Transmission / distribution network emergency cooperative control method for extreme weather conditions

Abstract

The invention discloses a transmission / distribution network emergency cooperative control method for extreme weather conditions, and the method comprises the following steps: firstly, comprehensively considering the coupling relation between a transmission network and a distribution network, and building a transmission / distribution cooperative emergency control model; secondly, the power distribution network operation center constructs a linear relation model among the variables by using historical operation data to replace an original power distribution network nonlinear power flow model; then, on the basis of a multi-parameter planning theory, the power distribution network emergency control model is converted into a model with boundary variables between power transmission networks and power distribution networks as planning parameters, and the model is reported to a power transmission network operation center; and the power transmission network operation center solves the emergency control model uploaded by each power distribution network. According to the method, the solving speed of the transmission network and power distribution network emergency control collaborative optimization optimal solution can be increased, and the communication burden is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system operation, and particularly relates to a multi-parameter planning emergency collaborative control method for a transmission network and a distribution network facing extreme weather conditions. Background Technique

[0002] With the continuous increase in the penetration rate of renewable energy sources (RES) represented by distributed photovoltaic (PV) in the active distribution network (ADN), its impact on the operation of the power grid has become increasingly significant. On the one hand, the integration of renewable energy sources has changed the traditional power supply structure of the power grid, resulting in reverse power flow phenomena in the distribution network. On the other hand, the uncertainty of its output has exacerbated the complexity of the operation of the power system. Especially in the context of high penetration of renewable energy sources, extreme weather events have amplified the operation risks, posing new challenges to the safe and stable operation of the power grid.

[0003] In order to meet the power flow safety requirements of the power grid under extreme weather conditions, it is necessary to strengthen the power and voltage connections between the transmission network and the distribution network, and give full play to the ability of the transmission and distribution networks to provide power support for each other under extreme weather conditions. The transmission and distribution networks are physically interconnected, and theoretically, centralized optimization of the transmission and distribution networks can be achieved, and then global optimization of the transmission and distribution networks can be realized. However, they are independently managed by the transmission system operator (TSO) and the distribution system operator (DSO) respectively, and require a large amount of computing resources and data support. Therefore, a distributed transmission and distribution coordination optimization method is needed. In the field of global distributed collaborative optimization of the transmission and distribution networks, the reactive power optimization of the transmission and distribution networks can be decomposed into a master problem and a sub-problem with additional cutting constraints through generalized Benders decomposition (GBD), and global optimization can be achieved through distributed iteration between the master problem and the sub-problem. The ADMM method can be used to coordinate generation resources, allowing the TSO and the DSO to independently solve the robust reserve scheduling problem in their respective regions. In addition, the convergence of ADMM (Alternating Direction Method of Multipliers) can be accelerated by introducing additional terms in the distributed iteration, but it brings errors to the model optimization and solution. The quadratic programming problem with parameters can be effectively solved through multi-parameter programming, and it has been applied in the distributed economic dispatch of the transmission and distribution networks, verifying that it is superior to the GBD and ADMM methods in terms of convergence speed and other aspects, and this method has not been applied in the emergency control of the transmission and distribution networks. However, the above-mentioned distributed iterative calculation methods are all calculated based on the condition that the distribution network model parameters are known. In fact, in the optimization problem of the distribution network with a high proportion of distributed photovoltaic, due to the strong non-linear characteristics of the distribution network power flow and the difficulty of accurately obtaining parameters in practical applications, etc., the above-mentioned traditional control methods relying on mechanism models are difficult to effectively carry out the collaborative optimization of the transmission network and the distribution network.

[0004] With the wide deployment of high-precision measurement terminals, data-driven methods have promoted research in the field of ADN control, effectively solving problems such as inaccurate parameters and time-consuming iterative solutions in traditional physics-based distribution network optimization control methods. Scholars use LSTM to establish a mapping between injection power and topology reconstruction solutions, thus significantly reducing the operating cost and calculation time of the distribution network. Other scholars adopt deep reinforcement learning methods to optimize the day-ahead scheduling strategy of the distribution network to ensure safe and efficient operation. However, these methods require a large amount of sampling data and complex training processes, and lack physical interpretability.

[0005] Due to the advantages of global linearization, Koopman operator theory has been applied to fitting nonlinear dynamic models. Based on Koopman operator theory, the nonlinear dynamic algebraic model in the low-dimensional state space can be transformed into a high-precision global linear form through data-driven methods. In practical applications, by appropriately increasing the dimension, the nonlinear model can be transformed into a high-precision linear model, which dynamically updates the global sensitivity information and optimizes the model according to the system operating state, and has an accuracy advantage in strongly nonlinear scenarios. Summary of the Invention

[0006] To solve the problem of coordinated optimization of emergency control for transmission and distribution networks, as well as the problem that it is difficult to accurately obtain the strong nonlinear characteristics of distribution network power flow and parameters in practical applications, the present invention proposes an emergency coordinated control method for transmission / distribution networks facing extreme weather conditions, realizes the design of a coordinated emergency control strategy for transmission and distribution networks based on multi-parameter programming, and uses data-driven methods in the distribution network to solve a high-precision linear model that does not depend on model parameters.

[0007] The present invention is realized by the following technical solutions:

[0008] An emergency coordinated control method for transmission / distribution networks facing extreme weather conditions proposed by the present invention specifically includes the following steps:

[0009] Comprehensively considering the coupling relationship between the transmission network and the distribution network, an emergency coordinated control model for transmission / distribution network is established, including:

[0010] Objective function equation of the transmission network: Among them, f trans represents the objective function of the transmission network, P g,i' represents the active power output of thermal power unit i', a i' , b i' , c i' represent the coal consumption coefficients of thermal power unit i', represents the set of thermal power units;

[0011] Constraint conditions of the transmission network:

[0012] ∑ i∈π(j) P ij -P j =∑ l∈σ(j) P jl

[0013] ∑ i∈π(j) Q ij -Q j =∑ l∈σ(j) Q jl

[0014]

[0015]

[0016]

[0017]

[0018] Among them, E represents the set of transmission network lines, represents the set of transmission network nodes, and respectively represent the active power and reactive power flowing from the transmission network node i t to the transmission network node j t π(j t ) and ψ(j t ) respectively represent the set of the parent node and the child node of the transmission network node j t , and represent the active power and reactive power of the load at the transmission network node j t , and respectively represent the minimum active power and reactive power of the thermal power unit i', and respectively represent the maximum active power and reactive power of the thermal power unit i', S ij,max represents the maximum apparent power allowed to pass through the transmission network line i t j t , and are respectively the squares of the voltages at the transmission network nodes i t and the transmission network j t , and respectively represent the resistance and reactance values of the transmission network line i t j t , and are the lower limit value and the upper limit value of the square of the voltage at the transmission network node i t ;

[0019] And, establish an emergency control optimization model for the distribution network, including:

[0020] Objective function of the distribution network: minf dis = minX T HX + dX + e, where f dis represents the objective function of the active distribution network (ADN), X = [ΔP 1 ,…ΔP n T represents the optimization variables of the ADN, and H, d, and e are the price coefficients of the load shedding cost and the energy storage output cost in the ADN;

[0021] Constraints of the distribution network:

[0022]

[0023]

[0024] Among them, represents the set of distribution network nodes, represents the set of distribution network energy storage, represents the set of distribution network loads, α represents the power factor angle of the load, P j , Q j represent the active power and reactive power injection of distribution network node j, represents the active power and reactive power of the energy storage of the j-th element of the distribution network energy storage set e , represents the initial active power injection and initial reactive power injection of the j-th element of the distribution network load set c , represents the active power change and reactive power change of the j-th element of the distribution network load set c , represents the change of the j-th element of the distribution network energy storage set e , the active power and reactive power of the j-th element of the distribution network load set c , γ represents the maximum power factor angle of the energy storage;

[0025] Using the historical operation data in the database of the distribution network operation center, through state space mapping and least squares training, offline obtain the voltage V m , current I m , active power P DG,m and reactive power Q DG,m of distributed power sources, active power P ESS,m and reactive power Q ESS,m of energy storage, active power P CLD,m and reactive power Q CLD,m ​, and the active power P supplied to the distribution network τ,m and the reactive power Q τ,m between the state - space mapping linear function relationship model: Combined with the emergency control optimization model of the distribution network in step 1, to obtain the power flow equation and safety constraint linear representation of the distribution network as:

[0026]

[0027] Transform the transmission - distribution coordinated emergency control problem into a multi - parameter quadratic programming problem MPQP model, and obtain the transmission - distribution coordinated emergency control model as follows:

[0028]

[0029] s.t. m = 1,..., n dis

[0030] x dis,m ∈X dis,m , G dis,m (x dis,m ) ≤ 0

[0031] y trans ∈Y trans , G trans (y trans ) ≤ 0

[0032] H m (x (m) , y m ) = 0

[0033] Among them, f dis,m and f trans represent the objective functions of the distribution network m and the transmission network, X dis,m and Y trans represent the value ranges of the corresponding optimization variables, n dis represents the number of ADNs, G dis,m and G trans represent the operation constraints of the distribution network m and the transmission network respectively, represents the boundary variable of the transmission network supplying the distribution network m, represents the boundary variable of the distribution network m supplying the transmission network, H m is the corresponding boundary constraint;

[0034] Use the MPQP method to transform the distribution network optimization problem into a retrieval set containing the optimization variables of the transmission network, and through derivation, obtain the sectional retrieval analytical formula of the distribution network emergency control problem:

[0035]

[0036] s.t. ym ∈ FR m

[0037] FR m = CR1 ∪ CR2 ∪ … CR n

[0038] where FR m represents the feasible region with respect to the boundary optimization variables, and y m represents the boundary optimization variables of the power transmission network;

[0039] Based on the piecewise retrieval analytical formula for the distribution network emergency control problem, a distributed iterative algorithm for the power transmission and distribution network based on MPQP is designed until the optimal solution of the power transmission and distribution coordinated emergency control model is obtained, and used as the boundary variables for the optimization problems of the power transmission network and the distribution network to execute the scheduling strategies of the power transmission network and the distribution network.

[0040] In some embodiments, the method further includes establishing boundary equality constraints between the power transmission network and the distribution network, as shown in the following formula:

[0041]

[0042] where and respectively represent the voltage amplitude at the connection point m' between the power transmission network and the distribution network, the active and reactive powers supplied to the distribution network, and respectively represent the node voltage amplitude at the connection point m' of the distribution network, the active and reactive powers supplied to the power transmission network.

[0043] In some embodiments, the method further includes obtaining a high-precision global linearized power flow equation based on historical data samples, and on the basis of the high-precision global linearized power flow matrix, deriving it into a sensitivity coefficient matrix:

[0044]

[0045]

[0046] where respectively represent the sensitivity of the distribution network voltage to the active power of the distribution network nodes, the sensitivity of the distribution network current to the active power of the distribution network nodes, the sensitivity of the active power supplied by the power transmission network to the distribution network to the active power of the distribution network nodes, the sensitivity of the reactive power supplied by the power transmission network to the distribution network to the active power of the distribution network nodes, N represents the total number of nodes in the distribution network m, l represents the number corresponding to the distribution network line ij, M m,ij 、M m,(N+l),j 、M m,2N,j and M m,(2N+1),j respectively represent the linear PF matrix M m corresponding to the output variables Vm,i 、I m,l 、P τ,m 、Q τ,m are related to the elements of the input variable P m,j ; M m,i,(K+e) 、M m,(N+l),(K+e) 、M m,2N,(K+e) and M m,(2N+1),(K+e) correspond to the output variables V m,i 、I m,l 、P τ,m 、Q τ,m and the elements of the e-th dimensionality-increasing variable ψ m,e (x);

[0047] Moreover, based on the above derivation process, the active power P τ,m and reactive power Q τ,m supplied to the distribution network, voltage V m,i and current I m,l with respect to the node injection reactive power Q m,j sensitivity coefficient matrix

[0048] In some embodiments, the MPQP-based distribution network distributed iterative algorithm of the method further includes the following processes:

[0049] a) Solve the main problem of the transmission network through the following formula to calculate the boundary optimization variable y m of the transmission network, and pass it to the distribution network optimization sub-problem. The expression is as follows:

[0050] min f trans (y trans )

[0051] s.t. y trans ∈ Y trans

[0052] y m ∈ FR m

[0053] b) For the given y m , the distribution network optimization problem in the k-th iteration is as follows:

[0054]

[0055]

[0056]

[0057] where It represents minimizing the objective function of the distribution network at the k-th iteration. s.t. represents the constraint conditions. There are two constraint conditions. The first one represents the optimization variables of distribution network m and the boundary variables between the transmission and distribution networks satisfy constraints. The second represents that the value range of the optimization variables of the distribution network should be within ;

[0058] c) It includes:

[0059] 1) If the distribution network sub-problem is feasible, determine the critical domain of the boundary variables between the transmission and distribution networks at the k-th iteration and the optimal objective parameters of distribution network m

[0060] 2) If the distribution network sub-problem is infeasible, solve the Lagrange multiplier λ that satisfies step (40), and generate a feasible cut to supplement the main problem of the transmission network;

[0061]

[0062] s.t. λ T B k = 0

[0063] 0 ≤ λ ≤ 1

[0064] Solve equation (41) to obtain the optimal solution λ * , and update the feasible region FR through the following equation (42):

[0065]

[0066] d) Unify the optimization variables in the transmission and distribution network optimization model into the optimization variables of the transmission network, and solve the main problem:

[0067]

[0068] y trans ∈ Y trans

[0069] where represents minimizing the transmission and distribution collaborative objective function. s.t. represents the constraint conditions. In formula (43), there are 3 constraint conditions. The first one is representing that the boundary variables of the transmission and distribution network are within the feasible region, representing that the boundary variables of the transmission and distribution network are within the adjacency range, y trans ∈ Y trans representing that the optimization variables of the transmission network are within the allowed value range;

[0070] f) If the solutions to all sub - problems are feasible and the difference between the boundary variables in two adjacent iterations is small enough, the termination condition is met and the iteration ends, i.e.:

[0071]

[0072] where represents the boundary variables of the power transmission and distribution network in the k - th iteration, represents the boundary variables of the power transmission and distribution network in the (k + 1)-th iteration, and ε represents the maximum allowable error.

[0073] Compared with the prior art, the present invention has the following remarkable advantages:

[0074] 1) The distribution network operation center constructs a linear relationship model between these historical operation data variables by using historical operation data, replacing the original non - linear power flow model of the distribution network. The high - precision linear model realized has the advantage of not depending on model parameters;

[0075] 2) It can not only reduce the communication burden generated for the emergency control of the transmission network and the distribution network, but also simplify the iteration process of the distributed iteration algorithm for the power transmission and distribution network based on MPQP, thereby accelerating the solution speed of the collaborative optimization optimal solution for the emergency control of the transmission network and the distribution network;

[0076] 3) It does not depend on the accuracy of the static model parameters of the distribution network. The proposed algorithm can obtain the global optimal solution after only a limited number of information exchanges, and can effectively cope with the large - range power flow transfer problem caused by a high proportion of renewable energy and the resulting power mismatch problem between the transmission network and the distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 is an exemplary framework diagram of the collaborative optimization of the emergency control of the transmission network and the distribution network in the present invention;

[0078] Figure 2 is an exemplary transformation diagram of the distribution network optimization sub - problem based on multi - parameter programming in the present invention;

[0079] Figure 3 is an exemplary distributed iterative algorithm diagram of the power transmission and distribution network coordination based on MPQP in the present invention;

[0080] Figure 4 is an exemplary topology diagram of the transmission network - distribution network in the present invention;

[0081] Figure 5 is an exemplary visualization diagram of the data - driven voltage distribution and the actual voltage distribution in the present invention;

[0082] Figure 6 is an exemplary visualization diagram of the data - driven current distribution and the actual current distribution in the present invention;

[0083] Figure 7 This is the visualization diagram of the effects before and after the optimization of the ADN voltage under extreme weather conditions exemplary in the present invention;

[0084] Figure 8 This is the visualization diagram of the effects before and after the optimization of the ADN current under extreme weather conditions exemplary in the present invention;

[0085] Table 1 is the exemplary table diagram in the present invention - comparison of the global optimization calculation performances of different distributed algorithms. Detailed implementation manners

[0086] The present invention will be further described below in conjunction with embodiments. The descriptions of the following embodiments are only for helping to understand the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several modifications can still be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

[0087] The present invention proposes an emergency collaborative control method for transmission / distribution networks facing extreme weather conditions. As Figure 1 shown, it is the collaborative emergency control collaborative framework for the transmission network and the distribution network. Based on the multi-parameter programming theory, with the boundary variables between the transmission network and the distribution network as the programming parameters, the distributed emergency control problem is transformed into a multi-parameter quadratic programming (MPQP) problem, so as to obtain the distributed iterative analytical expression of the emergency control model for the transmission and distribution networks. The method specifically includes the following steps:

[0088] Step 1: Comprehensively consider the coupling relationship between the transmission network and the distribution network, and establish an emergency collaborative control model for the transmission / distribution network; this step is specifically described as follows:

[0089] Step 1-1: Establish an emergency control optimization model for the transmission network, with the minimum coal consumption cost as the objective function. The emergency control optimization model for the transmission network is shown as the following formula:

[0090]

[0091] where, f trans represents the objective function of the transmission network, P g,i' represents the active power output of thermal power unit i', a i' , b i' , c i' represent the coal consumption coefficients of thermal power unit i', represents the set of thermal power units;

[0092] Set the following constraint conditions that the transmission network should follow:

[0093]

[0094]

[0095] Among them, \(E\) represents the set of transmission network lines, represents the set of transmission network nodes, which consists of thermal power units and load units; where the node is composed of and respectively represent the active power and reactive power flowing from the transmission network node \(i\) t to the transmission network node \(j\) t , \(\pi(j\) t ) and \(\psi(j\) t ) respectively represent the sets of the parent node and child nodes of the transmission network node \(j\) t , and represent the active power and reactive power of the load at the transmission network node \(j\) t , and respectively represent the minimum active power and reactive power of the thermal power unit \(i'\), and respectively represent the maximum active power and reactive power of the generator thermal power unit \(i'\), \(S\) ij,max represents the maximum apparent power that the transmission network line \(i\) t \(j\) t allows to pass through, and are respectively the squares of the voltages at the transmission network nodes \(i\) t and the transmission network \(j\) t , and respectively represent the resistance and reactance values of the transmission network line \(i\) t \(j\) t , and are the lower limit value and upper limit value of the square of the voltage at the transmission network node \(i\) t , represents the reactive power of the transmission network line j t l t , represents the reactive power of the transmission network node \(j\) t , represents the transmission network line \(i\) t \(j\) t are all in the transmission network set, represents that the thermal power unit \(i'\) of the transmission network is in the set of thermal power units;

[0096] Step 1-2: In establishing the emergency control optimization model of the distribution network, for the extreme scenario where the large-scale distributed PV output suddenly drops to zero, with the load shedding cost and energy storage output cost as the objective function, the emergency control optimization model of the distribution network is shown as follows:

[0097] min f dis = min X T H X + d X + e (8)

[0098] where, f dis represents the objective function of the active distribution network (ADN), X = [ΔP 1 ,…ΔP n T represents the optimization variables of the ADN, and H, d, and e are the price coefficients of the load shedding cost and energy storage output cost in the ADN;

[0099]

[0100] where, E D represents the line set of the distribution network, represents the node set of the distribution network, represents the energy storage set of the distribution network, represents the load set of the distribution network, Θ(j) and ψ(j) represent the sets of the parent node and child node of distribution network node j, V j represents the voltage at distribution network node j, I ij represents the current amplitude on distribution network line ij, R ij and X ij represent the resistance and reactance of distribution network line ij, and represent the lower and upper limits of the voltage amplitude at distribution network node j respectively, represents the upper limit of the current amplitude on distribution network line ij, P j , Q j represent the active power and reactive power injection at distribution network node j, represents the energy storage active power and energy storage reactive power of the j-th element in the distribution network energy storage set e , represents the initial active power injection and initial reactive power injection of the j-th element in the distribution network load set c , represents the active power change and reactive power change of the j-th element in the distribution network load set c , represents the change of the j-th element in the distribution network energy storage set e , the j-th element in the distribution network load set c ​The active power and reactive power, where γ represents the maximum power factor angle of the energy storage;

[0101] Step 1-3: Establish the boundary equation constraint between the transmission network and the distribution network, as shown in the following formula:

[0102]

[0103] Among them, and respectively represent the voltage amplitude at the connection point m' between the transmission network and the distribution network, the active and reactive powers supplied to the distribution network, and respectively represent the node voltage amplitude at the connection point m' of the distribution network, the active and reactive powers supplied to the transmission network;

[0104] Step 2: Utilize the historical operation data in the database of the distribution network operation center, and through state-space mapping and least-squares training, offline obtain the state-space mapping linear function relationship models between the voltage V m 、current I m 、active power P DG,m and reactive power Q DG,m 、active power P ESS,m and reactive power Q ESS,m 、active power P CLD,m and reactive power Q CLD,m of each distribution network (taking the mth distribution network as an example), and the active power P τ,m and reactive power Q τ,m supplied to the distribution network. Among them, the historical operation data of the distribution network operation center includes the active power and reactive power supplied to the distribution network, voltage, current, distributed power sources, energy storage, and load data. This step is specifically described as follows:

[0105] Step 2-1: Each distribution network obtains G data samples. Taking the mth distribution network as an example, the parameters of the data samples include the active power P τ,m and reactive power Q τ,m 、voltage V m,g 、current I m,g 、active power P DG,m,g and reactive power Q DG,m,g 、active power P ESS,m,g and reactive power Q ESS,m,g 、active power P CLD,m,g and reactive power Q CLD,m,g supplied to the distribution network. Then, the net active power P m,g and reactive power Q m,g of the gth data sample in distribution network m are expressed as follows:

[0106]

[0107] Step 2-2: Construct input samples and output samples according to the data samples (taking the gth sample as an example, g ∈ G);

[0108] The input sample is defined as:

[0109] x m,g =[P m,g Q m,g T (19)

[0110] The output sample is defined as:

[0111] y m,g =[V m,g I m,g P τ,m,g Q τ,m,g T (20)

[0112] Step 2-3: Increase the dimension of the state space of the input sample to obtain the input sample after dimension increase, which is defined as:

[0113]

[0114] where, ψ m (x m,g ) represents the non-linear enhanced observation dimension mapping vector function of the gth data sample of the mth distribution network. Assuming the number of enhanced observation dimensions is E, then ψ m (x m,g ) is defined as:

[0115] ψ m (x m,g )=[ψ m,1 (x m,g ),...,ψ m,e (x m,g ),…,ψ m,E (x m,g )] T (22)

[0116] The non-linear enhanced observation dimension mapping vector function ψ m,e (x m,g ) of the eth dimension of the gth data sample of the mth distribution network is defined as:

[0117]

[0118] where, c m,g,e represents the basis vector with the same dimension as x m,g , ψ m,e (x​​m,g ) represents the scalar function of the non-linear enhanced observation dimension mapping in the e-th dimension; r m,g,e represents the Euclidean norm;

[0119] Step 2-4: Arrange the output samples and the input samples after dimension elevation in sequence to obtain the output sample set and the input sample set after dimension elevation. The input sample set after dimension elevation of the m-th distribution network is defined as:

[0120]

[0121] The output sample set of the m-th distribution network is defined as:

[0122]

[0123] Step 2-5: Through least squares data-driven training, construct the linear models between the net active power P τ,m,g and reactive power Q τ,m,g , voltage V m,g , current I m,g for the distribution network. The least squares data-driven matrix M m of the m-th distribution network is as shown in the following formula:

[0124]

[0125] where, represents the matrix transpose of the input sample set after dimension elevation , represents the matrix pseudo-inverse of;

[0126] The defined linear function relationship of the m-th distribution network constructed is:

[0127]

[0128] In the above manner, a high-precision global linearized power flow equation is obtained based on historical data samples. On the basis of the high-precision global linearized power flow equation, a more accurate sensitivity coefficient matrix is further derived:

[0129]

[0130]

[0131] where, respectively represent the sensitivity of the distribution network voltage to the active power of the distribution network nodes, the sensitivity of the distribution network current to the active power of the distribution network nodes, the sensitivity of the active power supplied by the transmission network to the distribution network to the active power of the distribution network nodes, the sensitivity of the reactive power supplied by the transmission network to the distribution network to the active power of the distribution network nodes, and N represents the m-th distribution network (ADNm ) The total number of nodes in it, l represents the number corresponding to the distribution network line ij, M m,ij , M m,(N+l),j , M m,2N,j and M m,(2N+1),j respectively represent the elements in the linear PF matrix M m corresponding to the output variables V m,i , I m,l , P τ,m , Q τ,m and the input variable P m,j , M m,i,(K+e) , M m,(N+l),(K+e) , M m,2N,(K+e) and M m,(2N+1),(K+e) respectively correspond to the output variables V m,i , I m,l , P τ,m , Q τ,m and the e-th lifted variable ψ m,e (x);

[0132] The partial differential terms on the right side of equations (25)-(27) are calculated as follows:

[0133]

[0134] Based on the above derivation process, the active power P τ,m and reactive power Q τ,m , voltage V m,i , current I m,l with respect to the sensitivity coefficient matrix of the node-injected reactive power Q m,j are obtained by the same method.

[0135] Combining with the emergency control optimization model of the distribution network in step 1, the power flow equation and safety constraints of the distribution network are linearly represented as:

[0136]

[0137] Therefore, equations (1)-(7) constitute a complete emergency control model for the transmission network, equations (8), (13)-(16), (33) constitute a complete emergency control model for the distribution network, and equation (17) describes the consistency condition of the interaction variables between the transmission network and the distribution network;

[0138] Step 3: Based on the multi-parameter programming theory, transform the transmission and distribution coordinated emergency control problem into a multi-parameter quadratic programming problem (MPQP), and the MPQP model is shown as equation (34) below:

[0139]

[0140] Among them, \(x\) is the optimization variable, \(\theta\) is the planning parameter variable, \(H\) and \(G\) are the equality constraint and inequality constraint respectively, and \(f(\cdot)\) represents the objective function of the transmission and distribution coordinated emergency control problem.

[0141] Based on the multi-parameter programming theory, for any feasible planning parameter variable \(y\), there must exist a critical region \(CR\) such that the optimal solution \(x\) under any parameter within this critical region \(CR\) * can be expressed as an affine function of the planning parameter variable \(y\):

[0142] \(x\) * = \(x\) * (\(y\)), \(x\in CR\) (35)

[0143] Therefore, when \(y\) is in the critical region \(CR\), the objective function is simplified to a function only about \(y\).

[0144] The transmission and distribution coordinated emergency control model is a quadratic programming model. Assume that the optimization variable of the transmission network is represented by \(y\) trans and the optimization variable of distribution network \(m\) is represented by \(x\) dis,m Then the compact form of the transmission and distribution coordinated emergency control model is expressed as follows:

[0145]

[0146] Among them, \(f\) dis,m and \(f\) trans represent the objective functions of distribution network \(m\) and the transmission network, \(X\) dis,m and \(Y\) trans represent the value ranges of the corresponding optimization variables, \(n\) dis represents the number of ADNs, \(G\) dis,m and \(G\) trans represent the operation constraints of distribution network \(m\) and the transmission network respectively, represents the boundary variable of the transmission network supplying distribution network \(m\), represents the boundary variable of distribution network \(m\) supplying the transmission network, \(H\) m is the corresponding boundary constraint;

[0147] Decompose Equation (36) to obtain the distribution network optimization sub-problem, as shown in (37):

[0148]

[0149] The MPQP method can be used to transform the distribution network optimization problem into a retrieval set containing the optimization variables of the transmission network, and its transformation idea is as Figure 2 shown.

[0150] After derivation, the piecewise retrieval analytical formula of the sub-problem objective function of the transmission network boundary optimization variable \(y\) m can be obtained, as shown in Equation (38):

[0151]

[0152] Among them, FR m represents the feasible region for the boundary optimization variables;

[0153] Based on the piecewise retrieval of the analytical formula (38) for the emergency control problem of the distribution network, a distributed iterative algorithm for the transmission and distribution network based on MPQP is designed; as Figure 3 shown, the specific steps of the MPQP iterative algorithm are as follows:

[0154] Step 3-1: Solve the main problem of the transmission network through the following formula (39) to calculate the boundary optimization variable y m of the transmission network, and transmit it to the sub-problem of the distribution network. The expression is as follows:

[0155]

[0156] Step 3-2: For the given y m , the optimization problem of the distribution network at the k-th iteration is shown in Equation (40)

[0157]

[0158] Among them, represents minimizing the objective function of the distribution network at the k-th iteration, s.t. represents the constraint conditions. In formula (40), there are two constraint conditions. The first one is that the optimization variable of distribution network m and the boundary variable of the transmission and distribution network satisfy constraint, and the second indicates that the value range of the optimization variable of the distribution network should be within ;

[0159] Step 3-3: 1) If the sub-problem of the distribution network is feasible, determine the critical region of the boundary variable of the transmission and distribution network at the k-th iteration and the optimal objective parameter

[0160] of distribution network m; 2) If the sub-problem of the distribution network is infeasible, solve the Lagrange multiplier λ that satisfies Equation (40) to generate a feasible cut to supplement the main problem of the transmission network;

[0161]

[0162] Solve Equation (41) to obtain the optimal solution λ * , and update the feasible region FR through the following formula (42):

[0163]

[0164] Step 3-4: Unify the optimization variables in the transmission and distribution network optimization model into transmission network optimization variables, and solve the master problem:

[0165]

[0166] Among them, represents minimizing the transmission and distribution coordination objective function, s.t. represents the constraint conditions. In formula (43), there are 3 constraint conditions. The first one is represents that the transmission and distribution network boundary variables are within the feasible region, represents that the transmission and distribution network boundary variables are within the adjacency range, y trans ∈Y trans represents that the optimization variables of the transmission network are within the allowable value range;

[0167] Step 3-5: If the solutions of all sub-problems are feasible and the difference between the boundary variables in two adjacent iterations is small enough, then the termination condition is satisfied and the iteration ends, that is:

[0168]

[0169] Among them, represents the transmission and distribution network boundary variables in the k-th iteration, represents the transmission and distribution network boundary variables in the (k + 1)-th iteration, and ε represents the maximum allowable error;

[0170] Finally, take the optimal solution of the obtained transmission and distribution coordinated emergency control model as the optimal solution of the boundary variables of the optimization problems of the transmission network and the distribution network (that is, the optimal solution of the transmission and distribution coordinated emergency control model in formula (36)) to execute the dispatching strategies of the transmission network and the distribution network.

[0171] Verify the above implementation process of the present invention, and the verification process is described as follows:

[0172] The topology of the transmission and distribution network is as Figure 4 shown. Among them, the distribution network with 3 large-scale distributed photovoltaics access is connected to the transmission network through buses 3, 7, and 14. Select a certain boundary section for transmission and distribution coordinated emergency optimization control. The total loads of the distribution network at this moment are set to 2.12 MW, 2.53 MW, and 2.23 MW respectively; the total initial active powers of the ESS are 0.2 MW, 0.34 MW, and 0.33 MW respectively; the safe voltage range is set to [0.95, 1.05], and the line current limit is 0.2 p.u.

[0173] First, scenario setting. During the sudden drop in the output of distributed photovoltaics in the distribution network caused by extreme weather, it may lead to line overload and voltage over-limit in both the transmission network and the distribution network. The present invention sets four scenarios for case analysis and verification after the weather conditions change suddenly:

[0174] Scenario 1: The transmission network and distribution network are not optimized;

[0175] Scenario 2: The transmission network is independently optimized, and the distribution network is not optimized;

[0176] Scenario 3: Transmission and distribution coordinated optimization based on generalized Benders decomposition;

[0177] Scenario 4: Transmission and distribution coordinated optimization based on MPQP.

[0178] Second, comparison of optimization results:

[0179] As Figures 5 to 6 shown, it is a comparison between the calculation results of data-driven and the power flow calculation results based on the Newton-Raphson method. It can be seen from the figure that the power flow calculation results based on data-driven have high calculation accuracy, which can ensure the effectiveness of the data-driven power flow model in solving the transmission and distribution coordinated emergency control.

[0180] As Figure 7 shown, it is a visualization comparison diagram of the voltage optimization effect of ADN1 under four scenarios. It can be known from Figure 7 that when extreme weather causes a sharp drop in the output of distributed photovoltaics in the distribution network, without any optimization measures, the voltage of some nodes of ADN1 will drop below the safety lower limit of 0.95 p.u. Although the optimization of TN can provide a certain level of power support for ADN, the voltage violation problem in the ADN nodes directly facing end-users has not been effectively solved. This shows that a single TN optimization strategy is not sufficient to cope with the challenges brought by extreme weather. In contrast, Scenario 3 and Scenario 4 use different distributed iterative methods to implement the TN-ADN coordinated optimization strategy. Under these two scenarios, the optimization strategy not only includes control adjustments within each network, but also involves cooperation and support between TN and ADN. It can be seen from Figure 7 that the coordinated optimization not only improves the overall voltage level of ADN, but also achieves a more balanced voltage distribution, demonstrating the potential of coordinated optimization to maintain grid stability under extreme weather conditions.

[0181] As Figure 8 shown, it shows the line current distribution under extreme weather conditions in four scenarios. In Scenario 1 and Scenario 2, no ADN optimization measures are implemented, and the ADN lines are overloaded, and the line current exceeds the set upper limit, reflecting the vulnerability of ADN under extreme conditions and highlighting the necessity of optimization control to ensure line safety. Scenario 3 and Scenario 4 introduce TN-ADN coordinated optimization measures, effectively reducing the line current, making its distribution more uniform, and keeping it within the safe operating range.

[0182] As shown in Table 1, a comparison of the method proposed in this solution and the GBD method in terms of computing performance is presented. It can be seen from the table that the method proposed in this solution is significantly superior to the GBD algorithm in terms of computing time and the number of iterations. Especially under extreme weather conditions where strategies need to be quickly formulated to ensure continuous power supply to the load, the computing time of this method is shorter, making it more suitable for emergency control problems under such conditions.

[0183] Table 1

[0184] Method Number of iterations Computation time GBD 19 59.02s MPQP 5 16.93s

[0185] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and the descriptions in the specification are only preferred examples of the present invention and are not used to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the appended claims and their equivalents.

Claims

1. An emergency collaborative control method for transmission / distribution networks facing extreme weather conditions, characterized in that, The specific steps include: Comprehensively considering the coupling relationship between the transmission network and the distribution network, establish a coordinated emergency control model for the transmission / distribution network, including: Objective function equation of the power transmission network: Among them, f trans represents the objective function of the power transmission network, P g,i' represents the active power output of thermal power unit i', a i' , b i' , c i' represent the coal consumption coefficients of thermal power unit i', represents the set of thermal power units; Constraints of the transmission network: ∑ i∈π(j) P ij -P j =∑ l∈σ(j) P jl ∑ i∈π(j) Q ij -Q j =∑ l∈σ(j) Q jl Among them, \(E\) represents the set of transmission network lines, represents the set of transmission network nodes, and respectively represent the active power and reactive power flowing from the transmission network node \(i\) t to the transmission network node \(j\) t . \(\pi(j\) t ) and \(\psi(j\) t ) respectively represent the sets of the parent node and child nodes of the transmission network node \(j\) t . and represent the active power and reactive power of the load at the transmission network node \(j\) t . and respectively represent the minimum active power and reactive power of the thermal power unit \(i'\), and respectively represent the maximum active power and reactive power of the thermal power unit \(i'\), \(S\) ij,max represents the maximum apparent power allowed to pass through the transmission network line \(i\) t \(j\) t . and are respectively the squares of the voltages at the transmission network nodes \(i\) t and \(j\) t of the transmission network. and respectively represent the resistance and reactance values of the transmission network line \(i\) t \(j\) t . and are the lower limit value and upper limit value of the square of the voltage at the transmission network node \(i\) t ; And establish an emergency control optimization model for the distribution network, including: Objective function of the distribution network: min f dis = min X T HX + dX + e, where f dis represents the objective function of the active distribution network (ADN), X = [ΔP 1 , … ΔP n T represents the optimization variables of the ADN, and H, d, and e are the price coefficients of the load shedding cost and the energy storage output cost in the ADN;​ Constraints of the distribution network: Among them, represents the set of distribution network nodes, represents the set of distribution network energy storage, represents the set of distribution network loads, α represents the power factor angle of the load, P j , Q j represent the active power and reactive power injection of distribution network node j, represents the j-th element of the distribution network energy storage set e the active power of energy storage and the reactive power of energy storage, represents the j-th element of the distribution network load set c the initial active power injection and initial reactive power injection, represents the j-th element of the distribution network load set c the active power change and reactive power change, represents the j-th element of the distribution network energy storage set e the change amount, the j-th element of the distribution network load set c the active power and reactive power, γ represents the maximum power factor angle of energy storage; Using historical operation data in the database of the distribution network operation center, through state space mapping and least squares training, obtain the voltage V of each distribution network offline m , current I m , active power P of distributed power sources DG,m and reactive power Q DG,m , active power P of energy storage ESS,m and reactive power Q ESS,m , active power P of loads CLD,m and reactive power Q CLD,m , and the state space mapping linear function relationship model between the active power P τ,m and reactive power Q τ,m supplied to the distribution network: Combine with the emergency control optimization model of the distribution network in step 1 to obtain the power flow equation and safety constraint linear representation of the distribution network as: Transform the coordinated emergency control problem of the transmission and distribution network into a multi-parameter quadratic programming problem (MPQP) model, and the coordinated emergency control model of the transmission and distribution network is obtained as follows: s.t. m = 1, …, n dis x dis,m ∈X dis,m ,G dis,m (x dis,m )≤0 y trans ∈Y trans ,G trans (y trans )≤0 H m (x (m) ,y m ) = 0 Among them, f dis,m and f trans represent the objective functions of the distribution network m and the transmission network, X dis,m and Y trans represent the value ranges of the corresponding optimization variables, n dis represents the number of ADNs, G dis,m and G trans represent the operation constraints of the distribution network m and the transmission network respectively, represents the boundary variable of the transmission network supplying the distribution network m, represents the boundary variable of the distribution network m supplying the transmission network, H m is the corresponding boundary constraint; Use the MPQP method to transform the distribution network optimization problem into a retrieval set containing the optimization variables of the transmission network, and through derivation, obtain the piecewise retrieval analytical formula for the distribution network emergency control problem: s.t.y m ∈FR m FR m = CR1 ∪ CR2 ∪ … CR n Among them, FR m represents the feasible region for the boundary optimization variable, and y m represents the boundary optimization variable of the power transmission network; Based on the piecewise retrieval analytical formula for the distribution network emergency control problem, design a distributed iterative algorithm for the transmission and distribution network based on MPQP until the optimal solution of the coordinated emergency control model of the transmission and distribution network is obtained, and use it as the boundary variable for the optimization problems of the transmission network and the distribution network to execute the dispatching strategies of the transmission network and the distribution network.

2. The emergency collaborative control method for a power transmission / distribution network facing extreme weather conditions according to claim 1, wherein This method also includes establishing boundary equality constraints between the transmission network and the distribution network, as shown in the following formula: Among them, and respectively represent the voltage amplitude at the connection point m' between the transmission network and the distribution network, and the active and reactive powers supplied to the distribution network. and respectively represent the node voltage amplitude at the connection point m' of the distribution network and the active and reactive powers supplied to the transmission network.

3. A method for emergency collaborative control of a transmission / distribution network for extreme weather conditions according to claim 1, characterized in that, This method further includes obtaining a high-precision global linearized power flow equation based on historical data samples, and on the basis of the high-precision global linearized power flow matrix, deriving it into a sensitivity coefficient matrix: Among them, respectively represent the sensitivity of the distribution network voltage to the active power of the distribution network nodes, the sensitivity of the distribution network current to the active power of the distribution network nodes, the sensitivity of the active power supplied by the transmission network to the distribution network to the active power of the distribution network nodes, the sensitivity of the reactive power supplied by the transmission network to the distribution network to the active power of the distribution network nodes, N represents the total number of nodes in the distribution network m, l represents the number corresponding to the distribution network line ij, M m,ij 、M m,(N+l),j 、M m,2N,j and M m,(2N+1),j respectively represent the elements in the linear PF matrix M m corresponding to the output variables V m,i 、I m,l 、P τ,m 、Q τ,m and the input variable P m,j ; M m,i,(K+e) 、M m,(N+l),(K+e) 、M m,2N,(K+e) and M m,(2N+1),(K+e) respectively correspond to the elements of the output variables V m,i 、I m,l 、P τ,m 、Q τ,m and the e-th dimensionality-increased variable ψ m,e (x); And, based on the above derivation process, the active power P supplied to the distribution network is obtained using the same method τ,m and the reactive power Q τ,m , voltage V m,i , current I m,l The sensitivity coefficient matrix with respect to the nodal injected reactive power Q m,j ​ 4. A method for emergency collaborative control of a transmission / distribution network for extreme weather conditions according to claim 1, characterized in that The distributed iterative algorithm for the transmission and distribution network based on MPQP of this method further includes the following process: a) Solve the main problem of the transmission network by the following formula, calculate the boundary optimization variable y of the transmission network m , and pass it to the distribution network optimization sub-problem. The expression is as follows: minf trans (y trans ) s.t.y trans ∈Y trans y m belongs to FR m b) For a given y m , the distribution network optimization problem at the k-th iteration is as follows: Among them, represents minimizing the objective function of the distribution network under the k-th iteration. s.t. represents the constraint conditions. There are two constraint conditions. The first one represents the optimization variables of distribution network m and the boundary variables between the transmission and distribution networks satisfy constraint, and the second indicates that the value range of the optimization variables of the distribution network should be within ; c) Includes: 1) If the sub-problem of the distribution network is feasible, determine the critical domain of the boundary variables of the transmission and distribution network in the k-th iteration and the optimal objective parameters of distribution network m 2) If the distribution network sub-problem is infeasible, then solve the Lagrange multiplier λ that satisfies step formula (40), and generate a feasible cut to supplement the transmission network main problem; s.t. λ T B k = 0 0 ≤ λ ≤ 1 Solve Equation (41) to obtain the optimal solution λ * , and update the feasible region FR through the following Equation (42): d) Unify the optimization variables in the transmission and distribution network optimization model into the optimization variables of the transmission network, and solve the main problem: y trans ∈Y trans Among them, represents minimizing the objective function of the coordinated operation of power transmission and distribution. s.t. represents the constraints. In formula (43), there are three constraints. The first one is indicating that the boundary variables of the power transmission and distribution network are within the feasible region, indicating that the boundary variables of the power transmission and distribution network are within the adjacent range, y trans ∈Y trans indicating that the optimization variables of the power transmission network are within the allowable value range; e) If the solutions of all sub-problems are feasible, and the difference between the boundary variables between two adjacent iterations is small enough, then the termination condition is satisfied, and the iteration ends, that is: Among them, represents the boundary variables of the power transmission and distribution network at the k-th iteration, represents the boundary variables of the power transmission and distribution network at the (k + 1)-th iteration, and ε represents the maximum allowable error.

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