A multi-stage unit commitment method for power system with high proportion of new energy

Abstract

The application discloses a kind of multi-stage unit commitment methods of power system containing high proportion new energy, including constructing the unit commitment model covering day-ahead and real-time scheduling two stages, the uncertainty of new energy output prediction error is described using fuzzy set based on Wasserstein metric, mixed approximation rule is introduced, the start-stop state of quick start-stop unit is represented as the linear function of new energy output prediction error in previous stage, the model is converted into mixed integer linear programming problem easy to solve using dual theory, and combined with rolling optimization framework and real-time new energy output prediction information, obtain the final unit commitment scheme;The method is simple and easy to operate, can effectively reduce system cost, improve new energy consumption level, enhance power system reliability and flexibility, provide technical support for high proportion new energy power system safe and economic operation.

Description

Technical field

[0001] The present invention belongs to the technical field of power system operation control, and specifically relates to a multi-stage unit combination method for a power system containing a high proportion of new energy, which is particularly suitable for a power system with a high proportion of renewable energy access. [Background Technology]

[0002] As the penetration of renewable energy sources, such as wind and solar, in power systems continues to increase, the uncertainty surrounding power system operation and dispatch is also increasing. The intermittent and fluctuating output of renewable energy sources poses challenges to the safe and reliable operation of power systems. To effectively manage the uncertainty of renewable energy and ensure reliable and economical power system operation, advanced unit commitment optimization methods are required.

[0003] Traditional deterministic unit commitment methods struggle to effectively address the uncertainty introduced by fluctuations in renewable energy output. While stochastic optimization methods can account for uncertainty, they require precise probability distribution information, which is often difficult to accurately obtain. Robust optimization methods ensure system robustness by considering worst-case operating scenarios, but their solutions are often overly conservative, leading to higher operating costs.

[0004] Distributionally Robust Optimization (DRO) has garnered widespread attention in recent years as a compromise between stochastic optimization and robust optimization. Rather than relying on precise probability distributions, DRO utilizes a fuzzy set encompassing multiple possible probability distributions to describe uncertain parameters and optimizes the worst-case system operating cost (i.e., the most unfavorable probability distribution in the fuzzy set). This approach effectively reduces conservatism while maintaining system robustness.

[0005] In recent years, the Wasserstein metric-based DRO method has been applied to power system optimal scheduling problems. The Wasserstein metric quantifies the distance between two probability distributions and constructs fuzzy sets based on this metric. Traditional two-stage robust optimization models, when dealing with fast-start units, typically assume that their start and stop states remain unchanged during the second stage (real-time scheduling) and optimize only their output. This approach ignores the ability of fast-start units to start and stop rapidly within a day, limiting their ability to respond to fluctuations in renewable energy output.

[0006] Multi-stage optimization models can more accurately describe the dynamic decision-making process of power system operation, but their solution complexity is relatively high. The Mixed Approximation Rule (MAR), a dimensionality reduction technique, can effectively simplify the solution of multi-stage DRO models. MAR reduces the model's dimensionality by expressing future decision variables as functions of uncertainty parameters in previous stages, such as linear or affine functions.

[0007] This paper combines the Wasserstein metric, hybrid approximation rule and multi-stage optimization framework to propose a new multi-stage fully adaptive distributed robust unit combination method, aiming to fully utilize the flexibility of fast-start units to cope with the challenges brought by renewable energy output fluctuations. [Summary of the invention]

[0008] The purpose of the present invention is to provide a multi-stage unit combination method for an electric power system containing a high proportion of new energy, which can overcome the shortcomings of the existing technology. It is a simple, easy-to-implement unit combination method that can fully utilize the intraday start-up and shutdown flexibility of the fast-start unit, effectively respond to the challenges brought by fluctuations in the output of renewable energy, reduce system operating costs, improve the level of renewable energy absorption, and enhance the reliability and economy of the electric power system operation.

[0009] The technical solution of the present invention is a method for combining multi-stage units in a power system containing a high proportion of new energy, characterized in that it includes the following steps:

[0010] Step 1: Construct a multi-stage fully adaptive distributed broiler unit combination model considering the uncertainty of wind power output; the model takes minimizing the total system operating cost as the objective function and constructs the constraints of pre-dispatch operation and real-time dispatch operation;

[0011] The minimized total system operating cost in step one includes unit fuel cost, start-up and shutdown cost, output adjustment cost, and wind and load abandonment penalty cost set to ensure system reliability; the constraints are used to accurately characterize the dynamic decision-making process in the actual operation of the power system to distinguish the two stages of day-ahead scheduling and real-time scheduling, specifically referring to: 1) pre-scheduling operation constraints, mainly including unit start-up and shutdown state constraints, minimum start-up and shutdown time constraints, day-ahead output upper and lower limit constraints, and ramp rate constraints, to ensure that the unit meets safe operation requirements in the day-ahead scheduling stage; 2) real-time scheduling operation constraints, mainly including system power balance constraints and transmission line flow constraints, to ensure safe and stable operation of the power system in the real-time scheduling stage. At the same time, in the real-time scheduling stage, the unit output must meet the output adjustment upper and lower limit constraints.

[0012] The step 1 specifically includes the following contents:

[0013] Step 1.1 Considering the uncertainty of wind power output, the goal of the power system unit combination model is set to minimize the total system operation cost, that is, the objective function is shown in formula (1):

[0014]

[0015] Where: is the fuel price of unit i; Represents the startup cost of unit i; binary variable u i,t represents the startup variable of unit i in period t; represents the upper / lower reserve capacity price of unit i; P i,t is the base output of unit i in period t; f i (P i,t ) represents the power generation cost function, let f i (P i,t )=a i (P i,t ) 2 +b i P i,t +c i , a i 、b i 、c i is the power generation cost coefficient of unit i, The up / down reserve capacity provided for unit i in time period t; Indicates the price of adjusting the output of unit i upward / downward; W is the upward / downward output adjustment value provided by unit i in time period t; cur and L cur They represent the unit penalty costs of wind curtailment and load curtailment respectively; and They represent the wind curtailment and load curtailment of wind farm j and load node d in time period t respectively; D is the number of load nodes; N g is the number of units; ω [t] represents the set of wind power prediction errors from stage 1 to stage t, that is, x and y b are the discrete decision variables and continuous decision variables in the benchmark scenario of the pre-scheduling stage respectively; y r is the real-time scheduling decision variable;

[0016] Step 1.2: Determine the pre-scheduling operation constraints as shown in formulas (2)-(8):

[0017]

[0018] Where, v i,t is the shutdown variable of unit i in period t; binary variable I i,tis the start-up and shutdown status of unit i in period t, which is 1 when it is on and 0 when it is off. If unit i is in the start-up process in period t, the startup variable u of unit i in period t is i,t The value is 1; if unit i is in the shutdown process during period t, the shutdown variable v i,t The value is 1; is the minimum start / stop time of unit i; P is the duration of start / stop of unit i to period t-1; imin / P imax is the minimum / maximum technical output of unit i; is the upward / downward climbing rate of unit i; is the day-ahead output forecast value of wind farm j in period t; L d,t is the power load value of user d in time period t; k l,b is the sensitivity factor of line l to bus b; P l max is the maximum transmission power of line l;

[0019] Step 1.3: Determine the real-time scheduling constraints as shown in formulas (9)-(14):

[0020]

[0021] The decision variables in the benchmark scenario of the pre-scheduling stage are shown in formula (15):

[0022]

[0023] Decision variable y of the real-time scheduling model r Decision variables at each stage The composition is shown in formula (16):

[0024]

[0025] It can be seen that the decision variables x and y in the pre-scheduling stage b It is a here-and-now decision, which is determined before the uncertainty is realized; the real-time scheduling process includes 1-T scheduling stages, with a total of T scheduling stages. The decision variables in stage t are is a wait-and-see decision, whose uncertainty ω at the end of time t is [t] Determined when implemented, indicating multi-stage decision variables The unpredictability of the wait-and-see decision variables is a significant difference between the multi-stage model and the two-stage model. The two-stage model assumes that all the uncertainty information of all scheduling periods 1-T has been obtained when determining the wait-and-see decision variables. This assumption is inconsistent with the principle of time-series formulation of wait-and-see decisions in the real-time scheduling process. The feasible domain of the wait-and-see decision variables in multi-stage real-time scheduling is Ω t (x,y b ,ω [t] ,y [t-1] ), the decision variables in stage t depend on the decision variables and the uncertain variables ω1,ω2,…,ω t ;

[0026] Step 1.4 constructs a multi-stage fully adaptive distributed rod unit combination model based on the objective function determined in step 1.1 and the constraints determined in steps 1.2 and 1.3, as shown in formula (17):

[0027]

[0028] in, and Represent the states of slow-starting units and flexible units respectively; construct the affine function of random variable ξ, and let ξ 0，0 =1ξ:=[ξ 0,0 =1;ξ i,t =ω i,t ]; D t and d t is the coefficient matrix / vector related to the current stage number t in the constraints; is the probability distribution of the random variable ξ, which satisfies is the uncertainty set of wind power forecast errors, D is fuzzy uncertain set.

[0029] Step 2: Construct a fuzzy uncertainty set based on the Wasserstein metric, that is: according to the historical wind power output data and the corresponding forecast data, calculate the sample set of wind power output forecast errors, standardize the wind power output forecast error samples, and obtain a random variable that obeys the standard normal distribution; according to the pre-set confidence level and data sample size, use the probability inequality to determine the boundary of the standard normal distribution random variable, and obtain the fuzzy set of standardized wind power output forecast errors; according to the inverse transformation of the standardization process, restore the fuzzy set of standardized wind power output forecast errors to the fuzzy set of actual wind power output forecast errors. This fuzzy set takes the empirical distribution as the center and the radius determined by the pre-set confidence level as the boundary, and can cover the true distribution of wind power output forecast errors with a certain confidence level.

[0030] The fuzzy set construction process described in step 2 specifically includes:

[0031] Step 2.1: Establish a fuzzy uncertainty set based on Wasserstein distance;

[0032] Step 2.1.1 In order to accurately estimate the expected power generation cost, first use the sample set of historical data {ξ1,ξ2,…,ξ K Constructing an empirical distribution of wind power output forecast errors and take it as the true distribution approximation, that is: the sample set of historical data {ξ1,ξ2,…,ξ K} is divided into N equally spaced intervals, sorted by numerical value, and then the frequency of samples in each interval is counted to obtain the probability distribution of wind power output forecast error in each interval, that is, the empirical distribution

[0033] Step 2.1.2 Based on empirical distribution and Wasserstein metric, constructing a distribution that includes the true The fuzzy uncertain set D; Wasserstein metric is used to measure the “distance” between two probability distributions, and is defined as shown in formula (18):

[0034]

[0035] In the formula, the uncertain parameter | k 、 Obey respectively and for and The distance calculation method shown in formula (18) is to find an optimal joint distribution so that the cost of "transferring" the probability mass from one distribution to another is minimized, that is: Formula (18) represents the uncertainty set of wind power prediction errors. Above, experience distribution and the true distribution The Wasserstein distance between For all possible joint distributions In the example, the sample point ξ of the empirical distribution k and the sample points of the true distribution The expected value corresponding to the joint distribution with the smallest expected value of the distance between them;

[0036] The fuzzy uncertainty set D in step 2.1.2 is based on the empirical distribution As the center, with a radius ε determined by a pre-set confidence level a as the boundary, it can contain the true distribution with a confidence level of 1-a

[0037] Step 2.1.3 defines the fuzzy uncertainty set D as:

[0038]

[0039] In the formula represents the total probability distribution; the distance ε is the radius of the fuzzy uncertainty set D, which is determined by the size K of the given historical data, the number of equally spaced intervals N, the confidence α, and the diameter δ of the support space, as shown in formula (20);

[0040]

[0041] Step 2.1.4 In order to use the fuzzy uncertainty set D more conveniently in practical applications, the fuzzy uncertainty set D is mathematically described equivalently through the constraints shown in formulas (21)-(24), and the fuzzy uncertainty set based on Wasserstein distance is converted into a set of linear constraints, so that it can be conveniently applied to the optimization model to describe the uncertainty of wind power output prediction error.

[0042]

[0043] In formula (21), q nm Represents the nth sample point from the empirical distribution "Transport" to the mth sample point ξ of the true distribution m The probability mass of represents the sample point ξ m and The distance between them; in formulas (22)-(24), p mRepresents the mth sample point ξ in the true distribution m The probability of occurrence, Represents the nth sample point in the empirical distribution Probability of occurrence;

[0044] The constraint (21) in step 2.1.4 restricts the To the true distribution The “transportation” cost, that is, the weighted sum of the distances between sample points does not exceed the preset radius ε; the constraints (22) and (23) ensure that the marginal distribution of the joint distribution is respectively consistent with the empirical distribution and the true distribution Consistent; the constraint (24) ensures the true distribution It is a valid probability distribution, that is, the sum of the probabilities of all sample points is equal to 1.

[0045] Step 2.2: Establish a data-driven support set;

[0046] The probability distribution of wind power output forecast error should satisfy the assumption of light-tail distribution. In practical applications, this can be achieved by limiting the range of wind power forecast error. Therefore, in addition to the fuzzy uncertainty set D, the uncertainty set of wind power forecast error is It also has an important impact on the model results. In order to facilitate calculation, the prediction error sample set {ω1,ω2,…,ω K}Standardize according to formula (25):

[0047]

[0048] Where ∑ is the variance of the sample. Assuming that ∵ is an uncertain set of uncertain parameters θ, the uncertain set ∵ can be defined as follows:

[0049] ∵={θ∈R T ∣-γ≤θ i ≤γ} (26)

[0050] Where γ represents the boundary of the uncertain parameter θ;

[0051] Step 2.3: The uncertainty set of wind power forecast error is converted into the boundary γ, and then a support set with data-driven properties is established;

[0052] The uncertainty set should have the following two characteristics: 1) it covers the probability distribution of wind power output forecast error with a certain confidence level; 2) it should be as small as possible to reduce the conservatism of the model;

[0053] Therefore, the bound γ can be obtained by solving problem (27):

[0054]

[0055] Where, and ψ are the probability distribution of the uncertain parameter θ and the fuzzy uncertain set, respectively. η represents the confidence level of the uncertain set ∵. The constraint of problem (27) is a chance-constrained optimization problem that is difficult to solve. According to the duality theory, it can be transformed into an optimization problem that is easy to solve (28):

[0056]

[0057] Where, (·) + =max(·,0), the solution method of the optimization problem (28) is well known to those skilled in the art, for example, the nested bisection method can be used to solve it;

[0058] When the boundary γ is obtained by solving formula (28), the support set with data-driven properties can be obtained, as shown in formula (29):

[0059]

[0060] Formula (29) can be written as (30), where ω - and ω + represents the boundary of the uncertain variable ξ;

[0061]

[0062] For each uncertain variable ξ i,t Insert r within the boundary range i,t -1 breakpoint, i.e.

[0063] Step 2.4 introduces a nonlinear operator for the uncertain variable ξ, thereby constructing a flexible hybrid approximation rule as shown in formulas (31)-(34):

[0064]

[0065] Uncertain set of wind power forecast errors Reconstruct and obtain the reconstructed uncertainty set as shown in formula (35) and formula (36):

[0066]

[0067] Due to the introduction of uncertain variables of nonlinear operators The discontinuous characteristics of the wind power forecast error after reconstruction make the uncertainty set It is an open set. In order to simplify the difficulty of solving the model, the reconstructed wind power prediction error uncertainty set is constructed. The closed convex hull of As shown in formula (37) and formula (38):

[0068]

[0069] in, represents the normalized wind power output prediction error, Is the vertex Correlation coefficient;

[0070] From formulas (35) and (36), we can see that the reconstructed wind power forecast error uncertainty set is In each component and Therefore, formulas (37) and (38) can be organized into the form shown in formula (39), and finally the closed convex hull of the wind power output prediction error is obtained: The closed convex hull can be represented by the linear constraints shown in formula (39);

[0071]

[0072] Where,

[0073] Step 3: In order to reduce the solution complexity of the multi-stage fully adaptive distributed rod unit combination model constructed in step 1 as shown in formula (17), so that it can be applied to the actual power system operation optimization problem, and considering that the model contains a large number of decision variables and constraints, the computational complexity of directly solving the model is very large, especially when rapid decision-making is required in the real-time scheduling stage, a hybrid approximation rule is introduced to reduce the dimensionality of the model to simplify the model structure and improve the solution efficiency;

[0074] The step three specifically refers to: setting the start-stop state decision variable y of the rapid start-up unit at time t t It is expressed as a linear function of the wind power output forecast error in the previous stage, that is: where ξ [t]^ represents the wind power output forecast error vector from moment 1 to moment t, is the coefficient matrix of the linear function; similarly, the output decision variable x of the fast start unit at time t is t It can also be expressed as a linear function of the wind power output forecast error in the previous stage, that is:

[0075] Step 4: Convert the multi-stage fully adaptive distributed blue-rod unit commitment model after the hybrid approximation rule is introduced in step 3 into a mixed integer linear programming problem that is easy to solve;

[0076] The step 4 specifically includes:

[0077] Step 4.1 Reconstruct the inequality constraints:

[0078] Substituting the mixed approximation rule into the first constraint of formula (17) in step 1.4, we obtain formula (40):

[0079]

[0080] Introducing the closed convex hull of wind power output prediction error where S^={(i,T)|i∈[R],T∈[t]}∪{(0,0)}, Indicates that the set includes the wind power output forecast errors of all fast-start units in each time period;

[0081] make right Reconstruct as formula (42):

[0082]

[0083] Then, formula (40) can be rewritten as:

[0084]

[0085] in,

[0086]

[0087] Formula (42) performs standard robust equivalence reconstruction and uses duality theory to transform the inequality constraints containing uncertain parameters into linear matrix inequalities without uncertain parameters, as shown in formula (43);

[0088]

[0089] Step 4.2 Reconstruction of equality constraints:

[0090] Substituting the mixed approximation rule into the second constraint of formula (17) in step 1.4, we can obtain:

[0091]

[0092] Formula (44) is processed in the same way as formula (40), and the closed convex hull is introduced. Then formula (44) can be reconstructed as:

[0093]

[0094] Closed convex hull based on wind power output prediction error The separable characteristics of , formula (45) can be rewritten as:

[0095]

[0096] Therefore, by performing an equivalent transformation on formula (44), we can obtain formulas (47) and (48):

[0097]

[0098] Among them Z0 t and Z [t] t are the coefficient vector and matrix without uncertain parameters, respectively, and e is a unit vector; formulas (47) and (48) no longer contain the wind power output prediction error vector and This eliminates the influence of uncertainty on the equality constraints, making formulas (47) and (48) easier to solve;

[0099] Step 4.3 Reconstruction of the objective function:

[0100] By introducing the closed convex hull of wind power output prediction error The objective function in formula (17) can be transformed as shown in formula (49):

[0101]

[0102] Since the distributional robust optimization problem is to solve the optimal objective function expectation under the condition that the probability distribution of uncertain factors varies within a certain range, the objective function needs to be reformulated. Therefore, according to the strong duality theory, the inner layer of the objective function described by formula (17) can be reconstructed as:

[0103]

[0104] Other,

[0105]

[0106] According to the minimax theorem, applying the mixed approximation rule and formula (51) to the constraints in (50), we can obtain:

[0107]

[0108] According to the duality theory, the second part of formula (52) can be equivalent to:

[0109]

[0110] Furthermore, we can get:

[0111]

[0112] Therefore, formula (50) is equivalent to formula (55), which is the reconstructed objective function;

[0113]

[0114] Step 4.4 combines formulas (43), (47), (48) and (55) to obtain the reconstructed multi-stage fully adaptive distributionally robust unit commitment (MFA-DRUC) model shown in formula (56).

[0115]

[0116] Step 5: Based on the solution method of the rolling optimization framework, the multi-stage fully adaptive distributed robust unit combination model containing hybrid approximate rules established in steps 1 to 4 is solved, and the final practical unit combination scheme is obtained. The process is as follows: Figure 2 shown.

[0117] The model solution based on the rolling optimization framework in step 5 specifically includes the following steps:

[0118] Step 5.1: Divide the entire scheduling cycle by time, initialize the current time period t, and set it as the first time period, that is, t = 1;

[0119] Step 5.2: Obtain wind power output forecast information for the current time period t This information can come from weather forecasts, historical wind farm output data, etc.

[0120] Step 5.3: Get the latest wind power output forecast information from step 5.2 Update the fuzzy uncertainty set D constructed in step 2 to accurately describe the uncertainty of wind power output in the current time period;

[0121] Step 5.4: Using the updated fuzzy uncertainty set D obtained in step 5.3, retrain the hybrid approximation rule introduced in step 3 to obtain the updated hybrid approximation rule, such as the updated coefficient matrix and To better capture the relationship between the start-up and shutdown status of the fast-start units in the current time period and the wind power output in the previous period;

[0122] Step 5.5: Substitute the retrained hybrid approximation rule into the mixed integer linear programming model (Formula (56)) obtained in step 4, and solve it using a known solver to obtain the optimal unit combination plan for the current time period t, including the start and stop status and output of each unit in the current time period;

[0123] Step 5.6: Determine whether the current time period t reaches the end time T of the scheduling cycle; if t <T,则将当前时间段更新为下一个时间段,即t=t+1,并返回步骤5.2继续执行上述流程;如果t=T,则结束滚动优化过程,此时已经得到了整个调度周期的最优机组组合方案。

[0124] The beneficial effects of the technical solution provided by the present invention are:

[0125] ① Improve the reliability of system operation: The multi-stage fully adaptive distributed blue-rod unit combination method proposed in the present invention can effectively deal with uncertain factors such as wind power output fluctuations. Under the premise of ensuring system safety constraints, it can find the optimal unit combination scheme that meets various possible scenarios and improve the reliability of power system operation.

[0126] ② Reduce system operating costs: The present invention reduces the complexity of solving the multi-stage distributed robust optimization problem by introducing a hybrid approximation rule. At the same time, it fully considers the intraday start-stop flexibility of the fast-start unit, and can more economically utilize the fast-start unit to cope with wind power output fluctuations, thereby reducing the total operating cost of the system.

[0127] ③ Improve the level of renewable energy consumption: The present invention can better coordinate the rapid start-up of units and the output of renewable energy, reduce the phenomenon of wind and solar power abandonment, and improve the utilization rate of renewable energy.

[0128] ④ Enhanced model adaptability: The present invention adopts a fuzzy set construction method based on Wasserstein metric, which does not require precise probability distribution information and is more suitable for practical application scenarios. It enhances the model's adaptability to different types of renewable energy and power system operating environments.

Brief Description of the Drawings

[0129] Figure 1 The figure is a flow chart of a multi-stage unit combination method for a power system containing a high proportion of new energy sources according to the present invention.

[0130] Figure 2 This is a schematic diagram of a rolling optimization process of a multi-stage unit combination method for a power system containing a high proportion of new energy sources involved in the present invention.

[0131] Figure 3This is a 6-node system architecture diagram of Example 3 of a multi-stage unit combination method for a power system containing a high proportion of new energy sources involved in the present invention.

[0132] Figure 4 This is a schematic diagram of the in-sample cost comparison of the MFA-DRUC and MA-DRUC methods in a 6-node system of Example 3 of a multi-stage unit combination method for a power system containing a high proportion of renewable energy according to the present invention.

[0133] Figure 5 Schematic diagram showing the cost comparison between the MFA-DRUC and MA-DRUC methods under different distributions in a 6-node system of Example 3 of a multi-stage unit combination method for a power system with a high proportion of renewable energy involved in the present invention (wherein, Figure 5 -a is the result based on 20 days of historical data, Figure 5 -b is the result based on 365 days of historical data).

[0134] Figure 6 The cost comparison of the three methods MFA-DRUC, ROUC and SOUC under different distributions in the 6-node system of Example 3 of a multi-stage unit combination method for a power system with a high proportion of renewable energy involved in the present invention (wherein, Figure 6 -a is the result based on 20 days of historical data, Figure 6 -b is the result based on 365 days of historical data). [Specific implementation method]

[0135] To make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments and features in the embodiments of this application can be combined with each other unless there is a conflict.

[0136] Example 1

[0137] The embodiment of the present invention establishes a multi-stage unit combination method for a power system containing a high proportion of new energy, such as Figure 1 As shown in the figure, it can effectively reduce the total operating cost of the system, improve the level of renewable energy consumption, and enhance the reliability and economy of power system operation. It includes the following steps:

[0138] 101: Based on the actual operation of the power system, a multi-stage fully adaptive distributed blue-type unit combination model is constructed. The model aims to minimize the total operating cost of the system, with the constraints of pre-dispatch operation and real-time dispatch operation. The uncertain parameters in the model, such as wind power output, are represented as random variables obeying specific fuzzy sets.

[0139] Among them, minimizing the total system operating cost includes unit fuel cost, start-up and shutdown cost, output adjustment cost, and wind and load curtailment penalty cost set to ensure system reliability; the constraints are used to accurately characterize the dynamic decision-making process in the actual operation of the power system to distinguish the two stages of day-ahead scheduling and real-time scheduling, specifically: 1) pre-dispatch operation constraints, mainly including unit start-up and shutdown status constraints, minimum start-up and shutdown time constraints, day-ahead output upper and lower limits constraints, and ramp rate constraints, to ensure that the unit meets safe operation requirements in the day-ahead scheduling stage; 2) real-time scheduling operation constraints, mainly including system power balance constraints and transmission line flow constraints, to ensure the safe and stable operation of the power system in the real-time scheduling stage. At the same time, in the real-time scheduling stage, the unit output must meet the output adjustment upper and lower limit constraints.

[0140] Different from the traditional deterministic unit combination model or the random unit combination model that relies on the precise probability distribution, the present invention constructs a multi-stage fully adaptive distributed robust unit combination model to effectively characterize the uncertainty brought about by the wind power output forecast error and be closer to the actual operation of the power system. Specifically, in order to better describe the uncertainty and volatility of wind power output forecasts, the model represents the actual output of the wind farm as a random variable that obeys a specific fuzzy set, rather than using traditional deterministic variables or random variables that rely on precise probability distribution, thereby improving the model's coverage of various possible output scenarios and enhancing its robustness. In addition, considering the close temporal dependency between day-ahead scheduling and real-time scheduling in the actual operation of the power system, the present invention adopts a multi-stage decision framework to simulate this process, rather than simplifying the decision problem to a single-stage optimization, so as to be closer to the actual operation of the power system and improve the practicality of the model.

[0141] 102: Use historical data to estimate the empirical distribution of wind power output forecast errors, and construct a fuzzy set containing the true distribution based on the Wasserstein metric. The fuzzy set is centered on the empirical distribution and bounded by a radius determined by a pre-set confidence level.

[0142] In order to accurately describe the probability distribution information of wind power output forecast error, the present invention uses historical data to estimate the empirical distribution of wind power output forecast error, and constructs a fuzzy set containing the true distribution based on the Wasserstein metric. Specifically, first, based on the historical wind power output data and the corresponding forecast data, a sample set of wind power output forecast error is calculated. In order to eliminate the influence of dimension, the wind power output forecast error samples are standardized to obtain a random variable that obeys the standard normal distribution. Then, based on the pre-set confidence level and data sample size, the probability inequality is used to determine the boundary of the standard normal distribution random variable to obtain the standardized fuzzy set of wind power output forecast error. Finally, based on the inverse transformation of the standardization process, the standardized fuzzy set of wind power output forecast error is restored to the fuzzy set of actual wind power output forecast error. This fuzzy set is centered on the empirical distribution and bounded by a radius determined by the pre-set confidence level, and can cover the true distribution of wind power output forecast error with a certain degree of confidence.

[0143] 103: In order to reduce the solution complexity of the multi-stage fully adaptive distributed robust unit combination model constructed in step 1 so that it can be applied to actual power system operation optimization problems, and considering that the model contains a large number of decision variables and constraints, the computational complexity of directly solving the model is very large, especially when quick decisions need to be made in the real-time scheduling stage. Therefore, a hybrid approximation rule is introduced to express the start and stop state decision variables of the fast-start unit in the model as a linear function of the uncertainty parameters of the previous stage, simplifying the complex relationship between the decision variables and the uncertainty parameters, reducing the dimension of the problem, and embedding the linear function into the multi-stage fully adaptive distributed robust unit combination model.

[0144] The core idea of ​​the hybrid approximation rule is to express some decision variables as functions of the uncertainty parameters of the previous stage, thereby reducing the number of decision variables and the complexity of the constraints. In this invention, since the start and stop status of slow-start units (such as coal-fired units) is usually determined in the day-ahead scheduling stage, the hybrid approximation rule is mainly applied to the start and stop status decision variable y of fast-start units (such as gas turbine units). t and output decision variable x t .

[0145] 104:The multi-stage fully adaptive distributed rod unit combination model with mixed approximation rules is transformed into an easy-to-solve mixed integer linear programming problem using duality theory.

[0146] Since the start-stop state and output decision variables of the rapid start-stop unit are expressed as linear functions of the wind power output prediction error of the previous stage in step 103, and these linear functions are substituted into the multi-stage fully adaptive distributed Robust unit combination model, a multi-stage fully adaptive distributed Robust unit combination model containing mixed approximation rules is obtained. However, the model still contains complex fuzzy sets and nonlinear constraints, and it is difficult to solve it directly using the existing optimization solver. Therefore, the present invention uses duality theory to perform an equivalent transformation on the model, converting it into a mixed integer linear programming problem that is simpler in form and easier to solve.

[0147] Specifically, the present invention first converts the inequality constraints in the model into equivalent semi-infinite norm constraints. The semi-infinite norm constraints can concisely express the worst-case considerations under all possible probability distributions, because the model needs to ensure that the constraints hold in all cases.

[0148] The present invention then uses duality theory to transform the semi-infinite norm constraint into a finite number of linear constraints. Duality theory provides an effective method for converting complex constraints into simpler ones. By introducing dual variables, the previously difficult semi-infinite norm constraint can be converted into a finite number of linear constraints, thereby reducing the difficulty of solving the model.

[0149] At the same time, considering that the equality constraints in the model may contain uncertain parameters such as wind power output, the present invention performs an equivalent transformation so that these uncertain parameters are no longer explicitly included. The purpose of this step is to further simplify the model structure and make it easier to solve.

[0150] Finally, the present invention utilizes duality theory to transform the model's objective function into a form that is easier to solve. Similar to the transformation of constraints, duality theory can also be applied to transform the objective function into a more easily solvable form. For example, a complex objective function containing expected values ​​can be transformed into a series of linear expressions.

[0151] Through the four steps described above, the present invention successfully transforms the multi-stage fully adaptive distributed robust unit commitment model with hybrid approximation rules into an equivalent mixed-integer linear programming problem. This problem can be efficiently solved using existing mature optimization solvers (such as GUROBI and CPLEX), resulting in an optimal unit commitment solution that accounts for wind power output uncertainty.

[0152] 105: Model solving is performed using a rolling optimization framework, the entire scheduling period is divided into multiple time periods, the fuzzy set and the hybrid approximation rule are updated using the latest wind power output prediction information in each time period, and the updated model is solved to obtain the optimal unit commitment scheme in the current time period, so that the dynamic decision-making process of the actual operation of the power system is more accurately described, and the process is as shown in Figure 2

[0153] Specifically, it refers to:

[0154] Step 5.1 divides the entire scheduling period (for example, 24 hours) into multiple time periods (for example, one time period per hour), and sequentially makes decisions for each time period;

[0155] Step 5.2 At the beginning of each time period, first obtain the latest wind power output prediction information, and update the fuzzy uncertainty set D constructed in step two according to the information to accurately describe the uncertainty of the wind power output;

[0156] Step 5.3 According to the updated fuzzy uncertainty set D in step 5.2, retrain the hybrid approximation rule introduced in step three to better capture the relationship between the start-stop state of the fast-starting unit and the wind power output in the previous stage;

[0157] Step 5.4 Substitute the retrained hybrid approximation rule into the mixed integer linear programming model obtained by transformation in step four, and use a mature solver to solve it to obtain the optimal unit commitment scheme in the current time period, including the start-stop state and output of each unit in the current time period.

[0158] Through this rolling optimization method, the application can adjust the unit commitment scheme in real time according to the latest wind power output prediction information to better cope with the impact of wind power output fluctuations. At the same time, since each time period only needs to consider the system operation in the current time period and a short period of time thereafter, the scale of the model is relatively small, which can meet the requirements of actual power system operation and dispatch for calculation efficiency.

[0159] In summary, the embodiment of the application can effectively reduce the total system operation cost, improve the renewable energy consumption level, and enhance the reliability and economy of the power system operation through the above steps 101-105.

[0160] Example 2

[0161] This embodiment combines mathematical models to describe the specific implementation process of the multi-stage fully adaptive distribution robust unit commitment method based on hybrid approximation rules, including model establishment, model reconstruction and model solving.

[0162] ​201 Multi-time scale unit combination model with wind power uncertainty:

[0163] This section corresponds to step one in the specification, namely, constructing a multi-stage fully adaptive distributed blue-rod unit combination model. In order to accurately describe the dynamic decision-making process in the actual operation of the power system, the present invention adopts a multi-stage fully adaptive distributed blue-rod unit combination model, and refines the model into two stages: day-ahead scheduling and real-time scheduling. In the day-ahead scheduling stage, the model takes into account constraints such as unit start and stop status, output limit, ramp rate limit, system power balance, and transmission line flow limit, and constructs a deterministic optimization model with minimizing the total operating cost of the system as the objective function. On this basis, the present invention represents uncertainty parameters such as wind power output as random variables that obey specific fuzzy sets, and expands the day-ahead scheduling model into a multi-stage model to characterize the impact of wind power output fluctuations on the unit combination scheme during real-time scheduling.

[0164] Wherein, step 201 includes:

[0165] 1) Objective function

[0166] Considering the uncertainty of wind power output, the goal of the power system unit combination model is set to minimize the total system operation cost, that is, the objective function is shown in formula (1):

[0167]

[0168] Where: is the fuel price of unit i; Represents the startup cost of unit i; binary variable u i,t represents the startup variable of unit i in period t; represents the upper / lower reserve capacity price of unit i; P i,t is the base output of unit i in period t; f i (P i,t ) represents the power generation cost function, let f i (P i,t )=a i (P i,t ) 2 +b i P i,t +c i , a i 、b i 、c i is the power generation cost coefficient of unit i, The up / down reserve capacity provided for unit i in time period t; Indicates the price of adjusting the output of unit i upward / downward; W is the upward / downward output adjustment value provided by unit i in time period t; cur and Lcur They represent the unit penalty costs of wind curtailment and load curtailment respectively; and They represent the wind curtailment and load curtailment of wind farm j and load node d in time period t respectively; D is the number of load nodes; N g is the number of units; ω [t] represents the set of wind power prediction errors from stage 1 to stage t, that is, x and y b are the discrete decision variables and continuous decision variables in the benchmark scenario of the pre-scheduling stage respectively; y r is the real-time scheduling decision variable;

[0169] 2) Determine the pre-scheduling operation constraints as shown in formulas (2)-(8):

[0170]

[0171] Where, ν i,t is the shutdown variable of unit i in period t; binary variable I i,t is the start-up and shutdown status of unit i in period t, which is 1 when it is on and 0 when it is off. If unit i is in the start-up process in period t, the startup variable u of unit i in period t is i,t The value is 1; if unit i is in the shutdown process during period t, the shutdown variable ν i,t The value is 1; is the minimum start / stop time of unit i; P is the duration of start / stop of unit i to period t-1; imin / P imax is the minimum / maximum technical output of unit i; is the upward / downward climbing rate of unit i; is the day-ahead output forecast value of wind farm j in period t; L d,t is the power load value of user d in time period t; k l,b is the sensitivity factor of line l to bus b; P l max is the maximum transmission power of line l.

[0172] 3) Determine the real-time scheduling constraints as shown in formulas (9)-(14):

[0173]

[0174] The decision variables in the benchmark scenario of the pre-scheduling stage are shown in formula (15):

[0175]

[0176] Decision variable y of the real-time scheduling model rDecision variables at each stage The composition is shown in formula (16):

[0177]

[0178] It can be seen that the decision variables x and y in the pre-scheduling stage b It is a here-and-now decision, which is determined before the uncertainty is realized; the real-time scheduling process includes 1-T scheduling stages, with a total of T scheduling stages. The decision variables in stage t are is a wait-and-see decision, whose uncertainty ω at the end of time t is [t] Determined when implemented, indicating multi-stage decision variables The unpredictability of the wait-and-see decision variables is a significant difference between the multi-stage model and the two-stage model. The two-stage model assumes that all the uncertainty information of all scheduling periods 1-T has been obtained when determining the wait-and-see decision variables. This assumption is inconsistent with the principle of time-series formulation of wait-and-see decisions in the real-time scheduling process. The feasible domain of the wait-and-see decision variables in multi-stage real-time scheduling is Ω t (x,y b ,ω [t] ,y [t-1] ), the decision variables in stage t depend on the decision variables and the uncertain variables ω1,ω2,…,ω t ;

[0179] 202 points Blue Rod Model Description:

[0180] This section corresponds to step two and step three in the specification, namely, constructing a fuzzy uncertainty set and introducing a hybrid approximation rule. In order to improve the model's description accuracy of the wind power output forecast error, the present invention first constructs a fuzzy uncertainty set containing the true distribution based on the Wasserstein metric. The fuzzy set is centered on the empirical distribution of the wind power output forecast error estimated using historical data and has a radius determined by a pre-set confidence level as the boundary, thereby improving the model's description accuracy of the wind power output forecast error. In order to reduce the complexity of the model solution, the present invention introduces a hybrid approximation rule to reduce the model's dimensionality, and expresses the start-stop state decision variables of the fast-start unit in the model as linear functions of the uncertainty parameters of the previous stage.

[0181] The compact form of the multi-stage fully adaptive distributed rod unit combination model is shown in formula (17).

[0182]

[0183] in, and Represent the states of slow-starting units and flexible units respectively; to construct the affine function of random variable ξ, let ξ 0，0 =1ξ:=[ξ 0,0 =1;ξ i,t =ω i,t ]; D t and d t is the coefficient matrix / vector related to the current stage number t in the constraints. is the probability distribution of ξ, which satisfies is the uncertainty set of wind power forecast errors, D is fuzzy uncertain set.

[0184] 1) Fuzzy uncertain sets based on Wasserstein distance

[0185] Specifically, the sample set of historical data {ξ1,ξ2,…,ξ K Constructing an empirical distribution of wind power output forecast errors and take it as the true distribution Specifically, the sample set {ξ1,ξ2,…,ξ K} is divided into several intervals, and the frequency of samples in each interval is counted to obtain the probability distribution of wind power output forecast error in each interval, that is, the empirical distribution Since the true distribution is often difficult to obtain accurately, this invention is based on the empirical distribution and Wasserstein metric to construct a distribution that includes the true distribution The fuzzy uncertain set D is based on the empirical distribution As the center, with a radius ε determined by a pre-set confidence level α as the boundary, it can contain the true distribution with a confidence level of 1-α The Wasserstein metric is used to measure the "distance" between two probability distributions and is defined as shown in formula (18):

[0186]

[0187] In the formula, the uncertain parameter ξ k 、 Obey respectively and for and The joint distribution of

[0188] Formula (18) defines the Wasserstein distance, which is used to measure the distance between two probability distributions. The distance is calculated by finding an optimal joint distribution that minimizes the cost of "transferring" probability mass from one distribution to another. Specifically, the formula represents the uncertainty set of wind power forecast errors. Above, experience distribution and the true distribution The Wasserstein distance between For all possible joint distributions In the empirical distribution, the sample point ξ k and the sample points of the true distribution The expected value corresponding to the joint distribution with the smallest expected value of the distance between them.

[0189] The fuzzy uncertain set D is defined as:

[0190]

[0191] In the formula represents the entire probability distribution; the distance ε is determined by the size K of the given historical data, the number of bins N, the confidence α, and the diameter δ of the support space, as shown in formula (20);

[0192]

[0193] In order to more conveniently use fuzzy uncertainty sets in practical applications, the present invention provides an equivalent mathematical description of them through constraints (21)-(24). These constraints transform the calculation of the Wasserstein distance into a series of linear constraints, which are easier to solve in the optimization model.

[0194]

[0195] Specifically, constraint (21) restricts the To the true distribution The “transportation” cost, that is, the weighted sum of the distances between sample points does not exceed the pre-set radius ε. nm Represents the nth sample point from the empirical distribution "Transport" to the mth sample point ξ of the true distribution m The probability mass of represents the sample point ξ m and The distance between them.

[0196] Constraints (22) and (23) ensure that the marginal distribution of the joint distribution is respectively equal to the empirical distribution and the true distribution Consistent. Among them, p m Represents the mth sample point ξ in the true distribution m The probability of occurrence, Represents the nth sample point in the empirical distribution Probability of occurrence.

[0197] Constraint (24) ensures the true distribution It is a valid probability distribution, that is, the sum of the probabilities of all sample points is equal to 1.

[0198] Through the above constraints, the present invention transforms the fuzzy uncertainty set based on Wasserstein distance into a set of linear constraints, so that it can be conveniently applied to the optimization model to describe the uncertainty of wind power output prediction error.

[0199] 2) Data-driven support set

[0200] The probability distribution of wind power output forecast error should satisfy the assumption of light-tail distribution. In practical applications, this can be achieved by limiting the range of wind power forecast error. Therefore, in addition to the fuzzy uncertainty set D, the uncertainty set of wind power forecast error is It also has an important impact on the model results. In order to facilitate calculation, the prediction error sample set {ω1,ω2,…,ω K}Standardize according to formula (25):

[0201]

[0202] Where ∑ is the variance of the sample. Assuming that ∵ is an uncertain set of uncertain parameters θ, the uncertain set ∵ can be defined as follows:

[0203] ∵={θ∈R T ∣-γ≤θ i ≤γ} (26)where γ represents the bound of the uncertain parameter θ;

[0204] The uncertainty set should have the following two characteristics: 1) it covers the probability distribution of wind power output forecast error with a certain confidence level; 2) it should be as small as possible to reduce the conservatism of the model;

[0205] Therefore, the bound γ can be obtained by solving problem (27):

[0206]

[0207] Where, and ψ are the probability distribution of the uncertain parameter θ and the fuzzy uncertain set, respectively. η represents the confidence level of the uncertain set ∵. The constraint of problem (27) is a chance-constrained optimization problem that is difficult to solve. According to the duality theory, it can be transformed into an optimization problem that is easy to solve (28):

[0208]

[0209] Where, (·) + =max(·,0), the solution method of the optimization problem (28) is well known to those skilled in the art, for example, the nested bisection method can be used to solve it;

[0210] When the boundary Y is obtained by solving formula (28), the support set with data-driven properties can be obtained:

[0211]

[0212] Formula (29) can be written as (30), where ω - and ω + represents the boundary of the uncertain variable ξ;

[0213]

[0214] For each uncertain variable ξ i,t Insert r within the boundary range i,t -1 breakpoint, i.e.

[0215] A nonlinear operator is introduced for the uncertain variable ξ to construct a flexible hybrid approximation rule.

[0216]

[0217] Uncertain set of wind power forecast errors Reconstruct and obtain the reconstructed uncertainty set as shown in formula (35) and formula (36):

[0218]

[0219] Due to the introduction of nonlinear operator uncertainty variables The discontinuous characteristics of the wind power forecast error after reconstruction make the uncertainty set It is an open set. In order to simplify the difficulty of solving the model, the reconstructed wind power prediction error uncertainty set is constructed. The closed convex hull of As shown in formula (37) and formula (38):

[0220]

[0221] in, represents the normalized wind power output forecast error, Is the vertex Correlation coefficient;

[0222] From formulas (35) and (36), we can see that the reconstructed wind power forecast error uncertainty set is In each component and is separable, so formulas (37) and (38) can be arranged as:

[0223]

[0224] Where,

[0225] In summary, in step 2, the closed convex hull of the wind power output forecast error is finally obtained by standardizing the wind power output forecast error, constructing the fuzzy uncertainty set using the Wasserstein metric, and introducing the nonlinear operator to construct a flexible hybrid approximation rule. The closed convex hull can be represented by a series of linear constraints, as shown in Equation (39). This closed convex hull can cover the true distribution of wind power output forecast errors with a certain degree of confidence, while being compact and easy to calculate, laying the foundation for solving subsequent models.

[0226] 3) Hybrid approximation rule

[0227] Assuming that the decision of the current stage depends linearly on the random variables of the previous stage, that is, an approximation of the complex relationship between decision variables and random variables, thereby reducing the dimension of the distributionally robust optimization problem: The coefficient matrix of the linear function can be obtained by solving the corresponding optimization model, and the solution method is well known to those skilled in the art. For example, the least squares method can be used for parameter estimation.

[0228] By introducing hybrid approximation rules, the present invention directly links the start-stop status and output decision of the rapid start-stop unit with the wind power output forecast error in the previous stage, thereby effectively reducing the number of decision variables, simplifying the model structure, and reducing the complexity of the solution, laying the foundation for the subsequent use of duality theory for model transformation and the use of a rolling optimization framework for solution.

[0229] 203 model reconstruction:

[0230] This section corresponds to step 4 of the technical solution in the specification, and elaborates on how to use duality theory and mixed approximation rules to transform the multi-stage fully adaptive distributed rod unit combination model into an easy-to-solve mixed integer linear programming problem.

[0231] The model reconstruction process is mainly divided into three steps: first, the mixed approximation rules are substituted into the inequality constraints and equality constraints of the original model, and the duality theory is used to transform the inequality constraints containing semi-infinite norm constraints into a finite number of linear constraints; second, the equality constraints are equivalently transformed so that they do not contain uncertain parameters; finally, the duality theory is used to transform the expectation of the random variables in the objective function of the original model into a deterministic expression, and finally a mixed integer linear programming problem that is easy to solve is obtained.

[0232] Wherein, step 203 includes:

[0233] 1) Reconstruction of inequality constraints

[0234] Substituting the mixed approximation rule into the first constraint of formula (17), we get formula (40):

[0235]

[0236] Introducing the closed convex hull of wind power output prediction error where S^={(i,T)|i∈[R],T∈[t]}∪{(0,0)}, Indicates that the set includes the wind power output forecast errors of all fast-start units in each time period;

[0237] make Closed convex hull of wind power output prediction error Reconstruct as formula (42):

[0238]

[0239] Then, formula (40) can be rewritten as:

[0240]

[0241] in,

[0242]

[0243] Formula (42) is subjected to a standard robust equivalence reconstruction. This process uses duality theory to transform the inequality constraints containing uncertain parameters into linear matrix inequalities without uncertain parameters, as shown in Formula (43). A well-known optimization solver (such as GUROBI, CPLEX, etc.) is used to efficiently solve Formula (43).

[0244]

[0245] 2) Reconstruction of equality constraints

[0246] Substituting the mixed approximation rule into the second constraint of formula (17), we can obtain:

[0247]

[0248] Formula (44) is processed in the same way as formula (40), and Then formula (44) can be reconstructed as:

[0249]

[0250] Closed convex hull based on wind power output prediction error The separable characteristics of , formula (45) can be rewritten as:

[0251]

[0252] Therefore, by performing an equivalent transformation on formula (44), we can obtain formulas (47) and (48), where Z0 t and Z [t] t are the coefficient vector and matrix without uncertain parameters, respectively, and e is a unit vector. Formulas (47) and (48) no longer contain the wind power output prediction error vector and This eliminates the influence of uncertainty on the equality constraints, making them easier to solve.

[0253]

[0254] Among them Z0 t and Z [t] t are the coefficient vector and matrix without uncertain parameters, respectively, and e is a unit vector; formulas (47) and (48) no longer contain the wind power output prediction error vector and This eliminates the influence of uncertainty on the equality constraints, making formulas (47) and (48) easier to solve;

[0255] 3) Reconstruction of the objective function

[0256] By introducing the closed convex hull of wind power output prediction error The objective function in formula (17) can be transformed as shown in formula (49):

[0257]

[0258] Since the distributional robust optimization problem is to solve the optimal objective function expectation under the condition that the probability distribution of uncertain factors varies within a certain range, the objective function needs to be reformulated. Therefore, according to the strong duality theory, the inner layer of the objective function described by formula (17) can be reconstructed as:

[0259]

[0260] Other,

[0261]

[0262] According to the minimax theorem, applying the mixed approximation rule and formula (51) to the constraints in (50), we can obtain:

[0263]

[0264] According to the duality theory, the second part of formula (52) can be equivalent to:

[0265]

[0266] Furthermore, we can get:

[0267]

[0268] Therefore, formula (50) is equivalent to formula (56), which is the reconstructed objective function:

[0269]

[0270] 4) Combining formulas (43), (47), (48) and (55), we can obtain the reconstructed multi-stage fully adaptive distributionally robust unit commitment (MFA-DRUC) model shown in formula (56).

[0271]

[0272] The model solution based on the rolling optimization framework in step 105 specifically includes the following steps:

[0273] Step 5.1: Divide the entire scheduling cycle by time, initialize the current time period t, and set it as the first time period, that is, t = 1;

[0274] Step 5.2: Obtain wind power output forecast information for the current time period t This information can come from weather forecasts, historical wind farm output data, etc.

[0275] Step 5.3: Get the latest wind power output forecast information from step 5.2 Update the fuzzy uncertainty set D constructed in step 2 to accurately describe the uncertainty of wind power output in the current time period;

[0276] Step 5.4: Using the updated fuzzy uncertainty set D obtained in step 5.3, retrain the hybrid approximation rule introduced in step 3 to obtain the updated hybrid approximation rule, such as the updated coefficient matrix and To better capture the relationship between the start-up and shutdown status of the fast-start units in the current time period and the wind power output in the previous period;

[0277] Step 5.5: Substitute the retrained hybrid approximation rule into the mixed integer linear programming model (Formula (56)) obtained in step 4, and solve it using a known solver (such as GUROBI, CPLEX, etc.) to obtain the optimal unit combination plan for the current time period t, including the start and stop status and output of each unit in the current time period;

[0278] Step 5.6: Determine whether the current time period t reaches the end time T of the scheduling cycle; if t <T,则将当前时间段更新为下一个时间段,即t=t+1,并返回步骤5.2继续执行上述流程;如果t=T,则结束滚动优化过程,此时已经得到了整个调度周期的最优机组组合方案。

[0279] In summary, step five combines the models established in steps 101 to 104 with the actual power system dispatch process through a rolling optimization framework, achieving real-time optimization and adjustment of the unit combination plan. The final unit combination plan can effectively reduce system operating costs, improve the level of renewable energy absorption, and enhance the reliability and economy of power system operation.

[0280] Example 3

[0281] To verify the effectiveness of the multi-stage fully adaptive distributed brute force unit combination method proposed in this invention, this example applies it to an IEEE 6-bus system and an IEEE 118-bus system for case analysis. According to step 5, the entire scheduling cycle is divided into 24 time periods, each representing one hour.

[0282] At the beginning of each time period, the latest wind power output forecast data is first called up, and the fuzzy uncertainty set constructed in step two is updated based on this data to accurately describe the uncertainty caused by wind power output fluctuations in the current time period and the future period. Then, based on the updated fuzzy set, the hybrid approximation rule introduced in step three is retrained to more accurately characterize the relationship between the start-up and shutdown status of the fast-start units in the future time period and the wind power output. Finally, the updated hybrid approximation rule is substituted into the mixed integer linear programming model converted in step four and solved using the mature optimization solver Gurobi to obtain the optimal unit combination solution for the current time period.

[0283] Through this rolling optimization approach, decisions made in each time period fully account for the uncertainty of future wind power output forecasts, making the resulting unit combination plan more robust and better able to cope with the impact of wind power output fluctuations, thereby improving the reliability and economic efficiency of power system operation. In this example, we designed different simulation scenarios for a 6-node system and a 118-node system, and conducted comparative analysis with other methods, verifying the effectiveness of the proposed method in reducing system operating costs and improving renewable energy absorption.

[0284] The method is applied to a 6-node system and a modified IEEE118-node system. GUROBI 9.5.2 is used to solve the reconstructed distributed robust model on a computer equipped with an Intel Core i9-11900 CPU and 64GB RAM.

[0285] 3016-node system:

[0286] The test system consists of 6 nodes and 8 transmission lines. It includes three conventional thermal power units (G1, G2 and G4), one flexible unit (G3) and a wind farm. The wind farm is located on bus No. 4 and has an installed capacity of 100MW. Detailed system data is as follows: Figure 3 , as shown in Table 1-3.

[0287] Table 16 Node system generator parameters

[0288]

[0289] Table 26 Node system generator cost parameters

[0290]

[0291] Table 36 Node system transmission line parameters

[0292]

[0293] A key feature of the proposed MFA-DRUC is its ability to adjust the startup and shutdown of flexible units in near real time within a day. To demonstrate the advantages of the proposed model, a typical MA-DRUC model, whose internal layers do not make decisions regarding the startup and shutdown of flexible units, was used. Numerical experiments were conducted using 365 days of historical data for both the MFA-DRUC and MA-DRUC cases, with a confidence level of 0.98 and a number of bins of 20.

[0294] Table 46 MFA-DRUC solution in node system

[0295]

[0296] Table 56 MA-DRUC solution in node system

[0297]

[0298] Tables 4 and 5 present the unit commitment solutions for the MFA-DRUC and MA-DRUC models, respectively. As shown in Table 4, conventional units G1 and G4 are shut down, while G2 is dispatched day-ahead to meet the system's baseload demand. During real-time intraday dispatch, flexible unit G3 can quickly decide on its start / stop status based on actual wind power output (i.e., G3 is activated in scenarios S1-S4 with high wind power uncertainty and is not deployed in other scenarios). Although conventional thermal unit G1 has lower fuel costs than G3, G1's longer start / stop times and higher minimum output allow flexible unit G3 to more economically meet the load in these scenarios. In contrast, conventional thermal unit G1 is dispatched day-ahead, which is unnecessary for most scenarios. The proposed MFA-DRUC model effectively leverages the rapidity of flexible units to offset the uncertainty risk of wind power generation. However, in the MA-DRUC solution in Table 5, it can be observed that conventional thermal units G1 and G2 are dispatched, while flexible unit G3 is not deployed. This is because the typical MA-DRUC model does not determine the start and stop status of flexible units in the second (intraday) stage of the model. Therefore, the start and stop status of all thermal power units are determined in the first (day-ahead) stage. Furthermore, due to the lower fuel price of conventional thermal power units, G1 is scheduled day-ahead and remains online during periods when G1 output is not required.

[0299] Continue to perform a cost analysis for each scenario to uncover the benefits of flexibility. Figure 4A detailed cost comparison of the two models for each scenario based on 365 days of historical data is presented. Numerical experiments show that the total costs of the typical MA-DRUC and the proposed MFA-DRUC solutions are $36,790.2 and $35,355.8, respectively, representing a 3.89% cost reduction. Flexible generator G3 only needs to be dispatched in four scenarios. In S1 and S2, the MA-DRUC solution has a cost advantage over the MFA-DRUC solution due to the large fluctuations in wind power output and the lower fuel costs of G1. In S3 and S4, even if G3 is dispatched, the MFA-DRUC solution has lower costs. This is because as wind power volatility further decreases and generator G1 is subject to start-up and shutdown duration constraints, its online operation becomes unnecessary for an increasing period of time, requiring only short-term dispatch of the flexible generator to meet net load demand. In other scenarios, S5 to S20, the MFA-DRUC solution is more advantageous because flexible generator G3 does not need to be dispatched and the MA-DRUC solution must dispatch generator G1. In summary, by using the MFA-DRUC model, the rapid start and stop characteristics of flexible units can be utilized to reduce the allocation cost in the worst scenario.

[0300] The costs of MA-DRUC and MFA-DRUC were tested using historical data of varying sizes. To quantify the benefits of flexibility, this paper proposes a metric, Value of Flexibility (VF), to measure the cost improvement of the proposed MFA-DRUC model compared to traditional models.

[0301]

[0302] Among them, C MA-DRUC and C MFA-DRUC are the costs of MA-DRUC and MFA-DRUC respectively.

[0303] To test the out-of-sample robustness of MFA-DRUC and MA-DRUC, a Monte Carlo method was used to generate 3,000 samples for the worst-case probability distribution in each test. The test results are shown in Table 6. It can be observed that: 1. Under the same scale of historical data, the out-of-sample and in-sample costs of MA-DRUC exceed those of MFA-DRUC; 2. Under the same model, the out-of-sample and in-sample costs are close; 3. The VF value gradually increases with the increase in historical data. These data demonstrate that the proposed MFA-DRUC model can reduce system costs by unleashing the rapid daily startup and shutdown capabilities of flexible units.

[0304] In addition, to further verify the cost advantage of the MFA-DRUC model proposed in this paper in more scenarios and with different historical data sizes, 500 distributions with different standard deviations were generated in the corresponding fuzzy sets of the two cases. For the above-mentioned distributions, 3000 samples were used to calculate the system cost. The obtained numerical results are shown in Figure 5 (The blue data points are the system operating costs obtained based on the MA-DRUC model, and the red data points are the system operating costs obtained based on the MFA-DRUC model). Figure 5 -a is the result based on 20 days of historical data, Figure 5 -b is the result based on 365 days of historical data. It can be seen that under different distributions, MFA-DRUC has a greater cost advantage than MA-DRUC.

[0305] Table 6 Comparison of in-sample and out-of-sample system operating costs under different historical data sizes

[0306]

[0307] 5.1.3 Examples of Simple Models in Extreme Scenarios

[0308] This paper designs a simplified system to illustrate that the MA-DRUC model is infeasible in some extreme scenarios, while the proposed MFA-DRUC model can make the correct combination decisions. This simplified system consists of only generators G2 and G3 and a single wind turbine to meet the system load. Table 7 shows the extreme scenarios faced by the system over three consecutive time periods.

[0309] Table 7 Load and power generation data in extreme scenarios

[0310]

[0311] Substituting the data in Table 7 into the MFA-DRUC model, we obtain the optimal combination decision for Scenario 1: uG2 = (1,1,1), uG3 = (0,1,1). The optimal combination decision for Scenario 2: uG2 = (1,1,1), uG3 = (0,0,0). However, when the combination decision is obtained using the MA-DRUC model, it is reported as infeasible by GUROBI. This shows that MA-DRUC is conflicting in the two extreme scenarios. Specifically, at time t2 in Scenario 1, because the system net load of 170 MW is greater than the rated capacity of unit G2 (160 MW), unit G3 should be online. Conversely, at time t2 in Scenario 2, because the system net load of 55 MW is less than the sum of the minimum outputs of units G2 and G3 (56 MW), unit G3 should be offline. This creates an irreconcilable contradiction. In MA-DRUC, the combination decision for flexible generator G3 is obtained in the first stage. Therefore, the model cannot adapt to this extreme scenario and cannot obtain a feasible solution. In other words, MFA-DRUC expands the feasible domain of the traditional model and demonstrates the advantages of the model's rapid daily startup and shutdown of flexible resources in terms of system operating costs.

[0312] Numerical experiments were conducted on this six-bus system using both the Robust Optimal Unit Commitment (ROUC) and Stochastic Optimal Unit Commitment (SOUC) models. In the actual modeling process, SOUC was implemented based on a scenario approach and implemented using the Benders decomposition method. In fact, as historical data increases, the traditional DRUC model's description of the uncertainty probability distribution becomes increasingly accurate, and the resulting decision results may be closer to the true optimal solution. However, while the system cost of MFA-DRUC approaches that of SOUC, there is still a certain difference. This is because the inclusion of a hybrid approximation rule in the DRUC model restricts the feasible set of decision variables, leading to different UC decision results. On the other hand, by setting the confidence level α to 1, the DRUC model can be transformed into a special case of ROUC.

[0313] Table 86 Out-of-sample system cost ratios of MFA-DRUC, ROUC, and SOUC in the node system at different historical data sizes

[0314]

[0315] Table 8 summarizes the out-of-sample system costs of MFA-DRUC, ROUC, and SOUC for different historical data sizes. As shown in Table 8, when historical data is limited, SOUC suffers from infeasibility issues. Specifically, the stochastic optimization model inaccurately estimates the probabilities of certain scenarios, resulting in infeasible solutions. Therefore, MFA-DRUC is more robust than SOUC. As historical data increases, the system operating costs of MFA-DRUC based on the worst-case distribution approach those of SOUC with moderate risk. Meanwhile, the objective function of ROUC is to minimize the system operating costs under the worst-case scenario, which leads to more conservative decisions. The data demonstrates that the MFA-DRUC proposed in this paper is more economical than ROUC.

[0316] The above three models are further tested for system costs under 500 different distributions, such as Figure 6 As shown (the blue data points are the system operating costs obtained based on the ROUC model, the red data points are the system operating costs obtained based on the MFA-DRUC model, and the green data points are the system operating costs obtained based on the SOUC model). Figure 6 -a only shows the feasible results of SOUC. This further verifies that when there is less historical data, it will encounter infeasible problems. Figure 6 -b shows that as the amount of data increases, MFA-DRUC has a greater cost advantage than ROUC. Compared with SOUC, although the cost is higher, the model is more robust.

[0317] 302118 node system

[0318] The scalability of the proposed model was tested using a modified IEEE 118-node system. This system consists of three wind farms, 54 thermal power units, and 188 transmission lines. The newly added wind farms are located at nodes 36, 69, and 77, with installed capacities of 400 MW, 800 MW, and 650 MW, respectively. The thermal power units include 11 gas-fired units with fast start and shutdown capabilities. To alleviate transmission congestion caused by the new wind farms, three transmission lines, 23-32, 34-36, and 77-78, were added.

[0319] Similar to the numerical experiments for the six-bus system, the confidence level in the model was set to 0.99. In each test, a Monte Carlo method was used to generate 3,000 samples for the worst-case distribution to evaluate out-of-sample costs. The in-sample and out-of-sample results are presented in Table 9. Table 9 shows that under the worst-case distribution, the system operating costs of the MFA-DRUC are lower than those of the MA-DRUC. This further confirms that utilizing the rapid start-up and shutdown characteristics of flexible units within the day can help reduce costs.

[0320] Taking into account the actual situation of decommissioning thermal power units and adding flexible units, the aforementioned IEEE118 node system was further modified. Eight thermal power units with a capacity less than 100 MW were decommissioned, and gas units of the same capacity were added at the same nodes. Numerical experimental results obtained using the same method are shown in Table 10, which also show that the system operating cost of the MFA-DRUC is lower than that of the MA-DRUC. Compared with Table 9, the addition of flexible units (gas turbines) further unlocks their flexibility and reduces system operating costs.

[0321] Table 9 Comparison of in-sample and out-of-sample costs for the IEEE 118 node system at different historical data sizes

[0322]

[0323] Table 10 Comparison of in-sample and out-of-sample costs for the IEEE118-node system considering the retirement of thermal power units at different historical data sizes

[0324]

[0325] Those skilled in the art will understand that the accompanying drawings are only a schematic diagram of a preferred embodiment, and the serial numbers of the embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0326] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-stage unit combination method for a power system containing a high proportion of renewable energy, characterized in that It includes the following steps: Step 1: Construct a multi-stage fully adaptive distributed broiler unit combination model considering the uncertainty of wind power output; the model takes minimizing the total system operating cost as the objective function and constructs the constraints of pre-dispatch operation and real-time dispatch operation; Considering the uncertainty of wind power output, the goal of the power system unit combination model is set to minimize the total system operation cost, that is, the objective function is shown in formula (1): Where: is the fuel price of unit i; Represents the startup cost of unit i; binary variable u i,t represents the startup variable of unit i in period t; represents the upper / lower reserve capacity price of unit i; P i,t is the base output of unit i in period t; f i (P i,t ) represents the power generation cost function, let f i (P i,t )=a i (P i,t ) 2 +b i P i,t +c i , a i 、b i 、c i is the power generation cost coefficient of unit i, The up / down reserve capacity provided for unit i in time period t; Indicates the price of adjusting the output of unit i upward / downward; W is the upward / downward output adjustment value provided by unit i in time period t; cur and L cur They represent the unit penalty costs of wind curtailment and load curtailment respectively; and They represent the wind curtailment and load curtailment of wind farm j and load node d in time period t respectively; D is the number of load nodes; N g is the number of units; ω [t] represents the set of wind power prediction errors from stage 1 to stage t, that is, x and y b are the discrete decision variables and continuous decision variables in the benchmark scenario of the pre-scheduling stage respectively; y r is the real-time scheduling decision variable; Step 2: Construct a fuzzy uncertainty set based on the Wasserstein metric, that is: according to the historical wind power output data and the corresponding forecast data, calculate the sample set of wind power output forecast errors, standardize the wind power output forecast error samples, and obtain a random variable that obeys the standard normal distribution; according to the pre-set confidence level and data sample size, use the probability inequality to determine the boundary of the standard normal distribution random variable, and obtain the fuzzy set of standardized wind power output forecast errors; according to the inverse transformation of the standardization process, restore the fuzzy set of standardized wind power output forecast errors to the fuzzy set of actual wind power output forecast errors. This fuzzy set takes the empirical distribution as the center and the radius determined by the pre-set confidence level as the boundary, and can cover the true distribution of wind power output forecast errors with a certain confidence level. Step 3: Introduce the hybrid approximation rule to reduce the dimension of the multi-stage fully adaptive distributed blue stick unit combination model and simplify the model structure; Step 4: Convert the multi-stage fully adaptive distributed blue-rod unit commitment model after the hybrid approximation rule is introduced in step 3 into a mixed integer linear programming problem that is easy to solve; Step 5: Based on the solution method of the rolling optimization framework, the multi-stage fully adaptive distributed robust unit combination model containing hybrid approximation rules established in steps 1 to 4 is solved, and the final practical unit combination scheme is obtained.

2. A multi-stage unit combination method for a power system containing a high proportion of new energy according to claim 1, characterized in that The minimized total system operating cost in step one includes unit fuel cost, start-up and shutdown cost, output adjustment cost, and wind and load abandonment penalty cost set to ensure system reliability; the constraints are used to accurately characterize the dynamic decision-making process in the actual operation of the power system to distinguish the two stages of day-ahead scheduling and real-time scheduling, specifically referring to: 1) pre-scheduling operation constraints, mainly including unit start-up and shutdown state constraints, minimum start-up and shutdown time constraints, day-ahead output upper and lower limit constraints, and ramp rate constraints, to ensure that the unit meets safe operation requirements in the day-ahead scheduling stage; 2) real-time scheduling operation constraints, mainly including system power balance constraints and transmission line flow constraints, to ensure safe and stable operation of the power system in the real-time scheduling stage. At the same time, in the real-time scheduling stage, the unit output must meet the output adjustment upper and lower limit constraints.

3. A multi-stage unit combination method for a power system containing a high proportion of new energy according to claim 1, characterized in that The step three specifically refers to: setting the start-stop state decision variable y of the rapid start-up unit at time t t It is expressed as a linear function of the wind power output forecast error in the previous stage, that is: where ξ [t]^ represents the wind power output forecast error vector from moment 1 to moment t, is the coefficient matrix of the linear function; similarly, the output decision variable x of the fast start unit at time t is t It can also be expressed as a linear function of the wind power output forecast error in the previous stage, that is:

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