Multi-stage unit combination method for power system containing high-proportion new energy

Abstract

The invention discloses a multi-stage unit commitment method for a power system containing high-proportion new energy, and the method comprises the steps: constructing a unit commitment model covering a day-ahead stage and a real-time scheduling stage, describing the uncertainty of a new energy output prediction error through employing a fuzzy set based on Wasserstein measurement, introducing a hybrid approximation rule, and carrying out the prediction of a new energy output prediction error. The start-stop state of the quick start-stop unit is expressed as a linear function of a new energy output prediction error in a previous stage, the model is converted into a mixed integer linear programming problem easy to solve by using a duality theory, and a final unit combination scheme is obtained in combination with a rolling optimization framework and real-time new energy output prediction information; the method is simple and easy to implement, the system cost can be effectively reduced, the new energy consumption level is improved, the reliability and flexibility of the power system are enhanced, and technical support is provided for safe and economical operation of the high-proportion new energy power system.

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, and is particularly suitable for a power system with a high proportion of renewable energy access. [Background technology]

[0002] As the penetration of renewable energy, such as wind and solar, in the power system continues to increase, the uncertainty faced by the operation and dispatch of the power system is also increasing. The intermittent and fluctuating output of renewable energy has brought challenges to the safe and reliable operation of the power system. In order to effectively manage the uncertainty of renewable energy and ensure the reliable and economic operation of the power system, advanced unit combination optimization methods are needed.

[0003] Traditional deterministic unit combination methods are difficult to effectively deal with the uncertainty caused by fluctuations in renewable energy output. Although stochastic optimization methods can take uncertainty into account, they require accurate probability distribution information, and the probability distribution of renewable energy output is often difficult to obtain accurately. Robust optimization methods ensure the robustness of the system by considering the worst-case operating scenario, but their solutions are often too conservative, resulting in high operating costs.

[0004] As a compromise between stochastic optimization and robust optimization, the distributionally robust optimization (DRO) method has attracted widespread attention in recent years. The DRO method does not rely on precise probability distribution, but uses a fuzzy set containing multiple possible probability distributions to describe uncertainty parameters and optimize the system operation cost in the worst case (i.e., the most unfavorable probability distribution in the fuzzy set). This method can effectively reduce conservatism while ensuring the robustness of the system.

[0005] In recent years, the DRO method based on the Wasserstein metric has been applied to the problem of optimal dispatching of power systems. The Wasserstein metric can quantify the distance between two probability distributions and construct fuzzy sets based on this. When dealing with fast-start units, traditional two-stage robust optimization models usually assume that their start and stop states remain unchanged in the second stage (real-time dispatch) and only optimize their output. This method ignores the ability of fast-start units to start and stop quickly during the 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 high. Mixed Approximation Rule (MAR) is a dimensionality reduction technique that can effectively simplify the solution of multi-stage DRO models. MAR reduces the dimensionality of the model by expressing future decision variables as functions of uncertainty parameters in previous stages, such as linear functions or affine functions.

[0007] The present invention combines Wasserstein metric, hybrid approximation rule and multi-stage optimization framework to propose a new multi-stage fully adaptive distributed robust unit combination method, which aims to make full use of the flexibility of fast-start units to cope with the challenges brought by fluctuations in renewable energy output. [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 prior art and is a simple, easy-to-implement unit combination method that can fully utilize the intraday start-stop 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 consumption, and enhance the reliability and economy of the operation of the electric power system.

[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 comprises the following steps:

[0010] Step 1: Construct a multi-stage fully adaptive distributed BRU 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 the step 1 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 dispatch and real-time dispatch, specifically referring to: 1) pre-dispatch operation constraints, mainly including unit start-up and shutdown state 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 the safety operation requirements in the day-ahead dispatch stage; 2) real-time dispatch 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 dispatch stage. At the same time, in the real-time dispatch stage, the unit output must meet the output adjustment upper and lower limits 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; is the upward / downward output adjustment value provided by unit i in period t; W 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 For real-time scheduling decision variables;

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

[0017]

[0018] In the formula, 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 started and 0 when it is stopped; if unit i is in the start-up process in period t, then the startup variable u of unit i in period t 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 operation 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] The decision variable y of the real-time scheduling model r Decision variables at each stage The composition is as 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 period t is [t] Determined when implemented, indicating multi-stage decision variables The unexpectedness of the wait-and-see decision 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 from 1 to T has been obtained when determining the wait-and-see decision variables. This assumption is inconsistent with the principle of timing 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 variable at stage t depends on the decision variable and the uncertain variables ω1,ω2,…,ω t ;

[0026] Step 1.4 constructs a multi-stage fully adaptive distributed robust 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, and D is fuzzy uncertain set.

[0029] Step 2: Construct a fuzzy uncertain 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 error, 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 standardized fuzzy set of wind power output forecast error; according to the inverse transformation of the standardization process, restore the standardized fuzzy set of wind power output forecast error to the fuzzy set of actual wind power output forecast error. The fuzzy set is centered on the empirical distribution and bounded by the 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;

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

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

[0032] Step 2.1.1 In order to accurately estimate the expected power generation cost, we first use the sample set of historical data {ξ1,ξ2,…,ξ K}Constructing the empirical distribution of wind power output forecast error 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, and the frequency of samples in each interval is counted to obtain the probability distribution of wind power output prediction 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 its definition is as shown in formula (18):

[0034]

[0035] In the formula, the uncertain parameter | k , Obey 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 On the distribution of experience 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 The center is the radius ε determined by the preset confidence level a, which can contain the true distribution with a confidence level of 1-a.

[0037] Step 2.1.3 defines the fuzzy uncertain 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 equivalently described mathematically 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 easily 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 empirical distribution 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-tailed 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 It also has an important impact on the model results. In order to facilitate calculation, the prediction error sample set {ω1,ω2,…,ω K}Standardization is performed according to formula (25):

[0047]

[0048] In the formula, ∑ 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] In the formula, γ represents the boundary of the uncertain parameter θ;

[0051] Step 2.3: Solving the uncertainty set of wind power prediction error is transformed into solving the boundary γ, and then establishing a support set with data-driven properties;

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

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

[0054]

[0055] In the formula, and ψ are the probability distribution of the uncertain parameter θ and the fuzzy uncertain set, respectively. η represents the confidence of the uncertain set ∵. The constraint of problem (27) is a chance-constrained optimization problem that is not easy to solve. According to the duality theory, it can be transformed into an optimization problem that is easy to solve (28):

[0056]

[0057] In the formula, (·) + =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 uncertain set 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 The coefficient of correlation;

[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 as shown in formula (39), and finally the closed convex hull of wind power output prediction error is obtained: The closed convex hull can be represented by the linear constraints shown in formula (39);

[0071]

[0072] In the formula,

[0073] Step 3: In order to reduce the solution complexity of the multi-stage fully adaptive distributed robust 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 amount of calculation required to directly solve the model is very large, especially when rapid decisions need to be made in the real-time scheduling stage. Therefore, 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 quick start 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 prediction error vector from the first moment to the tth moment, 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 rod unit combination model after the mixed 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] Closed convex hull with wind power output prediction error where S^={(i,T)|i∈[R],T∈[t]}∪{(0,0)}, Indicates that the set contains the wind power output prediction 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), introducing the closed convex hull 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] 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 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 distributed 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) simultaneously, we can obtain:

[0107]

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

[0109]

[0110] Further, 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 as 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 commitment model containing hybrid approximate rules established in steps 1 to 4 is solved, and the final practical unit commitment 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: Obtain 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 an updated hybrid approximation rule, such as updating the coefficient matrix and To better capture the relationship between the start-stop status of the fast-start unit in the current time period and the wind power output in the previous stage;

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

[0123] Step 5.6: Determine whether the current time period t has reached the end time T of the scheduling period; if t < T, update the current time period to the next time period, i.e., t = t + 1, and return to Step 5.2 to continue executing the above process; if t = T, end the rolling optimization process, and at this time, the optimal unit commitment plan for the entire scheduling period has been obtained.

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

[0125] ① Improve the reliability of system operation: The multi-stage fully adaptive distributionally robust unit commitment method proposed by the present invention can effectively cope with uncertainty factors such as wind power output fluctuations, and find the optimal unit commitment plan that meets various possible scenarios on the premise of ensuring system safety constraints, thereby improving the reliability of power system operation.

[0126] ② Reduce the system operation cost: By introducing the hybrid approximation rule, the present invention reduces the solution complexity of the multi-stage distributionally robust optimization problem, and at the same time fully considers the intra-day start-stop flexibility of fast-start units, and can more economically utilize fast-start units to cope with wind power output fluctuations, thereby reducing the total system operation cost.

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

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

Description of the Drawings

[0129] Figure 1 It is a schematic flow chart of a multi-stage unit commitment method for a power system with a high proportion of new energy involved in the present invention.

[0130] Figure 2 It is a schematic diagram of the rolling optimization process of a multi-stage unit commitment method for a power system with a high proportion of new energy 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 an electric 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 of cost comparison between MFA-DRUC and MA-DRUC methods under different distributions in a 6-node system of Embodiment 3 of a multi-stage unit combination method for a power system with a high proportion of new 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 the embodiment 3 of the multi-stage unit combination method of the power system with a high proportion of new 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 solution and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments and features in the embodiments of the present application can be combined with each other without 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 renewable energy, such as Figure 1 As shown, 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 robust unit combination model is constructed. The model aims to minimize the total operating cost of the system, with constraints of pre-dispatch operation and real-time dispatch operation, and the uncertainty parameters such as wind power output in the model are expressed as random variables subject to specific fuzzy sets;

[0139] Among them, the minimized total system operating cost 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 dispatch and real-time dispatch, specifically referring to: 1) pre-dispatch operation constraints, mainly including unit start-up and shutdown state 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 the safety operation requirements in the day-ahead dispatch stage; 2) real-time dispatch 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 dispatch stage. At the same time, in the real-time dispatch stage, the unit output must meet the output adjustment upper and lower limits 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 caused 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 uses 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: The empirical distribution of wind power output forecast error is estimated using historical data, and a fuzzy set containing the true distribution is constructed 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 prediction error, the present invention uses historical data to estimate the empirical distribution of wind power output prediction 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 prediction data, a sample set of wind power output prediction error is calculated. In order to eliminate the influence of dimension, the wind power output prediction error samples are standardized to obtain random variables that obey the standard normal distribution. Then, according to the pre-set confidence level and data sample size, the boundary of the standard normal distribution random variable is determined using the probability inequality to obtain the standardized fuzzy set of wind power output prediction error. Finally, according to the inverse transformation of the standardization process, the fuzzy set of the standardized wind power output prediction error is restored to the fuzzy set of the actual wind power output prediction error. The fuzzy set is centered on the empirical distribution and bounded by the radius determined by the pre-set confidence level, and can cover the true distribution of the wind power output prediction 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 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 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, simplify the complex relationship between the decision variables and the uncertainty parameters, reduce the dimension of the problem, and embed the linear function into the multi-stage fully adaptive distributed robust unit combination model.

[0144] The core idea of ​​the hybrid approximate 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 the present 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 approximate rule is mainly applied to the start and stop status decision variables 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 robust 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 fast start-stop unit are represented 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 approximate rules is obtained. However, the model still contains complex fuzzy sets and nonlinear constraints, and it is difficult to solve directly using the existing optimization solver. Therefore, the present invention uses the 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] Then, the present invention uses duality theory to transform the semi-infinite norm constraint into a finite number of linear constraints. Duality theory provides an effective method for transforming complex constraints into simpler constraints. By introducing dual variables, the semi-infinite norm constraint that is originally difficult to handle can be transformed 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 on them so that they no longer explicitly contain these uncertain parameters. The purpose of this step is to further simplify the model structure and make it easier to solve.

[0150] Finally, the present invention uses duality theory to transform the objective function of the model into a form that is easy to solve. Similar to the transformation of constraint conditions, duality theory can also be applied to the transformation of the objective function, transforming it into a form that is easier to solve. For example, a complex objective function containing an expected value can be transformed into a series of linear expressions.

[0151] After the above four steps, the present invention successfully transforms the multi-stage fully adaptive distributed robust unit combination model containing mixed approximation rules into an equivalent mixed integer linear programming problem. This problem can be efficiently solved using existing mature optimization solvers (such as GUROBI, CPLEX, etc.), thereby obtaining the optimal unit combination scheme that takes into account the uncertainty of wind power output.

[0152] 105: The model is solved using a rolling optimization framework, and the entire dispatch cycle is divided into multiple time periods. The fuzzy set and hybrid approximation rules are updated in each time period using the latest wind power output forecast information, and the updated model is solved to obtain the optimal unit combination plan for the current time period, thereby more accurately describing the dynamic decision-making process of the actual operation of the power system. The process is as follows: Figure 2 shown.

[0153] Specifically:

[0154] Step 5.1: Divide the entire scheduling cycle (e.g., 24 hours) into multiple time periods (e.g., one time period per hour), and make decisions for each time period in turn;

[0155] Step 5.2: At the beginning of each time period, first obtain the latest wind power output forecast information, and update the fuzzy uncertainty set D constructed in step 2 based on the information to accurately describe the uncertainty of wind power output;

[0156] Step 5.3: Based on the fuzzy uncertainty set D updated in step 5.2, retrain the hybrid approximation rule introduced in step 3 to better capture the relationship between the start-stop state of the fast-start unit and the wind power output in the previous stage;

[0157] Step 5.4 substitutes the retrained hybrid approximation rule into the mixed integer linear programming model converted in step 4, and uses a mature solver to solve it to obtain the optimal unit combination plan for the current time period, including the start and stop status and output of each unit in the current time period.

[0158] Through this rolling optimization method, the present invention can be based on the latest wind power output forecast information in real time. Adjust the unit combination plan 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 model solution scale is relatively small, which can meet the requirements of actual power system operation and dispatching for calculation efficiency.

[0159] In summary, the embodiment of the present invention 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 through the above steps 101 to 105.

[0160] Example 2

[0161] This embodiment describes in detail the specific implementation process of the multi-stage fully adaptive distributed rod unit combination method based on hybrid approximate rules in combination with a mathematical model, including three main parts: model establishment, model reconstruction and model solution.

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

[0163] This section corresponds to step one in the specification, i.e., constructing a multi-stage fully adaptive distributed robust 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 robust 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 limitation, ramp rate limitation, system power balance, and transmission line flow limitation, and constructs a deterministic optimization model with minimizing the total system operating cost 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; is the upward / downward output adjustment value provided by unit i in period t; W 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 For real-time scheduling decision variables;

[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 started and 0 when it is stopped; if unit i is in the start-up process in period t, then the startup variable u of unit i in period t 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 predicted output value of wind farm j in time period t; L d,t is the power load value of user d in 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 operation 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] The decision variable y of the real-time scheduling model rDecision variables at each stage The composition is as 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 period t is [t] Determined when implemented, indicating multi-stage decision variables The unexpectedness of the wait-and-see decision 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 from 1 to T has been obtained when determining the wait-and-see decision variables. This assumption is inconsistent with the principle of timing 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 variable at stage t depends on the decision variable and the uncertain variables ω1,ω2,…,ω t ;

[0179] 202 points blue stick 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 wind power output forecast errors, the present invention first constructs a fuzzy uncertainty set containing a true distribution based on the Wasserstein metric. The fuzzy set is centered on the empirical distribution of wind power output forecast errors estimated using historical data and has a radius determined by a pre-set confidence level as a boundary, thereby improving the model's description accuracy of wind power output forecast errors. In order to reduce the complexity of the model solution, the present invention introduces a hybrid approximation rule to reduce the dimensionality of the model, and represents the start-stop state decision variables of the quick 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 the 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 in the constraints related to the current stage number t. is the probability distribution of ξ, which satisfies is the uncertainty set of wind power forecast errors, and 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 the empirical distribution of wind power output forecast error 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, so as to obtain the probability distribution of wind power output prediction error in each interval, that is, the empirical distribution Since the real distribution is often difficult to obtain accurately, the present invention is based on the empirical distribution and the Wasserstein metric to construct a distribution that includes the true distribution The fuzzy uncertain set D is based on the empirical distribution The center is the radius ε determined by the preset confidence level α, which 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 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, this formula represents the uncertainty set of wind power prediction errors. On the distribution of experience 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 of 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 use the fuzzy uncertainty set more conveniently in practical applications, the present invention provides an equivalent mathematical description of the fuzzy uncertainty set 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 empirical distribution To the true distribution The “transportation” cost is the weighted sum of the distances between sample points, which does not exceed the preset 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.

[0196] Constraints (22) and (23) ensure that the marginal distribution of the joint distribution is equal to the empirical distribution and the true distribution 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-tailed 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 It also has an important impact on the model results. In order to facilitate calculation, the prediction error sample set {ω1,ω2,…,ω K}Standardization is performed according to formula (25):

[0201]

[0202] In the formula, ∑ 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 boundary of the uncertain parameter θ;

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

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

[0206]

[0207] In the formula, and ψ are the probability distribution of the uncertain parameter θ and the fuzzy uncertain set, respectively. η represents the confidence of the uncertain set ∵. The constraint of problem (27) is a chance-constrained optimization problem that is not easy to solve. According to the duality theory, it can be transformed into an optimization problem that is easy to solve (28):

[0208]

[0209] In the formula, (·) + =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 uncertain variables The discontinuous characteristics of the wind power forecast error after reconstruction make the uncertain set 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 prediction error, is the vertex The coefficient of correlation;

[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 rearranged as:

[0223]

[0224] In the formula,

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

[0226] 3) Mixed approximation rules

[0227] Assuming that the decision of the current stage depends linearly on the random variables of the previous stage, which is an approximation of the complex relationship between decision variables and random variables, it reduces the dimension of the distributional 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 the hybrid approximation rule, the present invention directly links the start-stop state and output decision of the fast start-stop unit with the wind power output prediction 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 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 comprises:

[0233] 1) Reconstruction of inequality constraints

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

[0235]

[0236] Closed convex hull with wind power output prediction error where S^={(i,T)|i∈[R],T∈[t]}∪{(0,0)}, Indicates that the set contains the wind power output prediction 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 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), introducing 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 impact of uncertainty on the equality constraints, making them easier to solve.

[0253]

[0254] 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 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 distributed 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) simultaneously, we can obtain:

[0263]

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

[0265]

[0266] Further, we can get:

[0267]

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

[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 as 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 output data of wind farms, etc.

[0275] Step 5.3: According to the latest wind power output prediction information obtained in 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: Use the updated fuzzy uncertainty set D obtained in Step 5.3 to retrain the hybrid approximation rule introduced in Step 3 to obtain an updated hybrid approximation rule, such as updating the coefficient matrix and to better capture the relationship between the start-stop state of the fast-starting unit in the current time period and the wind power output in the previous stage;

[0277] Step 5.5: Substitute the retrained hybrid approximation rule into the mixed-integer linear programming model (Formula (56)) transformed in Step 4, and use a well-known solver (such as GUROBI, CPLEX, etc.) to solve it to obtain the optimal unit commitment plan for the current time period t, including the start-stop state 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, update the current time period to the next time period, i.e., t = t + 1, and return to Step 5.2 to continue executing the above process; if t = T, end the rolling optimization process, and at this time, the optimal unit commitment plan for the entire scheduling cycle has been obtained.

[0279] In summary, Step 5 combines the models established in Steps 101 to 104 with the actual power system scheduling process through a rolling optimization framework, realizes the real-time optimization and adjustment of the unit commitment plan, and the finally obtained unit commitment plan can effectively reduce the system operation cost, improve the renewable energy consumption level, and enhance the reliability and economy of the power system operation.

[0280] Embodiment 3

[0281] To verify the effectiveness of the multi-stage fully adaptive distributionally robust unit commitment method proposed in the present invention, this embodiment applies it to the IEEE 6-bus system and the IEEE 118-bus system for case analysis. According to Step 5, the entire scheduling cycle is divided into 24 time periods, and each time period represents 1 hour.

[0282] At the beginning of each time period, the latest wind power output forecast data is first called, and the fuzzy uncertainty set constructed in step 2 is updated based on the data to accurately describe the uncertainty caused by the fluctuation of wind power output in the current time period and the future period. Then, based on the updated fuzzy set, the hybrid approximation rule introduced in step 3 is retrained to more accurately characterize the relationship between the start-stop state of the fast-start unit and the wind power output in the future time period. Finally, the updated hybrid approximation rule is substituted into the mixed integer linear programming model converted in step 4, and the mature optimization solver Gurobi is used to solve it to obtain the optimal unit combination plan for the current time period.

[0283] Through this rolling optimization method, the decision of each time period fully considers the uncertainty of wind power output forecast in the future, making the final unit combination scheme more robust and better able to cope with the impact of wind power output fluctuations, thereby improving the reliability and economy of power system operation. In this embodiment, we designed different simulation scenarios for the 6-node system and the 118-node system respectively, and compared and analyzed them with other methods to verify the effectiveness of the method of the present invention in reducing system operating costs and improving the level of renewable energy consumption.

[0284] The method is applied on 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 includes 6 nodes and 8 transmission lines. It contains 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 with an installed capacity of 100MW. The detailed data of the system 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] The key feature of the constructed MFA-DRUC is that it can adjust the start or shutdown of flexible units in near real time within the day. In order to demonstrate the advantages of the proposed constructed model, a typical MA-DRUC model is used, and the inner layer of the model does not make decisions on the start and shutdown of flexible units. In the numerical experiments, 365 days of historical data are used in the MFA-DRUC and MA-DRUC cases respectively, where the confidence level is set to 0.98 and the number of bins is set to 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 show the unit combination solutions of the MFA-DRUC and MA-DRUC models, respectively. As shown in Table 4, conventional units G1 and G4 are in a closed state, G2 is dispatched on the day before to meet the basic load demand of the system, and in the real-time dispatch process during the day, the flexible unit G3 can quickly decide the start and stop state according to the actual wind power output (that is, G3 is started in the scenarios S1-S4 with large wind power uncertainty, and is not combined in other scenarios). Although the fuel cost of the conventional thermal power unit G1 is cheaper than that of G3, the longer start and stop time and larger minimum output of G1 enable the flexible unit G3 to meet the load more economically in the above scenarios. On the contrary, the conventional thermal power unit G1 is dispatched on the day before, which is not necessary for most scenarios. The MFA-DRUC model proposed in the present invention actually uses the rapidity of the flexible unit to hedge the uncertainty risk of wind power generation. However, from the MA-DRUC solution in Table 5, it can be observed that the conventional thermal power units G1 and G2 are dispatched, while the flexible unit G3 is not combined. This is because in the typical MA-DRUC model, the start and stop states of the flexible units are not decided in the second stage (i.e., intraday) model, so the start and stop states of all thermal power units are decided in the first stage (i.e., day-ahead). At the same time, due to the lower fuel price of conventional thermal power units, G1 is scheduled day-ahead and remains online during the period when G1 output is not needed.

[0299] Continue to perform cost analysis for each scenario to uncover the benefits of flexibility. Figure 4The detailed cost comparison of the two models in each scenario based on 365 days of historical data is shown. From the numerical experiments, the total cost of the typical MA-DRUC and the MFA-DRUC solution proposed in this invention is $36,790.2 and $35,355.8 respectively, with a cost reduction of 3.89%. The flexible unit G3 only needs to be dispatched in 4 cases. In S1 and S2, because the output power fluctuation of wind power generation is large and the fuel cost of G1 is low, MA-DRUC has a cost advantage over MFA-DRUC. In S3 and S4, even if G3 is dispatched, the cost of the MFA-DRUC solution is lower. Because as the volatility of wind power is further weakened and there is a start-stop duration constraint on unit G1, it is unnecessary for the unit to be online for more time, and the net load demand can be met by dispatching the flexible unit for a short time. For other scenarios, that is, S5 to S20, because the flexible unit G3 does not need to be dispatched and the MA-DRUC solution must dispatch unit G1, the decision-making scheme of MFA-DRUC is more advantageous. In summary, by using the MFA-DRUC model, the fast 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 are tested with historical data of different sizes. In order to quantify the benefits of flexibility, the present invention proposes a metric, namely, the value of flexibility (VF), to measure the improvement of the cost of the MFA-DRUC model proposed in the present invention compared with the traditional model.

[0301]

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

[0303] In order to test the robustness of MFA-DRUC and MA-DRUC out of sample, the Monte Carlo method is used to generate 3000 samples for the worst 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 cost of MA-DRUC both out of sample and in sample exceeds the cost of MFA-DRUC; 2. The out-of-sample cost under the same model is close to the in-sample cost; 3. With the increase of historical data, the value of VF gradually increases. The above data show that the proposed MFA-DRUC model can achieve the purpose of reducing system costs by releasing the rapid start-up and shutdown capabilities of flexible units within the day.

[0304] In addition, in order to further verify the cost advantage of the MFA-DRUC model proposed in this invention in more scenarios and with different historical data sizes, 500 distributions with different standard deviations are generated in the corresponding fuzzy sets of the two cases. For the above-mentioned distributions, 3000 samples are 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 simple system to illustrate that the MA-DRUC model is not feasible in some extreme scenarios, and the proposed MFA-DRUC can make the correct combination decision. In this simplified system, there are only generators G2, G3 and a wind turbine to meet the load demand of the system. Table 7 shows the extreme scenarios faced by the system in 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 get the optimal combination decision in 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, in the process of obtaining the combination decision through the MA-DRUC model, it will be reported as infeasible by GUROBI. This shows that MA-DRUC is conflicting in two extreme scenarios. Specifically, at t2 in scenario 1, since the net load of 170MW in the system is greater than the rated capacity of unit G2 (160MW), unit G3 should be online; on the contrary, at t2 in scenario 2, since the net load of 55MW in the system is less than the sum of the minimum outputs of units G2 and G3 (56MW), unit G3 should be offline. This creates an irreconcilable contradiction. In MA-DRUC, the combined decision of the flexible unit G3 is obtained in the first stage. Therefore, the model cannot adapt to this extreme scenario, that is, it 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 in reducing system operating costs by quickly starting and stopping flexible resources within a day.

[0312] Numerical experiments were conducted on the 6-node system using the robust optimization unit commitment (ROUC) and stochastic optimization unit commitment (SOUC) models. In the actual modeling process, SOUC is implemented based on the scenario and is implemented by the Benders decomposition method. In fact, as the amount of historical data increases, the traditional DRUC model describes the probability distribution of uncertainty more accurately, and the decision results obtained may be closer to the true optimal solution. However, the system cost of MFA-DRUC is close to SOUC, but there is still a certain difference. This is because the mixed approximation rule is added to the DRUC model. The existence of the mixed approximation rule will limit the feasible set of decision variables, resulting in 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] The out-of-sample system costs of MFA-DRUC, ROUC, and SOUC at different historical data sizes are statistically analyzed and shown in Table 8. As shown in Table 8, when there is less historical data, SOUC will have an infeasible problem, that is, the random optimization model will have inaccurate probability estimates for certain scenarios and produce infeasible solutions. Therefore, MFA-DRUC is more robust than SOUC, and as the historical data increases, the system operating cost of MFA-DRUC based on the worst distribution is close to the cost of SOUC with moderate risk. At the same time, the objective function of ROUC is to minimize the system operating cost under the worst scenario, which will lead to a more conservative decision-making result. It can be seen from the data that the MFA-DRUC proposed in the present invention has better economy 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 also 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 has stronger robustness.

[0317] 302118 Node System

[0318] The scalability of the proposed model is tested using a modified IEEE118 node system. The system has 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 400MW, 800MW, and 650MW, respectively. The thermal power units include 11 gas units with fast start and stop functions. In order to alleviate the transmission congestion problem caused by the newly added wind farms to the power system, three lines 23-32, 34-36, and 77-78 were added to the transmission lines.

[0319] Similar to the numerical experiments of the 6-bus system, the confidence level in the model is set to 0.99. In each test, 3000 samples are generated for the worst distribution using the Monte Carlo method to evaluate the out-of-sample cost. The obtained in-sample and out-of-sample results are shown in Table 9. Table 9 shows that under the worst distribution, the system operation cost of MFA-DRUC is lower than that of MA-DRUC. This further verifies that releasing the fast start-stop characteristics of flexible units within the day is conducive to reducing costs.

[0320] Taking into account the actual situation of the retirement of thermal power units and the new installation of flexible units, the above IEEE118 node system was further modified. Eight thermal power units with a capacity of less than 100MW were retired, and gas units of the same capacity were added at the same nodes. The numerical experimental results obtained using the same method are shown in Table 10, and it can also be concluded that the system operating cost of MFA-DRUC is lower than that of MA-DRUC. Compared with Table 9, with the increase of flexible units (gas turbines), their flexibility can be further released and the system operating cost can be reduced.

[0321] Table 9 Comparison of in-sample and out-of-sample costs of IEEE118 node system under different historical data sizes

[0322]

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

[0324]

[0325] Those skilled in the art will appreciate that the accompanying drawing is 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 principle of the present invention should be included in the protection scope 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 BRU 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; Step 2: Construct a fuzzy uncertain 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 error, 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 standardized fuzzy set of wind power output forecast error; according to the inverse transformation of the standardization process, restore the standardized fuzzy set of wind power output forecast error to the fuzzy set of actual wind power output forecast error. The fuzzy set is centered on the empirical distribution and bounded by the 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; Step 3: Introduce the hybrid approximation rule to reduce the dimension of the multi-stage fully adaptive distributed robust unit combination model and simplify the model structure; Step 4: Convert the multi-stage fully adaptive distributed rod unit combination model after the mixed 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 approximate rules established in steps 1 to 4 is solved, and the final practical unit combination scheme is obtained.

2. According to claim 1, a multi-stage unit combination method for a power system containing a high proportion of renewable energy is characterized in that The minimized total system operating cost in the step 1 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 dispatch and real-time dispatch, specifically referring to: 1) pre-dispatch operation constraints, mainly including unit start-up and shutdown state 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 the safety operation requirements in the day-ahead dispatch stage; 2) real-time dispatch 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 dispatch stage. At the same time, in the real-time dispatch stage, the unit output must meet the output adjustment upper and lower limits constraints.

3. A multi-stage unit combination method for a power system containing a high proportion of renewable energy according to claim 2, characterized in that The step 1 specifically includes the following contents: 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): 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; is the upward / downward output adjustment value provided by unit i in period t; W 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 For real-time scheduling decision variables; Step 1.2: Determine the pre-scheduling operation constraints as shown in formulas (2)-(8): In the formula, v 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 started and 0 when it is stopped; if unit i is in the start-up process in period t, then the startup variable u of unit i in period t 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; The duration of start / stop of unit i to period t-1; P 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 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; Step 1.3: Determine the real-time scheduling operation constraints as shown in formulas (9)-(14): The decision variables in the benchmark scenario of the pre-scheduling stage are shown in formula (15): The decision variable y of the real-time scheduling model r Decision variables at each stage The composition is as shown in formula (16): 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 period t is [t] Determined when implemented, indicating multi-stage decision variables The unexpectedness of the wait-and-see decision 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 from 1 to T has been obtained when determining the wait-and-see decision variables. This assumption is inconsistent with the principle of timing 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 variable at stage t depends on the decision variable and the uncertain variables ω1,ω2,…,ω t ; Step 1.4 constructs a multi-stage fully adaptive distributed robust 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): 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 constraint conditions; P is the probability distribution of the random variable ξ, which satisfies P(A): = P TY ({ξ [T] |[1;ξ [T] ∈A}), is the uncertain set of wind power prediction error, and D is the fuzzy uncertainty set of P.

4. According to claim 1, a multi-stage unit combination method for a power system containing a high proportion of renewable energy is characterized in that The fuzzy set construction process described in step 2 specifically includes: Step 2.1 Establish the fuzzy uncertainty set based on Wasserstein distance; Step 2.1.1 In order to accurately estimate the expected power generation cost, we first use the sample set of historical data {ξ1,ξ2,…,ξ K }Construct the empirical distribution P of wind power output forecast error K , and use it as an approximation of the true distribution P, that is: the sample set of historical data {ξ1,ξ2,…,ξ K } is divided into N equally spaced intervals, and the frequency of samples in each interval is counted to obtain the probability distribution of wind power output prediction error in each interval, that is, the empirical distribution P K ; Step 2.1.2 Based on the empirical distribution P K and Wasserstein metric to construct a fuzzy uncertain set D containing the true distribution P; Wasserstein metric is a quantity used to measure the "distance" between two probability distributions, and its definition is shown in formula (18): In the formula, the uncertain parameter ξ k , Obey P K and P; P K 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 On the empirical distribution P K and the Wasserstein distance W(P K ,P) is 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; Step 2.1.3 defines the fuzzy uncertain set D as: 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 a, and the diameter δ of the support space, as shown in formula (20); Step 2.1.4 In order to use the fuzzy uncertainty set D more conveniently in practical applications, the fuzzy uncertainty set D is equivalently described mathematically 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 easily applied to the optimization model to describe the uncertainty of wind power output prediction error. 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 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; The constraint (21) in step 2.1.4 restricts the empirical distribution P K The "transportation" cost to the true distribution P, 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 P K is consistent with the true distribution P; the constraint (24) ensures that the true distribution P is a valid probability distribution, that is, the sum of the probabilities of all sample points occurring is equal to 1. Step 2.2: Establish a data-driven support set; The probability distribution of wind power output forecast error should satisfy the assumption of light-tailed 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 It also has an important impact on the model results. In order to facilitate calculation, the prediction error sample set {ω1,ω2,…,ω K }Standardization is performed according to formula (25): In the formula, Σ is the variance of the sample. Assuming that ∵ is an uncertain set of uncertain parameters θ, the uncertain set ∵ can be defined as follows: ∵={θ∈R T ∣-γ≤θ i ≤γ} (26) where γ represents the boundary of the uncertain parameter θ; Step 2.3 solves the uncertainty set of wind power prediction error ∵ and transforms it into solving the boundary γ, and then establishes a support set with data-driven properties; The boundary γ can be obtained by solving problem (27): Where P std and ψ are the probability distribution of the uncertain parameter θ and the fuzzy uncertain set, respectively. η represents the confidence of the uncertain set ∵. The constraint of problem (27) is a chance-constrained optimization problem that is not easy to solve. According to the duality theory, it can be transformed into an optimization problem that is easy to solve (28): In the formula, (·) + =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; 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): Formula (29) can be written as (30), where ω - and ω + represents the boundary of the uncertain variable ξ; For each uncertain variable ξ i,t Insert r within the boundary range i,t -1 breakpoint, i.e. 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): Uncertain set of wind power forecast errors Reconstruct and obtain the reconstructed uncertainty set as shown in formula (35) and formula (36): Due to the introduction of uncertain variables of nonlinear operators The discontinuous characteristics of the wind power forecast error after reconstruction make the uncertain set 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): in, represents the normalized wind power output prediction error, is the vertex The coefficient of correlation; 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 as shown in formula (39), and finally the closed convex hull of wind power output prediction error is obtained: The closed convex hull can be represented by the linear constraints shown in formula (39); In the formula, 5. A multi-stage unit combination method for a power system containing a high proportion of renewable energy according to claim 4, characterized in that The fuzzy uncertainty set D in step 2.1.2 is based on the empirical distribution P K With as the center and the radius ε determined by the pre-set confidence level a as the boundary, it can contain the true distribution P with a confidence level of 1-a.

6. A multi-stage unit combination method for a power system containing a high proportion of renewable energy according to claim 4 or 5, characterized in that The uncertain set in step 2.3 should have the following two characteristics: 1) Cover the probability distribution of wind power output prediction error with a certain confidence level; 2) Keep it as small as possible to reduce the conservatism of the model.

7. A multi-stage unit combination method for a power system containing a high proportion of renewable energy according to claim 1, characterized in that The step three specifically refers to: setting the start-stop state decision variable y of the quick start 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 prediction error vector from the first moment to the tth moment, 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:

8. A multi-stage unit combination method for a power system containing a high proportion of renewable energy according to claim 3, characterized in that The step 4 specifically includes: Step 4.1 Reconstruct the inequality constraints: Substituting the mixed approximation rule into the first constraint of formula (17) in step 1.4, we obtain formula (40): Closed convex hull with wind power output prediction error where S^={(i,T)|i∈[R],T∈[t]}∪{(0,0)}, Indicates that the set contains the wind power output prediction errors of all fast-start units in each time period; make right Reconstruct as formula (42): Then, formula (40) can be rewritten as: in, 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); Step 4.2 Reconstruction of equality constraints: Substituting the mixed approximation rule into the second constraint of formula (17) in step 1.4, we can obtain: Formula (44) is processed in the same way as formula (40), introducing the closed convex hull Then formula (44) can be reconstructed as: Closed convex hull based on wind power output prediction error The separable characteristics of , formula (45) can be rewritten as: 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 formulas (47) and (48) easier to solve; Step 4.3 Reconstruction of the objective function: 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): Since the distributed 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: Other, According to the minimax theorem, applying the mixed approximation rule and formula (51) to the constraints in (50) simultaneously, we can obtain: According to the duality theory, the second part of formula (52) can be equivalent to: Further, we can get: Therefore, formula (50) is equivalent to formula (55), that is, the reconstructed objective function is obtained; Combining formulas (43), (47), (48) and (55) in step 4.4, the reconstructed multi-stage fully adaptive distributionally robust unit commitment model as shown in formula (56) can be obtained.

9. A multi-stage unit combination method for a power system containing a high proportion of renewable energy according to claim 8, characterized in that The model solution based on the rolling optimization framework in step five specifically includes the following steps: Step 5.1: Divide the entire scheduling period by time, initialize the current time period t, and set it as the first time period, that is, t = 1; Step 5.2: Obtain wind power output forecast information for the current time period t Step 5.3: Obtain 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; Step 5.4: Use the updated fuzzy uncertainty set D obtained in step 5.3 to retrain the hybrid approximation rule introduced in step three to obtain the updated hybrid approximation rule; Step 5.5: Substitute the retrained hybrid approximation rule into the mixed-integer linear programming model as shown in formula (56) transformed in step four and solve it to obtain the optimal unit commitment plan for the current time period t, including the start-stop status and output of each unit in the current time period; Step 5.6: Determine whether the current time period t reaches the end time T of the scheduling period; if t < T, update the current time period to the next time period, that is, t = t + 1, and return to step 5.2 to continue executing the above process; if t = T, end the rolling optimization process, and at this time, the optimal unit commitment plan for the entire scheduling period has been obtained.

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