A method for unit commitment based on historical data under renewable energy penetration rate

Abstract

This invention discloses a unit combination method based on historical data under renewable energy penetration, comprising the following steps: S1. Constructing standby constraints in the unit combination problem; S2. Constructing a prediction error dataset consisting of prediction errors at various times within the data collection period; S3. Dividing the error dataset into two parts: a dataset and a set of uncertainties; S4. Dividing the dataset into uncertainties and constructing an uncertain set, and estimating its shape parameters; S5. Transforming robust constraints with uncertainties into deterministic constraints for direct solution; S6. Reconstructing the uncertain set and introducing a transformation function to transform and solve the optimization problem. This invention reduces the impact of prediction errors on solving the unit combination problem by using historical data of renewable energy prediction errors, effectively improving energy utilization.

Description

Technical Field

[0001] This invention relates to unit combination, and in particular to a unit combination method based on historical data under renewable energy penetration. Background Technology

[0002] Unit commissioning (UC) is a classic process executed by system operators (ISOs) in the electricity market. By solving UC, ISOs determine generator dispatch plans, minimizing the cost of meeting forecasted loads while considering various generation resource and system reliability constraints. Although the UC problem has been extensively studied in the literature, it now faces new challenges due to the high penetration rate of renewable energy. Because of the variability and intermittency of renewable energy sources, the forecasting error for renewable energy generation is typically much larger than that of traditional load forecasting. This large forecasting error introduces significant uncertainty into the UC problem, making it more challenging to obtain a suitable solution.

[0003] Traditional approaches to address uncertainty in Uncertainty Constraints (UC) include stochastic programming (SP) and robust optimization (RO). Chance-constrained programming (CCP) is one of the most popular types of SP, utilizing distributional information to model uncertainty. However, we encounter difficulties in obtaining accurate distributional information about renewable energy generation, forcing us to estimate the distribution. Furthermore, UC problems often involve complex joint chance constraints (CCs) due to the consideration of multiple periods, further limiting the accuracy of quantification. While CCP provides a concise and intuitive model of uncertainty, inaccurate estimations of the distribution can lead to unreliable solutions. Unlike CCP, RO utilizes a set of uncertainties to characterize uncertainty, requiring only the range of parameters. While RO guarantees best performance in the worst-case scenario, it can be overly conservative. Moreover, traditional reserve power also faces challenges in obtaining favorable solutions due to its lack of dispatch flexibility. In practice, ISOs cannot continuously dispatch spinning reserves (SR) because committing a unit results in discrete changes in SR. Faced with high renewable energy penetration, ISOs may have to start additional generators to provide sufficient reserve power, which is detrimental to improving energy utilization efficiency. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a unit combination method based on historical data under renewable energy penetration. By using historical data on renewable energy prediction errors, the impact of prediction errors on solving unit combination problems can be reduced, thereby effectively improving energy utilization.

[0005] S1. Constructing the reserve constraints in the unit combination problem;

[0006] S2. At each moment within the data collection period, collect the actual output power and predicted output power of renewable energy. Subtract the predicted output power from the actual output power to obtain the prediction error. Construct a prediction error dataset consisting of the prediction errors at each moment within the data collection period.

[0007] S3. Divide the error dataset into datasets. and dataset Two parts;

[0008] S4. Transfer the dataset Divided into and Construct an uncertainty set and estimate the shape parameters;

[0009] S5. Transform robust constraints with uncertain sets into deterministic constraints for direct solution;

[0010] S6. Reconstruct the uncertain set and introduce a transformation function to transform and solve the optimization problem.

[0011] The beneficial effects of this invention are: by using historical data on renewable energy prediction errors, this invention reduces the impact of prediction errors on solving unit combination problems, thereby effectively improving energy utilization. Attached Figure Description

[0012] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0013] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description.

[0014] like Figure 1 As shown, a unit combination method based on historical data under renewable energy penetration includes the following steps:

[0015] S1. Constructing the reserve constraints in the unit combination problem;

[0016] Reserve constraints in deterministic unit combination problems:

[0017]

[0018] This indicates whether the generator is on or off; 1 means the generator is on, and 0 means the generator is off. This is the unit's maximum output power. (D) t It is the load in the system, R t This redundancy is set up to deal with uncertainties in the system, and it is generally 5% of the load.

[0019] Under uncertainty, the reserve constraints in the unit combination problem involving renewable energy are as follows:

[0020]

[0021] Due to the uncertainty introduced by renewable energy forecasting errors, we generally modify deterministic constraints into chance constraints, i.e., the probability that the constraint can be satisfied. 1-ρ represents the probability of satisfying the constraint, and ξ is the forecasting error. Since renewable energy cannot be dispatched like traditional energy sources and is generally treated as a negative load, the forecasting error is added to the load. superior, This is the predicted load.

[0022] Introducing the uncertainty of statistical feasibility, we introduce the reserve constraint in the renewable energy unit combination problem:

[0023]

[0024] For a given dataset D ξ An algorithm is considered statistically feasible if it can guarantee that its solution satisfies the constraint with a confidence level of 1-δ. 1-δ is the confidence level at which the internal constraint is satisfied.

[0025] S2. At each moment within the data collection period, collect the actual output power and predicted output power of renewable energy. Subtract the predicted output power from the actual output power to obtain the prediction error. Construct a prediction error dataset consisting of the prediction errors at each moment within the data collection period.

[0026] In the embodiments of this application, the actual output power of renewable energy is obtained by actual measurement of renewable energy, and the predicted output power refers to the predicted time domain published in advance before the actual measurement; for historical information, both the measured output power and the predicted output power of renewable data can be regarded as known data that can be directly collected; for example, for wind power data, forecasting agencies (such as Bonneville Power Administration) will publish wind power forecast data for different time periods.

[0027] S3. Divide the error dataset into datasets. and dataset Two parts (of which, For step S4, For use in step S5);

[0028] S4. Transfer the dataset Divided into and Construct an uncertainty set and estimate the shape parameters;

[0029] S401. Transfer the dataset It is then divided into two parts, namely and in and Their sizes are z1 and z2, respectively;

[0030] S402. Construct the uncertainty set and estimate the shape parameters:

[0031] (1) Use To approximate the basic shape of an elliptic, for an elliptic uncertainty set It can be represented as:

[0032]

[0033] Where μ is the mean of the prediction error, and ξ is the prediction error; μ is a vector of the same length as ξ; for example, if there are 1000 predicted wind power outputs and their corresponding actual wind power outputs over 24 hours, ξ is the actual power minus the predicted power. Similarly, with 1000 data points, ξ... i The error represents the error corresponding to the i-th data point out of one thousand data points. μ is the average of the errors obtained from the one thousand data points over time (24 hours), that is, the average error at each moment.

[0034] M is The relevant symmetric matrix, s e It is a scalar, μ and M affect the shape of the uncertainty set, s e Characterizes the size of the ellipsoid;

[0035] (2) Through μ is estimated using the sample mean.

[0036]

[0037] ξ i Dataset The i-th data in the data;

[0038] (3) For a symmetric matrix M, estimate ξ using the sample covariance matrix or the diagonalized covariance matrix to provide the geometric distribution of ξ:

[0039] when When the size of the matrix is ​​greater than the dimension of ξ, use the covariance matrix; otherwise, use the diagonalized covariance matrix.

[0040]

[0041] (4) Define a transformation function y(ξ1). For an elliptic, set:

[0042] y(ξ1)=(ξ1-μ) T M -1 (ξ1-μ).

[0043] Calculate y(ξ) for each ξ i exist Obtain scalar s j Then, scalar [s1,s2,…,s z2 The values ​​are sorted in ascending order, and the index j of the ideal scalar is... * The following conditions must be met:

[0044]

[0045] in,

[0046] S5. Transform robust constraints with uncertain sets into deterministic constraints for direct solution;

[0047] By selecting scalars using the same method as for elliptic uncertainty sets, we obtain an uncertainty set that guarantees statistical feasibility.

[0048] Robustness constraints with uncertain sets should be transformed into deterministic constraints for direct solution. For elliptic uncertain sets, chance constraints are transformed into the following linear constraints:

[0049]

[0050] Where α t satisfy:

[0051]

[0052] In the above formula, M t It is a submatrix of M, representing the matrix corresponding to the error ξ at time t, α t These are intermediate variables, representing the parameters obtained after transforming the uncertain set into a linear constraint;

[0053] By solving this linear constraint problem, we can obtain... The solution is denoted as

[0054] The estimated parameters determine the shape of the ellipsoid, while the estimated parameters determine its size, resulting in a definite set of uncertainties that can be solved using solvers such as gurobi and standard robust optimization methods.

[0055] S6. Reconstruct the uncertain set and introduce a transformation function to transform and solve the optimization problem.

[0056] S601. Derive the form of the reconstructed uncertainty set:

[0057]

[0058] in It is the solution returned by solving the problem using the result obtained in step S3;

[0059] S602. Introduction of conversion functions

[0060]

[0061] Use h(ξ) The samples are transformed, and each sample will obtain a scalar h(ξ). Then, they are sorted in ascending order, still using the index j of the ideal scalar defined in step S3. * Find the j-th * A scalar, namely s;

[0062] The robustness constraint is transformed into a deterministic constraint to solve the problem. The original constraint is:

[0063]

[0064] After conversion, we get:

[0065]

[0066] S603. Solve the transformed optimization problem to obtain the unit combination scheduling scheme. This represents the on / off state of the i-th unit at time t, and allows us to obtain the on / off state of the unit at each time.

[0067] In the embodiments of this application, IEEE 14-node and 39-node standard test cases are used to simulate the unit combination problem during simulation experiments. The start-up and shutdown states and costs of the units are obtained, and the proportion of constraints violated is calculated. Lower costs are better, and a violation proportion as close to 0.05 as possible is preferable.

[0068] The final results are shown in the table below:

[0069] Table 8: Pcrformance on IEEE 14-bus System with 1-ρ=0.95,1-η=0.95

[0070]

[0071] Table 9: Performance on IEEE 39-bus System with 1-ρ=0.95,1-η=0.g5

[0072]

[0073] Validated on IEEE 14-bus and 39-bus systems, the method proposed in this application can minimize REP (the smaller the better) while closely matching the stability requirement.

[0074] The foregoing description illustrates and describes a preferred embodiment of the present invention. However, as previously stated, it should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the inventive concept described herein through the foregoing teachings or techniques or knowledge in related fields. Any modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for unit combination based on historical data under renewable energy penetration, characterized in that: Includes the following steps: S1. Constructing the reserve constraints in the unit combination problem; Step S1 includes: First, construct the reserve constraints in the deterministic unit combination problem: ； This indicates whether the generator unit is on or off; 1 indicates the unit is on, and 0 indicates the unit is off. It is the maximum output power of the unit. It is the load in the system. It is redundancy set up to deal with uncertainties in the system; Then, under uncertainty, the reserve constraint in the unit combination problem involving renewable energy is as follows: ； The uncertainty introduced by renewable energy forecasting errors will lead to the modification of deterministic constraints into chance constraints, i.e., the probability at which the constraints can be satisfied. That is, the probability of satisfying the constraints. The error is in the forecast, which treats renewable energy as a negative load, so the forecast error is added to it. superior, This is the predicted load; Finally, by introducing the uncertainty of statistical feasibility, we obtain the reserve constraint in the renewable energy unit combination problem: ； For a given dataset If an algorithm can guarantee that its solution has a... The confidence level satisfies this constraint, therefore the algorithm is considered statistically feasible. It represents the confidence level at which internal constraints are satisfied. S2. At each moment within the data collection period, collect the actual output power and predicted output power of renewable energy. Subtract the predicted output power from the actual output power to obtain the prediction error. Construct a prediction error dataset consisting of the prediction errors at each moment within the data collection period. ; S3. Divide the error dataset into datasets. and dataset Two parts; S4. Transfer the dataset Divided into and Construct an uncertainty set and estimate the shape parameters; Step S4 includes: S401. Transfer the dataset It is then divided into two parts, namely and ,in and The sizes are respectively and ; S202. Construct the uncertainty set and estimate the shape parameters: (1) Use To approximate the basic shape of an elliptic, for an elliptic uncertainty set This can be represented as: ； in, It is the mean of the prediction error. It is the prediction error; Is with Vectors of the same length; yes Related symmetric matrices, It is a scalar. and Influences the shape of the uncertainty set Characterizes the size of the ellipsoid; (2) Through Estimate by the sample mean .: ； Dataset The i-th data in the data; (3) For symmetric matrices Estimate using the sample covariance matrix or the diagonalized covariance matrix, providing... Geometric distribution: when Size greater than When the dimension is zero, use the covariance matrix; otherwise, use the diagonalized covariance matrix. ； (4) Define a transformation function For an elliptic, the following settings are used: ； calculate For each exist Obtain scalar Then scalar Values ​​sorted in ascending order, ideal scalar index. The following conditions must be met: ； in, ; S5. Transform robust constraints with uncertain sets into deterministic constraints for direct solution; Step S5 includes: Using the same method as for elliptic uncertainty sets, scalars are selected to obtain an uncertainty set that guarantees statistical feasibility; Robustness constraints with uncertain sets should be transformed into deterministic constraints for direct solution. For elliptic uncertain sets, chance constraints are transformed into the following linear constraints: ； in satisfy: ； In the above formula, yes The submatrix representing the error The matrix corresponding to time t, These are intermediate variables, representing the parameters obtained after transforming the uncertain set into a linear constraint; By solving this linear constraint problem, we can obtain... The solution is denoted as ; S6. Reconstruct the uncertain set and introduce a transformation function to transform and solve the optimization problem.

2. The method for unit combination based on historical data under renewable energy penetration according to claim 1, characterized in that: Step S6 includes: S601. Derive the form of the reconstructed uncertainty set: ； in It is the solution returned by solving the problem using the result obtained in step S3; S602. Introducing conversion functions ； use right The samples are transformed, and each sample will yield a scalar. Then sort them in ascending order, still using the index of the ideal scalar defined in step S3. Find the first A scalar, namely s; The robustness constraint is transformed into a deterministic constraint to solve the problem. The original constraint is: ； After conversion, we get: ； S603. Solve the transformed optimization problem to obtain the unit combination scheduling scheme. , This represents the on / off state of the i-th unit at time t, and allows us to obtain the on / off state of the unit at each time.

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