A power distribution network operation stability evaluation method considering entropy space

Abstract

The application discloses a power distribution network operation stability evaluation method considering entropy space, constructs a distributed power supply dynamic model, and designs a distributed power supply energy function; based on the distributed power supply energy function, an energy value of a leading unstable balance point is selected as critical energy, and a critical energy surface is fitted; a system entropy index representing power flow balance and static voltage safety of the power distribution network is constructed, the system entropy index is dispersed to a distributed power supply level to obtain a distributed power supply entropy index; a distributed power supply entropy boundary condition is designed, a distributed power supply entropy space representing safety and stability is constructed based on a boundary projection method; energy values of a steady state working point and a given expected accident are quickly solved, and the energy values are quickly positioned in and outside the entropy space; and based on positioning results and the distributed power supply entropy space, the power distribution network operation stability is evaluated. Compared with the prior art, the application evaluates the power distribution network operation stability according to the distributed power supply entropy space, and simplifies a traditional safety and stability evaluation method.

Description

Technical Field

[0001] This invention relates to a method for evaluating the operational stability of a distribution network that takes into account entropy space, and belongs to the field of distribution network optimization. Background Technology

[0002] While distributed power sources have driven the construction of distribution networks under new conditions and promoted the clean and low-carbon transformation of distribution networks, they have also brought varying degrees of impact on the safety, economy, and reliable operation of distribution networks. It is necessary to strengthen the construction of distribution networks in a targeted manner, assess the carrying capacity of distribution networks, guide the scientific layout, orderly development, nearby access, and local consumption of distributed new energy sources, and reduce the impact of the volatility and randomness of distributed power sources on the safety and stability of distribution networks. Summary of the Invention

[0003] Purpose of the invention: To address the shortcomings of existing technologies, this invention proposes a method for evaluating the operational stability of distribution networks that takes into account entropy space.

[0004] Technical solution: This invention discloses a method for evaluating the operational stability of a distribution network that takes into account entropy space, comprising the following steps:

[0005] Step 1: Construct a dynamic model of distributed generation, perform price reduction processing on it, and use the first integration method to design the distributed generation energy function that characterizes the multidimensional stability of the distribution network.

[0006] Step 2: Based on the constructed distributed power source energy function, select the energy value of the dominant unstable equilibrium point as the critical energy, and fit the critical energy surface at different operating points based on the hyperplane piecewise affine method;

[0007] Step 3: Normalize the power flow balance entropy index and voltage security entropy index to obtain the system entropy index characterizing the power flow balance and static voltage security of the distribution network. Based on the branch-bound method, distribute the system entropy index to the distributed generation level to obtain the distributed generation entropy index characterizing the power flow balance and static voltage security.

[0008] Step 4: Design distributed power source entropy boundary conditions. Based on the boundary conditions, construct the distributed power source entropy boundary on the two-dimensional PQ plane. Based on the critical energy surface obtained in Step 2, construct the distributed power source entropy space characterizing security and stability based on the boundary projection method.

[0009] Step 5: Quickly solve for the steady-state operating point and the energy value under a given contingency scenario, rapidly locate the location within and outside the entropy space, and evaluate the stability of the distribution network operation based on the location results and the distributed power source entropy space obtained in Step 4.

[0010] Furthermore, the dynamic model of distributed power sources in step 1 is as follows:

[0011] Analyzing the distribution network topology, we model the distribution network topology as an undirected graph, describing the connection relationships between distributed generation nodes, and considering the network structure characteristics, the power injected into the distributed generation nodes is:

[0012]

[0013] In the formula, A represents the directed incidence matrix, and Z... v Here is the branch impedance parameter matrix, δ is the voltage phase angle vector, and B ii represents the off-diagonal elements in the admittance matrix, and V is the nodal voltage magnitude vector;

[0014] The relative gain matrix is ​​used to quantify and evaluate the coupling strength between different loops in a multivariable control system, with the control variable Δx as the control variable. i With the controlled variable ΔS i Interaction strength z ij for:

[0015]

[0016] n is the number of distributed power nodes.

[0017] Control variable Δx i With the controlled variable ΔS i The relative gain matrix R RGA for:

[0018]

[0019] Based on R RGA Quantitatively assess the interaction between electrical quantities of various distributed power sources in the distribution network:

[0020]

[0021] In the formula, γ ij A value of 1 indicates a strong interaction between distributed power generation nodes, and their mutual influence cannot be ignored; γ ij A value of 0 indicates that the interaction between distributed power nodes is weak;

[0022] Ignore γ ij The interaction between distributed power nodes with a value of 0, and the network coupling effect on distributed power node i, i.e., the transfer function relationship of the state variables of the stable branch is:

[0023]

[0024] In the formula, G i (s) represents the closed-loop transfer function of distributed source i acting alone, J ij(s) represents the network transfer function between distributed source i and distributed source j, J ji (s) represents the network transfer function between distributed source j and distributed source i; G j,j+1 (s) represents the mutual coupling between distributed source j and distributed source j+1;

[0025] The equivalent decoupling power of a distributed power node is:

[0026] ΔS′ i =M i (s)Δx i

[0027] The decoupled distributed power source dynamic model is represented as follows:

[0028]

[0029] In the formula, x t These are system state variables, including the frequency and phase angle states within the phase-locked loop, the states of the inner and outer loop PI controllers, the states of the filter inductors and capacitors, the DC voltage states, and the decoupled state variables, y. t The variables are algebraic variables, including the active power P and reactive power Q at the steady-state operating point of the distributed power source, and w is the disturbance.

[0030] Furthermore, the method for reducing the order of the distributed power dynamic model in step 1 is as follows:

[0031] The dynamic components of a distributed power source include a phase-locked loop (PLL), inner and outer loop PI controllers, filters, and DC-side dynamics. By utilizing intrinsic orthogonal decomposition during the construction of the reduced-order system, partial modes corresponding to key state variables are extracted. The key state variables of interest are retained, and the influence of non-key state variables is compensated for, resulting in the reduced-order dynamic model of the distributed power source.

[0032]

[0033] In the formula, x r =[δ i ,ω i ,e i ] represents the key system state variables retained after order reduction, δ i The power angle of the distributed power source; ω i = 2πf, where f is the frequency of the distributed power source, e i For the electromotive force of the distributed power source, y r For algebraic variables;

[0034] Furthermore, the distributed generation energy function designed in step 1 using the first integration method to characterize the multidimensional stability features of the distribution network is as follows:

[0035] Distributed power structure preservation model:

[0036]

[0037] In the formula, T i M is the stiffness coefficient. i D is the equivalent inertial time constant. i The damping coefficient;

[0038] The energy function of a distributed generation is constructed using the first integration method, and its form is as follows:

[0039]

[0040] In the formula, E Ki and E Pi These represent the kinetic and potential energy of the distributed power source, respectively, F. i (δ i ,e i ) corresponds to the system after being disturbed, (ω is ,δ is ,e is This corresponds to the state before the disturbance.

[0041] Furthermore, step 2, which involves fitting the critical energy surface at different operating points using a piecewise affine method based on a hyperplane, includes the following steps:

[0042] Based on the energy function construction, the energy value of the dominant unstable equilibrium point is selected as the critical energy. Using the homotopy method, let Π(x) r )=f(x r ,y r )+w=0, introducing parameter t and auxiliary function Ψ(x) r Construct the homotopy mapping and solve for it:

[0043]

[0044] Where, x r0 It is x r The initial value is used to define the initial condition x. r (0);

[0045] The dominant unstable equilibrium point is obtained as (δ) ub ,ω ub ,e ub The corresponding potential energy is the critical energy Ecr. If the energy of the distributed power source exceeds the critical energy Ecr, then... cr This indicates instability. Based on the critical energy solution method, different system dynamic models are used at different steady-state operating points to calculate different critical energies E. crTo obtain the critical energy surface at different operating points, we first solve for the scatter plot of the critical energy at different operating points, and then fit the critical energy surface by piecewise affine fitting of the hyperplane.

[0046] Using the critical energy as the boundary value, a two-stage solution model is established to characterize the critical energy surface: the inner model determines the stability of the system based on boundary condition constraints, while the outer model searches for boundary points along the power growth direction until the system loses stability, taking the previous boundary point as the critical stable point. The inner model needs to determine the operating conditions for solution, while the limit of the outer model is constrained by the stability margin of the inner model. The final critical energy surface consists of multiple critical stable hyperplanes, and the fitting function of the critical energy surface is expressed as:

[0047] E cr =g(P i Q i )

[0048] Among them, (P) i Q i ) represents the steady-state operating point of the distributed source i, and g represents the polynomial function, which is generally of order 2-3.

[0049] Furthermore, the distributed power source entropy indicators characterizing power flow balance and static voltage security in step 3 are as follows:

[0050] H0=α1H′ r +α2H' V (8)

[0051] In the formula, α1 and α2 are the weights of the power flow balance entropy index and the voltage safety entropy index, respectively, and H′ r H' V These are the normalized results of the power flow balance entropy index and the voltage safety entropy index, respectively.

[0052] Furthermore, the process of constructing the distributed power source entropy space characterizing security and stability in step 4 is as follows:

[0053] Design the entropy boundary conditions for distributed power sources, expressed as follows:

[0054] f(P i Q i )=H0

[0055] Based on the boundary conditions, a distributed source entropy boundary is constructed on the two-dimensional PQ plane. Using the fitted critical energy surface, the entropy boundary in the two-dimensional PQ plane is projected onto the critical energy surface in the three-dimensional PQE space. The projected distributed source entropy space is represented as follows:

[0056]

[0057] Furthermore, in step 5, the steady-state operating point and the energy value under a given anticipated accident are quickly solved, and the location is rapidly determined both inside and outside the entropy space, as detailed below:

[0058] (1) Based on Gradient Boosting Decision Tree (GBDT), a fast mapping is performed between the steady-state operating point and the energy value under a given anticipated accident, and rapid localization is achieved within and outside the entropy space. The input and output of the GBDT network are:

[0059]

[0060] In the formula, X represents the input of the decision tree network, Y is the output value of the decision tree mapping, (P i Q i Let ) represent the steady-state operating point of distributed source i, w be the given anticipated disturbance, and E i i represents the energy value at the corresponding steady-state operating point and under the expected disturbance, measuring the stability of i. y is a 0-1 variable label used to determine whether the system is safe and stable.

[0061] The weak learner is initialized to f0(x) i The loss function is r. ti The strong learner is updated by the loss function:

[0062]

[0063] In the formula, x i For the input variable, y i For the corresponding real label, L(y) i f(x) is the loss function, c is the learner output value, m is the number of training rounds, and f(x) is the learning function. i ) is the decision tree function, f t (x) is the learner function for this round of training, f t-1 (x) is a function of the learner from the previous training round, f t (x i ) is for input x i The learner is set to time, where J is the number of iterations and c is the number of iterations. tj Let I be the learner output after t rounds and j iterations, and let I be the compensation coefficient.

[0064] The system safety and stability assessment method is divided into offline and online components. Offline training relies on historical data, obtained through measurements in the distribution network. Online sensing relies on real-time measurement or prediction data, requiring data from a single time segment to obtain the location of the steady-state operating point in entropy space in real time, thereby determining whether the system is in a safe and stable state. For the entropy value, no anticipated disturbance is required; the input is power, i.e., X = [P]. i Q i ] T;

[0065] (2) Local linearization relationship of entropy change trend based on least squares method

[0066] To locally linearize the entropy value, we first apply several sets of small fluctuations to the mapping model between entropy and power, obtaining the corresponding entropy fluctuations. The relationship between local entropy and power can then be approximated as follows:

[0067] ΔH=CΔP+DΔQ+θ H (14)

[0068] In the formula, ΔH is the entropy change, ΔP is the active power change, ΔQ is the reactive power change matrix, C and D are local linearization parameters, and θ H This is a higher-order parameter of entropy;

[0069] Solving the overdetermined system of equations using the least squares method yields the local linear matrix under this operating condition. The established overdetermined system of equations is as follows:

[0070]

[0071] Among them, Z ij Let be the matrix parameter of matrix Z in row i and column j, M be the total number of rows, N be the total number of columns, and β be the matrix parameter of matrix Z. j For the corresponding coefficients; when solving, find β, introduce the residual sum of squares function F(β)=||Zβ-H||, differentiate with respect to β to find the maximum and minimum values, and after simplification, get β=(Z T Z) - 1 Z T H; After obtaining the linear trend, it can quickly locate the working point in the entropy space and simultaneously obtain the safest, most stable, and orderly position.

[0072] Beneficial effects:

[0073] 1. This invention simplifies traditional safety and stability assessment methods by establishing a distributed generation entropy space characterizing "multi-dimensional stability issues such as system voltage stability and synchronization stability." Through energy function analysis, and by employing model decoupling and order reduction, the complex system characteristics of the distribution network are simplified for analysis. The energy function describes the grid's ability to absorb accumulated energy during a disturbance. The conversion between the system's kinetic and potential energy can well explain the system's complex motion trajectory, and the system's true critical transient energy is close to the potential energy at the unstable equilibrium point. Under random disturbances, analogous to the motion equations of a synchronous machine, a mapping relationship is established between the individual kinetic energy and trajectory of the distributed generation after system decoupling. The stability is described through the energy conversion process of the distributed generation nodes.

[0074] 2. The distribution network stability assessment method proposed in this invention reduces the error of the optimized scheduling model and improves scheduling efficiency, system economy, security and orderliness by considering multi-objective optimization of stability and adopting a mapping relationship positioning method. Attached Figure Description

[0075] Figure 1 This is a schematic diagram of the entropy space of the present invention. Detailed Implementation

[0076] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0077] This invention discloses a method for evaluating the operational stability of a distribution network that takes into account entropy space, comprising the following steps:

[0078] Step 1: Construct a dynamic model of distributed generation, perform price reduction processing on it, and use the first integration method to design the distributed generation energy function that characterizes the multidimensional stability features of the distribution network.

[0079] 1) Construct a dynamic model of distributed generation considering the coupling mechanism of the distribution network.

[0080] First, the distribution network topology is analyzed. Using graph theory, the topology is modeled as an undirected graph, describing the connections between distributed generation nodes. Considering the network structure characteristics, the injected power of the distributed generation nodes is:

[0081] P = AZ v sin(Α T δ)

[0082] Q = -|Α|Z v cos(Α T δ)-[V]diag[B ii V

[0083] In the formula, A represents the directed incidence matrix, and Z... v Let B be the branch impedance parameter matrix. ii The non-diagonal elements in the admittance matrix are represented by δ, where δ is the voltage phase angle vector and V is the node voltage magnitude vector.

[0084] Secondly, considering the complex interactions between distributed power sources, a relative gain matrix quantification method is used to evaluate the coupling strength between different loops in a multivariable control system, with the control variable Δx in the closed-loop system being considered. i With the controlled variable ΔS iInteraction strength between:

[0085]

[0086] n is the number of distributed power nodes.

[0087] Control variable Δx i With the controlled variable ΔS i The relative gain matrix R RGA for:

[0088]

[0089] Based on R RGA Quantitatively assess the interaction between electrical quantities of various distributed power sources in the distribution network:

[0090]

[0091] In the formula, γ ij A value of 1 indicates a strong interaction between distributed power generation nodes, and their mutual influence cannot be ignored; γ ij A value of 0 indicates that the interaction between distributed power nodes is weak and can be ignored.

[0092] Ignoring the weaker interactions between distributed power nodes, distributed power node i is subject to network coupling, i.e., the transfer function relationship of the state variables of the stable branch is:

[0093]

[0094] In the formula, G i (s) represents the closed-loop transfer function of distributed source i acting alone, J ij (s) represents the network transfer function between distributed source i and distributed source j, J ji (s) represents the network transfer function between distributed source j and distributed source i; G j,j+1 (s) represents the mutual coupling between distributed source j and distributed source j+1.

[0095] The equivalent decoupling power of a distributed power node is: ΔS i '=M i (s)Δx i The decoupled distributed power source dynamic model can be represented as: In the formula, x t These are system state variables, including the frequency and phase angle states within the phase-locked loop, the states of the inner and outer loop PI controllers, the states of the filter inductors and capacitors, the DC voltage states, and the decoupled state variables, y. tThe variables are algebraic variables, including the steady-state operating point of the distributed power source, such as active power P and reactive power Q, and w is the disturbance quantity.

[0096] The method for reducing the order of the dynamic model of distributed power sources is as follows:

[0097] The dynamic components of a distributed power source include a phase-locked loop (PLL), inner and outer loop PI controllers, filters, and DC-side dynamics. By utilizing intrinsic orthogonal decomposition during the construction of the reduced-order system, partial modes corresponding to key state variables are extracted. The key state variables of interest are retained, and the influence of non-key state variables is compensated for, resulting in the reduced-order dynamic model of the distributed power source.

[0098]

[0099] In the formula, x r =[δ i ,ω i ,e i ] represents the key system state variables retained after order reduction, δ i The power angle of the distributed power source; ω i = 2πf, where f is the frequency of the distributed power source, e i For the electromotive force of the distributed power source, y r It is an algebraic variable.

[0100] 2) Distributed Generator Energy Function Design Based on First Integration Method: The energy function describes the grid's ability to absorb accumulated energy during a disturbance. The conversion between the system's kinetic and potential energy can well explain the system's complex trajectory. The system's true critical transient energy is close to the potential energy at the unstable equilibrium point. Under random disturbances, analogous to the equations of motion of a synchronous machine, a mapping relationship is established between the kinetic energy and trajectory of a single distributed generator after decoupling from the system. The stability is described through the energy conversion process of the distributed generator nodes. Distributed Generator Structure Preservation Model:

[0101]

[0102] In the formula, T i M is the stiffness coefficient. i D is the equivalent inertial time constant. i is the damping coefficient.

[0103] Considering the physical interpretation of state variables mapped to energy space, during system state changes, a portion of the system's energy is converted into work, while another portion is dissipated as heat in a disordered manner. The definition of the energy function reflects the portion of energy transfer converted into work. Based on the correspondence between key system state variables and system energy, the distributed source energy function is constructed using the first integration method, and its form is as follows:

[0104]

[0105] In the formula, E Ki and E Pi These represent the kinetic and potential energy of the distributed power source, respectively, F. i (δ i ,e i ) corresponds to the system after being disturbed, (ω is ,δ is ,e is This corresponds to the state before the disturbance.

[0106] Step 2: Based on the constructed distributed power source energy function, select the energy value of the dominant unstable equilibrium point as the critical energy, and fit the critical energy surface at different operating points based on the hyperplane piecewise affine method.

[0107] Based on the construction of the energy function, the energy value of the dominant unstable equilibrium point is selected as the critical energy. Considering that the equilibrium point calculation method based on Newton's method has high requirements for the selection of the initial value of the iteration, the homotopy method is adopted to overcome the sensitivity of Newton's iteration method to the initial value (δ0,ω0,e0).

[0108] Let Π(x) r )=f(x r ,y r )+w=0, introducing parameter t and auxiliary function Ψ(x) r Construct the homotopy mapping and solve for it:

[0109]

[0110] Where, x r0 It is x r The initial value is used to define the initial condition x. r (0).

[0111] The dominant unstable equilibrium point is obtained as (δ) ub ,ω ub ,e ub The corresponding potential energy is the critical energy Ecr. If the energy of the distributed power source exceeds the critical energy Ecr... cr This indicates instability. Based on the critical energy solution method, different system dynamic models correspond to different steady-state operating points, and different critical energies E can be calculated. cr To obtain the critical energy surface at different operating points, we first solve for the scatter plot of the critical energy at different operating points, and then fit the critical energy surface using a piecewise affine hyperplane.

[0112] A two-stage solution model is established using the critical energy as the boundary value to characterize the critical energy surface. The inner model determines system stability based on boundary condition constraints, while the outer model searches for boundary points along the power growth direction until the system loses stability, taking the previous boundary point as the critical stable point. The inner model needs to determine the operating conditions for solution, while the limit of the outer model is constrained by the stability margin of the inner model. The final critical energy surface consists of multiple critical stable hyperplanes.

[0113] The fitting function for the critical energy surface can be expressed as: E cr =g(P i Q i ), (P i Q i ) represents the steady-state operating point of distributed source i, and g represents a polynomial function, which is generally of order 2-3.

[0114] Step 3: Normalize the power flow balance entropy index and voltage security entropy index to obtain the system entropy index characterizing the power flow balance and static voltage security of the distribution network. Based on the branch-bound method, distribute the system entropy index to the distributed generation level to obtain the distributed generation entropy index characterizing the power flow balance and static voltage security.

[0115] The distributed generation entropy characterizing the safe and orderly operation of the distribution network system is constructed as follows:

[0116] In the field of distribution network system research, information entropy is combined with the static security concept related to distribution networks to propose a unique entropy concept for distribution network systems, which is used to characterize their static orderliness and security.

[0117] The mathematical expression for the power flow equilibrium entropy of a distribution network is: In the formula, Let n be the number of branches in the system whose load rate falls within the safe range (A, B). i The percentage of the total number of branch roads is calculated using the following formula: The power flow equilibrium entropy is minimized when all branch load rates fall within the same range; conversely, it is maximized when all branch load rates fall within different ranges. Power flow equilibrium entropy, from the perspective of load rate, quantitatively describes the balance of power flow distribution across all lines at a given power flow cross-section.

[0118] Static voltage safety typically considers the voltage distribution and level during system operation. Distributed power sources containing power electronic equipment have lower withstand voltage capabilities and are at risk of voltage exceeding limits under faults or disturbances. Voltage safety entropy is defined as follows: The number of nodes in the distribution network system whose voltage deviations from the rated operating voltage are within the safe range (C, D). The percentage of nodes is calculated using the following formula: A higher voltage safety entropy value indicates a more uneven voltage distribution at nodes, with a few nodes potentially having larger over-limit values. A lower voltage safety entropy value indicates a smaller voltage difference between nodes and a more uniform voltage distribution. However, when the node voltage deviates significantly from the rated operating voltage, the entire distribution network may experience voltage collapse.

[0119] Normalizing the power flow balance entropy index and the voltage security entropy index yields a system entropy index characterizing the power flow balance and static voltage security of the distribution network. Based on the branch-bound method, the system-level index is distributed to the distributed generation level to obtain a distributed generation entropy index characterizing the power flow balance and static voltage security.

[0120] H0=α1H r '+α2H' V

[0121] In the formula, α1, α2 and H r '、H' V These are the weights and normalized results of the power flow balance entropy index and the voltage safety entropy index, respectively.

[0122] Step 4: Design distributed power source entropy boundary conditions. Based on the boundary conditions, construct the distributed power source entropy boundary on the two-dimensional PQ plane. Based on the critical energy surface obtained in Step 2, construct the distributed power source entropy space characterizing security and stability based on the boundary projection method.

[0123] The method for constructing the distributed power entropy space based on boundary projection is as follows:

[0124] Based on the definition of distributed source entropy, the boundary condition for distributed source entropy can be expressed as: f(P) i Q i H0. Based on this boundary condition, a distributed source entropy boundary is constructed on the two-dimensional PQ plane. Based on the fitted critical energy surface, a distributed source entropy space characterizing security and stability is constructed. The entropy boundary in the two-dimensional PQ plane is projected onto the critical energy surface in the three-dimensional PQE space. The projected distributed source entropy space can be expressed as:

[0125] E cr =g(P i Q i )

[0126] f(P i Q i -H0≤0

[0127] The physical meaning of distributed power source entropy space is: the system's steady-state operating point simultaneously satisfies the distributed power source entropy constraints of safety and orderliness, as well as the energy constraints of stability. As long as the system's steady-state operating point and its corresponding energy under the expected disturbance are within the space, the system will definitely satisfy the defined safety, orderliness, and stability constraints.

[0128] Step 5: Quickly solve for the steady-state operating point and the energy value under a given contingency scenario, rapidly locate the location within and outside the entropy space, and evaluate the stability of the distribution network operation based on the location results and the distributed power source entropy space obtained in Step 4.

[0129] 1) Fast localization within entropy space

[0130] Considering the difficulty in quickly calculating the energy function value under a given anticipated event, a Gradient Boosting Decision Tree (GBDT) is used to rapidly map the steady-state operating point to the energy value under a given anticipated event, and to achieve rapid localization within and outside the entropy space, in order to improve the speed of safety and stability determination. The input and output of the GBDT network are:

[0131]

[0132] In the formula, X represents the input of the decision tree network, Y is the output value of the decision tree mapping, (P i Q i Let ) represent the steady-state operating point of distributed source i, w be the given anticipated disturbance, and E i The energy value at the corresponding steady-state operating point and under the expected disturbance is used to measure the stability of i. y is a 0-1 variable label used to determine whether the system is safe and stable.

[0133] The weak learner is initialized to f0(x) i Its loss function is r ti The strong learner is updated by the loss function:

[0134]

[0135] In the formula, x i For the input variable, y i For the corresponding real label, L(y) i f(x) is the loss function, c is the learner output value, m is the number of training rounds, and f(x) is the learning function. i ) is the decision tree function, f t (x) is the learner function for this round of training, f t-1 (x) is a function of the learner from the previous training round, f t (x i ) is for input x iThe learner is set to time, where J is the number of iterations and c is the number of iterations. tj Let I be the learner output after t rounds and j iterations, and let I be the compensation coefficient.

[0136] The system safety and stability assessment method is divided into offline and online components. Offline training relies on historical data, which can be obtained through power distribution network measurements. Online sensing, on the other hand, relies on real-time measurement or prediction data, requiring only data from a single time segment to obtain the location of the steady-state operating point in entropy space in real time, thereby determining whether the system is in a safe and stable state. For the entropy value, no anticipated disturbance is required; the input is power, i.e., X = [P]. i Q i ] T .

[0137] 2) Local linearization relationship of entropy change trend based on least squares method

[0138] Considering the need to minimize entropy, variations near the same operating point require finding the direction that minimizes entropy. Therefore, local linearization of the entropy is performed. First, several sets of small fluctuations are given to the mapping model between entropy and power to obtain the corresponding entropy fluctuations. The relationship between local entropy and power can be approximated as:

[0139] ΔH=CΔP+DΔQ+θ H

[0140] In the formula, ΔH is the entropy change, ΔP is the active power change, ΔQ is the reactive power change matrix, C and D are local linearization parameters, and θ H is a higher-order parameter of entropy.

[0141] Solving this overdetermined system of equations using the least squares method yields the local linear matrix under this operating condition. The overdetermined system of equations is established as follows:

[0142]

[0143] Among them, Z ij Let be the matrix parameter of matrix Z in row i and column j, M be the total number of rows, N be the total number of columns, and β be the matrix parameter of matrix Z. j The corresponding coefficients. To find a suitable β that makes the equation hold true as much as possible when solving this equation, we introduce the residual sum of squares function F(β)=||Zβ-H||, and find the maximum or minimum value of the derivative of β. After simplification, we can obtain β=(Z T Z) -1 Z T H. After obtaining the linear trend, it is possible to quickly locate the working point in the entropy space and simultaneously obtain the safest, most stable, and ordered position.

[0144] In this specification, the terms "an embodiment," "example," "specific example," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0145] 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 to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A power distribution network operation stability assessment method considering entropy space, characterized in that, The method comprises the following steps: Step 1: constructing a distributed power supply dynamic model, performing a reduction process on the distributed power supply dynamic model, and designing a distributed power supply energy function representing multi-dimensional stability characteristics of the power distribution network by using a first integral method; The network topology of the power distribution network is analyzed, the network topology of the power distribution network is modeled as an undirected graph, the connection relationship between the distributed power supply nodes is described, and the network structure characteristic is considered, and the distributed power supply node injection power is: wherein A represents a directed incidence matrix, Z v is a branch impedance parameter matrix, δ is a voltage phase angle vector, B ii represents off-diagonal elements in the admittance matrix, and V is a node voltage magnitude vector. The relative gain matrix is used to quantify the interaction strength between different loops of a multivariable control system. The control variable Δx i and the controlled variable ΔS i are related by: ij ​ n is the number of distributed power supply nodes; Control variable Δx i Relative gain matrix R i of the controlled variable ΔS RGA is: Based on R RGA Quantitative evaluation of the interaction between the electrical quantities of each distributed power supply in the distribution network: In the formula, γ ij The value of 1 indicates that there is strong interaction between the distributed power nodes, and the mutual influence cannot be ignored. gamma ij a value of 0 indicates weak interaction between the distributed power supply nodes; Neglecting γ ij The interaction between the distributed power supply nodes with the value of 0, the distributed power supply node i is subjected to the network coupling effect, that is, the stable branch state quantity transfer function relationship is: where G i (s) represents the closed-loop transfer function of the distributed generator i acting alone, J ij (s) represents the network transfer function between the distributed generator i and the distributed generator j, J ji (s) represents the network transfer function between the distributed generator j and the distributed generator i; G j,j+1 (s) represents the mutual coupling part between the distributed generator j and the distributed generator j+1; The decoupled power of the distributed power supply node is: ΔS i ' = M i (s) Δx i The decoupled distributed power supply dynamic model is represented as: where x t are system state variables, including the frequency and phase angle states in the phase-locked loop, the PI controller states in the inner and outer loops, the filter inductance and capacitance states, the DC voltage state, and the decoupled state variables, y t are algebraic variables, including the active power P and the reactive power Q of the steady-state operating point of the distributed power supply, and w is the disturbance quantity. Step 2: based on the constructed distributed power supply energy function, the energy value of a dominant unstable equilibrium point is selected as critical energy, and a hyperplane piecewise affine method is used to fit the critical energy surface at different operating points; Step 3: the power flow balance entropy index and the voltage safety entropy index are normalized to obtain a system entropy index representing the power flow balance and the static voltage safety of the power distribution network, the system entropy index is dispersed to the distributed power supply level based on a branch definition method, and a distributed power supply entropy index representing the power flow balance and the static voltage safety is obtained; Step 4: designing a distributed power supply entropy boundary condition, according to the boundary condition, constructing a distributed power supply entropy boundary on a two-dimensional P-Q plane, according to the critical energy surface fitted in step 2, constructing a distributed power supply entropy space representing safety and stability based on a boundary projection method; Step 5: the energy value of the steady-state operating point and the given expected accident is quickly solved, and the inside and outside of the entropy space is quickly located, and the running stability of the power distribution network is evaluated based on the positioning result and the distributed power supply entropy space obtained in step 4.

2. The method for power grid operation stability assessment considering entropy space according to claim 1, characterized in that, The order reduction method of the distributed power supply dynamic model in step 1 is as follows: The dynamic link of the distributed power supply includes a phase-locked loop, an inner and outer loop PI controller, a filter and a direct current side dynamic, intrinsic orthogonal decomposition is used to intercept the part of the mode corresponding to the key state variable in the process of constructing the order reduction system, the key state variable is retained, and the influence caused by the non-key state variable is compensated, and the reduced distributed power supply dynamic model is obtained: where x r = [δ i , ω i , e i ] is the reduced system key state variables, δ i is the power angle of the distributed power source; ω i = 2πf, f is the frequency of the distributed power source, e i is the electromotive force of the distributed power source, and y r is an algebraic variable.

3. The method for power grid operation stability assessment considering entropy space according to claim 2, characterized in that, The distributed power supply energy function representing the multi-dimensional stability characteristics of the power distribution network is designed by using the first integral method in step 1, and the specific process is as follows: The distributed power supply structure retention model is: where T i is the stiffness coefficient, M i is the equivalent inertial time constant, D i is the damping coefficient; The first integral method is used to construct the distributed power supply energy function, and the form is as follows: where E Ki and E Pi are the kinetic and potential energy of the distributed power source, respectively, F i (δ i , e i ) corresponds to the system after the disturbance, and (ω is , δ is , e is ) corresponds to the state before the disturbance.

4. The power grid operation stability evaluation method considering entropy space according to claim 3, characterized in that, The step 2 based on the hyperplane piecewise affine method to fit the critical energy surface at different operating points comprises the following steps: Based on the energy function construction, the energy value of the dominant unstable equilibrium point is selected as the critical energy. The homotopy method is used to make Π(x r ) = f(x r ,y r ) + w = 0, introduce the parameter t and the auxiliary function Ψ(x r ), construct the homotopy mapping, and solve: where x r0 is the initial value of x r used to define the initial condition x r (0); The dominant unstable equilibrium point is obtained as (δ ub ,ω ub ,e ub ), which corresponds to the critical energy E cr . If the energy of the distributed power supply exceeds the critical energy E cr , instability is considered; based on the critical energy solving method, different system dynamic models correspond to different steady-state operating points, and different critical energies E cr are calculated. In order to obtain the critical energy surface at different operating points, first, the scatter plot of the critical energy at different operating points is obtained, and then the critical energy surface is fitted by hyperplane segmentation. A two-stage solving model is established to describe the critical energy surface by taking the critical energy as a boundary value: the inner model judges whether the system is stable or not based on the boundary condition constraint, and the outer model searches for the boundary point along the power growth direction until the system loses stability, and the previous boundary point is taken as a critical stable point, the inner model needs to determine the operating condition for solving, and the limit of the outer model is restricted by the stability margin of the inner model, finally, the critical energy surface is composed of a plurality of critical stable hyperplanes, and the fitting function of the critical energy surface is represented as: E cr = g(P i , Q i ) where (P i , Q i ) denotes the steady state operating point of distributed generator i, and g denotes a polynomial function, typically of order 2-3.

5. The method for power grid operational stability assessment considering entropy space according to claim 4, characterized in that, The distributed power supply entropy index representing the power flow balance and the static voltage safety in step 3 is as follows: H0= a1H' r + a2H' V (9) In the formula, α1 and α2 are respectively the weight of the power flow balance entropy index and the voltage safety entropy index, H' r , H' V are respectively the normalized results of the power flow balance entropy index and the voltage safety entropy index.

6. The power grid operational stability assessment method considering entropy space according to claim 5, wherein, The distributed power supply entropy space representing safety and stability in step 4 is constructed as follows: The distributed power entropy boundary condition is designed and expressed as: f(P i ,Q i ) = H0 According to the boundary condition, the distributed power entropy boundary is constructed on the two-dimensional P-Q plane, and the entropy boundary in the two-dimensional P-Q plane is projected onto the critical energy surface in the three-dimensional P-Q-E space according to the fitted critical energy surface, and the projected distributed power entropy space is expressed as:

7. The method of claim 1, wherein, The step 5 is to quickly solve the steady-state operating point and the energy value under the given contingency, and to quickly locate in and out of the entropy space, and the specific steps are as follows: (1) Based on the gradient boosting decision tree GBDT, the steady-state operating point and the energy value under the given contingency are quickly mapped, and the quick positioning in and out of the entropy space is realized, and the input and output of the GBDT network are: where X represents the input of the decision tree network, Y is the output value of the decision tree mapping, (P i , Q i ) represents the steady state operating point of the distributed power supply i, w is a given expected disturbance, E i is the energy value under the corresponding steady state operating point and the expected disturbance, measures the stability degree of i, and y is a 0-1 variable label used to determine whether the system is safe and stable. Initialize the weak learner setting f0(x i ) as the loss function r ti , update the strong learner by the loss function: In the formula, x i is an input variable, y i is a corresponding real label, L(y i , c) is a loss function, c is a learner output value, m is a number of rounds of training, f(x i ) is a decision tree function, f t (x) is a learner function of this round of training, f t-1 (x) is a function of a learner of the last round of training, f t (x i ) is a learner when the input is x i , J is a number of iterations, c tj is a learner output of the t rounds of j iterations, and I is a compensation coefficient. The system security and stability discrimination method is divided into offline and online two parts, the offline training depends on historical data, which is obtained through power distribution network measurement; the online perception depends on real-time measurement or prediction data, which needs single time section data, the position of steady-state operating point in entropy space is obtained in real time, and then it is judged whether the system is in a safe and stable state. For the entropy value, it is not necessary to give the expected disturbance, and the input is power, that is, X = [P i , i ] T ; (2) Local linearization relationship of entropy value change trend based on least square method The entropy value is locally linearized, and first, a plurality of small fluctuations are given to the mapping model of the entropy value and the power to obtain the corresponding entropy value fluctuation, and the relationship between the local entropy value and the power is approximately expressed as: AH = CΔP + DΔQ + Θ H (14) where ΔH is the entropy change, ΔP is the active change, ΔQ is the reactive change matrix, C, D are local linearization parameters, θ H is the high order parameter of entropy; The over-determined equation set is solved by the least square method, that is, the local linear matrix under the running state is obtained, and the over-determined equation set is established as: Wherein, Z ij is the matrix parameter of the matrix Z in i row j column, M is the total number of rows, N is the total number of columns, β j is the corresponding coefficient; when solving, find β, introduce the residual sum of squares function F(β) = ||Zβ-H||, and find the maximum value by differentiating β, and after arranging, β = (Z T Z) -1 Z T H; after obtaining the linear change trend, the most safe, stable and orderly position of the working point is quickly obtained while quickly positioning in the entropy space.

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