Power system wind power consumption capability limit evaluation method considering transient stability

Abstract

The invention relates to the technical field of electric power system automation, and particularly discloses an electric power system wind power consumption capability limit evaluation method considering transient stability, and the method comprises the steps: carrying out the sampling in a feasible space of an electric power system, and generating a sample data set; using the sample data set to offline train a deep neural network as a transient stability evaluator, and predicting a transient stability index of the power system; based on the wind power output short-term prediction data and the load prediction data, considering the transient stability constraint of the power system, and determining a day-ahead scheduling plan of each generator in the power system; and constructing an evaluation model of the wind power consumption capability limit under the current scheduling plan, and accelerating the solving process by means of constructing an initial solution in an auxiliary manner through constraint preprocessing and a heuristic algorithm. The method has the advantages that the calculation speed of the evaluation model is effectively improved, the transient stability of the power system is considered, the wind power consumption capability limit is quickly evaluated, and auxiliary opinions and decision support are provided for real-time dispatching of dispatchers.

Description

Technical Field

[0001] The present invention relates to the technical field of power system automation, and in particular to a method for evaluating the wind power absorption capacity limit of a power system considering transient stability. Background Art

[0002] With the large-scale access of wind power, problems such as reduced inertia of the power system and reduced transient stability margin have become increasingly prominent. The uncertainty of wind power poses a major challenge to the safe and stable operation of the system. Unlike thermal power generation, dispatchers have limited control over wind power output, and wind abandonment measures will only be taken when there is a safety violation in the system. Therefore, there is an urgent need for a method to evaluate the limit of wind power absorption capacity and guide its dispatching.

[0003] Traditional assessment methods are mainly based on static safety constraints. Although the calculation is relatively simple, they ignore transient stability constraints, resulting in overly optimistic assessment results. In addition, as the high penetration rate of wind power makes the operating state of the power system highly diversified, traditional methods can no longer meet the current speed and accuracy requirements for assessing the limit of wind power absorption capacity.

[0004] Therefore, under the premise of considering the transient stability of the power system, rapid assessment of the limit of wind power absorption capacity has become a key task that needs to be solved urgently. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method for evaluating the wind power absorption capacity limit of a power system taking transient stability into consideration.

[0006] The object of the present invention is achieved by the following technical solution: a method for evaluating the wind power absorption capacity limit of a power system considering transient stability, the method comprising the following steps:

[0007] Step S1, sampling in the feasible space of the power system to generate a sample data set;

[0008] Step S2: using the sample data set to train a deep neural network offline as a transient stability evaluator to predict transient stability indicators of the power system;

[0009] Step S3: Based on the short-term forecast data of wind power output and the load forecast data, considering the transient stability constraints of the power system, determine the day-ahead dispatch plan of each generator in the power system;

[0010] Step S4: Based on the determined day-ahead dispatch plan, taking into account the uncertainty of wind power output and the transient stability constraints of the power system, an evaluation model for the wind power absorption capacity limit under the current dispatch plan is constructed, and the initial solution is accelerated by means of constraint preprocessing and heuristic algorithm to assist in constructing the initial solution, thereby achieving rapid evaluation.

[0011] Specifically, the specific steps of step S1 include:

[0012] The feature vector of each sample in the sample data set follows the following formula:

[0013]

[0014] In the formula, s is a sample; S represents the sample set; X s and Y s Respectively represent the input features and label vector of sample s; u g represents the start and stop state vector of the generator g. g =1, the generator is in the starting state, otherwise it is in the shut-down state; g represents the active output vector of generator g; P load represents the active power of the load; V represents the node voltage amplitude vector; δ represents the node voltage phase angle vector; Г line A quantitative indicator that represents the transient stability of the power system.

[0015] Specifically, the quantitative characterization index Г line Calculated by the following formula:

[0016]

[0017] In the formula, x con and x sta are control variables and state variables respectively; F l (·) is used to calculate Г line ζ is a scalar parameter of the increase in power system node load power or generator output power;

[0018] The following calculation model is used to quantify the characterization index Г line Perform the calculation:

[0019]

[0020] Where ζ is a scalar parameter indicating the increase in power system node load power or generator output power; H c (·) and G c (·) are the equality constraints and inequality constraints in the optimization problem respectively; c and C represent the expected accident and the expected accident set; (τ 0 ,τ end ] represents the duration of the transient process; γ c (·) represents a set of differential algebraic equations that describe the change process of various variables in the power system during the transient process; Represents the differential function, describing the transient process of the power system; Ψ c (·) represents the transient stability criterion, which is determined by the following formula:

[0021]

[0022] In the formula, δ g and δ COI are the power angle and inertia center of generator g respectively; δ max is the maximum allowable power angle deviation; M g is the moment of inertia; G represents the generator set.

[0023] Specifically, the step S1 further includes constructing an n-dimensional classification distribution of the unit status based on historical statistical data, and its probability distribution function is as follows:

[0024] p(u g =1) = α g

[0025] In the formula, α g is the probability of generator g starting, and the probability vector ξ=[α 1 ,…,α g ,…,α G ] is input into the constructed classification distribution.

[0026] Specifically, the transient stability evaluator in step S2 is a fully connected deep neural network with L layers, and its expression is:

[0027]

[0028] Where w and b are weight and bias sets respectively; Represents the predicted value of sample s. All hidden layers are activated by the ReLU function, while the output layer uses a linear activation function.

[0029] The loss function of a deep neural network is defined as minimizing the prediction error of all samples, as follows:

[0030]

[0031] Where Y s represents the actual value of sample s; n s Indicates the number of samples.

[0032] Specifically, the specific steps of step S3 include:

[0033] A safety constraint unit combination model is constructed with the goal of minimizing the power system operation cost. The objective function of the safety constraint unit combination model is:

[0034] R all =R G +R SU +R SD+R wind

[0035]

[0036] In the formula, R all is the total operating cost of the power system; R G , R SU and R SD are the power generation cost, startup cost and shutdown cost of the generator respectively; R wind Penalty costs for wind power output reduction; a 1 ,g、a 2,g and a 3,g is the cost coefficient of the generator; P g,t is the output of generator g at time t; u g,t is the start-stop state variable of the generator. g,t =1, the generator starts, otherwise the generator stops; T is the entire dispatching cycle; su g and sd g is the cost of starting and stopping the generator once; wind is the unit wind abandonment cost of wind turbines; P pre wind,t and P wind,t is the predicted output and actual output of the wind turbine at time t; G is the generator set;

[0037] The constraints of the safety constraint unit commitment model include:

[0038] System power balance constraints:

[0039]

[0040] Where P load,t represents the load power at time t;

[0041] Generator output upper and lower limit constraints:

[0042] u g,t P g,min ≤P g,t ≤u g,t P g,max

[0043] Where P g,max and P g,min Indicates the upper and lower limits of the generator output;

[0044] Minimum generator on / off duration constraint:

[0045]

[0046] In the formula, tsu and t sd Respectively represent the minimum start-up and shutdown duration of the generator;

[0047] Generator output climbing constraint:

[0048] P g,t -P g,t-1 ≤u g,t-1 r g,up +(u g,t -u g,t-1 ) g,min +(1-u g,t ) g,max

[0049] P g,t-1 -P g,t ≤u g,t r g,down +(u g,t-1 -u g,t ) g,min +(1-u g,t-1 ) g,max

[0050] -r g,down u g,t ≤P g -P g,sch ≤r g,up u g,t

[0051] In the formula, r g,up and r g,down Indicates the up and down climbing power of the generator; P g,sch Represents the dispatch plan value of the generator;

[0052] Transmission line power flow constraints:

[0053] -P line,max ≤P line ≤P line,max

[0054] Where P line and P line,max They represent the transmission power of the transmission line and its upper power limit respectively;

[0055] Wind farm output constraints:

[0056]

[0057] Where P wind,rate Indicates the rated installed capacity of the wind turbine;

[0058] Transient stability constraints:

[0059] Pline ≤Γ line

[0060] The neural network model includes multiple nonlinear and non-convex functions, as shown below:

[0061]

[0062] Where σ(·) and O(·) are the ReLU function and the activation function of the output layer, respectively;

[0063] A binary auxiliary variable is introduced to transform the deep neural network into a mixed integer linear programming form as follows:

[0064]

[0065] In the formula, is the activation state of the σ(·) function in the lth layer of the neural network; N l represents the number of neurons in the lth layer; ε represents any extreme small number; m represents a relatively large number. For a neuron n, if This means that its ReLU function is activated, that is and On the contrary, if Then the σ(·) function is not activated, that is ≤0, and y l =0;

[0066] The transient stability estimator obtained by training the deep neural network is converted into the following transient stability constraints and then incorporated into the safety constraint unit commitment model:

[0067]

[0068] The security constrained unit commitment model considering transient stability constraints is regarded as a mixed integer linear programming problem and is calculated by cplex or gurobi commercial solvers to obtain the day-ahead dispatch plan of each generator.

[0069] Specifically, the evaluation model of wind power consumption limit in step S4 is described as follows:

[0070]

[0071] Among them, P wind,max and P wind,min Indicates the upper and lower limits of wind power output that the power system can carry under the current dispatch plan; N wind Assemble for wind turbines;

[0072] In the evaluation model, wind power output is regarded as an uncertain variable, and the uncertainty set can be expressed as:

[0073]

[0074] The constraints of the evaluation model include system power balance constraints, upper and lower limit constraints of generator output, minimum generator on / off duration constraints, generator output ramp constraints, transmission line flow constraints and transient stability constraints.

[0075] Specifically, in order to solve the evaluation model in step S4, an auxiliary continuous variable is introduced to associate the decision variables of the two stages of the robust optimization problem, as shown in the following formula:

[0076] P wind =ρ wind P wind,min +(1-ρ wind ) wind,max ,ρ wind ∈[0,1]

[0077] In the formula, ρ wind represents the ratio of the actual wind power output to the wind power consumption carrying capacity boundary, converting the uncertain parameters into ρ wind , so that the evaluation model of wind power consumption limit is transformed into a standard two-stage robust optimization problem. wind When the range of is determined, the objective function is minimized by solving the decision variables of the first stage, while in the second stage, the worst-case wind power abandonment is minimized by solving the decision variables of the second stage.

[0078] Specifically, in step S4, the two-stage robust optimization problem is solved and divided into two independent problems. When the variables of the first stage are determined, the objective function of the inner layer problem can be expressed as:

[0079]

[0080] In the formula, △P wind The wind curtailment power of wind power output is represented by simplifying the constraints in the evaluation model into the following two items, where the former is the active real-time balance constraint of the power system and the latter is the ramp constraint during generator rescheduling:

[0081] J 1 ≤β 1 P g +χP wind +μ△P wind

[0082] J 2 ≤β 2 P g +θPg,sch

[0083] In the formula, β 1 , χ and μ represent the power balance constraint matrix in the real-time scheduling stage, corresponding to different types of generation and load, where β 1 represents the variable or parameter in the power constraint of thermal power units, χ represents the variable or parameter in the power constraint of wind power units, μ represents the variable or parameter in the wind power curtailment constraint; similarly, β 2 and θ represent the power ramp constraint matrix of thermal power units during the redispatching process, where β 2 corresponds to the real-time dispatch power, θ corresponds to the generator power in the day-ahead dispatch plan; J 1 and J 2 They represent the constant terms on the right side of the power balance equation in the real-time scheduling stage and the rescheduling power constraint respectively.

[0084] Based on the strong duality theorem, the above two-stage robust optimization problem is transformed into the following dual form:

[0085] max(J 1 -χP wind )'η 1 +(J 2 -θP b,sch )'η 2 ,η 1 ,η 2 ≥0

[0086]

[0087] P wind χ=ρ wind P wind,min χ+(1-ρ wind ) wind,max χ,ρ wind ∈[0,1]

[0088] Where η 1 and η 2 is the dual variable; θ is the auxiliary variable;

[0089] Introducing the Big M method to deal with continuous variables ρ wind , add the following constraints:

[0090]

[0091] In the formula, π wind is a newly introduced auxiliary variable. If ρ wind =0, then the wind power output P windis constrained to the upper bound of the uncertainty set; otherwise, it is constrained to the lower bound of the uncertainty set. At this time, the above two-stage robust optimization problem is transformed into the following mixed integer programming model:

[0092] min(P wind,min -P wind,max )+θ

[0093] (J 1 -χP wind )'η 1 +(J 2 -θP b,sch )'η 2 ≤θ

[0094] Among them, θ is an auxiliary variable, which represents the maximum value of the second stage.

[0095] The present invention has the following advantages:

[0096] In view of the problem of heavy calculation burden of transient stability index, the present invention constructs a transient stability index evaluator; in view of the problem of generating training samples, a discrete sampling algorithm and synthetic minority oversampling technology are used to generate and expand sample data sets, ensuring that the trained transient stability index estimator can more accurately capture the nonlinear form of the index; considering the non-convexity and nonlinearity in the evaluator model, which makes it difficult to directly embed it into the day-ahead dispatch optimization model, it is converted into the form of mixed integer programming by introducing auxiliary integer variables; in view of the real-time dispatch challenge caused by random fluctuations in wind power, a rapid assessment model of wind power absorption capacity limit is constructed to quickly assess the maximum loadable range of wind power output under the current dispatch plan. The proposed method can effectively improve the calculation speed of the assessment model, and while considering the transient stability of the power system, it realizes the rapid assessment of the wind power absorption capacity limit, providing auxiliary opinions and decision support for dispatchers in real-time dispatch. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 Schematic diagram of the evaluation method of the present invention. DETAILED DESCRIPTION

[0098] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the embodiments described are only part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0099] 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 invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0100] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "including a..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0101] The present invention is further described below in conjunction with the accompanying drawings, but the protection scope of the present invention is not limited to the following description. Figure 1 As shown, a method for evaluating the wind power absorption capacity limit of a power system considering transient stability includes the following steps:

[0102] Step S1, sampling in the feasible space of the power system to generate a sample data set;

[0103] Step S2: using the sample data set to train a deep neural network offline as a transient stability evaluator to predict transient stability indicators of the power system;

[0104] Step S3: Based on the short-term forecast data of wind power output and the load forecast data, considering the transient stability constraints of the power system, determine the day-ahead dispatch plan of each generator in the power system;

[0105] Step S4: Based on the determined day-ahead dispatch plan, taking into account the uncertainty of wind power output and the transient stability constraints of the power system, an evaluation model for the wind power absorption capacity limit under the current dispatch plan is constructed, and the initial solution is accelerated by means of constraint preprocessing and heuristic algorithm to assist in constructing the initial solution, thereby achieving rapid evaluation.

[0106] Furthermore, the specific steps of step S1 include:

[0107] Sampling is performed in the feasible space to cover all operating scenarios as much as possible. The feature vector of each sample in the sample data set follows the following formula:

[0108]

[0109] In the formula, s is a sample; S represents the sample set; X s and Y s Respectively represent the input features and label vector of sample s; u g represents the start and stop state vector of the generator g. g =1, the generator is in the starting state, otherwise it is in the shut-down state; g represents the active output vector of generator g; P load represents the active power of the load; V represents the node voltage amplitude vector; δ represents the node voltage phase angle vector; Г line The quantitative characterization index representing the transient stability of the power system is selected as the ultimate transmission capacity of the transmission line as the transient stability constraint in this method in combination with actual engineering applications.

[0110] The quantitative characterization index Г line Calculated by the following formula:

[0111]

[0112] In the formula, x con and x sta are control variables and state variables respectively; F l (·) is used to calculate Г line ζ is a scalar parameter of the increase in power system node load power or generator output power;

[0113] This indicator is usually calculated using the repeated power flow method, and its calculation model can be expressed as an optimization problem as follows:

[0114]

[0115] Where ζ is a scalar parameter indicating the increase in power system node load power or generator output power; H c (·) and G c (·) are the equality constraints and inequality constraints in the optimization problem respectively; c and C represent the expected accident and the expected accident set; (τ 0 ,τ end ] represents the duration of the transient process; γ c (·) represents a set of differential algebraic equations describing the change process of various variables in the power system during the transient process; Represents the differential function, describing the transient process of the power system; Ψ c (·) represents the transient stability criterion, which is determined by the following formula:

[0116]

[0117] In the formula, δ g and δ COI are the power angle and inertia center of generator g respectively; δ max is the maximum allowable power angle deviation; M g is the moment of inertia; G represents the generator set.

[0118] However, when the eigenvector X s When binary variables are added to the data, the traditional uniform sampling method is no longer applicable. As the number of generator sets increases, the number of combinations of their start and stop states also increases exponentially, affecting the efficiency of sample generation, and many of the samples lack feasibility. Therefore, a discrete sampling algorithm is proposed to specifically construct an n-dimensional classification distribution of the unit state based on historical statistical data, and its probability distribution function is shown below:

[0119] p(u g =1) = α g

[0120] In the formula, α g is the probability of generator g starting, and the probability vector ξ=[α 1 ,…,α g ,…,α G ] is input into the constructed classification distribution, and the generator state is sampled according to the given probability to obtain the matching one-hot encoding. Afterwards, in order to ensure the generalizability of the transient stability index estimator trained using this sample data set, the synthetic minority oversampling technique is further used to expand the marginal distribution samples in the sample data set, especially the samples near the transient stability boundary, which provides richer information for the estimator to identify the transient stability of power transmission.

[0121] Different from the traditional uniform sampling of input data, the synthetic minority oversampling technology helps the estimator to more accurately capture the nonlinear form of the transient stability index by locally enhancing the samples of the transient stability boundary contour, thereby reflecting the true situation of the transient stability of the power system. The expanded samples will be merged into the data set for subsequent transient stability estimator training. Since the use of this indicator to quantitatively analyze the transient stability of the power system requires traversing and verifying multiple expected fault sets, and repeated time domain simulations in a large discrete decision space, the nonlinear and high-dimensional characteristics of the quantitative analysis indicator calculation process are further amplified, which further aggravates its computational burden. Therefore, in this method, a deep neural network is trained offline as a transient stability evaluator to predict the transient stability index;

[0122] The transient stability evaluator is a fully connected deep neural network with L layers. The model can be simplified as follows:

[0123]

[0124] Where w and b are weight and bias sets respectively; Represents the predicted value of sample s. All hidden layers are activated by the ReLU function, while the output layer uses a linear activation function.

[0125] The loss function of a deep neural network is defined as minimizing the prediction error of all samples, as follows:

[0126]

[0127] Where Y s represents the actual value of sample s; n s Indicates the number of samples.

[0128] Furthermore, the specific steps of step S3 include:

[0129] A safety constraint unit combination model is constructed with the goal of minimizing the power system operation cost. The objective function of the safety constraint unit combination model is:

[0130] R all =R G +R SU +R SD +R wind

[0131]

[0132]

[0133] In the formula, R all is the total operating cost of the power system; R G , R SU and R SD are the power generation cost, startup cost and shutdown cost of the generator respectively; R wind Penalty costs for wind power output reduction; a 1,g 、a 2,g and a 3,g is the cost coefficient of the generator; P g,t is the output of generator g at time t; u g,t is the start-stop state variable of the generator. g,t =1, the generator starts, otherwise the generator stops; T is the entire dispatching cycle; su g and sd g is the cost of starting and stopping the generator once; wind is the unit wind abandonment cost of wind turbines; P pre wind,t and P wind,tis the predicted output and actual output of the wind turbine at time t; G is the generator set;

[0134] The constraints of the safety constraint unit commitment model include:

[0135] System power balance constraints:

[0136]

[0137] Where P load,t represents the load power at time t;

[0138] Generator output upper and lower limit constraints:

[0139] u g,t P g,min ≤P g,t ≤u g,t P g,max

[0140] Where P g,max and P g,min Indicates the upper and lower limits of the generator output;

[0141] Minimum generator on / off duration constraint:

[0142]

[0143] Where, t su and t sd Respectively represent the minimum start-up and shutdown duration of the generator;

[0144] Generator output climbing constraint:

[0145] P g,t -P g,t-1 ≤u g,t-1 r g,up +(u g,t -u g,t-1 ) g,min +(1-u g,t ) g,max

[0146] P g,t-1 -P g,t ≤u g,t r g,down +(u g,t-1 -u g,t ) g,min +(1-u g,t-1 ) g,max

[0147] -r g,down u g,t ≤P g-P g,sch ≤r g,up u g,t

[0148] In the formula, r g,up and r g,down Indicates the up and down climbing power of the generator; P g,sch Represents the dispatch plan value of the generator;

[0149] Transmission line power flow constraints:

[0150] -P line,max ≤P line ≤P line,max

[0151] Where P line and P line,max They represent the transmission power of the transmission line and its upper power limit respectively;

[0152] Wind farm output constraints:

[0153]

[0154] Where P wind,rate Indicates the rated installed capacity of the wind turbine;

[0155] Transient stability constraints:

[0156] P line ≤Γ line

[0157] Although a deep neural network is trained to replace the time-consuming transient stability index calculation process, there are multiple nonlinear and non-convex functions involved in the neural network model, as shown below:

[0158]

[0159] Where σ(·) and O(·) are the ReLU function and the activation function of the output layer, respectively;

[0160] When the deep neural network is directly added to the safety constraint unit combination, the nonlinear and non-convex functions in it will increase the burden of optimizing the dispatch model. Therefore, a binary auxiliary variable is introduced to transform the deep neural network into a mixed integer linear programming form, as shown below:

[0161]

[0162] In the formula, is the activation state of the σ(·) function in the lth layer of the neural network; N lrepresents the number of neurons in the lth layer; ε represents any extreme small number; m represents a relatively large number. For a neuron n, if This means that its ReLU function is activated, that is and On the contrary, if Then the σ(·) function is not activated, that is ≤0, and y l =0;

[0163] The transient stability estimator obtained by training the deep neural network is converted into the following transient stability constraints and then incorporated into the safety constraint unit commitment model:

[0164]

[0165] The security constrained unit commitment model considering transient stability constraints is regarded as a mixed integer linear programming problem and is calculated by cplex or gurobi commercial solvers to obtain the day-ahead dispatch plan of each generator.

[0166] The random fluctuation of wind power output inevitably causes a deviation between its actual output and the predicted output. When this deviation exceeds the upper limit of the flexible adjustment resources that can be carried under the current operating state of the power system, the formulated dispatch plan will no longer be able to guarantee the real-time balance of the active power of the power system. This means that in order to ensure the safe and stable operation of the power system, wind power output will be abandoned due to restrictions such as generator climbing constraints and transmission line flow constraints. At this time, the evaluation model of the wind power absorption limit of the power system considering wind power uncertainty and transient stability can be described as:

[0167]

[0168] Among them, P wind,max and P wind,min Indicates the upper and lower limits of wind power output that the power system can carry under the current dispatch plan; N wind Assemble for wind turbines;

[0169] Due to the randomness and uncertainty of wind power, wind power output is regarded as an uncertain variable in the evaluation model, and the uncertainty set can be expressed as:

[0170]

[0171] The constraints of the evaluation model include system power balance constraints, upper and lower limits of generator output constraints, minimum generator on / off duration constraints, generator output ramp constraints, transmission line power flow constraints and transient stability constraints:

[0172]

[0173] u g,t P g,min ≤P g,t ≤u g,t P g,max

[0174]

[0175] P g,t -P g,t-1 ≤u g,t-1 r g,up +(u g,t -u g,t-1 ) g,min +(1-u g,t ) g,max

[0176] P g,t-1 -P g,t ≤u g,t r g,down +(u g,t-1 -u g,t ) g,min +(1-u g,t-1 ) g,max

[0177] -r g,down u g,t ≤P g -P g,sch ≤r g,up u g,t

[0178] -P line,max ≤P line ≤P line,max

[0179]

[0180] Obviously, the wind power output range that the power system can carry under the current dispatch plan needs to be obtained by solving the above robust optimization problem. Generally speaking, a standard two-stage robust optimization problem aims to optimize the system by selecting decision variables in the first stage so as to adapt to the uncertainty concentration P in the second stage. wind However, in the above evaluation model, the upper / lower bounds of the uncertainty set P wind,max and P wind,min Again, it is a decision variable, not a predetermined parameter in a standard robust optimization problem. This means that the existing solution cannot be used directly to solve the above robust optimization problem. Therefore, an auxiliary continuous variable is introduced to associate the decision variables of the two stages of the robust optimization problem, as shown in the following formula:

[0181] P wind =ρ wind P wind,min +(1-ρ wind ) wind,max ,ρ wind ∈[0,1]

[0182] In the formula, ρ wind represents the ratio of the actual wind power output to the wind power consumption carrying capacity boundary, converting the uncertain parameters into ρ wind , so that the evaluation model of wind power consumption limit is transformed into a standard two-stage robust optimization problem. wind When the range of is determined, the objective function is minimized by solving the decision variables of the first stage, while in the second stage, the worst-case wind power abandonment is minimized by solving the decision variables of the second stage.

[0183] Furthermore, in step S4, the two-stage robust optimization problem is solved and divided into two independent problems. When the variables of the first stage are determined, the objective function of the inner layer problem can be expressed as:

[0184]

[0185] In the formula, △P wind The wind curtailment power of wind power output is represented by simplifying the constraints in the evaluation model into the following two items, where the former is the active real-time balance constraint of the power system and the latter is the ramp constraint during generator rescheduling:

[0186] J 1 ≤β 1 P g +χP wind +μ△P wind

[0187] J 2 ≤β 2 P g +θP g,sch

[0188] In the formula, β 1 , χ and μ represent the power balance constraint matrix in the real-time scheduling stage, corresponding to different types of generation and load, where β 1 represents the variable or parameter in the power constraint of thermal power units, χ represents the variable or parameter in the power constraint of wind power units, μ represents the variable or parameter in the wind power curtailment constraint; similarly, β 2 and θ represent the power ramp constraint matrix of thermal power units during the redispatching process, where β 2 corresponds to the real-time dispatch power, θ corresponds to the generator power in the day-ahead dispatch plan; J 1and J 2 They represent the constant terms on the right side of the power balance equation in the real-time scheduling stage and the rescheduling power constraint respectively.

[0189] In order to cope with the forecast deviation of wind power output, the power system balances the active power in real time through the flexible adjustment capability of thermal power units. Based on the strong duality theorem, the above two-stage robust optimization problem is transformed into the following dual form:

[0190] max(J 1 -χP wind )'η 1 +(J 2 -θP b,sch )'η 2 ,η 1 ,η 2 ≥0

[0191]

[0192] P wind χ=ρ wind P wind,min χ+(1-ρ wind ) wind,max χ,ρ wind ∈[0,1]

[0193] Where η 1 and η 2 is the dual variable; θ is the auxiliary variable;

[0194] The transformed constraints determine the feasible domain of the dual problem and are only related to the decision variables in the second stage, while the decision variables in the first stage will only change the objective function of the dual problem. Furthermore, the large M method is introduced to deal with the continuous variable ρ wind , add the following constraints:

[0195]

[0196] In the formula, π wind is a newly introduced auxiliary variable. If ρ wind =0, then the wind power output P wind is constrained to the upper bound of the uncertainty set; otherwise, it is constrained to the lower bound of the uncertainty set. At this time, the above two-stage robust optimization problem is transformed into the following mixed integer programming model:

[0197] min(P wind,min -P wind,max )+θ

[0198] (J 1 -χP wind )'η 1 +(J 2-θP b,sch )'η 2 ≤θ

[0199] Among them, θ is an auxiliary variable, which represents the maximum value of the second stage.

[0200] Afterwards, in order to improve the efficiency of solving mixed integer programming, a multi-level constraint preprocessing strategy is adopted. Constraints are tightened by boundary tightening and coefficient scaling to ensure numerical stability; linearly related or implicit redundant constraints are identified and deleted, and constraints with similar structures are aggregated or decomposed and reconstructed. At the variable level, the problem dimension can be reduced by fixing variables with certain values ​​and algebraic substitution. In addition, when it is necessary to repeatedly solve the mixed integer programming model, a feasible solution is quickly generated by a greedy algorithm, and then a local search method is used to improve it. After obtaining the initial solution, it can be used as the hot start solution of the solver, and the characteristic information in the solution can be extracted to guide the variable selection and branch direction in the branch and bound process. The implementation of these auxiliary acceleration strategies needs to follow the order from simple to difficult, and dynamically adjust according to the characteristics of the problem in practical applications, while weighing the computational overhead of preprocessing and the improvement of solution efficiency.

[0201] The above is only a preferred embodiment of the present invention and does not limit the present invention in any form. Any technician familiar with the art can make many possible changes and modifications to the technical solution of the present invention by using the above-mentioned technical content without departing from the scope of the technical solution of the present invention, or modify it into an equivalent embodiment of equivalent changes. Therefore, any changes, modifications, equivalent changes and modifications made to the above embodiments based on the technology of the present invention without departing from the content of the technical solution of the present invention belong to the protection scope of the present technical solution.

Claims

1. A method for evaluating the wind power absorption capacity limit of a power system considering transient stability, characterized by: The method comprises the following steps: Step S1, sampling in the feasible space of the power system to generate a sample data set; Step S2: using the sample data set to train a deep neural network offline as a transient stability evaluator to predict transient stability indicators of the power system; Step S3: Based on the short-term forecast data of wind power output and the load forecast data, considering the transient stability constraints of the power system, determine the day-ahead dispatch plan of each generator in the power system; Step S4: Based on the determined day-ahead dispatch plan, taking into account the uncertainty of wind power output and the transient stability constraints of the power system, an evaluation model for the wind power absorption capacity limit under the current dispatch plan is constructed, and the initial solution is accelerated by means of constraint preprocessing and heuristic algorithm to assist in constructing the initial solution, thereby achieving rapid evaluation.

2. The method for evaluating the wind power absorption capacity limit of a power system considering transient stability according to claim 1 is characterized in that: The specific steps of step S1 include: The feature vector of each sample in the sample data set follows the following formula: In the formula, s is a sample; S represents the sample set; X s and Y s Respectively represent the input features and label vector of sample s; u g represents the start and stop state vector of the generator g. g =1, the generator is in the starting state, otherwise it is in the shut-down state; g represents the active output vector of generator g; P load represents the active power of the load; V represents the node voltage amplitude vector; δ represents the node voltage phase angle vector; Г line A quantitative indicator that represents the transient stability of the power system.

3. The method for evaluating the wind power absorption capacity limit of a power system considering transient stability according to claim 2 is characterized in that: The quantitative characterization index Г line Calculated by the following formula: In the formula, x con and x sta are control variables and state variables respectively; F l (·) is used to calculate Г line function; ζ is a scalar parameter of the increase in power system node load power or generator output power; The following calculation model is used to quantify the characterization index Г line Perform the calculation: Where ζ is a scalar parameter indicating the increase in power system node load power or generator output power; H c (·) and G c (·) are the equality constraints and inequality constraints in the optimization problem respectively; c and C represent the expected accident and the expected accident set; (τ0,τ end ] represents the duration of the transient process; γ c (·) represents a set of differential algebraic equations describing the change process of various variables in the power system during the transient process; Represents the differential function, describing the transient process of the power system; Ψ c (·) represents the transient stability criterion, which is determined by the following formula: In the formula, δ g and δ COI are the power angle and inertia center of generator g respectively; δ max is the maximum allowable power angle deviation; M g is the moment of inertia; G represents the generator set.

4. The method for evaluating the wind power absorption capacity limit of a power system considering transient stability according to claim 2 is characterized in that: The step S1 also includes constructing an n-dimensional classification distribution of the unit status based on historical statistical data, and its probability distribution function is as follows: p(u g =1)=a g In the formula, α g is the probability of generator g starting, and the probability vector ξ=[α1,…,α g ,…,α G ] is input into the constructed classification distribution.

5. The method for evaluating the wind power absorption capacity limit of a power system considering transient stability according to claim 2 is characterized in that: The transient stability evaluator in step S2 is a fully connected deep neural network with L layers, and its expression is: Where w and b are weight and bias sets respectively; Represents the predicted value of sample s. All hidden layers are activated by the ReLU function, while the output layer uses a linear activation function. The loss function of a deep neural network is defined as minimizing the prediction error of all samples, as follows: Where Y s represents the actual value of sample s; n s Indicates the number of samples.

6. The method for evaluating the wind power absorption capacity limit of a power system considering transient stability according to claim 5 is characterized in that: The specific steps of step S3 include: A safety constraint unit combination model is constructed with the goal of minimizing the power system operation cost. The objective function of the safety constraint unit combination model is: minR all =R G +R SU +R SD +R wind In the formula, R all is the total operating cost of the power system; R G , R SU and R SD are the power generation cost, startup cost and shutdown cost of the generator respectively; R wind Penalty costs for wind power output reduction; a 1,g 、a 2,g and a 3,g is the cost coefficient of the generator; P g,t is the output of generator g at time t; u g,t is the start-stop state variable of the generator. g,t =1, the generator starts, otherwise the generator stops; T is the entire dispatching cycle; su g and sd g is the cost of starting and stopping the generator once; wind is the unit wind abandonment cost of wind turbines; P pre wind,t and P wind,t is the predicted output and actual output of the wind turbine at time t; G is the generator set; The constraints of the safety constraint unit commitment model include: System power balance constraints: Where P load,t represents the load power at time t; Generator output upper and lower limit constraints: u g,t Q g,min ≤P g,t ≤u g,t Q g,max Where P g,max and P g,min Indicates the upper and lower limits of the generator output; Minimum generator on / off duration constraint: Where, t su and t sd Respectively represent the minimum start-up and shutdown duration of the generator; Generator output climbing constraint: P g,t -P g,t-1 ≤u g,t-1 r g,up +(u g,t -u g,t-1 )P g,min +(1-u g,t )P g,max P g,t-1 -P g,t ≤u g,t r g,down +(u g,t-1 -u g,t )P g,min +(1-u g,t-1 )P g,max -r g,down u g,t ≤P g -P g,sch ≤r g,up u g,t In the formula, r g,up and r g,down Indicates the up and down climbing power of the generator; P g,sch Represents the dispatch plan value of the generator; Transmission line power flow constraints: -P line,max ≤P line ≤P line,max Where P line and P line,max They represent the transmission power of the transmission line and its upper power limit respectively; Wind farm output constraints: Where P wind,rate Indicates the rated installed capacity of the wind turbine; Transient stability constraints: P line ≤Γ line The neural network model includes multiple nonlinear and non-convex functions, as shown below: Where σ(·) and O(·) are the ReLU function and the activation function of the output layer, respectively; A binary auxiliary variable is introduced to transform the deep neural network into a mixed integer linear programming form as follows: In the formula, is the activation state of the σ(·) function in the lth layer of the neural network; N l is the number of neurons in the lth layer; ε is any extreme small number; m is a real number. For a neuron n, if This means that its ReLU function is activated, that is and On the contrary, if Then the σ(·) function is not activated, that is And y l =0; The transient stability estimator obtained by training the deep neural network is converted into the following transient stability constraints and then incorporated into the safety constraint unit commitment model: The security constrained unit commitment model considering transient stability constraints is regarded as a mixed integer linear programming problem and is calculated by cplex or gurobi commercial solvers to obtain the day-ahead dispatch plan of each generator.

7. The method for evaluating the wind power absorption capacity limit of a power system considering transient stability according to claim 5 is characterized in that: The evaluation model of wind power consumption limit in step S4 is described as follows: Among them, P wind,max and P wind,min Indicates the upper and lower limits of wind power output that the power system can carry under the current dispatch plan; N wind Assemble for wind turbines; In the evaluation model, wind power output is regarded as an uncertain variable, and the uncertainty set can be expressed as: The constraints of the evaluation model include system power balance constraints, upper and lower limit constraints of generator output, minimum generator on / off duration constraints, generator output ramp constraints, transmission line flow constraints and transient stability constraints.

8. The method for evaluating the wind power absorption capacity limit of a power system considering transient stability according to claim 7 is characterized in that: In order to solve the evaluation model in step S4, an auxiliary continuous variable is introduced to associate the decision variables of the two stages of the robust optimization problem, as shown in the following formula: P wind =ρ wind P wind,min +(1-p wind )P wind,max ,r wind ∈[0,1] In the formula, ρ wind represents the ratio of the actual wind power output to the wind power consumption carrying capacity boundary, converting the uncertain parameters into ρ wind , so that the evaluation model of wind power consumption limit is transformed into a standard two-stage robust optimization problem. wind When the range of is determined, the objective function is minimized by solving the decision variables of the first stage, while in the second stage, the worst-case wind power abandonment is minimized by solving the decision variables of the second stage.

9. The method for evaluating the wind power absorption capacity limit of a power system considering transient stability according to claim 8 is characterized in that: In step S4, the two-stage robust optimization problem is solved and divided into two independent problems. When the variables of the first stage are determined, the objective function of the inner layer problem can be expressed as: In the formula, △P wind The wind curtailment power of wind power output is represented by simplifying the constraints in the evaluation model into the following two items, where the former is the active real-time balance constraint of the power system and the latter is the ramp constraint during generator rescheduling: J1≤β1P g +χP wind +μ△P wind J2≤β2P g +θP g,sch In the formula, β1, χ and μ represent the power balance constraint matrix in the real-time dispatch stage, corresponding to different types of power generation and load, where β1 represents the variable or parameter in the power constraint formula of the thermal power unit, χ represents the variable or parameter in the power constraint formula of the wind power unit, and μ represents the variable or parameter in the wind power reduction constraint; β2 and θ represent the power ramp constraint matrix of the thermal power unit in the redispatch process, where β2 corresponds to the real-time dispatch power, and θ corresponds to the generator power in the day-ahead dispatch plan; J1 and J2 represent the right-hand constant terms of the power balance equation in the real-time dispatch stage and the redispatch power constraint, respectively; Based on the strong duality theorem, the above two-stage robust optimization problem is transformed into the following dual form: max(J1-χP wind )'η1+(J2-θP b,sch )'η2,η1,η2≥0 P wind x=r wind P wind,min x+(1-p wind )P wind,max h,r wind ∈[0,1] In the formula, η1 and η2 are dual variables; θ is an auxiliary variable; Introducing the Big M method to deal with continuous variables ρ wind , add the following constraints: In the formula, π wind is a newly introduced auxiliary variable. If ρ wind =0, then the wind power output P wind is constrained to the upper bound of the uncertainty set; otherwise, it is constrained to the lower bound of the uncertainty set. At this time, the above two-stage robust optimization problem is transformed into the following mixed integer programming model: min(P wind,min -P wind,max )+θ (J1-χP wind )'η1+(J2-θP b,sch )'η2≤θ Among them, θ is an auxiliary variable, which represents the maximum value of the second stage.

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