Embedded linear constraint generation method and system for inverter power distribution network stability

Abstract

The application discloses an embedded linear constraint generation method and system for inverter power distribution network stability, determines inverter stability indexes and system stability indexes; a double-layer machine learning method framework is used to establish an inverter power distribution network stability constraint fitting model, including an outer model and an inner model; the trained inverter power distribution network stability constraint fitting model is used to obtain the system stability indexes and the inverter stability indexes according to input data; and a big M method is used to generate index codes of the system stability indexes and the inverter stability indexes respectively, and the index codes are embedded into a target function. The method realizes the satisfaction of a prediction error tolerance accuracy while ensuring the embeddability of the constraint, achieves an ideal trade-off between prediction accuracy and embedding complexity, helps inverter power distribution network system operators to consider small disturbance stability and frequency stability indexes in inverter droop parameter adjustment, and reduces stability risks.

Description

Technical Field

[0001] The present invention belongs to the technical field of distribution network operation, and in particular relates to an embedded linear constraint generation method and system for small-disturbance stability and frequency stability of an inverter distribution network. Background Art

[0002] As more distributed renewable energy sources are connected to distribution networks via power electronic converters, the network is gradually transforming into one dominated by inverter-based power generation. This results in lower inertia and weaker damping, significantly reducing the system's ability to withstand disturbances and making it highly susceptible to frequency violations after disturbances. Furthermore, the fast response of inverters, as power electronic devices, increases the risk of sustained and severe oscillations, exacerbating the system's stability issues with small disturbances and jeopardizing the safe operation of the distribution network.

[0003] Incorporating system stability constraints into system operation is a key issue. Due to the adjustability of the inverter power control outer loop parameters, the existing technology ensures system stability by adjusting the inverter power outer loop control parameters. In power systems dominated by synchronous machines, the method of incorporating transient stability and voltage stability constraints into operation and optimal power flow models is adopted to determine transient transmission power or re-dispatch generators to maintain system stability limits. With the advent of power systems dominated by inverter power generation, from the perspective of frequency stability, the existing technology uses inverters to provide inertia and fast frequency reserve technology to improve transient performance. Based on the difference in inertia between grid-following inverters and grid-forming inverters, it is proposed to adopt a strategic inertia layout to optimize the inverter power outer loop parameters and improve key system frequency dynamic performance indicators.

[0004] Furthermore, in power systems with a high penetration of inverters, small-disturbance stability is crucial, with damping playing a more critical role than inertia. For the spatial configuration of inverter damping, the damping coefficients of each inverter in the system are adjusted to improve small-disturbance stability. During the planning phase, increasing inverter damping at specific locations effectively increases grid strength, thereby improving stability. During real-time operation, the damping coefficients of the inverters are directly adjusted in real time to achieve optimal performance. Existing methods use non-convex models to configure oscillation damping. For example, they use sensitivity factors of the oscillation modes to iteratively adjust the modal damping ratio, but this leads to iterative complexity. Alternatively, they use analytical calculations of oscillation modes and time-domain response simulations, but their non-convex nature and complex computational form still limit the embeddability of stability constraints. Existing methods assume that all inverter units have the same inertia-damping ratio. Furthermore, due to the limitations of non-convexity or uniform inertial damping assumptions, incorporating these methods into system operation presents significant challenges, hindering the development of adjustable inverter oscillation damping operations. Summary of the Invention

[0005] To solve the problems in the prior art, the application provides an embedded linear constraint generation method and system for inverter power distribution network stability, realizes inverter parameter adjustment operation considering stability constraints of the power distribution network, and realizes the consideration of small signal stability and frequency stability constraints of the inverter power distribution network system and the reduction of optimization calculation complexity in the inverter power outer loop parameter adjustment operation based on the embedded linear constraints of the system small signal stability and frequency stability of the inverter power outer loop parameters.

[0006] The application adopts the technical scheme as follows.

[0007] The application provides an embedded linear constraint generation method for inverter power distribution network stability, and the linear constraint is a constraint condition of the objective function, including:

[0008] A system state space model of the inverter power distribution network is established, the damping ratio of the inverter is defined according to the eigenvalue of the system state space model, and is used as an inverter stability index;

[0009] A dynamic model of the inverter power distribution network system is established, including: a small signal model of power measurement filtering, a small signal model of droop control link, a small signal model of the power distribution network line and a small signal model of the power distribution network load; the time when the frequency deviation of the inverter power distribution network reaches the maximum and the control parameters of the inverter are obtained, the maximum frequency deviation and the steady-state frequency deviation of the inverter power distribution network are calculated based on the dynamic model of the inverter power distribution network system, and are used as system stability indexes; wherein the control parameters of the inverter include: disturbance power, droop coefficient, system equivalent damping, system inertia constant, system equivalent damping, natural oscillation frequency, equivalent time constant and equivalent turbine coefficient;

[0010] Based on a double-layer machine learning method framework, an inverter power distribution network stability constraint fitting model is established, including: an outer model and an inner model; in the outer model, input data is divided into multiple linear regions according to the stable working point of the power distribution network system and the stable working point of the inverter; the input data includes the operation data of the power distribution network and the control parameters of the inverter; in the inner model, a regularized ridge regression method is used to perform linear mapping fitting on the system stability indexes in each linear region, and a regularized softmax regression method is used to perform linear mapping fitting on the inverter stability indexes in each linear region; the trained inverter power distribution network stability constraint fitting model is used to obtain the system stability indexes and the inverter stability indexes according to the input data;

[0011] The index codes of the system stability indexes and the inverter stability indexes are respectively generated by using the big M method, and the index codes are embedded into the objective function.

[0012] Preferably, the damping ratio of the inverter is defined as an index of inverter stability according to the eigenvalues of the system state space model in the following relation:

[0013]

[0014] wherein, is the damping ratio of the ith inverter, is a set of real numbers, σ i is the real part of the ith eigenvalue of the system state space model, ω i is the imaginary part of the ith eigenvalue of the system state space model.

[0015] Preferably, the dynamic model of the power measurement filter is as follows:

[0016]

[0017] wherein, P, Q are the active and reactive power measured at the node by the inverter, ω c is the cut-off frequency of the low-pass filter, v oD and v oQ are the d and q axis components of the node voltage based on the common reference point voltage, i od and i oq are the d and q axis components of the node current based on the common reference point current, s is the Laplace operator;

[0018] The dynamic model of the droop control loop is as follows:

[0019]

[0020] wherein, is the frequency of the ith inverter, ω n is the reference nominal frequency, is the d axis component of the voltage of the ith inverter, V n is the reference nominal voltage of the inverter, and are the active and reactive control loop droop parameters of the ith inverter;

[0021] The dynamic model of the distribution network line is as follows:

[0022]

[0023] wherein, v Di , v Qi are the d and q axis components of the voltage of the node i based on the common reference point voltage, v Dj , v Qj are the d and q axis components of the voltage of the node j based on the common reference point voltage, ilineDij and i lineQij are the d-axis and q-axis components of the line ij current based on the common reference point current, R lineij , L lineij are the resistance and inductance of the line ij, ω com is the frequency under the common coordinate system;

[0024] The dynamic model of the distribution network load is as follows:

[0025]

[0026] In the formula, i loadDi and i loadQi are the d-axis and q-axis components of the load node i current based on the common reference point current, R loadi , L load are the resistance and inductance of the load node i.

[0027] Preferably, after the dynamic model of the power measurement filtering, the dynamic model of the droop control link, the dynamic model of the distribution network line and the dynamic model of the distribution network load are once Taylor expanded, the corresponding small signal models are obtained; the small signal model of the inverter distribution network system obtained by integrating each small signal model is taken as the dynamic model of the inverter distribution network system.

[0028] Preferably, based on the dynamic model of the inverter distribution network system, the maximum frequency deviation Δf max and the steady-state frequency deviation Δf qss of the inverter distribution network are calculated, which constitute the system stability index and satisfy the following relationship respectively:

[0029]

[0030] In the formula, ΔP L is the disturbance power; R P is the equivalent droop parameter of the system synthesized by the droop coefficient R P,i of the i th inverter; D and H are the equivalent damping and inertia constant of the system respectively; ξ, ω n , T and F are the equivalent damping, natural oscillation frequency, equivalent time constant and equivalent turbine coefficient of the system respectively; t max is the time when the frequency deviation of the inverter distribution network reaches the maximum; N DG is the set of inverters; K P,i is the participation factor of the i th inverter, which is 1 when the inverter is running and 0 when the inverter is shut down.

[0031] Preferably, in the outer model, the input data is divided into multiple linear regions according to the stable working point of the distribution network system and the stable working point of the inverter, including:

[0032] The input data vector {x k} is clustered into W linear regions C1, C2, …, C j , …, C W , and simultaneously satisfies the following two optimization objectives:

[0033] 1) In the same linear region C j , the coefficients and intercepts can achieve the fitting of all samples and indicators;

[0034] 2) The W linear regions C1, C2, …, C j , …, C W are represented in the form of a polyhedron of linear separation of region properties.

[0035] Preferably, the system stability indicators in each linear region are linearly mapped and fitted by using a regularized ridge regression method, including:

[0036] In the W linear regions C1, C2, …, C j , …, C W , for each system stability indicator linearly mapped and fitted by using a regularized ridge regression method, satisfying the following relationship:

[0037]

[0038] In the formula, is the linearly mapped and fitted system stability indicator, are the coefficients and intercepts obtained by linearly mapping and fitting the i-th system stability indicator in the j-th linear region C j , J j is the j-th linear region C j , α > 0 is an l2-regularization parameter, y ki is the i-th system stability indicator corresponding to the k-th sample, x k is the k-th sample, k ∈ J j indicates that the sample x k comes from the j-th linear region C j .

[0039] Preferably, the inverter stability indicators in each linear region are linearly mapped and fitted by using a regularized softmax regression method, including:

[0040] In the W linear regions C1, C2, …, C j , …, C W , for each inverter stability indicator The linear mapping fitting is performed by using the softmax regression method with regularization, and the following relationship is met:

[0041]

[0042] In the formula, is the linear mapping fitting of the inverter stability index, I(i) is the category set of the i-th inverter stability index, are the coefficients and intercepts of the linear mapping fitting of the i-th inverter stability index in the j-th linear region C j are the coefficients and intercepts of the linear mapping fitting of the i-th inverter stability index in the j-th linear region C are the coefficients and intercepts of the linear mapping fitting of the i-th inverter stability index in the j-th linear region C i is the number of categories of the i-th inverter stability index, [y dk ] i is the category value of the i-th inverter stability index of the k-th sample, is the h-th category of the i-th inverter stability index, x k is the k-th sample, k∈J j represents that the sample x k comes from the j-th linear region C j , and α is a positive number.

[0043] Preferably, the block coordinate descent method is used to train the inverter power distribution network stability constraint fitting model to determine the parameters of the inverter power distribution network stability constraint fitting model with the minimum loss function as the target.

[0044] Preferably, the big M method is used to convert the system stability index into the following relationship:

[0045]

[0046] In the formula, p ji is the auxiliary variable corresponding to the i-th system stability index in the j-th linear region, δ j is the classification mark of the system stability index belonging to the j-th linear region, and is a binary vector, δ j ∈{0,1} K , and K is the number of linear regions, satisfying x is input data, and are the lower limit constraint coefficient and the upper limit constraint coefficient of the i-th system stability index in the j-th linear region in the stable state determined by the big M method, respectively;

[0047] The auxiliary variable p jiTo represent the index code of the threshold range of the i th system stability index corresponding to the j th linear region, the index code is embedded into the objective function.

[0048] Preferably, the inverter stability index is converted into the following relationship by using the large M method:

[0049]

[0050] In the formula, ν ih is the classification mark of the h th inverter stability index belonging to the i th inverter, and is a binary vector, v ih ∈{0,1}, x is input data, I(i) is the category set of the i th inverter stability index, δ j is the classification mark of the system stability index belonging to the j th linear region, and is a binary vector, δ j ∈{0,1} K , K is the number of linear regions, and satisfies is the constraint coefficient between the h th inverter stability index and the t th inverter stability index determined by using the large M method, and satisfies B is an input data set;

[0051] The binary vector ν ih is the index code representing the h th inverter stability of the i th inverter, and the index code is embedded into the objective function.

[0052] The application further provides an embedded linear constraint generation system for inverter power distribution network stability, and the linear constraint is a constraint condition of the objective function, and comprises:

[0053] The index establishment module is used for establishing a system state space model of the inverter power distribution network, defining a damping ratio of the inverter as an inverter stability index according to eigenvalues of the system state space model, and further used for establishing a dynamic model of the inverter power distribution network system, including: a small signal model of power measurement filtering, a small signal model of droop control link, a small signal model of the power distribution network line and a small signal model of the power distribution network load; obtaining a time when a frequency deviation of the inverter power distribution network reaches a maximum and a control parameter of the inverter, calculating a maximum frequency deviation and a steady-state frequency deviation of the inverter power distribution network as system stability indexes based on the dynamic model of the inverter power distribution network system; wherein the control parameter of the inverter includes: disturbance power, droop coefficient, system equivalent damping, system inertia constant, system equivalent damping, inherent oscillation frequency, equivalent time constant and equivalent turbine coefficient.

[0054] The stability index generation module is used for establishing an inverter power distribution network stability constraint fitting model based on a double-layer machine learning method framework, including an outer model and an inner model.

[0055] The index embedding module is used for generating index codes of the system stability index and the inverter stability index respectively by using the large M method, and embedding the index codes into the objective function as embedded linear constraints of the objective function.

[0056] The beneficial effects of the present application at least include that, compared with the prior art, the double-layer multi-region linear machine learning representation algorithm and the encoding method thereof realize the satisfaction of the prediction error tolerance accuracy while ensuring the embeddability of the constraints, achieve an ideal trade-off between prediction accuracy and embedding complexity, and help the inverter power distribution network system operator to consider small disturbance stability and frequency stability indexes in inverter droop parameter adjustment, thereby reducing the stability risk. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 It is a flowchart of an embedded linear constraint generation method for inverter power distribution network stability proposed by the present application. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical scheme and advantages of the present application clearer, the technical scheme of the present application will be described clearly and completely below in combination with the drawings in the embodiments of the present application. The embodiments described in the present application are only a part of the embodiments of the present application, but not all the embodiments. Based on the spirit of the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0059] The present application proposes an embedded linear constraint generation method for inverter power distribution network stability, as shown in Figure 1 , including:

[0060] Step 1, establish a system state space model of the inverter power distribution network, define the damping ratio of the inverter as the inverter stability index according to the eigenvalue of the system state space model.

[0061] Specifically, the system state space model of the linearized system satisfies the following relationship:

[0062]

[0063] y = Cx + Du

[0064] wherein, are the state vector, the output vector and the control input vector of the linearized system respectively; represents a differential operation; are system state space matrices; is a real number set, and n, m and p are the dimension of the state vector, the dimension of the output vector and the dimension of the control input vector respectively.

[0065] Let represent the ith eigenvalue of the system state space model, is a complex number set, and are the real part and the imaginary part of the ith eigenvalue respectively; λ i corresponding left and right eigenvectors satisfy the following relationship:

[0066] Au i = λ i u i

[0067] v i T A = v i T λ i

[0068] wherein, u i is the left eigenvector of the ith eigenvalue λ i , and v i is the right eigenvector of the ith eigenvalue λ i ;

[0069] According to the eigenvalue of the system state space model, the damping ratio of the inverter is defined as the following relationship, as an inverter stability index:

[0070]

[0071] wherein, is the damping ratio of the ith inverter, is a real number set, σ i is the real part of the ith eigenvalue λ i of the system state space model, and ω i is the imaginary part of the ith eigenvalue λ i of the system state space model.

[0072] Step 2: Establish a dynamic model of the inverter distribution network system, including: a small signal model of the power measurement filter, a small signal model of the droop control link, a small signal model of the distribution network line, and a small signal model of the distribution network load; obtain the time when the frequency deviation of the inverter distribution network reaches the maximum and the control parameters of the inverter, and based on the dynamic model of the inverter distribution network system, calculate the maximum frequency deviation and steady-state frequency deviation of the inverter distribution network as system stability indicators; wherein the control parameters of the inverter include: disturbance power, droop coefficient, system equivalent damping, system inertia constant, system equivalent damping, natural oscillation frequency, equivalent time constant and equivalent turbine coefficient.

[0073] Specifically, step 2 includes:

[0074] Step 2.1, respectively establish the dynamic model of power measurement filtering, the dynamic model of droop control link, the dynamic model of distribution network line and the dynamic model of distribution network load;

[0075] Specifically, a low-pass filter is used in the power controller module to perform power measurement filtering. The dynamic model of power measurement filtering is as follows:

[0076]

[0077] Where P and Q are the node active power and reactive power measured by the inverter, respectively, c is the cutoff frequency of the low-pass filter, v oD and v oQ are the d-axis component and q-axis component of the node voltage based on the common reference point voltage, i od and i oq are the d-axis component and q-axis component of the node current based on the common reference point current, and s is the Laplace operator.

[0078] Specifically, for the droop control link of the power outer loop of the inverter frequency and voltage, the dynamic model of the droop control link is as follows:

[0079]

[0080] Where, is the frequency of the i-th inverter, ω n is the reference nominal frequency, is the d-axis component of the i-th inverter voltage, V n is the reference nominal voltage of the inverter, and are the active power control loop droop parameters and reactive power control loop droop parameters of the i-th inverter.

[0081] Specifically, the dynamic model of the distribution network line is as follows:

[0082]

[0083] where v Di and v Qi are the d-axis and q-axis components of the node i voltage based on the common reference point voltage, respectively, v Dj and v Qj are the d-axis and q-axis components of the node j voltage based on the common reference point voltage, respectively, i lineDij and i lineQij are the d-axis and q-axis components of the line ij current based on the common reference point current, R lineij , L lineij are the resistance and inductance of the line ij, respectively, and ω com is the frequency under the common coordinate system.

[0084] Specifically, the dynamic model of the distribution network load is as follows:

[0085]

[0086] where i loadDi and i loadQi are the d-axis and q-axis components of the load node i current based on the common reference point current, respectively, R loadi , L load are the resistance and inductance of the load node i, respectively.

[0087] Step 2.2, after the dynamic model of the power measurement filter, the dynamic model of the droop control link, the dynamic model of the distribution network line and the dynamic model of the distribution network load are once Taylor expanded, the corresponding small signal model is obtained; the small signal model obtained by integrating each small signal model is the small signal model of the inverter distribution network system as the dynamic model of the inverter distribution network system;

[0088] Specifically, the dynamic model of the inverter distribution network system satisfies the following relationship:

[0089]

[0090] where Δx sys , Δu sys are the system state variables and input variables, · represents the differential operation, A sys , B sys are the system state space matrices.

[0091] In the embodiment, A sys , B sys are the fine modeling forms of the state space matrices used for system characteristic root and damping ratio calculation in step 1.

[0092] Step 2.3, obtaining the time when the frequency deviation of the inverter distribution network reaches the maximum and the control parameters of the inverter, based on the dynamic model of the inverter distribution network system, calculating the maximum frequency deviation and the steady-state frequency deviation of the inverter distribution network as the system stability index; wherein the control parameters of the inverter include: disturbance power, droop coefficient, system equivalent damping, system inertia constant, system equivalent damping, natural oscillation frequency, equivalent time constant and equivalent turbine coefficient.

[0093] The frequency dynamics under disturbance conditions are mainly controlled by the primary frequency regulation of all online units. By aggregating all individual generators into a single generator, the frequency dynamics can be modeled using a swing equation. The aggregated frequency is also known as the center of inertia frequency. Considering the distribution network power system dominated by inverters for generator groups, distributed new energy units can provide frequency support by operating in load shedding mode or installing energy storage. The electromagnetic transient of power electronic equipment is fast enough, and the present application mainly focuses on the control strategy of new energy units and energy storage using droop control for network support.

[0094] Specifically, the P / f droop control parameters of the inverter include but are not limited to: disturbance power, droop coefficient, system equivalent damping, system inertia constant, system equivalent damping, natural oscillation frequency, equivalent time constant and equivalent turbine coefficient.

[0095] Specifically, the system stability index of the inverter distribution network includes: maximum frequency deviation, steady-state frequency deviation.

[0096] Based on the P / f droop control parameters of the inverter, the maximum frequency deviation Δf max and the steady-state frequency deviation Δf qss constitute the system stability index, respectively satisfying the following relationship:

[0097]

[0098] In the formula, ΔP L is the disturbance power; R P is the droop coefficient R P,i of the i-th inverter; D and H are the system equivalent damping and system inertia constant, respectively; ξ, ω n , T and F are the system equivalent damping, natural oscillation frequency, equivalent time constant and equivalent turbine coefficient, respectively; t max is the time when the frequency deviation of the inverter distribution network reaches the maximum; N DG is the set of inverters; K P,i is the participation factor of the i-th inverter, which is 1 when the inverter is running and 0 when the inverter is shut down.

[0099] Specifically, the Monte Carlo method is used to sample the inverter control parameters, and simulation is performed on the sampling samples to obtain associated data of the inverter control parameters and the system stability index, and a training data set is established based on the associated data.

[0100] Step 3, based on the double-layer machine learning method framework, an inverter power distribution network stability constraint fitting model is established, including an outer model and an inner model; wherein,

[0101] In the outer model, the input data is divided into multiple linear regions according to the stable working points of the power distribution network system and the inverter; the input data includes the operating data of the power distribution network and the control parameters of the inverter;

[0102] In the inner model, the system stability index in each linear region is linearly mapped and fitted by using a regularized ridge regression method, and the inverter stability index in each linear region is linearly mapped and fitted by using a regularized softmax regression method;

[0103] Using the trained inverter power distribution network stability constraint fitting model, the linear constraints of the inverter power distribution network stability in each linear region are output according to the input data.

[0104] In the embodiment, according to the double-layer multi-region linear machine learning representation algorithm framework, through the mode of outer data multi-region linear division-inner linear mapping, the inverter stability index and the system stability index, which are two types of nonlinear indexes, are accurately linearly fitted; wherein, the inverter stability index and the system stability index correspond to the stable working points of the inverter and the stable working points of the power distribution network system respectively, and the operating data of the power distribution network and the control parameters of the inverter are nonlinear data or functions, which cannot be embedded into a general optimization operation problem, so it is necessary to linearly divide these nonlinear data or functions to obtain multiple linear regions, and the operating data of the power distribution network and the control parameters of the inverter present linear characteristics in each linear region.

[0105] In the embodiment, the system stability index is regarded as a regression problem of numerical index, so the regularized ridge regression method is used to linearly map and fit the system stability index in each linear region, and the inverter stability index is regarded as a classification problem of category index, so the regularized softmax regression method is used to linearly map and fit the inverter stability index in each linear region.

[0106] Through the above fitting, the inverter stability index and the system stability index are converted into linear constraint forms that can be embedded into a general optimization problem.

[0107] Specifically, in the outer model, the input data is divided into multiple linear regions according to the stable working points of the power distribution network system and the inverter, including:

[0108] The input data vector {x k} is clustered into W linear regions C1, C2, …, C j , …, C W , x k is the kth sample, and simultaneously satisfies the following two optimization objectives:

[0109] 1) In the same linear region C j , the coefficients and intercepts can achieve the fitting of all samples and indicators;

[0110] 2) The W linear regions C1, C2, …, C j , …, C W are represented in the form of a polyhedron of linear separation as the region properties.

[0111] Specifically, the regularized ridge regression method is used to perform linear mapping fitting on the system stability indicators in each linear region, including:

[0112] In the W linear regions C1, C2, …, C j , …, C W , for each system stability indicator , the regularized ridge regression method is used to perform linear mapping fitting, satisfying the following relationship:

[0113]

[0114] In the formula, is the linear mapping fitting of the system stability indicator, are the coefficients and intercepts obtained by using the regularized ridge regression method to perform linear mapping fitting on the ith system stability indicator in the jth linear region C j , J j is the sample set in the jth linear region C j , α>0 is an l2-regularization parameter, y ki is the ith system stability indicator corresponding to the kth sample, x k is the kth sample, k∈J j indicates that the sample x k comes from the sample set J j in the jth linear region C j .

[0115] Specifically, the regularized softmax regression method is used to perform linear mapping fitting on the inverter stability indicators in each linear region, including:

[0116] In the W linear regions C1, C2, …, C j , …, CW For each inverter stability index The linear mapping fitting is performed by using the softmax regression method with regularization, and the following relationship is met:

[0117]

[0118] In the formula, is the linear mapping fitting of the inverter stability index, I(i) is a category set of the i-th inverter stability index, is the coefficient and intercept obtained by performing linear mapping fitting on the j-th linear region C j The coefficient and intercept obtained by performing linear mapping fitting on the h-th inverter stability index in the j-th linear region, is the coefficient and intercept obtained by performing linear mapping fitting on the t-th inverter stability index in the j-th linear region C i is the number of categories of the i-th inverter stability index, [y dk ] i is the category value of the i-th inverter stability index of the k-th sample, is the h-th category of the i-th inverter stability index, x k is the k-th sample, J j is the j-th linear region C j is the sample set, k∈J j indicates that the sample x k comes from the j-th linear region C j is the sample set J j , and alpha is an l2-regularization parameter.

[0119] By setting alpha>0, the ridge regression and the softmax regression are strict convex problems, and therefore, the optimal solutions are unique.

[0120] The block coordinate descent method is used to train the inverter power distribution network stability constraint fitting model, so as to determine the parameters of the inverter power distribution network stability constraint fitting model, with the minimum loss function as the target. The input data is input into the trained inverter power distribution network stability constraint fitting model, and the linear constraint of the inverter power distribution network stability is obtained.

[0121] In the embodiment, the training and construction of the double-layer multi-region linear machine learning representation are realized, the optimization minimization of the sub-problems is alternately performed, since the sub-optimization problem in the block coordinate descent is solved as a global optimum, therefore, the algorithm converges to a local optimum solution; the double-layer multi-region linear machine learning representation algorithm proposed in the application can converge to a local optimum solution of the following mixed integer optimization problem within a limited number of steps.

[0122] Step 4, using the big M method, respectively generate system stability index and inverter stability index index code, the index code embedded in the objective function, as the embedded linear constraints of the objective function.

[0123] Specifically, using the big M method, the system stability index is converted into the following relationship:

[0124]

[0125] In the formula, p ji is the auxiliary variable corresponding to the i-th system stability index under the j-th linear region, δ j is the classification mark of the system stability index belonging to the j-th linear region, and is a binary vector, δ j ∈{0,1} K , K is the number of linear regions, satisfying x is the input data, and are the lower limit constraint coefficient and the upper limit constraint coefficient of the i-th system stability index in the j-th linear region under the stable state determined by using the big M method.

[0126] In the embodiment, the binary vector δ j and the coefficients and intercepts obtained by using the regularized ridge regression method to perform linear mapping fitting on the i-th system stability index under the j-th linear region C j The lower limit constraint coefficient and the upper limit constraint coefficient of the i-th system stability index in the j-th linear region under the stable state are determined by using the big M method and Thus, the system stability index in each linear region is coded, and a mixed integer linear inequality is obtained. In the mixed integer linear inequality, the auxiliary variable p ji is the index code representing the threshold range corresponding to the i-th system stability index under the j-th linear region, and the index code can be embedded into the objective function to be optimized, thereby realizing the embedding of the system stability index.

[0127] Using the big M method, the inverter stability index is converted into the following relationship:

[0128]

[0129] In the formula, v ih is the classification mark of the h-th type inverter stability index belonging to the i-th inverter, and is a binary vector, v ih ∈{0,1}, x is the input data, I(i) is the category set of the i-th inverter stability index, δ j ​is the classification mark of the system stability index belonging to the jth linear region, which is a binary vector, δ j ∈{0,1} K , K is the number of linear regions, satisfying is the constraint coefficient between the stability index of the h-th inverter and the stability index of the t-th inverter determined by the large M method, satisfying B is the input dataset.

[0130] In the embodiment, the binary vector δ is used j and ν ih , use the regularized softmax regression method to calculate the j-th linear region C j The coefficients and intercepts obtained by linear mapping fitting of the stability index of the h-th inverter are The coefficients and intercepts obtained by linearly mapping the stability index of the t-type inverter in the j-th linear region using the regularized softmax regression method are: And the constraint coefficient between the stability index of the h-th inverter and the stability index of the t-th inverter determined by the big M method Thus, the inverter stability index is encoded and a mixed integer linear inequality is obtained. In the mixed integer linear inequality, the binary vector ν ih is the index code that characterizes the stability of the h-th type inverter of the i-th inverter. The index code can be embedded into the objective function to be optimized, thereby realizing the embedding of the inverter stability index.

[0131] Simple machine learning methods are difficult to accurately characterize complex stability constraints. Therefore, the present invention proposes a two-layer machine learning method framework to establish an inverter distribution network stability constraint fitting model to obtain system stability indicators and inverter stability indicators; and in order to avoid introducing too many variables that make it difficult to embed system stability indicators and inverter stability indicators into the objective function, the present invention proposes using the big M method to process the system stability indicators and inverter stability indicators to obtain the corresponding mixed integer linear form, and use the auxiliary variables in the mixed integer linear form as index codes to embed them into the objective function, thereby realizing the embedding processing of system stability indicators and inverter stability indicators. The index code is not only a classification mark for each indicator, but also represents the threshold range corresponding to each indicator, and completely retains the numerical characteristics of the system stability indicator and inverter stability indicator, meeting the needs of optimization operation problems in different scenarios.

[0132] The present invention also proposes an embedded linear constraint generation system for inverter distribution network stability. The linear constraint is a constraint condition of the objective function, including:

[0133] The index establishing module is configured to establish a system state space model of the inverter power distribution network, define a damping ratio of the inverter as an inverter stability index according to a characteristic value of the system state space model, and establish a dynamic model of the inverter power distribution network system, including a power measurement filter small signal model, a droop control link small signal model, a power distribution network line small signal model, and a power distribution network load small signal model.

[0134] The stability index generation module is configured to establish an inverter power distribution network stability constraint fitting model based on a double-layer machine learning method framework, including an outer model and an inner model.

[0135] The index embedding module is configured to generate index encodings of the system stability index and the inverter stability index respectively by using the big M method, and embed the index encodings into a target function as embedded linear constraints of the target function.

[0136] The IEEE 37-node power distribution network system is selected to briefly verify the present application.

[0137] The system includes 37 nodes, and a grid-connected inverter based on droop control is connected to the node {1318212933}. and The adjustable range of the droop parameters -6 , 1e -4 , 1e -5 , and 2e -4). The simulation platform adopts MATLAB-Simulink platform. Based on the typical working conditions of the system, the Monte Carlo method is used to sample and simulate the droop parameters of the inverter, and the sample data set (x k ,y k ) corresponding to the droop parameters and the related system stability performance indicators is obtained. Based on the data set, the embeddable linear constraint generation method for small signal stability and frequency stability of the inverter power distribution system proposed in the application is used. The application generates a data set containing 10,000 samples, uses 80% of the available data for training, and the remaining 20% for testing the prediction of the results. In the verification description of the application, the frequency minimum point indicator is a numerical indicator, and the small signal stability indicator and the damping ratio indicator are category indicators. Those skilled in the art can change them according to specific problems in specific use, which will not be described here.

[0138] The accurate performance verification of the embeddable linear constraint generation method for small signal stability and frequency stability of the inverter power distribution system is shown in Table 1. The average error is used for accuracy analysis of the numerical indicator of the frequency minimum point, and the accuracy rate is used for accuracy analysis of the category indicators of small signal stability and damping ratio. The results show that the double-layer multi-region linear machine learning representation proposed in the application has high accuracy for both numerical indicators and categories.

[0139] Table 1 Accuracy of small signal stability and frequency stability indicators of inverter power distribution system

[0140]

[0141] In order to compare the embeddable constraint generation method, the application considers three types of machine learning algorithms, ridge regression (for numerical indicators), softmax regression (for category indicators), and artificial neural network (for numerical indicators and category indicators), to generate embeddable constraints. Table 2 compares the effects of the method proposed in the application and the above methods.

[0142] Table 2 Accuracy of small signal stability and frequency stability indicators of inverter power distribution system under different methods

[0143]

[0144] As can be seen from the results in Table 2, the simple linear form-based machine learning regression and classification methods such as ridge regression and softmax regression have lower accuracy in characterizing the small signal stability and frequency stability indicators of the inverter distribution network system than the method proposed in the application. The double-layer multi-region linear machine learning characterization algorithm proposed in the application can make the linear fitting of the nonlinear indicators more accurate through the mode of outer data multi-region linear division-inner linear mapping. The nonlinear form-based machine learning regression and classification methods such as artificial neural networks have higher accuracy in characterizing the small signal stability and frequency stability indicators of the inverter distribution network system than the method proposed in the application, but will introduce too many binary variables, making the global optimization after embedding more complex and reducing the embeddability of the constraints. The double-layer multi-region linear machine learning characterization algorithm proposed in the application can guarantee the embeddability of the constraints while meeting the tolerance accuracy, making it possible to consider the small signal stability and frequency stability indicators in the droop parameter adjustment operation of the inverter distribution network system.

[0145] The existing power system stability constraint embedding methods such as simple machine learning regression and classification methods in the form of embeddable coding (support vector machine based on linear kernel, optimal decision tree, etc.) have simple structure and are easy to embed, but sacrifice the fitting accuracy of the target nonlinear features. Deep learning regression and classification methods based on complex structures (such as deep neural networks) can accurately capture nonlinear features, but will introduce too many binary variables in the embedding code, making the global optimization after embedding more complex and reducing the embeddability of the constraints.

[0146] The present disclosure can be a system, a method, and / or a computer program product. The computer program product can include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present disclosure.

[0147] Computer readable storage media can be tangible storage media which can retain and store instructions for use by an instruction execution device. Computer readable storage media can be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer readable storage media include the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire.

[0148] Computer readable program instructions described herein can be downloaded to respective computing / processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and / or a wireless network. The network can comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and / or edge servers. A network adapter card or network interface in each computing / processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing / processing device.

[0149] Computer readable program instructions for carrying out operations of the present disclosure can be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state setting data, or any combination of source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++ or the like, and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The computer readable program instructions can execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) can execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present disclosure.

[0150] Finally, it should be noted that the above-mentioned embodiments are merely used to illustrate the technical solutions of the present application, but not to limit it. Although the present application has been described in detail with reference to the above-mentioned embodiments, those skilled in the art should understand that the specific embodiments of the present application can be modified or replaced, and any modification or replacement without departing from the spirit and scope of the present application should be covered in the protection scope of the claims of the present application.

Claims

1. A method for generating embedded linear constraints for inverter distribution network stability, wherein the linear constraints are constraints of the objective function, characterized in that: include: Establish a system state space model of the inverter distribution network, and define the inverter's damping ratio as an inverter stability indicator based on the eigenvalues ​​of the system state space model. A dynamic model of the inverter distribution network system is established, including: a small signal model of the power measurement filter, a small signal model of the droop control link, a small signal model of the distribution network line, and a small signal model of the distribution network load; the time when the frequency deviation of the inverter distribution network reaches the maximum and the inverter control parameters are obtained; based on the dynamic model of the inverter distribution network system, the maximum frequency deviation and steady-state frequency deviation of the inverter distribution network are calculated as system stability indicators; the inverter control parameters include: disturbance power, droop coefficient, system equivalent damping, system inertia constant, natural oscillation frequency, equivalent time constant, and equivalent turbine coefficient; Based on a two-layer machine learning framework, an inverter distribution network stability constraint fitting model is established, including an outer model and an inner model. In the outer model, the input data is divided into multiple linear regions according to the stable operating point of the distribution network system and the stable operating point of the inverter. The input data includes the operating data of the distribution network and the control parameters of the inverter. In the inner model, a regularized ridge regression method is used to perform linear mapping fitting on the system stability index in each linear region, and a regularized softmax regression method is used to perform linear mapping fitting on the inverter stability index in each linear region. Using the trained inverter distribution network stability constraint fitting model, the system stability index and the inverter stability index are obtained according to the input data. The big-M method is used to generate index codes of system stability index and inverter stability index respectively, and the index codes are embedded into the objective function.

2. The embedded linear constraint generation method for inverter distribution network stability according to claim 1, characterized in that: The damping ratio of the inverter is defined as the inverter stability indicator according to the eigenvalue of the system state space model using the following relationship: Where, ξ i ∈R is the damping ratio of the i-th inverter, R is a real number set, σ i is the real part of the i-th eigenvalue of the system state space model, ω i is the imaginary part of the i-th eigenvalue of the system state space model.

3. The embedded linear constraint generation method for inverter distribution network stability according to claim 1, characterized in that: The dynamic model of power measurement filtering is as follows: Where P and Q are the node active power and reactive power measured by the inverter, respectively, c is the cutoff frequency of the low-pass filter, v oD and v oQ are the d-axis component and q-axis component of the node voltage based on the common reference point voltage, i od and i oq are the d-axis component and q-axis component of the node current based on the common reference point current, and s is the Laplace operator; The dynamic model of the droop control link is as follows: Where, is the frequency of the i-th inverter, ω n is the reference nominal frequency, is the d-axis component of the i-th inverter voltage, V n is the reference nominal voltage of the inverter, and are the active power control loop droop parameters and reactive power control loop droop parameters of the i-th inverter, are the active power and reactive power of the i-th inverter frequency respectively; The dynamic model of the distribution network line is as follows: Where, v Di 、v Qi are the d-axis component and q-axis component of the node i voltage based on the common reference point voltage, v Dj 、v Qj are the d-axis component and q-axis component of the node j voltage based on the common reference point voltage, i lineDij and i lineQij are the d-axis component and q-axis component of the line ij current based on the common reference point current, R lineij 、L lineij are the resistance and inductance of line ij, ω com is the frequency in the common coordinate system; The dynamic model of distribution network load is as follows: Where i loadDi and i loadQi They are the d-axis component and q-axis component of the load node i current based on the common reference point current, R loadi 、L load are the resistance and inductance of the load node i respectively.

4. The embedded linear constraint generation method for inverter distribution network stability according to claim 3, characterized in that: After Taylor expansion of the dynamic model of the power measurement filter, the dynamic model of the droop control link, the dynamic model of the distribution network line, and the dynamic model of the distribution network load, the corresponding small signal model is obtained; the small signal model of the inverter distribution network system obtained by integrating the various small signal models is used as the dynamic model of the inverter distribution network system.

5. The embedded linear constraint generation method for inverter distribution network stability according to claim 4, characterized in that: Based on the dynamic model of the inverter distribution network system, the maximum frequency deviation Δf of the inverter distribution network is calculated max and steady-state frequency deviation Δf qss The system stability index satisfies the following relationships: Where, ΔP L is the disturbance power; R P is the droop coefficient R of the i-th inverter P,i The synthesized system equivalent droop parameters; D and H are the system equivalent damping and system inertia constant respectively; ξ, ω n , T and F are the system equivalent damping, natural oscillation frequency, equivalent time constant and equivalent turbine coefficient respectively; t max The time when the frequency deviation of the inverter distribution network reaches the maximum; N DG is the inverter set; K P,i is the participation factor of the i-th inverter. When the inverter is running, the participation factor is 1, and when the inverter is stopped, the participation factor is 0.

6. The embedded linear constraint generation method for inverter distribution network stability according to claim 1, characterized in that: In the outer model, the input data is divided into multiple linear regions according to the stable operating points of the distribution network system and the inverter, including: The input data vector {x k }Clustered into W linear regions C1, C2, ..., C j ,……,C W and simultaneously meet the following two optimization goals: 1) In the same linear region C j In , the coefficients and intercepts can achieve the fitting of all samples and indicators; 2) W linear regions C1, C2, ..., C j ,……,C W Represented as linearly separable polyhedra of regional properties.

7. The embedded linear constraint generation method for inverter distribution network stability according to claim 6, characterized in that: Regularized ridge regression method is used to perform linear mapping fitting on the system stability indicators in each linear region, including: In W linear regions C1, C2, ..., C j ,……,C W For each system stability index The regularized ridge regression method is used for linear mapping fitting, which satisfies the following relationship: Where, is the linear mapping fitting of the system stability index, The regularized ridge regression method is used to calculate the j-th linear region C j The coefficient and intercept obtained by linear mapping fitting of the i-th system stability index, J j is the jth linear region C j , α>0 is a l 2- Regularization parameter, y ki is the i-th system stability index corresponding to the k-th sample, x k is the kth sample, k∈J j Represents sample x k From the jth linear region C j .

8. The embedded linear constraint generation method for inverter distribution network stability according to claim 7, characterized in that: The regularized softmax regression method is used to perform linear mapping fitting on the inverter stability indicators in each linear region, including: In W linear regions C1, C2, ..., C j ,……,C W For each inverter stability index The regularized softmax regression method is used for linear mapping fitting, which satisfies the following relationship: Where, is the linear mapping fitting of the inverter stability index, I(i) is the category set of the i-th inverter stability index, The regularized softmax regression method is used for the j-th linear region C j The coefficients and intercepts obtained by linear mapping fitting of the stability index of the h-th type inverter are: are the coefficients and intercepts obtained by linear mapping fitting of the stability index of the t-type inverter in the j-th linear region using the regularized softmax regression method, m i is the number of categories of the stability index of the i-th inverter, [y dk ] i is the category value of the i-th inverter stability index of the k-th sample, is the hth category of the stability index of the i-th inverter, x k is the kth sample, k∈J j Represents sample x k From the jth linear region C j , α is a positive number.

9. The embedded linear constraint generation method for inverter distribution network stability according to claim 1, characterized in that: The block coordinate descent method is used to train the stability constraint fitting model of the inverter distribution network. The goal is to minimize the loss function to determine the parameters of the stability constraint fitting model of the inverter distribution network.

10. The embedded linear constraint generation method for inverter distribution network stability according to claim 7, characterized in that: Using the Big M method, the system stability index is converted into the following relationship: Where p ji is the auxiliary variable corresponding to the i-th system stability index in the j-th linear region, δ j is the classification mark of the system stability index belonging to the jth linear region, which is a binary vector, δ j ∈{0,1} K , K is the number of linear regions, satisfying x is the input data, and are the lower limit constraint coefficient and upper limit constraint coefficient of the i-th system stability index in the j-th linear region under the stable state determined by the big M method; With auxiliary variable p ji In order to characterize the index code corresponding to the threshold range of the i-th system stability index in the j-th linear region, the index code is embedded into the objective function.

11. The embedded linear constraint generation method for inverter distribution network stability according to claim 8, characterized in that: Using the Big M method, the inverter stability index is converted into the following relationship: Where, ν ih The h-th inverter stability index belongs to the classification mark of the i-th inverter, which is a binary vector. x is the input data, I(i) is the category set of the i-th inverter stability index, δ j is the classification mark of the system stability index belonging to the jth linear region, which is a binary vector, δ j ∈{0,1} K , K is the number of linear regions, satisfying is the constraint coefficient between the stability index of the h-th inverter and the stability index of the t-th inverter determined by the large M method, satisfying B is the input data set; Binary vector ν ih is the index code that characterizes the stability of the h-th inverter of the i-th inverter, and the index code is embedded into the objective function.

12. An embedded linear constraint generation system for inverter distribution network stability, wherein the linear constraint is a constraint condition of the objective function, characterized in that: include: An indicator establishment module is used to establish a system state space model of the inverter distribution network and define the damping ratio of the inverter according to the characteristic value of the system state space model as an inverter stability indicator; It is also used to establish a dynamic model of the inverter distribution network system, including: a small signal model of the power measurement filter, a small signal model of the droop control link, a small signal model of the distribution network line, and a small signal model of the distribution network load; obtain the time when the frequency deviation of the inverter distribution network reaches the maximum and the control parameters of the inverter, and based on the dynamic model of the inverter distribution network system, calculate the maximum frequency deviation and steady-state frequency deviation of the inverter distribution network as system stability indicators; among which, the control parameters of the inverter include: disturbance power, droop coefficient, system equivalent damping, system inertia constant, natural oscillation frequency, equivalent time constant and equivalent turbine coefficient; The stability index generation module is used to establish an inverter distribution network stability constraint fitting model based on a two-layer machine learning method framework, including: an outer model and an inner model; wherein, in the outer model, the input data is divided into multiple linear regions according to the stable operating point of the distribution network system and the stable operating point of the inverter; the input data includes the operating data of the distribution network and the control parameters of the inverter; in the inner model, the regularized ridge regression method is used to perform linear mapping fitting on the system stability index in each linear region, and the regularized softmax regression method is used to perform linear mapping fitting on the inverter stability index in each linear region; using the trained inverter distribution network stability constraint fitting model, the system stability index and the inverter stability index are obtained according to the input data; The indicator embedding module is used to generate index codes of the system stability indicator and the inverter stability indicator respectively by using the big M method, and embed the index codes into the objective function as the embedded linear constraints of the objective function.

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