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

Abstract

The invention discloses an embedded linear constraint generation method and system for inverter power distribution network stability. The method comprises the following steps: determining an inverter stability index and a system stability index; based on a double-layer machine learning method framework, establishing an inverter power distribution network stability constraint fitting model which comprises an outer layer model and an inner layer model; using the trained inverter power distribution network stability constraint fitting model to obtain a system stability index and an inverter stability index according to the input data; and respectively generating index codes of the system stability index and the inverter stability index by adopting a large M method, and embedding the index codes into the target function. According to the method, the constraint embeddability is ensured while the prediction error tolerance precision is met, the prediction accuracy and the embedding complexity are ideally balanced, an inverter power distribution network system operator is helped to consider small interference stability and frequency stability indexes in inverter droop parameter adjustment, and the stability risk is reduced.

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 and more distributed renewable energy sources are connected to the distribution network system through power electronic converters, the distribution network is gradually transformed into a power system dominated by inverter power generation, resulting in lower inertia and weaker damping, which greatly reduces the system's ability to resist interference and easily causes the system to exceed the frequency limit after interference. In addition, since the inverter has the characteristics of fast response of power electronic devices, it increases the risk of continuous and severe oscillation, exacerbating the problem of small disturbance stability of the system and endangering the safety of distribution network system operation.

[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 the power system dominated by synchronous machines, the method of incorporating transient stability and voltage stability constraints into the operation and optimal power flow model is adopted to determine the transient transmission power or re-dispatch the generator to maintain the system stability limit. With the birth of the power system 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-building 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] In addition, in power systems with high penetration of inverters, small disturbance stability is very important, and damping plays a more critical role than inertia. In the spatial configuration of inverter damping, the damping coefficient of each inverter in the system is adjusted to improve the small disturbance stability performance. In the planning stage, the damping of the inverter at a specific location is enhanced to effectively improve the strength of the power grid, thereby improving stability. In the real-time operation process, the damping coefficient of the inverter is directly adjusted in real time to achieve the best performance. The prior art establishes a non-convex model to configure oscillation damping, such as iteratively adjusting the modal damping ratio using the sensitivity factor of the oscillation mode, but it leads to the complexity of iteration, or by analyzing and calculating the oscillation mode and time domain response simulation, but its non-convex characteristics and complex calculation form still limit the embeddability of stability constraints. The prior art assumes that all inverter units have the same inertia-damping ratio. In addition, due to the limitations of non-convex problems or uniform inertial damping assumptions, incorporating these methods into system operation brings significant challenges, which hinders the development of adjusting inverter oscillation damping operations. Summary of the invention

[0005] In order to solve the deficiencies in the prior art, the present invention provides an embedded linear constraint generation method and system for the stability of an inverter distribution network, which realizes the distribution network inverter parameter adjustment operation considering the stability constraint, and the embedded linear constraints of the system small disturbance stability and frequency stability based on the inverter power outer loop parameters, which realizes the consideration of the inverter distribution network system small disturbance stability and frequency stability constraints in the inverter power outer loop parameter adjustment operation and reduces the optimization calculation complexity.

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

[0007] The present invention proposes an embedded linear constraint generation method for inverter distribution network stability. The linear constraint is a constraint condition of the objective function, including:

[0008] Establish a system state space model of the inverter distribution network, and define the damping ratio of the inverter according to the eigenvalue of the system state space model as the inverter stability index;

[0009] Establish a dynamic model of the inverter distribution network system, including: a small signal model of power measurement filtering, 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;

[0010] Based on a two-layer machine learning method framework, an inverter distribution network stability constraint fitting model is established, 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 operation 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; the trained inverter distribution network stability constraint fitting model is used to obtain the system stability index and the inverter stability index according to the input data;

[0011] 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.

[0012] Preferably, the damping ratio of the inverter is defined as the inverter stability index according to the characteristic value of the system state space model using the following relationship:

[0013]

[0014] In the formula, is the damping ratio of the ith inverter, is a set of real numbers, 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.

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

[0016]

[0017] In the formula, P and Q are the node active power and reactive power measured by the inverter, respectively, ω c is the low-pass filter cutoff frequency, 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;

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

[0019]

[0020] In the formula, is the i-th inverter frequency, ω n is the reference nominal frequency, is the d-axis component of the i-th inverter voltage, V n is the inverter reference nominal voltage, and are the active control loop droop parameters and reactive control loop droop parameters of the i-th inverter;

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

[0022]

[0023] In the formula, 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, ilineDij 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;

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

[0025]

[0026] In the formula, i loadDi and i loadQi 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 load node i respectively.

[0027] Preferably, 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 Taylor expanded to obtain the corresponding small signal model; the small signal model of the inverter distribution network system obtained by integrating the small signal models is used 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 of the inverter distribution network is calculated. max and steady-state frequency deviation Δf qss The system stability index satisfies the following relations:

[0029]

[0030] In the formula, 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 power distribution network reaches the maximum; N DG is the inverter set; K P,i is the participation factor of the ith inverter. When the inverter is running, the participation factor is 1, and when the inverter is stopped, the participation factor is 0.

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

[0032] The input data vector {x k}Clustering into W linear regions C1, C2, ..., C j ,……,C W And simultaneously meet the following two optimization goals:

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

[0034] 2) W linear regions C1, C2, ..., C j ,……,C W Represented as linearly separable polyhedral forms of regional properties.

[0035] Preferably, a regularized ridge regression method is used to perform linear mapping fitting on the system stability index in each linear region, including:

[0036] 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, satisfying the following relationship:

[0037]

[0038] In the formula, is the linear mapping fit 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 l2-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 .

[0039] Preferably, a regularized softmax regression method is used to perform linear mapping fitting on the inverter stability index in each linear region, including:

[0040] 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, satisfying the following relationship:

[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, 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 inverter are: are the coefficient and intercept obtained by linear mapping fitting of the stability index of the t-th inverter in the j-th linear region using the regularized softmax regression method, m 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 hth category of the i-th inverter stability index, 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.

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

[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 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 ith system stability index in the jth linear region under the stable state determined by the big M method;

[0047] With auxiliary variable p jiIn order to characterize the index code corresponding to the threshold range of the ith system stability index in the jth linear region, the index code is embedded into the objective function.

[0048] Preferably, the big M method is used to convert the inverter stability index into the following relationship:

[0049]

[0050] Where, ν ih is the h-th inverter stability index, which belongs to the classification mark of the i-th inverter and is a binary vector. 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 big M method, satisfying B is the input data set;

[0051] Binary vector ν ih is the index code that characterizes the stability of the h-th inverter of the ith inverter, and the index code is embedded into the objective function.

[0052] 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:

[0053] An index 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 index; it is also used to establish a dynamic model of the inverter distribution network system, including: a small signal model of power measurement filtering, a small signal model of a droop control link, a small signal model of a distribution network line, and a small signal model of a 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;

[0054] 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 operation 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; the trained inverter distribution network stability constraint fitting model is used to obtain the system stability index and the inverter stability index according to the input data;

[0055] The index embedding module is used to generate index codes of the system stability index and the inverter stability index respectively by adopting the big M method, and embed the index codes into the objective function as the embedded linear constraints of the objective function.

[0056] The beneficial effects of the present invention are that, compared with the prior art, at least the double-layer multi-region linear machine learning characterization algorithm and its encoding method proposed in the present invention achieve the embeddability of constraints while satisfying the prediction error tolerance accuracy, and achieve an ideal trade-off between prediction accuracy and embedding complexity, which helps the inverter distribution network system operator to consider small interference stability and frequency stability indicators in the inverter droop parameter adjustment, thereby reducing stability risks. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0058] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The embodiments described in this application are only embodiments of a part of the present invention, rather than all embodiments. Based on the spirit of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the protection scope of the present invention.

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

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

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

[0062]

[0063] y=Cx+Du

[0064] In the formula, are the state vector, output vector and control input vector of the linearized system respectively; . represents the differential operation; All are system state space matrices; is a set of real numbers, n, m, and p are the dimensions of the state vector, output vector, and control input vector, respectively.

[0065] set up represents the i-th eigenvalue of the system state space model, is a complex set, and are the real and imaginary parts of the ith eigenvalue respectively; λ i The corresponding left and right eigenvectors Satisfies the following relationship:

[0066] Au i =λ i u i

[0067] v i T A=v i T λ i

[0068] In the formula, u i is the i-th eigenvalue λ i The left eigenvector of i is the i-th eigenvalue λ i The right eigenvector of ;

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

[0070]

[0071] In the formula, is the damping ratio of the ith inverter, is a set of real numbers, σ i is the i-th eigenvalue λ of the system state space model i The real part of i is the i-th eigenvalue λ of the system state space model i The imaginary part of .

[0072] Step 2, establish a dynamic model of the inverter distribution network system, including: a small signal model of power measurement filtering, 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 establishing a dynamic model of power measurement filtering, a dynamic model of a droop control link, a dynamic model of a distribution network line, and a dynamic model of a distribution network load;

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

[0076]

[0077] In the formula, P and Q are the node active power and reactive power measured by the inverter, respectively, ω c is the low-pass filter cutoff frequency, 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] In the formula, is the i-th inverter frequency, 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 control loop droop parameters and reactive control loop droop parameters of the i-th inverter.

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

[0082]

[0083] In the formula, 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.

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

[0085]

[0086] In the formula, i loadDi and i loadQi 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 load node i respectively.

[0087] Step 2.2, 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 small signal models is used 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] In the formula, Δx sys , Δu sys are system state variables and input variables, · represents differential operation, A sys , B sys is the system state space matrix.

[0091] In the embodiment, A sys , B sys It is a refined modeling form of the state space matrix used in step 1 to calculate the system characteristic roots and damping ratio.

[0092] Step 2.3, obtain the time when the frequency deviation of the inverter distribution network reaches the maximum and the control parameters of the inverter, and calculate the maximum frequency deviation and steady-state frequency deviation of the inverter distribution network based on the dynamic model of the inverter distribution network system 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.

[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 aggregate frequency is also called the inertial center frequency. Considering the distribution power system dominated by inverter-based generator sets, distributed renewable energy units can provide frequency support by operating in load reduction mode or installing energy storage. The electromagnetic transients of power electronic equipment are fast enough, and the present invention mainly focuses on the control strategy of renewable 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 indicators of the inverter distribution network include: maximum frequency deviation and steady-state frequency deviation.

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

[0097]

[0098] In the formula, 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 power distribution network reaches the maximum; N DG is the inverter set; K P,i is the participation factor of the ith inverter. When the inverter is running, the participation factor is 1, and when the inverter is stopped, the participation factor is 0.

[0099] Specifically, the inverter control parameters are sampled using the Monte Carlo method, and simulation is performed using the sampled samples to obtain correlation data between the inverter control parameters and the system stability index, and a training data set is established using the correlation data.

[0100] Step 3: Based on the two-layer machine learning method framework, establish the inverter distribution network stability constraint fitting model, 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 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;

[0102] 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;

[0103] The trained inverter distribution network stability constraint fitting model is used to output the linear constraints of the inverter distribution network stability in each linear region according to the input data.

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

[0105] In the embodiment, the system stability index is regarded as a regression problem of a numerical index, and therefore a regularized ridge regression method is used to perform linear mapping fitting on the system stability index in each linear region. The inverter stability index is regarded as a classification problem of a category index, and therefore a regularized softmax regression method is used to perform linear mapping fitting on 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 a linear constraint form that can be embedded in a general optimization problem.

[0107] Specifically, 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, including:

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

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

[0110] 2) W linear regions C1, C2, ..., C j ,……,C W Represented as linearly separable polyhedral forms of regional 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 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, satisfying the following relationship:

[0113]

[0114] In the formula, is the linear mapping fit 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 Intrinsic sample set, α>0 is a l2-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 Internal sample set J 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 W linear regions C1, C2, ..., C j ,……,CW For each inverter stability index The regularized softmax regression method is used for linear mapping fitting, satisfying the following relationship:

[0117]

[0118] 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, 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 inverter are: are the coefficient and intercept obtained by linear mapping fitting of the stability index of the t-th inverter in the j-th linear region using the regularized softmax regression method, m 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 hth category of the i-th inverter stability index, x k is the kth sample, J j is the jth linear region C j Inner sample set, k∈J j Represents sample x k From the jth linear region C j Internal sample set J j , α>0 is a l2-regularization parameter.

[0119] By setting α>0, both ridge regression and softmax regression are strictly convex problems, and therefore, their optimal solutions are unique.

[0120] The block coordinate descent method is used to train the inverter distribution network stability constraint fitting model, with the goal of minimizing the loss function to determine the parameters of the inverter distribution network stability constraint fitting model. The input data is input into the trained inverter distribution network stability constraint fitting model to obtain the linear constraints of the inverter distribution network stability.

[0121] In the embodiment, the training construction of a two-layer multi-region linear machine learning representation is implemented. By alternately optimizing and minimizing sub-problems, the algorithm converges to a local optimal solution because the sub-optimization problems in the block coordinate descent are solved as global optimal solutions. The two-layer multi-region linear machine learning representation algorithm proposed in the present invention can converge to the local optimal solution of the following mixed integer optimization problem within a limited number of steps.

[0122] Step 4: Use the big M method to generate index codes for the system stability index and the inverter stability index respectively, and embed the index codes into the objective function as embedded linear constraints of the objective function.

[0123] Specifically, the big M method is used to convert the system stability index into the following relationship:

[0124]

[0125] 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 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 constraint coefficient and upper constraint coefficient of the ith system stability index in the jth linear region under the stable state determined by the big M method.

[0126] In the embodiment, the binary vector δ is used j And the regularized ridge regression method is used to find the jth linear region C j The coefficients and intercepts obtained by linear mapping fitting of the i-th system stability index are The big M method is used to determine the lower and upper limit constraint coefficients of the stability index of the ith system in the jth linear region under the stable state. and Thus, the system stability index in each linear region is encoded, and a mixed integer linear inequality is obtained. In the mixed integer linear inequality, the auxiliary variable p ji It is an index code that characterizes the threshold range corresponding to the ith system stability index in the jth linear region. The index code can be embedded into the objective function to be optimized, thereby realizing the embedding of the system stability index.

[0127] The big M method is used to convert the inverter stability index into the following relationship:

[0128]

[0129] Where, ν ih is the h-th inverter stability index, which belongs to the classification mark of the i-th inverter and is a binary vector. ih ∈{0,1}, x is the input data, I(i) is the category set of the i-th inverter stability index, δ jis 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 big M method, satisfying B is the input data set.

[0130] In the embodiment, the binary vector δ is used j and ν ih , use the regularized softmax regression method to calculate the jth 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-th 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 an index code that characterizes the stability of the h-th inverter of the ith 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. 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 into the objective function, thereby realizing the embedding processing of the system stability indicators and inverter stability indicators. The index code is not only a classification mark for each indicator, but also characterizes the threshold range corresponding to each indicator, and completely retains the numerical characteristics of the system stability indicators and inverter stability indicators to meet 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] An index 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 index; it is also used to establish a dynamic model of the inverter distribution network system, including: a small signal model of power measurement filtering, a small signal model of a droop control link, a small signal model of a distribution network line, and a small signal model of a 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;

[0134] 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 operation 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; the trained inverter distribution network stability constraint fitting model is used to obtain the system stability index and the inverter stability index according to the input data;

[0135] The index embedding module is used to generate index codes of the system stability index and the inverter stability index respectively by adopting the big M method, and embed the index codes into the objective function as the embedded linear constraints of the objective function.

[0136] The IEEE 37-node distribution network system is selected to briefly verify the present invention, and the accuracy and embeddability of the embeddable linear constraint generation method for small disturbance stability and frequency stability of the inverter distribution network system proposed in the present invention are mainly verified.

[0137] The system contains 37 nodes. The grid-connected inverter based on droop control is connected to node {1318212933}. The droop parameter and The adjustable range is (5e -6 ,1e -4 ) and (1e -5 ,2e -4The simulation calculation platform uses the MATLAB-Simulink platform. Based on the typical working conditions of the system, the Monte Carlo method is used to sample and simulate the inverter droop parameters to obtain a sample data set (x k ,y k ), based on the data set, the embedded linear constraint generation method for small disturbance stability and frequency stability of the inverter distribution network system proposed in the present invention is adopted. The present invention generates a data set containing 10,000 samples, uses 80% of the available data for training, and the remaining 20% ​​is used to predict the test results. In the verification description of the present invention, the frequency minimum point index is a numerical index, and the small disturbance stability index and the damping ratio index are category indicators. Those skilled in the art can make changes according to specific problems when using it, which will not be repeated here.

[0138] The accuracy of the embedded linear constraint generation method for small disturbance stability and frequency stability of the inverter distribution network system is verified as shown in Table 1. The average error is used for the accuracy analysis of the numerical index of the lowest frequency point, and the accuracy rate is used for the category index of small disturbance stability and damping ratio. The results show that the double-layer multi-region linear machine learning representation proposed in the present invention has high accuracy for both numerical indicators and categories.

[0139] Table 1 Accuracy of small disturbance stability and frequency stability indicators of inverter distribution network system

[0140]

[0141] In order to compare the embeddable constraint generation methods, the present invention 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) for embeddable constraint generation. Table 2 compares the effects of the method proposed in the present invention with the above methods.

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

[0143]

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

[0145] Existing power system stability constraint embedding methods, such as simple machine learning regression and classification methods in the form of embeddable coding (support vector machines based on linear kernels, optimal decision trees, etc.), have a simple structure and are easy to embed, but sacrifice the accuracy of fitting the target nonlinear characteristics; such as deep learning regression and classification methods based on complex structures (such as deep neural networks), while accurately capturing nonlinear characteristics, will introduce too many binary variables in the embedding code, making the global optimization after embedding more complicated and reducing the embeddability of the constraints.

[0146] The present disclosure may be a system, a method and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for causing a processor to implement various aspects of the present disclosure.

[0147] A computer-readable storage medium may be a tangible device that can hold and store instructions used by an instruction execution device. A computer-readable storage medium may be, for example, but not limited to, an electrical 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 of computer-readable storage media (a non-exhaustive list) include: a portable computer disk, 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 disk read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device, such as a punch card or a raised structure in a groove on which instructions are stored, and any suitable combination of the foregoing. As used herein, a computer-readable storage medium is not to be interpreted as a transient signal per se, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide or other transmission medium (e.g., a light pulse through a fiber optic cable), or an electrical signal transmitted through a wire.

[0148] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, optical fiber transmissions, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in the computer-readable storage medium in each computing / processing device.

[0149] The computer program instructions for performing the operation of the present disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-related instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages, such as Smalltalk, C++, etc., and conventional procedural programming languages, such as "C" language or similar programming languages. Computer-readable program instructions may be executed completely on a user's computer, partially on a user's computer, as an independent software package, partially on a user's computer, partially on a remote computer, or completely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., using an Internet service provider to connect via the Internet). In some embodiments, an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), may be customized by utilizing the state information of the computer-readable program instructions, and the electronic circuit may execute the computer-readable program instructions, thereby realizing various aspects of the present disclosure.

[0150] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents, and any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. An embedded linear constraint generation method for inverter distribution network stability, wherein the linear constraint is a constraint condition of the objective function, characterized in that: include: Establish a system state space model of the inverter distribution network, and define the damping ratio of the inverter according to the eigenvalue of the system state space model as the inverter stability index; Establish a dynamic model of the inverter distribution network system, including: a small signal model of power measurement filtering, 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; Based on a two-layer machine learning method framework, an inverter distribution network stability constraint fitting model is established, 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 operation 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; the trained inverter distribution network stability constraint fitting model is used to obtain the system stability index and the inverter stability index 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: According to the characteristic value of the system state space model, the damping ratio of the inverter is defined as the inverter stability index by the following relationship: In the formula, is the damping ratio of the ith inverter, is a set of real numbers, 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 the power measurement filter is as follows: In the formula, P and Q are the node active power and reactive power measured by the inverter, respectively, c is the low-pass filter cutoff frequency, 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: In the formula, is the i-th inverter frequency, 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 control loop droop parameters and reactive control loop droop parameters of the i-th inverter; The dynamic model of the distribution network line is as follows: In the formula, 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: In the formula, i loadDi and i loadQi 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 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 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, the corresponding small signal model is obtained; the small signal model of the inverter distribution network system obtained by integrating the 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 relations: 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 parameter; 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 power distribution network reaches the maximum; N DG is the inverter set; K P,i is the participation factor of the ith 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 point of the distribution network system and the stable operating point of the inverter, including: The input data vector {x k }Clustering 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 polyhedral forms of regional properties.

7. The embedded linear constraint generation method for inverter distribution network stability according to claim 6, characterized in that: The 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, satisfying the following relationship: In the formula, is the linear mapping fit 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 l2-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 6, 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, satisfying the following relationship: Where V yd 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 inverter are: are the coefficient and intercept obtained by linear mapping fitting of the stability index of the t-th inverter in the j-th linear region using the regularized softmax regression method, m 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 hth category of the i-th inverter stability index, 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 minimum loss function is taken as the goal 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: 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 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 ith system stability index in the jth 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 ith system stability index in the jth 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: The big M method is used to convert the inverter stability index into the following relationship: Where, ν ih is the h-th inverter stability index, which belongs to the classification mark of the i-th inverter and is a binary vector. 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 big 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 ith 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 index 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 index; It is also used to establish a dynamic model of the inverter distribution network system, including: a small signal model of power measurement filtering, a small signal model of a droop control link, a small signal model of a distribution network line, and a small signal model of a 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; 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 operation 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; the trained inverter distribution network stability constraint fitting model is used to obtain the system stability index and the inverter stability index according to the input data; The index embedding module is used to generate index codes of the system stability index and the inverter stability index respectively by adopting 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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