A two-stage robust equilibrium analysis method based on inexact dirichlet model

Abstract

The application discloses a two-stage robust balance analysis method based on an inexact Dirichlet model, obtains system basic technical information from a dispatching system, and obtains prediction error data of new energy history; according to the prediction error data of the new energy history, an inexact Dirichlet model is adopted to construct an uncertain set of new energy in each period; according to the element type of the dispatching system, operation constraints of the dispatching system are constructed, and a target function of system operation is set; a standard two-stage robust optimization model is formed; the original problem of the two-stage robust optimization model is divided into a main problem and a sub-problem, an improved C&CG algorithm is adopted to iteratively solve in the range of the constructed new energy uncertain set, and power and energy balance results of the dispatching system under extreme operation conditions are obtained; the method can reduce the conservativeness of the system under uncertain environment, and can find potential extreme scenarios in the system operation process, thereby providing a reference for early warning.

Description

Technical Field

[0001] This invention belongs to the field of power system optimization operation technology, specifically involving a two-stage robust balance analysis method based on an inaccurate Dirichlet model. Background Technology

[0002] To address environmental and climate issues and alleviate the current shortage of fossil fuels, vigorously developing renewable energy sources such as wind and solar power has gradually become a common choice for countries worldwide in formulating energy policies and promoting clean energy transitions. Under the standard paradigm of a high-proportion renewable energy power system, the supply side will be dominated by new energy power generation with significant uncertainties, such as wind and solar power, making it increasingly reliant on weather conditions. On the demand side, the proportion of loads with regulatory capabilities will also increase significantly, and the response will be increasingly influenced by user behavior, exhibiting greater uncertainty. Therefore, in the context of the new power system, the uncertainties on both the source and load sides will transform the system's supply-demand balance from "deterministic supply-side resources responding to uncertain loads" to "a probabilistic matching of uncertain supply-side resources with uncertain demand-side resources." This will greatly increase the balance risks faced by the system and the difficulty of balancing electricity supply and demand.

[0003] Flexible resources, such as cascade hydropower, have attracted widespread attention from researchers due to their rapid adjustment and short-term support capabilities. They can follow net load fluctuations when the grid's peak-shaving capacity is insufficient, improving the reliability and security of system operation. In the research on power source-side flexible resources, existing literature models the operating power of cascade hydropower as an affine function of the realized photovoltaic power value, constructing a short-term stochastic optimization model for cascade hydropower. This achieves rapid response to photovoltaic power fluctuations and reduces the amount of curtailed photovoltaic power. Other literature further considers ultra-short-term time scales, constructing an ultra-short-term scheduling model based on heuristic methods to follow the fluctuations of new energy sources in the system, achieving a connection between short-term and real-time scheduling. In the research on grid-side flexible resources, existing literature constructs an equivalent model of stepped high-voltage direct current (HVDC) lines, utilizing the flexibility of cascade hydropower stations to alleviate the peak-shaving pressure on the receiving-end grid while avoiding frequent switching of HVDC line converter devices, achieving multi-regional mutual assistance. Therefore, as the proportion of new energy sources continues to increase, flexible resources within the system will play a certain regulatory role in both time and space dimensions, which is beneficial for alleviating the supply and demand contradictions of the system. However, the short-term operation modeling of cascade hydropower in the aforementioned studies is not detailed enough, failing to consider the nonlinear relationship between power generation and head and flow rate, resulting in insufficient exploration of the flexibility of hydropower. Furthermore, most studies neglect the ecological, flood control, and irrigation water supply functions of cascade hydropower, making the resulting scheduling schemes difficult to use directly in practice.

[0004] Conducting power balance analysis is a crucial foundation and necessary task for understanding and regulating the power system. Its purpose is to maximize the utilization of power generation resources and optimize power generation costs across the entire grid by coordinating the allocation of primary power generation energy sources such as hydropower, coal, and wind power across regions and time periods. Currently, commonly used power balance analysis methods are mainly divided into stochastic production simulation and time-series production simulation. However, most models assume that the predicted renewable energy power is 100% accurate. As the proportion of renewable energy continues to increase, the impact of uncertainties in wind and solar power cannot be ignored. While robust optimization avoids the curse of dimensionality caused by the increase in scenario trees, the optimization results of the model may be relatively conservative. Furthermore, to fully explore the flexible regulation capabilities of hydropower, the start-up and shutdown variables of hydropower will be introduced in the second stage of the robust optimization problem, which may cause the strong duality theorem to fail, significantly increasing the difficulty of solving the model. Summary of the Invention

[0005] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing a two-stage robust balance analysis method based on an inaccurate Dirichlet model. This method is used to solve the technical problem that high-dimensional uncertainty in scenarios with a high proportion of new energy sources makes it difficult to accurately calculate the balance state. It enables short-term power balance analysis of high-proportion renewable energy power systems and serves as a reference for day-ahead dispatch.

[0006] The present invention adopts the following technical solution:

[0007] A two-stage robust equilibrium analysis method based on an inexact Dirichlet model includes the following steps:

[0008] Basic technical information of the system is obtained from the scheduling system, and historical prediction error data of new energy are obtained.

[0009] Based on the obtained historical prediction error data of new energy sources, an inaccurate Dirichlet model is used to construct the uncertainty set of new energy sources for each time period.

[0010] Based on the component types of the scheduling system, the operational constraints of the scheduling system are constructed, and the objective function of the system operation is set; thus forming a standard two-stage robust optimization model.

[0011] The original problem of the obtained two-stage robust optimization model is divided into a main problem and a sub-problem. The improved C&CG algorithm is used to iteratively solve the problem within the constructed new energy uncertainty set to obtain the power balance result of the scheduling system under extreme operating conditions.

[0012] Preferably, the basic technical information of the system includes:

[0013] Historical forecast errors and next-day forecast power information for renewable energy and loads; basic operating parameters and cost coefficients of thermal power units in the dispatching system; existing power networks, transformers and network parameters; basic operating descriptions of cascade hydropower in the dispatching system and their corresponding spatial relationships; and basic operating parameters of ultra-high voltage direct current transmission systems in the dispatching system.

[0014] Preferably, the uncertainty set of the new energy source is constructed time-by-time using an inexact Dirichlet model as follows:

[0015] The historical samples are sorted in ascending order according to the magnitude of the error, and the prediction error is divided into segments, and the number of power occurrences in each segment is counted.

[0016] Estimate the 1-α confidence band of the true distribution of new energy prediction errors based on the beta distribution;

[0017] By extracting the (1-γ) / 2 quantile of the upper bound of the confidence band and the (1+γ) / 2 quantile of the lower bound of the confidence band, the upper and lower bounds of the uncertainty set of the new energy are obtained.

[0018] More preferably, the true distribution P * The 1-α confidence band is calculated as follows:

[0019]

[0020]

[0021] in, For the mth j The lower probability limit of segment power occurrence. For random variables, For the mth j Upper limit of the probability of segment power occurring P (x) is the lower bound of the true probability distribution. This is the upper bound of the true probability distribution.

[0022] Preferably, the operational constraints of the scheduling system are as follows:

[0023] Wind power and solar power operation constraints include:

[0024] The relationship between the actual daily power of new energy sources and the uncertain set and predicted power:

[0025]

[0026] Spatiotemporal coupling constraints of new energy fluctuations:

[0027]

[0028] Mutual exclusion constraints on the selection of new energy power values:

[0029]

[0030] in, These represent the actual daily output and the predicted output of new energy sources, respectively. These are the flags representing the upper and lower boundaries of the new energy output, respectively. These represent the upper and lower boundaries of the uncertain set, respectively, and π. T For time-uncertainty budgeting, π S For the budget of spatial uncertainty, N RE The number of new energy generating units;

[0031] The operating constraints of thermal power units include:

[0032] Unit start-up and shutdown constraints:

[0033]

[0034] Minimum start-stop time constraints:

[0035]

[0036]

[0037] Output upper and lower limit constraints:

[0038]

[0039] Climbing constraints:

[0040]

[0041]

[0042] in, This represents the start / stop status of the thermal power unit and the start flag. These represent the minimum technical output and installed capacity of a thermal power unit, respectively. T represents the downhill and uphill ramp rates of the thermal power unit, respectively. i on Minimum boot time, For thermal power units in their start-up state, T i off Minimum shutdown time, This refers to the operating power of the thermal power unit.

[0043] The operational constraints of a cascade hydropower system include:

[0044] Power generation flow constraints:

[0045]

[0046] Water discharge constraints:

[0047]

[0048] Hydropower head and tailwater level constraints:

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] Spatial coupling constraints of cascade hydropower reservoirs:

[0055]

[0056] Reservoir capacity constraints:

[0057]

[0058]

[0059]

[0060] Hydroelectric coupling constraints:

[0061]

[0062] in, This represents the power generation flow rate of the hydroelectric generator unit, s k,t This refers to the amount of water wasted by the hydropower unit. These are the net head of the hydropower unit, the reservoir water level, the tailrace water level, and the head loss. It refers to the dead water level and maximum water level of the reservoir, V. x,t It refers to the reservoir's water storage capacity. These are the minimum and maximum storage capacities of the reservoir, respectively. These are the turbine conversion efficiency and power generation efficiency, respectively; ρ is the density of water; and g is the acceleration due to gravity.

[0063] UHVDC operation constraints include:

[0064] DC upper and lower limit constraints:

[0065]

[0066] DC ramp constraint:

[0067]

[0068]

[0069] Adjustment limit:

[0070]

[0071] in, and These represent the upward and downward adjustment flags, respectively.

[0072] By analogy with the minimum start-up and shutdown time constraints of thermal power units, the following constraints are obtained:

[0073]

[0074]

[0075] Among them, T i HVDC,min+ and T i HVDC,min- These are the minimum durations after regulation for high-voltage direct current transmission;

[0076] The number of times a high-voltage direct current transmission can be regulated in a single day is limited.

[0077]

[0078] in, This represents the maximum number of adjustments possible to the DC tie line.

[0079]

[0080] Where Q represents the daily planned transaction volume of the DC tie line.

[0081] More preferably, the objective function of the scheduling system is as follows:

[0082]

[0083]

[0084]

[0085]

[0086] Among them, C Th,Start / C Th,Oper These are the start-up cost and operating cost of a thermal power unit, respectively. These are the coefficients of the quadratic, linear, and constant terms of the thermal power plant operating cost, respectively, C. Hy,Start For the start-up cost of hydropower units, C HVDC,Adj Adjustment costs for ultra-high voltage direct current transmission, These are the single start-up costs for thermal power, hydropower, and ultra-high voltage direct current (UHVDC) power plants, respectively. N Th The number of thermal power units. This is the start / stop flag for thermal power units. N represents the operating power of the thermal power unit. Hy This refers to the number of hydropower units. N is the start / stop flag for the hydroelectric generator unit. HVDC This refers to the number of high-voltage direct current transmission devices. This is the upward adjustment flag for the high-voltage direct current transmission device. This is the down-adjustment flag for the high-voltage direct current transmission device;

[0087] The costs of power curtailment and load shedding in the dispatch system are expressed as follows:

[0088]

[0089]

[0090] Among them, C RE,Curtail / C L,Cut ω represents the cost of curtailing renewable energy and the cost of load shedding, respectively. WT / ω PV / ω L These represent the cost coefficients for wind curtailment, solar curtailment, and load shedding, respectively. These represent the amounts of wind curtailment, solar curtailment, and load shedding, respectively. T is the number of time periods to be solved, and N is the number of time periods to be solved. WT This refers to the number of wind turbine units.

[0091] Preferably, the two-stage robust optimization model is as follows:

[0092]

[0093] Among them, c T Let α be the coefficient matrix of integer variables. T Let be the coefficient matrix of the DC transmission variables, x be a vector of integer variables, p be a vector of DC transmission variables, U be the uncertain set, Y be the set of two-stage operation variables, and d be the variable vector. T Let f be the coefficient matrix of the two-stage integer variables, z be the vector composed of the two-stage integer variables, and f be the coefficient matrix of the two-stage integer variables. T This is a coefficient matrix consisting of the two-stage operating variables, where y represents the two-stage operating variables, and β represents the coefficient matrix. Ts is the coefficient matrix of the two-stage unbalance, s is the vector composed of the two-stage unbalance, A and E are the inequality constraint coefficient matrices related to integer variables, B and N are the inequality constraint coefficient matrices related to DC tie line variables, b, g, and h are the constant term vectors, F is the constraint condition coefficient matrix of the two-stage operating variables, M and T are the constraint condition coefficient matrices of the two-stage integer variables, D is the coefficient matrix of the uncertain variables, H is the constraint condition coefficient matrix of the unbalance, and u is the vector composed of uncertain variables.

[0094] Preferably, the improved C&CG algorithm is used to iteratively solve the problem within the constructed new energy uncertainty set, specifically as follows:

[0095] Solve the master problem of two-stage robust optimization and obtain the unit start-up and shutdown schedule and the operating status of DC tie lines of the system;

[0096] The subproblems of the two-stage robust optimization problem are further broken down into a main problem and subproblems. The main problem determines the start-up and shutdown states of the hydropower unit, while the subproblems find the worst operating scenario. Through continuous iteration of the main and subproblems, the most extreme scenario is finally found.

[0097] More preferably, the main problem is specifically:

[0098]

[0099] Among them, c T Let α be the coefficient matrix of integer variables. T Let be the coefficient matrix of the DC transmission variables, x be a vector of integer variables, p be a vector of DC transmission variables, U be the uncertain set, Y be the set of two-stage operation variables, and d be the variable vector. T Let f be the coefficient matrix of the two-stage integer variables, z be the vector composed of the two-stage integer variables, and f be the coefficient matrix of the two-stage integer variables. T This is a coefficient matrix consisting of the two-stage operating variables, where y represents the two-stage operating variables, and β represents the coefficient matrix. T Let be the coefficient matrix of the two-stage unbalance, s be the vector of the two-stage unbalance, A and E be the coefficient matrices of inequality constraints related to integer variables, B and N be the coefficient matrices of inequality constraints related to DC tie line variables, b, g, and h be the vector of constant terms, F be the coefficient matrix of constraint conditions for the two-stage operating variables, M and T be the coefficient matrices of constraint conditions for the two-stage integer variables, D be the coefficient matrix of uncertain variables, H be the coefficient matrix of constraint conditions for the unbalance, u be the vector of uncertain variables, and z be the coefficient matrix of the two-stage unbalance variables. r Let f be a two-stage integer variable in the r-th iteration. T y r β is the two-stage running variable for the r-th iteration. T As an auxiliary variable, s rLet be the two-stage imbalance variable in the r-th iteration, where r is the current iteration number of the algorithm.

[0100] More preferably, the sub-problems include:

[0101] The inner main problem of nested C&CG:

[0102]

[0103] Where θ is an auxiliary variable. For a one-stage solution with defined integer variables, For the DC tie-line operating power determined in the first-stage solution, λ l The dual multiplier is R, which is the current iteration number.

[0104] Nested C&CG inner subproblems:

[0105]

[0106] in, These are the selected extreme scenarios.

[0107] Compared with the prior art, the present invention has at least the following beneficial effects:

[0108] A two-stage robust balance analysis method based on an inaccurate Dirichlet model is proposed for short-term power balance analysis of high-proportion renewable energy power systems, especially bases where new energy is transmitted via UHVDC, and serves as a reference for day-ahead dispatch. Obtaining basic system technical information from provincial / central dispatch systems is a necessary condition for realizing short-term power balance analysis. Constructing a standard two-stage robust model of the system is the core step of this invention. Through this step, the components included in the system are integrated, and by setting the system operation objective function, the operational flexibility of DC interconnection lines and cascade hydropower is fully utilized to achieve optimal system operation and balance analysis.

[0109] Furthermore, statistical processing of historical data is a prerequisite for the rational construction of the uncertain set of new energy sources. Appropriate processing methods help to uncover potential information within historical data. Constructing the true distribution of prediction errors is a core step in constructing the uncertain set of new energy sources. This involves using an inexact Dirichlet model, based on existing historical information, to achieve an approximate estimate of the prediction error without assuming any errors. As historical samples accumulate, the approximate estimate will infinitely approximate the true distribution, which is an important step in reducing the model's conservatism. The final step in constructing the uncertain set of new energy sources is to obtain artificially set upper and lower bounds based on quantile theory and a defined confidence band.

[0110] Furthermore, by integrating the components included in the system and setting the system's operational objective function, the operational flexibility of the DC interconnection line and cascade hydropower is fully explored, thereby achieving optimal system operation and balance analysis.

[0111] Furthermore, solving the main problem of the two-stage robust optimization of the system is the first step of the solution algorithm proposed in this invention. By solving the main problem of the two-stage robust optimization, the unit combination scheme of the system and the operating power of the DC tie line can be obtained. Since only some constraints are considered, a lower bound is provided for the solution of the C&CG algorithm.

[0112] Furthermore, solving the sub-problem of two-stage robust optimization of the system greatly improves the flexibility of cascade hydropower development. By analogy with the traditional C&CG algorithm, this invention further divides the sub-problem into a main problem of solving the hydropower start-up and shutdown states and a sub-problem of solving extreme operating scenarios. Solving the main problem of solving the hydropower start-up and shutdown states, since it only considers some constraints and seeks the maximum value, provides an upper bound for the convergence of the sub-problems; solving the sub-problem of solving extreme operating scenarios provides a lower bound, and by iteratively finding extreme operating scenarios, these are fed back to the upper layer.

[0113] In summary, the method of this invention can reduce the conservatism of the system under uncertain environments and can detect potential extreme scenarios during system operation, providing a reference for early warning. The method of this invention establishes a two-stage robust optimization problem with mixed integer pursuit constraints, and iteratively solves it using an improved C&CG algorithm combined with common commercial solvers. Compared with previous research, the method proposed in this invention has the following advantages:

[0114] (1) In terms of component modeling, a refined model of high-proportion renewable energy bases transmitted via DC was constructed, and different linearization approximation techniques were introduced for different nonlinear constraints to reduce the computational burden.

[0115] (2) Regarding the construction of the uncertainty set, based on limited historical sample data, under the condition of satisfying a certain confidence level, the fuzzy set of the prediction error of new energy was characterized by the Inexact Dirichlet Model (IDM). It can approximate the real distribution without artificially assuming the distribution, which greatly reduces the subjectivity and conservatism of robust optimization.

[0116] (3) In terms of model solving, an improved nested C&CG algorithm was adopted to solve the proposed two-stage robust optimization model and obtain the power abandonment and load shedding results under extreme scenarios. For the mixed integration problem in the second stage, the two-layer problem was first extended to a three-layer problem, and iteratively solved by analogy with the traditional C&CG algorithm.

[0117] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0118] Figure 1 This is a flowchart of the method of the present invention;

[0119] Figure 2 Flowchart for the implementation of the improved nested C&CG algorithm;

[0120] Figure 3 Here is the network diagram of the XJTU-ROTS test system;

[0121] Figure 4 A schematic diagram of the uncertainty set and worst-case scenario for new energy sources;

[0122] Figure 5 Two-stage robust power balance diagram with HVDC;

[0123] Figure 6 Two-stage robust power balance diagram without HVDC;

[0124] Figure 7 A schematic diagram of a computer device provided in an embodiment of the present invention;

[0125] Figure 8 This is a block diagram of a chip provided according to an embodiment of the present invention. Detailed Implementation

[0126] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0127] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0128] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0129] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0130] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0131] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0132] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0133] This invention provides a two-stage robust balance analysis method based on an inexact Dirichlet model (IDM) for short-term power balance analysis of high-proportion renewable energy power systems, especially bases where renewable energy is transmitted via UHVDC, and serves as a reference for day-ahead dispatch. In terms of component modeling, a refined model of high-proportion renewable energy bases transmitting via DC is constructed, and different linearization approximation techniques are introduced for different nonlinear constraints, reducing the computational burden. Regarding uncertainty set construction, based on limited historical sample data and under certain confidence levels, an IDM is used to characterize the fuzzy set of prediction errors for renewable energy, which can approximate the true distribution without artificially assuming distributions, greatly reducing the subjectivity and conservatism of robust optimization. In terms of model solving, an improved nested C&CG algorithm is used to solve the proposed two-stage robust optimization model, and can obtain the power curtailment and load shedding results under extreme scenarios. For the mixed-integer linear programming problem in the second stage, the two-level problem is first extended to a three-level problem, and iteratively solved by analogy with the traditional C&CG algorithm. The computational efficiency of the algorithm is analyzed through numerical simulation. By constructing an uncertainty set and invoking cascade hydropower units, the conservatism of the model is reduced, the system's ability to cope with extreme scenarios is improved, and potential extreme imbalances can be identified, allowing for early warnings based on the balance analysis results.

[0134] Please see Figure 1 This invention discloses a two-stage robust equilibrium analysis method based on an inaccurate Dirichlet model, comprising the following steps:

[0135] S1. Obtain basic technical information of the system from the scheduling system and obtain historical prediction error data of new energy.

[0136] The system's basic technical information includes:

[0137] Historical forecast errors and next-day forecast power information for renewable energy and loads; basic operating parameters and cost coefficients of thermal power units in the system; existing power networks, transformers and network parameters; basic operating descriptions of cascade hydropower in the system and their corresponding spatial relationships; and basic operating parameters of the ultra-high voltage direct current transmission system in the system.

[0138] S2. Based on the historical prediction error data of new energy obtained in step S1, the uncertain set of new energy is constructed for each time period using the inaccurate Dirichlet model (IDM).

[0139] S201, Historical Data Processing;

[0140] The existing historical samples are sorted in ascending order according to the magnitude of the error, and the prediction error is segmented to count the number of power occurrences in each segment.

[0141] The IDM (Imprecise Dirichlet Model) is an extension of the deterministic Dirichlet model. It uses a single Dirichlet distribution as the prior distribution to evaluate the probability distribution of random variables. The IDM can provide objective statistics for random variables that follow a multinomial distribution, especially when prior information is lacking or completely unknown.

[0142] Suppose there are n possible outcomes at a random time, and each outcome is represented by ξ. i If we express this as an expression, then the sample space of the event is Ω={ξ1,ξ2,...,ξ}. n The occurrence of this event follows a probability distribution P{X=ξ}. i}=θ i Let i = 1, 2, ..., n, where X represents a random variable and θ = (θ1, θ2, ..., θn). n ) represents the probability of each event occurring in the sample space, and satisfies θ i ≥0,i=1,2,...,n and

[0143] The deterministic Dirichlet model for the random variable θ, using Bayesian statistical principles, has its Dirichlet prior distribution represented by the Dirichlet(s,r) distribution shown in equation (1) as follows:

[0144]

[0145] in, Represents the Gamma function, r j These are predefined weighting coefficients, related to prior experience, and represent θ. j The mean of the result; s is a hyperparameter that determines the degree of influence of prior experience on the statistical result. The larger s is, the more samples are needed to eliminate the influence of prior experience on the statistical result. Therefore, s is understood as the degree of caution for the latest information, and its value range is usually [1, 2].

[0146] Obtain sample observations X ob Then, the original prior Dirichlet distribution is updated to the posterior Dirichlet distribution shown in equation (2) through Bayesian inference.

[0147]

[0148] Where M is the total number of sample observations, m j Let be the number of times the j-th event occurs in M ​​sample observations. Therefore, after obtaining the posterior distribution, the expected value of the probability distribution is as follows:

[0149] E(θ j)=(m j +s·r j (s+X) ob ) -1 (3)

[0150] Therefore, as r takes different values, the event ξ is obtained. i The probability θ of occurrence i The range of values ​​for is:

[0151]

[0152] S202, Construct confidence bands for the true distribution;

[0153] The 1-α confidence band of the true distribution of new energy prediction error is estimated based on the beta distribution.

[0154] To adapt to the two-stage robust optimization method, it is also necessary to study the probability θ. i The confidence interval is given. Since the power generation levels of new energy sources are independent of each other at any given moment, the marginal distribution of the Dirichlet distribution can be used for calculation. Let... This represents the set of samples obtained by independently sampling the random variable X according to its true distribution and arranging them in ascending order. Represents the beta distribution β(m) j ,n+1-m j The α quantile of n. For any n and α, define... Where n represents the sample size. And introduce... Then for the true distribution P * The method for calculating the 1-α confidence band is as follows:

[0155]

[0156] S203. Construct the upper and lower bounds of the uncertain set of new energy sources.

[0157] The upper and lower bounds of the uncertainty set of new energy sources are obtained by extracting the (1-γ) / 2 quantile of the upper bound of the confidence band and the (1+γ) / 2 quantile of the lower bound of the confidence band.

[0158] Please see Figure 1 After obtaining the true distribution P * After the 1-α confidence band, truncate (1-γ) / 2 quantiles and P The upper and lower bounds of the fluctuation of the uncertain set can be obtained by using the (1+γ) / 2 quantile of (x), such as Figure 1 As shown.

[0159] S3. Based on the component types of the scheduling system, construct the operational constraints of the scheduling system and set the objective function for system operation, including economy and security; organize and form a standard two-stage robust optimization model.

[0160] S301. Construct the corresponding mathematical model based on the components contained in the system;

[0161] Mathematical models were developed for various power generation and flexibility resources in the system, including wind turbines, photovoltaic units, thermal power units, cascade hydropower, and ultra-high voltage direct current.

[0162] Let Ω represent a set of a certain type of resources, with its subscript representing the corresponding resource name, including new energy generating units (RE), thermal power units (Th), hydropower units (Hy), and ultra-high voltage direct current transmission (HVDC). T represents the total number of balance analysis periods; subscript i represents the number of a certain type of resource, and subscript t represents a certain scheduling time.

[0163] (1) Operational constraints of wind power and photovoltaic power

[0164] The uncertainty set is used to describe the uncertainty of wind power and photovoltaic output.

[0165] Equations (6) to (8) characterize the intraday stochastic fluctuations of new energy units. Equation (6) represents the relationship between the intraday actual power of new energy units and the uncertain set and predicted power. These represent the actual daily output and the predicted output of new energy sources, respectively. These are the flags indicating the upper and lower boundaries of the new energy output.

[0166]

[0167] Equation (7) describes the spatiotemporal coupling constraint of new energy fluctuations, which is beneficial to the conservatism of the control model.

[0168]

[0169] Equation (7) is a mutual exclusion constraint on the power values ​​of new energy sources, indicating that it is impossible to take the upper / lower boundary at the same time.

[0170]

[0171] in, These represent the upper and lower boundaries of the uncertain set, respectively.

[0172] (2) Operating constraints of thermal power units

[0173] Thermal power units are the most common type of power source in the system and also serve as the system's backup power source. Their operational constraints mainly include unit start-up and shutdown constraints (9), as follows:

[0174]

[0175] The minimum start-stop time constraints (10)-(11) are as follows:

[0176]

[0177]

[0178] Output upper and lower limit constraints (12), as follows:

[0179]

[0180] The climbing constraints (13)-(14) are as follows:

[0181]

[0182]

[0183] in, This represents the start / stop status of the thermal power unit and the start flag. These represent the minimum technical output and installed capacity of a thermal power unit, respectively. These represent the downhill and uphill speeds of the thermal power unit, respectively.

[0184] (3) Operational constraints of cascade hydropower systems

[0185] A cascade hydropower system refers to a series of hydropower stations running from upstream to downstream within the same or different river basins. These systems typically include reservoirs of a certain capacity and can be categorized as annual regulating power stations, seasonal regulating power stations, etc., based on the reservoir's regulation capacity. Cascade hydropower systems can receive instructions from dispatching agencies to achieve efficient utilization and rational development of water resources, while also meeting other water conservancy needs such as navigation, irrigation, and flood control.

[0186] For ease of subsequent modeling, let's assume there are N rivers in a certain watershed H. H There are cascade hydropower stations, numbered sequentially from upstream to downstream as {1,2,...,N}. H The operational constraints of a cascade hydropower system can be mainly divided into power constraints, hydraulic constraints, and hydropower coupling constraints.

[0187] Electricity constraints are similar to those of thermal power units, including start-stop constraints, upper and lower output limits, and ramping constraints, which will not be elaborated here.

[0188] Hydraulic constraints include power generation flow constraints (15), as detailed below:

[0189]

[0190] The wastewater discharge constraint (16) is as follows:

[0191]

[0192] The constraints on the hydroelectric head and tailwater level (17)-(21) are as follows:

[0193]

[0194]

[0195]

[0196]

[0197]

[0198] Spatial coupling constraints of cascade hydropower reservoirs (22) are as follows:

[0199]

[0200] Reservoir capacity constraints (23)-(25), as detailed below:

[0201]

[0202]

[0203]

[0204] Hydroelectric coupling constraints (26) are as follows:

[0205]

[0206] in, This represents the power generation flow rate of the hydroelectric generator unit, s k,t This refers to the amount of water wasted by the hydroelectric power unit. These are the net head of the hydropower unit, the reservoir water level, the tailrace water level, and the head loss. These are the dead water level and the maximum water level of the reservoir. V x,t It refers to the water storage capacity of the reservoir. These are the minimum and maximum storage capacities of the reservoir, respectively. These are the turbine conversion efficiency and power generation efficiency, respectively; ρ is the density of water; and g is the acceleration due to gravity.

[0207] However, the above model contains highly nonlinear constraints (18)-(20) and (26), which are difficult to solve directly; two different linearization methods will be given next to assist in the solution.

[0208] Taking the reservoir capacity-water level relationship in equation (18) as an example, we first introduce the piecewise linearization of its nonlinear relationship, and then introduce SOS-2 constraints to perform a convex combination of the endpoints of each piecewise linearized function to describe each value; the specific method is as follows:

[0209] Suppose that the reservoir's water capacity and water level are divided into K+1 points, then there are K piecewise linearized functions, and the reservoir's water capacity range is... Each point satisfies The reservoir water level can be expressed as Then, a set of continuous variables y varying in [0,1] is introduced to characterize the relationship between water capacity and reservoir water level using a convex combination:

[0210]

[0211]

[0212] To ensure that the y-values ​​of a given hydropower station at any given time have only two non-zero values ​​(representing the two endpoints of the interval) and to satisfy the convex combination property, a series of binary variables z and other constraints need to be introduced:

[0213]

[0214]

[0215]

[0216]

[0217]

[0218] For hydropower coupling constraints, the product of power generation flow and water head makes the mathematical model a bilinear nonlinear programming problem. The McCormick envelope method can eliminate the product term, ensuring the convexity of the problem and providing a sufficiently tight boundary, and has been widely used. Its form involves constructing a series of overestimated or underestimated cutting planes to approximate the original bilinear terms, with the added constraints as follows:

[0219]

[0220] (4) UHVDC operation constraints

[0221] Because of the large number of power electronic devices and the complexity of their adjustment, frequent adjustments to the output of the DC tie line may lead to commutation failure. Therefore, a "stepped" method is often used to adjust the transmission power of the DC tie line. This stepped characteristic is considered through constraints such as DC upper and lower limit constraints (35), DC ramp constraints (36)(37), and adjustment number limits (41).

[0222]

[0223] in, It refers to the transmission power of a high-voltage direct current line. P i HVDC and These are the minimum and maximum transmission power of the high-voltage direct current transmission line, respectively.

[0224]

[0225]

[0226] The following adjustment principles should be met when adjusting DC tie lines:

[0227] Both upward and downward adjustment states are not allowed to exist at the same time, therefore constraints need to be added:

[0228]

[0229] in, and These represent the upward and downward adjustment flags, respectively.

[0230] After the DC tie line adjustment is completed, the power transmission level should be maintained for a period of time. By analogy with the minimum start-up and shutdown time constraints of thermal power units, the following constraints are obtained:

[0231]

[0232]

[0233] Among them, T i HVDC,min+ and T i HVDC,min- These represent the minimum duration after regulation of high-voltage direct current transmission.

[0234] The number of times a high-voltage direct current transmission can be regulated in a single day is limited.

[0235]

[0236] in, This represents the maximum number of adjustments that can be made to the DC tie line.

[0237]

[0238] Where Q is the daily planned transaction volume of the DC tie line.

[0239] S302, The objective function of the system is as follows:

[0240] The objective function of the system is characterized as a multi-objective optimization problem. The first objective is to minimize the operating cost of the system, and the second objective is to minimize the curtailment cost and load shedding penalty of the system. The operating cost of the system includes the start-up and shutdown cost and operating cost of thermal power units, the start-up loss cost of cascade hydropower, and the adjustment cost of UHVDC transmission, as shown in equations (43)-(46).

[0241]

[0242]

[0243]

[0244]

[0245] Among them, C Th,Start / C Th,Oper These represent the start-up cost and operating cost of a thermal power unit, respectively. These represent the coefficients of the quadratic, linear, and constant terms of the thermal power plant operating cost, respectively. This part can be processed using certain linearization methods. Hy,Start C represents the startup cost of a hydroelectric power unit. HVDC,Adj This indicates the adjustment cost of ultra-high voltage direct current transmission. These represent the single start-up cost of thermal power, the single start-up cost of hydropower, and the single adjustment cost of ultra-high voltage direct current, respectively.

[0246] The system's power curtailment cost and load shedding cost are expressed by equations (47)-(48).

[0247]

[0248]

[0249] Among them, C RE,Curtail / C L,Cut ω represents the cost of curtailing renewable energy and the cost of load shedding, respectively. WT / ω PV / ω L These represent the cost coefficients for wind curtailment, solar curtailment, and load shedding, respectively. These represent the amounts of wind curtailment, solar curtailment, and load shedding, respectively.

[0250] S303. Establish a standard two-stage robust optimization problem for the scheduling system and formulate a compact format:

[0251] Based on the above analysis, the objective function and operational constraints of the system were established. Next, a two-stage robust optimization model as shown in (49) was established.

[0252]

[0253] Where χ is the set of integer variables in the first stage, U is the set of uncertain variables, and Y is the set of continuous variables in the second stage.

[0254] χ={x∈Z {0,1} ,p∈R + :} (50)

[0255] U=={u∈Z {0,1}:} (51)

[0256] Y = {z∈Z} {0,1},y∈R + :} (52)

[0257] The physical meaning of the above problem is that the first stage determines the start-up and shutdown status of thermal power units and the operation status of ultra-high voltage direct current transmission, and the second stage determines the start-up and shutdown status of hydropower units and the output status of various system resources under the worst-case scenario, minimizing system operating costs and imbalance.

[0258] For ease of analysis, the above form has been transformed into a compact format as shown in the following figure:

[0259]

[0260] S4. Divide the original problem into a main problem and subproblems, and use the improved C&CG algorithm to solve iteratively;

[0261] Please see Figure 2 The specific steps are as follows:

[0262] S401. Solve the master problem of the two-stage robust optimization and obtain the unit start-up and shutdown schedule and the operating status of the DC tie line of the system.

[0263] S402. The subproblems of the two-stage robust optimization problem are further broken down into a main problem and subproblems. The main problem determines the start-up and shutdown states of the hydropower unit, while the subproblems find the worst-case operating scenario. Through continuous iteration of the main and subproblems, the most extreme scenario is finally found.

[0264] (1) The outer main problem of nested C&CG

[0265] By analogy with the traditional C&CG solution approach, the problem shown in equation (53) can be divided into a main subproblem for solution, where the main problem takes the form shown in (54). Since the constraints contained in the main problem are only a part of the constraints in the original problem, solving the main problem will provide a lower bound for the optimal solution of the original problem, and at the same time obtain the thermal power unit combination results and the operating status of the UHVDC transmission system.

[0266]

[0267] (2) Nested C&CG outer subproblem

[0268] 1) Nested C&CG inner main problem

[0269] Considering the special characteristics of the subproblem, we first transform it into a three-level optimization model:

[0270]

[0271] Here, the set Φ represents all possible values ​​of the integer variable z, and is a countable set.

[0272] Suppose there are a total of R possible cases. If all integer variables are enumerated, we can obtain an equivalent large-scale mixed integer optimization problem. In this case, the subproblem is rewritten as the equivalent form shown in equation (56).

[0273]

[0274] Note that the minimization problem in the constraints is a linear programming model. We can obtain its dual problem and add the dual problem constraints to equation (56) to obtain a large-scale single-layer optimization problem, as shown in equation (57).

[0275]

[0276] For the bilinear term (Du) in equation (57) T λ, considering that variable u is a 0 / 1 variable, therefore let γ ij =λ i u j Then, the Big M method is used for exact linearization, and the additional constraints are shown in equation (58).

[0277]

[0278] Since the inner master problem also contains only partial constraints, solving the inner maximization master problem will yield the upper bound of the outer subproblems, as well as the worst-case uncertainty scenario, which will be passed on to subsequent inner subproblems.

[0279] 2) Nested C&CG inner subproblems

[0280] Considering that enumerating all integer variables is impractical and that only a small number of unit combinations can adequately address the worst-case scenario, the Recourse problem with inner integer variables can also be solved precisely through iterative methods, similar to the solution process of C&CG. The construction idea of ​​the nested C&CG inner subproblem is based on the idea of ​​C&CG, returning the key unit combination for the inner main problem, as shown in equation (59).

[0281]

[0282] Since the worst-case scenario selected through the inner master problem may lead to a better hydropower start-up and shutdown state after another round of optimization, solving the inner subproblem will obtain the lower bound of the outer subproblem, and at the same time, obtain a set of key unit combination results, which are then passed to the inner master problem to improve the upper bound. When the solutions to the inner master subproblem do not differ by more than a threshold, the subproblem is solved, and the process returns to the outer layer.

[0283] S5 outputs extreme operating scenarios and the power balance analysis results under extreme scenarios.

[0284] The system will analyze the power balance results under extreme operating conditions and return the power balance scheme with the least loss as a guide for short-term dispatching.

[0285] In another embodiment of the present invention, a two-stage robust equilibrium analysis system based on an inaccurate Dirichlet model is provided. This system can be used to implement the above-mentioned two-stage robust equilibrium analysis method based on an inaccurate Dirichlet model. Specifically, the two-stage robust equilibrium analysis system based on an inaccurate Dirichlet model includes a data module, a construction module, an optimization module, and an output module.

[0286] Among them, the data module obtains basic technical information of the system from the scheduling system and obtains historical prediction error data of new energy.

[0287] The module constructs the uncertainty set of new energy sources by time period using an inaccurate Dirichlet model based on the prediction error data of the new energy historical data obtained in step S1.

[0288] The optimization module constructs the operational constraints of the scheduling system based on the component types of the scheduling system, and sets the objective function for system operation; thus forming a standard two-stage robust optimization model.

[0289] The output module divides the original problem of the two-stage robust optimization model obtained by the optimization module into a main problem and sub-problems. It then uses an improved C&CG algorithm to iteratively solve the problem within the range of the new energy uncertainty set constructed by the construction module, thereby obtaining the power balance result of the scheduling system under extreme operating conditions.

[0290] In another embodiment of the present invention, a terminal device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or corresponding function. The processor described in this embodiment can be used for operation of a two-stage robust balance analysis method based on an inaccurate Dirichlet model, including:

[0291] Basic technical information of the system is obtained from the scheduling system, and historical prediction error data of new energy sources are obtained. Based on the historical prediction error data of new energy sources, an inaccurate Dirichlet model is used to construct the uncertainty set of new energy sources for each time period. According to the component type of the scheduling system, the operation constraints of the scheduling system are constructed, and the objective function of the system operation is set. A standard two-stage robust optimization model is formed. The original problem of the two-stage robust optimization model is divided into a main problem and a sub-problem. An improved C&CG algorithm is used to iteratively solve the problem within the constructed uncertainty set of new energy sources, and the power balance result of the scheduling system under extreme operating conditions is obtained.

[0292] Please see Figure 7The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When executed by the processor 61, the computer program 63 implements the fluid composition calculation method in the reservoir stimulation wellbore of this embodiment. To avoid repetition, details are omitted here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the two-stage robust equilibrium analysis system based on the inaccurate Dirichlet model of this embodiment. To avoid repetition, details are omitted here.

[0293] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 7 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0294] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0295] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or RAM of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on the computer device 60.

[0296] Furthermore, the memory 62 may include both internal storage units of the computer device 60 and external storage devices. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0297] Please see Figure 8 The terminal device is a chip. In this embodiment, the chip 600 includes a processor 622, which may be one or more, and a memory 632 for storing computer programs executable by the processor 622. The computer program stored in the memory 632 may include one or more modules, each corresponding to a set of instructions. Furthermore, the processor 622 may be configured to execute the computer program to perform the aforementioned two-stage robust balance analysis method based on an inaccurate Dirichlet model.

[0298] Additionally, chip 600 may also include a power supply component 626 and a communication component 650. The power supply component 626 can be configured to perform power management of chip 600, and the communication component 650 can be configured to enable communication of chip 600, such as wired or wireless communication. Furthermore, chip 600 may also include an input / output (I / O) interface 658. Chip 600 can operate on an operating system stored in memory 632.

[0299] In another embodiment of the present invention, a storage medium is also provided, specifically a computer-readable storage medium (memory). This computer-readable storage medium is a memory device in a terminal device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and extended storage media supported by the terminal device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device.

[0300] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the two-stage robust equilibrium analysis method based on the inaccurate Dirichlet model in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor to perform the following steps:

[0301] Basic technical information of the system is obtained from the scheduling system, and historical prediction error data of new energy sources are obtained. Based on the historical prediction error data of new energy sources, an inaccurate Dirichlet model is used to construct the uncertainty set of new energy sources for each time period. According to the component type of the scheduling system, the operation constraints of the scheduling system are constructed, and the objective function of the system operation is set. A standard two-stage robust optimization model is formed. The original problem of the two-stage robust optimization model is divided into a main problem and a sub-problem. An improved C&CG algorithm is used to iteratively solve the problem within the constructed uncertainty set of new energy sources, and the power balance result of the scheduling system under extreme operating conditions is obtained.

[0302] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0303] Case Analysis

[0304] The testing system comprises three zones: A, B, and C. Zone A is rich in renewable energy and serves as a high-proportion renewable energy transmission base. Zone B is a load center with the highest thermal power capacity in the entire zone. The main connections between the three zones are as follows: Zone A and Zone B are connected by four AC interconnection lines and one DC interconnection line, while Zone B and Zone C are connected by three AC interconnection lines. In this invention, the run-of-river hydropower is improved to cascade hydropower. Detailed cascade hydropower data and spatial relationships are as follows: Figure 3 As shown in Table 1.

[0305] Table 1. Operating parameters of the cascade hydropower infrastructure in the basin.

[0306]

[0307]

[0308] Case settings

[0309] To verify the effectiveness of the proposed model and algorithm, different computational examples were set up as shown in Table 2.

[0310] Table 2. Calculation Example Settings

[0311]

[0312] Effectiveness analysis of models and algorithms

[0313] Figure 4 The graph shows the worst-case operating scenario for renewable energy. As can be seen, the average output power of renewable energy is lower than the predicted power, resulting in higher operating costs and more severe consequences such as load shedding. Therefore, it is evident that... Figure 5 and Figure 6 It can be seen that wind curtailment occurred during periods 3 and 5 due to the ramp-up limitations of thermal power units. Due to insufficient wind power, load shedding occurred during periods 19-21. During periods of high renewable energy generation, HVDC also improved transmission levels, enabling flexible mutual assistance between multiple regional power grids, which is beneficial for the absorption of renewable energy.

[0314] However, discovering these potential imbalances using deterministic models is somewhat difficult. As shown in Table 3, this method is less conservative than the traditional two-stage RO model, reducing operating costs and load shedding penalties by 10.25%. Therefore, the method proposed in this invention provides an effective solution for identifying the worst-case imbalance state of a system and providing corresponding response strategies, which has significant engineering implications.

[0315] Table 3. Balance analysis results for different examples.

[0316]

[0317]

[0318] Next, a comparative analysis of Case 7 and Case 8 is used to analyze the role of HVDC in multi-regional complementarity. First, the results of the balance analysis using a deterministic model show that although no imbalance exists in either case, the target of Case 7 is 12.66% higher than the target of the deterministic model considering HVDC. This phenomenon arises because the constraints of the critical section limit the power transmission from A to load center B by cost-effective thermal power units, thus requiring the use of more expensive thermal power units to meet load demand. Table 3 shows that under the worst-case operating condition, the amount of renewable energy curtailed is 17462.22 MWh, and the load shedding is 1175.85 MWh. Therefore, HVDC helps to aggregate renewable energy and alleviate the peak-shaving pressure of the system.

[0319] Simulations of predicted data with varying sample sizes and uncertainty budgets revealed that as historical data accumulates and the spatiotemporal uncertainty budget decreases, the model's conservatism further diminishes, leading to a reduction in the target value. The overall system imbalance is also alleviated. This aligns with the actual system operation, demonstrating the model's correctness.

[0320] In summary, this invention provides a two-stage robust equilibrium analysis method based on an inaccurate Dirichlet model. In terms of component modeling, it constructs a refined model of a high-proportion renewable energy base transmitting electricity via DC, and introduces different linearization approximation techniques for different nonlinear constraints, thereby reducing the computational burden.

[0321] Regarding the construction of the uncertainty set, based on limited historical sample data and under certain confidence levels, the Inexact Dirichlet Model (IDM) was used to characterize the fuzzy set of prediction errors for new energy sources. This model can approximate the true distribution without making arbitrary assumptions about the distribution, greatly reducing the subjectivity and conservatism of robust optimization.

[0322] In terms of model solving, an improved nested C&CG algorithm was adopted to solve the proposed two-stage robust optimization model, and the results of power abandonment and load shedding under extreme scenarios were obtained. For the mixed integer linear programming problem in the second stage, the two-level problem was first extended to a three-level problem, and iteratively solved by analogy with the traditional C&CG algorithm.

[0323] The computational efficiency of the algorithm was analyzed through numerical simulation. By reasonably constructing the uncertainty set and incorporating cascade hydropower units, the conservatism of the model was reduced, the system's ability to cope with extreme scenarios was improved, and potential extreme imbalances could be identified, allowing for early warning based on the balance analysis results.

[0324] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A two-stage robust equilibrium analysis method based on an inexact Dirichlet model, characterized in that, Includes the following steps: Basic technical information of the system is obtained from the scheduling system, and historical prediction error data of new energy are obtained. Based on the obtained historical prediction error data of new energy sources, an inaccurate Dirichlet model is used to construct the uncertainty set of new energy sources for each time period. Based on the component types of the scheduling system, the operational constraints of the scheduling system are constructed, and the objective function of the system operation is set; a standard two-stage robust optimization model is formed, wherein the operational constraints of the scheduling system include the operational constraints of the cascade hydropower system, and when constructing the operational constraints of the cascade hydropower system, piecewise linearization and SOS-2 constraints are used to process the nonlinear relationship between reservoir capacity and water level. The original problem of the obtained two-stage robust optimization model is divided into a main problem and subproblems. An improved C&CG algorithm is used to iteratively solve the problem within the constructed new energy uncertainty set to obtain the power balance result of the dispatching system under extreme operating conditions. Specifically, the step of iteratively solving the problem using the improved C&CG algorithm includes: further decomposing the subproblems into inner main problems and inner subproblems to address the problem of the standard C&CG algorithm failing due to the introduction of integer variables in the second stage because of the operating constraints of the cascade hydropower system.

2. The two-stage robust equilibrium analysis method based on the inaccurate Dirichlet model according to claim 1, characterized in that, The system's basic technical information includes: Historical forecast errors and next-day forecast power information for renewable energy and loads; basic operating parameters and cost coefficients of thermal power units in the dispatching system; existing power networks, transformers and network parameters; basic operating descriptions of cascade hydropower in the dispatching system and their corresponding spatial relationships; and basic operating parameters of ultra-high voltage direct current transmission systems in the dispatching system.

3. The two-stage robust equilibrium analysis method based on the inaccurate Dirichlet model according to claim 1, characterized in that, The uncertainty set of new energy sources is constructed time-by-time using an inexact Dirichlet model as follows: The historical samples are sorted in ascending order according to the magnitude of the error, and the prediction error is divided into segments, and the number of power occurrences in each segment is counted. Estimate the true distribution of new energy prediction errors based on beta distribution Confidence band; Extract the upper bound of the confidence band respectively Quantiles and lower bound of confidence band Quantiles are used to obtain the upper and lower bounds of the uncertainty set of new energy sources.

4. The two-stage robust equilibrium analysis method based on the inaccurate Dirichlet model according to claim 3, characterized in that, True distribution of The confidence band is calculated as follows: in, For the first m j The lower probability limit of segment power occurrence. For random variables, For the first m j Upper limit of the probability of segment power occurring This is the lower bound of the true probability distribution. This is the upper bound of the true probability distribution.

5. The two-stage robust equilibrium analysis method based on the inaccurate Dirichlet model according to claim 1, characterized in that, The specific operational constraints of the scheduling system are as follows: Wind power and solar power operation constraints include: The relationship between the actual daily power of new energy sources and the uncertain set and predicted power: Spatiotemporal coupling constraints of new energy fluctuations: Mutual exclusion constraints on the selection of new energy power values: in, / These represent the actual daily output and the predicted output of new energy sources, respectively. / These are the flags representing the upper and lower boundaries of the new energy output, respectively. / These represent the upper and lower boundaries of the uncertain set, respectively. Budgeting for time uncertainty, Budgeting for spatial uncertainty, The number of new energy generating units; The operating constraints of thermal power units include: Unit start-up and shutdown constraints: Minimum start-stop time constraints: Output upper and lower limit constraints: Climbing constraints: in, / This represents the start / stop status of the thermal power unit and the start flag. / These represent the minimum technical output and installed capacity of a thermal power unit, respectively. / These represent the downhill and uphill ramp rates of the thermal power unit, respectively. Minimum boot time, This indicates the start-up status of the thermal power unit. Minimum shutdown time, This refers to the operating power of the thermal power unit. The operational constraints of a cascade hydropower system include: Power generation flow constraints: Water discharge constraints: Hydropower head and tailwater level constraints: Spatial coupling constraints of cascade hydropower reservoirs: Reservoir capacity constraints: Hydroelectric coupling constraints: in, This represents the power generation flow rate of the hydroelectric generator unit. This refers to the amount of water wasted by the hydropower unit. / / / These are the net head of the hydropower unit, the reservoir water level, the tailrace water level, and the head loss. / These are the dead water level and the maximum water level of the reservoir. It refers to the reservoir's water storage capacity. / These are the minimum and maximum storage capacities of the reservoir, respectively. / These are the turbine conversion efficiency and the power generation efficiency, respectively. It is the density of water. It is gravitational acceleration; UHVDC operation constraints include: DC upper and lower limit constraints: DC ramp constraint: Adjustment limit: in, and These represent the upward and downward adjustment flags, respectively. By analogy with the minimum start-up and shutdown time constraints of thermal power units, the following constraints are obtained: in, and These are the minimum durations after regulation for high-voltage direct current transmission; The number of times a high-voltage direct current transmission can be regulated in a single day is limited. in, This represents the maximum number of adjustments possible to the DC tie line. in, The daily planned trading volume for the DC interconnection line.

6. The two-stage robust equilibrium analysis method based on the inaccurate Dirichlet model according to claim 5, characterized in that, The objective function of the scheduling system is as follows: in, / These are the start-up cost and operating cost of a thermal power unit, respectively. / / These are the coefficients of the quadratic, linear, and constant terms of the thermal power plant operating cost, respectively. For the start-up cost of hydropower units, Adjustment costs for ultra-high voltage direct current transmission, / / These are the single start-up costs for thermal power, hydropower, and ultra-high voltage direct current (UHVDC) power plants, respectively. The number of thermal power units. This is the start / stop flag for thermal power units. This refers to the operating power of thermal power units. This refers to the number of hydropower units. This is the start / stop flag for the hydroelectric generator unit. This refers to the number of high-voltage direct current transmission devices. This is the upward adjustment flag for the high-voltage direct current transmission device. This is the down-adjustment flag for the high-voltage direct current transmission device; The costs of power curtailment and load shedding in the dispatch system are expressed as follows: in, / These represent the costs of curtailing renewable energy and the costs of load shedding, respectively. / / These represent the cost coefficients for wind curtailment, solar curtailment, and load shedding, respectively. / / These represent the amounts of wind curtailment, solar curtailment, and load shedding, respectively. To solve for the number of time periods, This refers to the number of wind turbine units.

7. The two-stage robust equilibrium analysis method based on the inaccurate Dirichlet model according to claim 1, characterized in that, The two-stage robust optimization model is as follows: in, The coefficient matrix is ​​a matrix of integer variables. This is the coefficient matrix of the DC transmission variables. A vector consisting of integer variables. A vector composed of DC transmission variables. For an uncertain set, It is a set of variables for the two-stage operation. The coefficient matrix of the two-stage integer variables. A vector consisting of two-stage integer variables. The coefficient matrix consists of variables from the two-stage operation. For the two-stage operation variables, This is the coefficient matrix of the two-stage imbalance. This is a vector composed of two-stage imbalance quantities. , This is the coefficient matrix of inequality constraints related to integer variables. , This is the inequality constraint coefficient matrix related to the DC tie-line variables. , , A vector of constant terms. This is the constraint coefficient matrix for the two-stage runtime variables. , This is the constraint coefficient matrix for two-stage integer variables. The coefficient matrix of the uncertain variables, This is the constraint coefficient matrix for the unbalanced quantity. A vector consisting of uncertain variables.

8. The two-stage robust equilibrium analysis method based on the inaccurate Dirichlet model according to claim 1, characterized in that, The improved C&CG algorithm is used to iteratively solve the problem within the constructed uncertainty set of new energy sources, specifically as follows: Solve the master problem of two-stage robust optimization and obtain the unit start-up and shutdown schedule and the operating status of DC tie lines of the system; The subproblems of the two-stage robust optimization problem are further broken down into a main problem and subproblems. The main problem determines the start-up and shutdown states of the hydropower unit, while the subproblems find the worst operating scenario. Through continuous iteration of the main and subproblems, the most extreme scenario is finally found.

9. The two-stage robust equilibrium analysis method based on the inaccurate Dirichlet model according to claim 8, characterized in that, The main question is as follows: in, The coefficient matrix is ​​a matrix of integer variables. This is the coefficient matrix of the DC transmission variables. A vector consisting of integer variables. A vector composed of DC transmission variables. For an uncertain set, It is a set of variables for the two-stage operation. The coefficient matrix of the two-stage integer variables. A vector consisting of two-stage integer variables. The coefficient matrix consists of variables from the two-stage operation. For the two-stage operation variables, This is the coefficient matrix of the two-stage imbalance. This is a vector composed of two-stage imbalance quantities. , This is the coefficient matrix of inequality constraints related to integer variables. , This is the inequality constraint coefficient matrix related to the DC tie-line variables. , , A vector of constant terms. This is the constraint coefficient matrix for the two-stage runtime variables. , This is the constraint coefficient matrix for two-stage integer variables. The coefficient matrix of the uncertain variables, This is the constraint coefficient matrix for the unbalanced quantity. A vector composed of uncertain variables. Let r be the two-stage integer variable in the r-th iteration. For the two-stage running variables of the r-th iteration, As an auxiliary variable, Let be the two-stage imbalance variable in the r-th iteration. This represents the current iteration number of the algorithm.

10. The two-stage robust equilibrium analysis method based on the inaccurate Dirichlet model according to claim 8, characterized in that, Sub-problems include: The inner main problem of nested C&CG: in, As an auxiliary variable, For a one-stage solution with defined integer variables, To determine the DC tie-line operating power in the first stage of the solution, As a dual multiplier, This represents the current iteration number; Nested C&CG inner subproblems: in, These are the selected extreme scenarios.

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