponding alpha and->Quantile estimates of quantile levels.
3. The probability prediction-based standby quantification method for the electric power system considering the uncertainty of multiple time scales of new energy, which is characterized by comprising the following steps of: the random process model of the illite in the step 2 is described by the following first-order random differential equation
dξ [m] (τ)＝-[ξ [m] (τ)-a [m] ]dτ+b [m] dW(τ),
Where τ is continuous time, dτ is time derivative, W (·) is the standard wiener process, ζ [m] (τ) represents the mth Gaussian component, dζ [m] (τ) is ζ [m] Differentiation of (τ), a [m] And b [m] Is a constant term; wherein a is [m] Expressing a regression target of the illite random process model, and determining the total level of new energy output; b [m] The strength of the new energy output fluctuation is represented; a, a [m] And b [m] Is estimated by the following procedure;
the probability distribution deduction process of the Ebrake random process in the step 2 under the second time scale is that
Firstly, calculating the solution of the first-order random differential equation based on the Earthway integral theory
Wherein τ 0 Is the initial time;
then, based on the Earthway differential theory, calculating the Gaussian component ζ [m] First and second moments of (τ)
Wherein E [ xi ] [m] (τ)]And Var [ zeta ] [m] (τ)]Respectively is xi [m] A first moment and a second moment of (τ); the mean value 0 and the variance of each Gaussian component in the Gaussian mixture model obtained in the step 1 are calculatedSubstituting into the following formula to obtain a [m] And b [m] The value of (2) is
Wherein T is the period of the minute-scale time scale; taking expectations from two sides of the first-order random differential equation to obtain dζ [m] First and second moments of (τ)
E[dξ [m] (τ)[＝(a [m] -E[ξ [m] (τ)])dτ,
Wherein E [ dζ ] [m] (τ)]And Var [ dζ ] [m] (τ)]Respectively dζ [m] A first moment and a second moment of (τ);
the new energy output multi-time scale uncertainty model in the step 2 is as follows:
under the specified confidence level, the probability interval of the uncertainty of the new energy output under the minute time scale is
Wherein alpha andlevel of division corresponding to lower and upper end points of interval,/->And->For corresponding alpha and->A quantile estimate of the quantile level;
under the specified confidence level, the probability interval of the uncertainty of the new energy output under the second time scale is
4. A probabilistic predictive power system backup quantization method for accounting for uncertainty in multiple time scales of new energy as claimed in claim 3, wherein: in the two-stage robust standby collaborative optimization model of the power system in the step 3, the requirement for standby adjustment is based on the zeta estimated in the step 2 t Probability intervalIs defined as
Wherein Ru is t And Rd t The standby requirement is adjusted up and down respectively for the period t;
the two-stage robust standby collaborative optimization model of the power system comprises a first-stage model and a second-stage model;
the objective function of the first stage model is
Wherein g is the number of the generator set,for the set of generator sets s is the energy storage device number,/-for>Is a collection of energy storage devices; />For generating power of the unit g in the period t, < >>And->The reserved upper and lower parts of the unit g are adjusted for standby; />And->Charging and discharging power of the energy storage s respectively, +.>And->The reserved upper and lower adjustment for the energy storage s is reserved for standby; />For the unit operating cost factor of the unit g, +.>And->Reserve cost is adjusted up and down for unit capacity of the unit g respectively; />And->The unit charge and discharge cost coefficients of the energy storage device s are respectively +.>And->Reserve cost is respectively adjusted up and down for unit capacity of the energy storage device s;
the first stage model contains power system operating constraints including:
a. generating set capacity constraints
Wherein,,and->The minimum output limit value and the maximum output limit value of the generator set are respectively;
b. climbing constraint of generator set
Wherein,,for the generating power of the unit g in the T-1 period, deltaT is 15 minutes scheduling time interval,/->And->Respectively regulating the power climbing rate limit value of the generator set downwards and upwards;
c. energy storage device operation constraints
Wherein,,andP s S the upper limit value and the lower limit value of the charge and discharge power of the energy storage device s;
d. energy storage device capacity constraints
Wherein,,E s andfor the lower and upper limits of the storage capacity of the energy storage device s, E s,t For storing energy of the energy storage device s in t period, E s,0 For storing energy of the energy storage means s at an initial moment, E s,T For storing energy at the end of a scheduling period, E, of the energy storage means s s,t-1 For storing energy of the energy storage means s during the period t-1 +.>And->The charge and discharge efficiency of the energy storage device s;
e. standby restraint for energy storage device
Wherein μ is a reserve capacity limit coefficient of the energy storage device;
f. standby demand constraint for power system
g. Node power balancing constraints
Wherein b is the node number of the power system,for the node set of the power system, w and v are the numbers of the wind farm and the photovoltaic power station respectively,/-for>Predicted force for wind farm w in period t,/->Predicting the power of the photovoltaic power station v in the t period;for the load power at node b, l is the branch number of the power system, +.>For the power transmitted by branch l fr (l) and to (l) are the start and end of branch l, respectively,/->Respectively collecting a generator set, a wind power plant, a photovoltaic power station and an energy storage device at the node b;
h. branch tide constraint
Wherein,,andP l F representing upper and lower limits of the line transmission power flow.
The objective function of the second stage model is
Wherein C is P,up And C P,dn The cost is penalized for upward and downward standby shortage respectively;and->The power balancing method is characterized in that the power balancing method is two relaxation variables, and the physical meaning of the power balancing method is that upward power and downward power which need to be compensated in a t period are needed for maintaining the real-time power balance of a node b when the climbing reserve is insufficient; />The power generation power is adjusted for the continuous change of the unit g in the t period, and is a function of time tau;and->Respectively adjusting charge and discharge power of the energy storage device s continuously changing in the t period;
the power system operation constraint conditions to be met by the second stage model include:
a. power generator set output adjustment constraint
b. Energy storage device output adjustment constraint
c. Real-time power balance constraint
Wherein,,for the possible prediction error of the generated power of the wind farm w in the t period, +.>Prediction error for the possible generation power of the photovoltaic power plant v in the t period, +.>And->Is->And->Probability intervals at 95% confidence level; />Climbing a slope for the possible generation power of the photovoltaic power station v in the t period, +.>Climbing a slope for the possible generation power of the photovoltaic power station v in the t period, +.>And->Is->Andprobability intervals at 95% confidence level.
5. The probability prediction-based standby quantification method for the electric power system considering the uncertainty of multiple time scales of new energy, which is characterized by comprising the following steps of: the model conversion method based on Bernstein polynomials in the step 4 is to make the continuous time variable in the second stage model By discrete time variable V t [i] And Bernstein base function +.>Is expressed mathematically as:
wherein I is the order of Bernstein polynomial, I is an integer less than I, V t [i] Is v t An ith control variable of (τ);
the general two-stage robust optimization model converted in the step 4 is as follows
Ω 0 ＝{E 0 x 0 +F 0 y 0 +G 0 z 0 ≤f}
Ω u ＝{E u x u ≤F u y 0 +Hu+d}
Wherein x is 0 And z 0 Continuous variable and integer variable, y, of the first stage, respectively 0 Is a coupling variable of two phases, x u As a continuous variable of the second stage Ω 0 And omega u For the feasible domain of the first and second stage models, u is the control variable of Bernstein polynomials corresponding to ζ (τ),set of u, b I (τ) is a vector form of the Bernstein basis function of the I order; />Respectively x 0 ,y 0 ,z 0 ,x u Coefficient of unit cost of E 0 ,F 0 ,G 0 ,E u ,F u H, d are constant coefficients in the inequality constraint.
6. The probabilistic prediction-based standby quantification method for the electric power system considering the uncertainty of multiple time scales of new energy, which is characterized by comprising the following steps of: the improved column and constraint generation algorithm in the step 5 decomposes the original problem into a main problem and a sub problem, and searches the optimal solution of the original problem in the iterative calculation process of the main problem and the sub problem;
for the r-th iteration, the mathematical model of the main problem is
s.t.E 0 x 0 +F 0 y 0 +G 0 z 0 ≤f
Wherein j is an integer from 1 to r, x u(j) Is the continuous variable optimal solution of the second stage obtained by the j-th iteration, u *(j) Is the value of u corresponding to the worst uncertainty scene obtained by the jth iteration, and eta isMaximum value of (2);
the mathematical model of the sub-problem is
s.t.E u x u ≤F u y 0 +Hu+d
λ(F u y 0*(r) +Hu+d-E u x u )＝0
Where lambda is the dual variable,and E is uT Respectively->And E is u Transpose of (y) 0*(r) Is y obtained by the r-th iteration 0 Is the optimal solution of (a);
in each iteration process, the lifting property of Bernstein polynomial is utilized to solve the u obtained by the sub-problem *(j) Bernstein space mapped to low dimensions is approximatedExpressed mathematically as
Wherein,,b is a positive integer less than I I (tau) and>respectively I-stage and->Compact form of the order Bernstein basis function, M e Is->Dimension mapping matrix, use +.>Approximately replace u *(j) Thereby reducing the model complexity of the main problem.
CN202310337026.4A 2023-03-31 2023-03-31 Power system standby quantification method based on probability prediction and considering uncertainty of multiple time scales of new energy Pending CN116502747A (en)

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