Comprehensive energy microgrid group scheduling optimization method based on small disturbance stability security domain

Abstract

The invention provides an integrated energy micro-grid group scheduling optimization method based on a small-disturbance stability security domain, and the method comprises the steps: constructing an algebraic-differential equation set of an integrated energy micro-grid group, carrying out the linearization, and further obtaining an integrated energy micro-grid group dynamic model; constructing a bifurcation equation of the comprehensive energy microgrid group and a small disturbance stability domain of the bifurcation equation, and selecting dominant bifurcation parameters; constructing a polynomial basis function set, constructing a polynomial approximation expression of each variable in the bifurcation equation by using a linear combination of polynomial basis functions, and then obtaining a Galerkin projection equation set; solving a Galerkin projection equation set by using a sparse Galerkin method based on equation residual, and substituting a solving result into a polynomial approximation expression to obtain a comprehensive energy microgrid group security domain considering small disturbance stability; scheduling optimization is carried out according to the integrated energy microgrid group security domain; according to the method, the calculation efficiency can be effectively improved, and effective coordination of system economy and safety is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of microgrid group optimization scheduling, and more specifically, to a comprehensive energy microgrid group scheduling optimization method based on a small disturbance stability safety domain. Background Art

[0002] Compared with traditional power systems dominated by synchronous generators, the dynamic response characteristics of various components in the power electronics integrated energy microgrid system have multiple uncertainties. Therefore, traditional stability judgment methods are no longer sufficient to analyze the operating mechanism characteristics within the integrated energy microgrid.

[0003] For a long time, the safety and stability of power systems have generally been analyzed by setting up specified scenarios and using simulation calculations under one or several fault modes to draw conclusions on whether the system is safe and stable. This type of method is called a point-by-point method, but the point-by-point method cannot make a holistic evaluation of the system's operating status. Moreover, as a deterministic analysis method, it is difficult to handle the probabilistic safety assessment of integrated energy systems with large-scale renewable energy grid connection.

[0004] To assess the small-disturbance stability of increasingly complex, multi-uncertainty integrated energy microgrids, researchers have used a domain perspective to analyze the distance between the system's current operating point and the stability domain boundary. This allows them to assess the relative relationship between the current operating point and the safety domain boundary, further deriving safety margins and optimal control directions. Mathematically, the small-disturbance stability domain boundary of an integrated energy system is characterized by a hypersurface defined by a criterion. Due to the system's high nonlinearity, sampling-fitting methods and Taylor series expansions are often used to approximate the precise expression for the stability domain boundary.

[0005] The sampling-fitting method uses some pre-given points to fit a function model composed of polynomial functions, exponential functions or trigonometric functions. The result is an approximate description of the functional relationship between the system state variables and parameters. However, the selection criteria for a single sample in this method are not easy to determine, and the number and location of sample points will inevitably have a significant impact on the final result. Moreover, it is also difficult to determine which basis functions to select for fitting, and there are also overfitting and underfitting phenomena caused by improper coordination between the number of basis functions and the number of sample points.

[0006] The calculation results of the Taylor series expansion method are only a rough approximation near the rated operating point, and are therefore only applicable in situations where parameter changes are small and the system nonlinearity is weak. Existing solutions generally only involve first-order or second-order sensitivity, and rarely involve third-order sensitivity, which makes it difficult to improve the accuracy of the sensitivity method by increasing the order. More importantly, sensitivity methods based on Taylor series expansion are only local methods, and their accuracy decreases rapidly after the parameter value moves away from this point, rather than being accurate across the entire range of the parameter variation.

[0007] In summary, there is an urgent need for a new solution that can quantitatively analyze the security of integrated energy microgrid systems and accurately characterize the system security domain, so as to achieve effective coordination between system economy and safety in the formulation of optimized scheduling plans. Summary of the Invention

[0008] In order to overcome the defect of the above-mentioned existing technologies that it is difficult to quantify and evaluate the safety margin of integrated energy microgrid groups efficiently and accurately, the present invention provides an integrated energy microgrid group scheduling optimization method based on a small-disturbance stable safety domain. The sparse Galerkin method is innovatively applied to the generation of a small-disturbance stable safety domain for integrated energy microgrid groups, which can effectively improve the calculation efficiency. At the same time, the generated safety domain can be directly used in the real-time online scheduling optimization of the integrated energy microgrid group system.

[0009] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0010] A method for optimizing the scheduling of integrated energy microgrids based on a small-disturbance stable safety region includes the following steps:

[0011] S1: Construct and linearize the algebraic-differential equations of the integrated energy microgrid group to further obtain the dynamic model of the integrated energy microgrid group;

[0012] S2: Construct the bifurcation equation of the integrated energy microgrid and its small perturbation stability domain, and select the dominant bifurcation parameters;

[0013] S3: Construct a set of polynomial basis functions and use linear combinations of polynomial basis functions to construct polynomial approximation expressions for each variable in the bifurcation equation;

[0014] S4: Substituting the polynomial approximation expression into the bifurcation equation, projecting the bifurcation equation onto each polynomial basis function by inner product calculation, and obtaining the Galerkin projection equation group;

[0015] S5: Obtain the initial values ​​of the approximation coefficients of each polynomial approximation expression, solve the Galerkin projection equations using the sparse Galerkin method based on the equation residual, and substitute the solution results into the polynomial approximation expression to obtain the safety domain of the integrated energy microgrid considering small disturbance stability;

[0016] Scheduling optimization is performed based on the security domain of the integrated energy microgrid group.

[0017] Preferably, in step S1, the algebraic-differential equations of the integrated energy microgrid group are expressed as:

[0018]

[0019] in, is the first-order derivative of the system dynamic state variable; x|t＝0 is the initial value of the system state variable; x is the dynamic state variable of the integrated energy microgrid; y is an algebraic variable; p is an independent variable parameter; f(x, y, p), g(x, y, p) and h(p) represent the initial values ​​of the differential equation, algebraic equation and dynamic system respectively;

[0020] When the independent parameter p is constant, the following equation is linearized at the equilibrium point (x0, y0):

[0021]

[0022] Where Δx and Δy are the increments of the differential and algebraic state variables relative to their equilibrium points, respectively;

[0023] when When it is non-singular, the state matrix A of the integrated energy microgrid group is further obtained:

[0024]

[0025] According to Lyapunov's first stability test, when all eigenvalues ​​of the state matrix A have negative real parts, the integrated energy microgrid group is small-disturbance stable.

[0026] Preferably, in step S1, the integrated energy microgrid group includes a plurality of single integrated energy microgrids with the same structure, each of which includes: a distributed wind turbine generator set, a distributed photovoltaic generator set, a split-shaft gas turbine, a distributed energy storage device, a control center and a power load;

[0027] The dynamic model of the integrated energy microgrid group includes several single integrated energy microgrid models; each of the single integrated energy microgrid models includes: a grid-type doubly-fed wind turbine generator model, a grid-type photovoltaic generator model, a split-shaft gas turbine generator model, and an energy storage device model;

[0028] The grid-type doubly-fed wind turbine generator model is specifically as follows:

[0029]

[0030] in, is the first-order derivative of the dynamic state variable of the grid-type doubly-fed wind turbine generator set; x WT is the dynamic state variable of the grid-type doubly-fed wind turbine generator set; WT is the algebraic variable of the grid-type doubly-fed wind turbine generator set; p WT is the independent variable parameter of the grid-type doubly-fed wind turbine generator set; f WT (x WT ,y WT ,p WT ) and gWT (x WT ,y WT ,p WT ) represent the differential equation and algebraic equation of the grid-type doubly-fed wind turbine generator model respectively;

[0031] The grid-type photovoltaic generator model is specifically as follows:

[0032]

[0033] in, is the first-order derivative of the grid-type photovoltaic generator configuration state variable; x PV is the dynamic state variable of the grid-type photovoltaic generator set; y PV is the algebraic variable of the grid-type photovoltaic generator set; p PV is the independent variable parameter of the grid-type photovoltaic generator set; f PV (x PV ,y PV ,p PV ) and g PV (x PV ,y PV ,p PV ) represent the differential equation and algebraic equation of the grid-type photovoltaic generator model respectively;

[0034] The energy storage device model is specifically:

[0035]

[0036] in, is the first-order derivative of the state variable of the energy storage device; x ESS is the dynamic state variable of the energy storage device; y ESS is the algebraic variable of the energy storage device; p ESS is the independent variable parameter of the energy storage device; f ESS (x ESS ,y ESS ,p ESS ) and g ESS (x ESS ,y ESS ,p ESS ) represent the differential equation and algebraic equation of the energy storage device model respectively;

[0037] The split-shaft gas turbine generator set model is specifically as follows:

[0038]

[0039] in, is the first-order derivative of the state variable of the split-shaft gas turbine generator set; x GTis the dynamic state variable of the split-shaft gas turbine generator set; y GT is the algebraic variable of the split-shaft gas turbine generator set; p GT is the independent variable parameter of the split-shaft gas turbine generator set; f GT (x GT ,y GT ,p GT ) and g GT (x GT ,y GT ,p GT ) represent the differential equation and algebraic equation of the split-shaft gas turbine generator model respectively;

[0040] The models of each feeder and tie line in the integrated energy microgrid system are:

[0041]

[0042] Where i TLi·D and i TLi·Q represents the current of the tie line connected to the i-th microgrid in the public DQ coordinate system; R TLi , L TLi is the resistance and inductance of the i-th tie line; v pcci·D and v pcci·Q is the voltage at the common coupling point where all distributed generation sources in the i-th microgrid are connected in the common DQ coordinate system; v pcc·D and v pcc·Q is the voltage of the common coupling point to which all microgrids are connected under the common DQ coordinate;

[0043] The local load in the i-th integrated energy microgrid can be described as:

[0044]

[0045] Where i loadi·D and i loadi·Q represents the current of the local load in the i-th microgrid in the public DQ coordinate system; R loadi , L loadi is the resistance and inductance of the local load;

[0046] Each single integrated energy microgrid model is specifically:

[0047]

[0048] in, is the first-order derivative of the state variable of the single integrated energy microgrid; x IMG is the dynamic state variable of the single integrated energy microgrid; y IMG is the variable of single integrated energy microgrid number; p IMG is the independent variable parameter of the single integrated energy microgrid; fIMG (x IMG ,y IMG ,p IMG ) and g IMG (x IMG ,y IMG ,p IMG ) represent the differential equation and algebraic equation of the single integrated energy microgrid model respectively;

[0049] The comprehensive energy microgrid model is specifically as follows:

[0050]

[0051] in, is the first-order derivative of the state variable of the integrated energy microgrid group; x IMGC is the dynamic state variable of the integrated energy microgrid group; y IMGC is the algebraic variable of the integrated energy microgrid group; p IMGC is the independent variable parameter of the integrated energy microgrid group; f IMGC (x IMGC ,y IMGC ,p IMGC ) and g IMGC (x IMGC ,y IMGC ,p IMGC ) represent the differential equation and algebraic equation of the integrated energy microgrid model respectively.

[0052] Preferably, in step S2, the bifurcation equation of the integrated energy microgrid is constructed, which is expressed as:

[0053] F class (x,y,x B ,p)=0

[0054] Among them, F class represents the value of the bifurcation equation with bifurcation type class, which includes any of Hopf bifurcation, saddle-node bifurcation, and singularity-induced bifurcation; x B is an additional variable;

[0055] The small perturbation stability region is expressed as:

[0056]

[0057] in, Represents the real number domain, Re(λ i ) represents the real part of the i-th eigenvalue;

[0058] The boundary of the small perturbation stability region is defined as:

[0059]

[0060] Among them, Σ SNB represents the set of all saddle bifurcation points; Σ Hopf represents the set of Hopf bifurcation points; Σ SIB represents the set of singularity-induced bifurcation points.

[0061] Preferably, in step S2, the dominant bifurcation parameters selected include:

[0062] p={p load ,p wind ,p pv ,p GT ,p k}

[0063] Among them, p load is the load factor of each single integrated energy microgrid; p wind is the wind power factor of each single integrated energy microgrid wind turbine unit; p pv is the optical power factor of each single integrated energy microgrid photovoltaic unit; p GT is the mechanical power of each single integrated energy microgrid gas turbine; p k is the gas turbine excitation regulator gain coefficient.

[0064] Preferably, in step S3, a set of polynomial basis functions is constructed for each dominant bifurcation parameter to construct a polynomial basis function set, and the polynomial basis function is expressed as:

[0065] Φ i,0 (q i ),Φ i,1 (q i ),Φ i,2 (q i ),...,Φ i,N (q i )∈U,i=1,2,…,s

[0066] Among them, q i is the i-th dominant bifurcation parameter to be analyzed, s is the number of dominant bifurcation parameters to be analyzed; Φ i,N (q i ) is the basis function of degree N corresponding to the i-th dominant bifurcation parameter; U is the inner product space;

[0067] The sum of the tensor product of the basis function groups corresponding to each parameter is not higher than the preset value N b The function of is used as the basis function of the inner product space U subspace to obtain the complete polynomial basis function, which is expressed as:

[0068]

[0069] Among them, N bis the number of basis functions, satisfying is the experimental basis function; q is the dominant bifurcation parameter to be analyzed selected from p, and p≠q; is the tensor product;

[0070] The polynomial approximation expression of each variable in the bifurcation equation is expressed as:

[0071]

[0072] in, is the value of the polynomial approximation expression of the i-th variable; c ij is the coefficient of the jth basis function in the polynomial approximation expression of the i-th variable.

[0073] Preferably, in step S4, the Galerkin projection equations are expressed as:

[0074]

[0075] Among them, B i It is the approximation equation of the boundary criterion of the small disturbance stability security region of the i-th integrated energy microgrid group.

[0076] Preferably, in step S5, an initial search direction vector is selected, and then the equations of Hopf bifurcation and saddle-node bifurcation are solved along the initial search direction to obtain the instability critical point on the boundary of the small perturbation stability region. and p * The corresponding state variable x * , algebraic variable y * With the eigenvector φ * ; If the calculated p * Not belonging to the preset parameter support domain Ω p , then update the search direction vector, adjust the search direction and calculate again;

[0077] The instability critical point p * The corresponding state variable x * , algebraic variable y * With the eigenvector φ * As the initial value of the constant coefficient in the polynomial approximation expression, and set the other non-constant coefficients to 0 to complete the initialization.

[0078] Preferably, in step S5, solving the Galerkin projection equations using a sparse Galerkin method based on equation residuals includes:

[0079] First-order approximation: Use the Newton-Raphson method to solve the Galerkin projection equations to obtain c ij The first-order approximation result of ;

[0080] Second-order and higher-order approximation: The importance of the second-order and higher-order terms of the Galerkin projection equation is quantified by using the weighted average of the absolute value of the residual equation and its inner product;

[0081] For each order of the second order and above, sort the items in each order according to their corresponding importance and take the top s τ Items, generate sparse bases of order 2 and above in turn;

[0082] The first-order approximation result and the sparse bases of the second order and above are used to replace the basis functions in the polynomial approximation expression respectively to obtain the safety domain of the integrated energy microgrid group considering small disturbance stability.

[0083] Preferably, the importance of the second-order and higher-order terms is expressed as:

[0084]

[0085] Among them, G r,s ({c j,k}) is the nonlinear equation system after Galerkin projection, and the unknown coefficients can be obtained by solving it; c (1,1) are the undetermined coefficients solved by the first-order approximation equation; represents the total amount of inner products of the second-order Galerkin projection equation to be solved and all quadratic basis function terms, is the number of quadratic basis functions;

[0086] The s τ satisfy:

[0087]

[0088] Among them, τ is the preset threshold.

[0089] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0090] The present invention provides a method for optimizing the scheduling of an integrated energy microgrid group based on a small-disturbance stable safety domain. The method comprises the following steps: first, constructing an algebraic-differential equation group of the integrated energy microgrid group and linearizing the equation group, and further obtaining a dynamic model of the integrated energy microgrid group; then, constructing a bifurcation equation of the integrated energy microgrid group and its small-disturbance stable domain, and selecting a dominant bifurcation parameter; then, constructing a set of polynomial basis functions, and using a linear combination of the polynomial basis functions to construct a polynomial approximation expression of each variable in the bifurcation equation; then, substituting the polynomial approximation expression into the bifurcation equation, and projecting the bifurcation equation onto each polynomial basis function through inner product calculation to obtain a Galerkin projection equation group; finally, obtaining an initial value of an approximation coefficient of each polynomial approximation expression, solving the Galerkin projection equation group using a sparse Galerkin method based on equation residuals, and substituting the solution result into the polynomial approximation expression to obtain a safety domain of the integrated energy microgrid group considering small-disturbance stability; and performing scheduling optimization according to the safety domain of the integrated energy microgrid group.

[0091] This invention innovatively applies the sparse Galerkin method to generate a safety domain for small-disturbance stability of an integrated energy microgrid cluster. Combined with the proposed bifurcation surface, it constitutes a small-disturbance stability boundary, which can be used to directly determine whether the system maintains small-disturbance stability after fluctuations and adjustments of parameters such as new energy, load, and gas turbine mechanical power. The present invention can effectively improve computational efficiency, and the safety domain it generates can be directly applied to real-time online scheduling optimization of the integrated energy microgrid cluster system. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 This is a flow chart of a method for optimizing the scheduling of an integrated energy microgrid group based on a small disturbance stability safety region provided in Example 1. DETAILED DESCRIPTION

[0093] The accompanying drawings are for illustrative purposes only and are not to be construed as limiting this patent;

[0094] In order to better illustrate this embodiment, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product size;

[0095] It is understandable to those skilled in the art that some well-known structures and descriptions thereof may be omitted in the drawings.

[0096] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0097] Example 1

[0098] like Figure 1 As shown, this embodiment provides a method for optimizing the scheduling of an integrated energy microgrid group based on a small disturbance stability safety region, comprising the following steps:

[0099] S1: Construct and linearize the algebraic-differential equations of the integrated energy microgrid group to further obtain the dynamic model of the integrated energy microgrid group;

[0100] S2: Construct the bifurcation equation of the integrated energy microgrid and its small perturbation stability domain, and select the dominant bifurcation parameters;

[0101] S3: Construct a set of polynomial basis functions and use linear combinations of polynomial basis functions to construct polynomial approximation expressions for each variable in the bifurcation equation;

[0102] S4: Substituting the polynomial approximation expression into the bifurcation equation, projecting the bifurcation equation onto each polynomial basis function by inner product calculation, and obtaining the Galerkin projection equation group;

[0103] S5: Obtain the initial values ​​of the approximation coefficients of each polynomial approximation expression, solve the Galerkin projection equations using the sparse Galerkin method based on the equation residual, and substitute the solution results into the polynomial approximation expression to obtain the safety domain of the integrated energy microgrid considering small disturbance stability;

[0104] Scheduling optimization is performed based on the security domain of the integrated energy microgrid group.

[0105] In the specific implementation process, the algebraic-differential equations of the integrated energy microgrid group are first constructed and linearized to further obtain the dynamic model of the integrated energy microgrid group;

[0106] Then, the bifurcation equation of the integrated energy microgrid and its small perturbation stability domain are constructed, and the dominant bifurcation parameters are selected;

[0107] Then, a set of polynomial basis functions is constructed, and the linear combination of the polynomial basis functions is used to construct the polynomial approximation expressions of each variable in the bifurcation equation;

[0108] Then, the polynomial approximation expression is substituted into the bifurcation equation, and the bifurcation equation is projected onto each polynomial basis function through inner product calculation to obtain the Galerkin projection equation group;

[0109] Finally, the initial values ​​of the approximation coefficients of each polynomial approximation expression are obtained, and the Galerkin projection equations are solved using the sparse Galerkin method based on the equation residual. The solution is substituted into the polynomial approximation expression to obtain the safety domain of the integrated energy microgrid group considering small disturbance stability. Real-time online scheduling optimization is performed based on the safety domain of the integrated energy microgrid group.

[0110] This method innovatively applies the sparse Galerkin method to generate a safety domain for small-disturbance stability in integrated energy microgrids. The Galerkin method belongs to the non-sampling approximation functional class of methods. It does not rely on discrete sampling calculation information of the system when the parameters change. Instead, it approximates the parameterized problem by minimizing the inner product projection of the system approximation error in the normed space, thereby obtaining global approximation accuracy characteristics. This method has strong adaptability to strongly nonlinear systems and multi-parameterized problems with large-scale parameter changes. Therefore, the Galerkin method can be used for quantitative safety analysis of integrated energy microgrids and accurately characterize the system safety domain.

[0111] The lack of an efficient quantitative assessment method for safety margins in existing integrated energy microgrid scheduling and operation schemes makes it difficult to achieve effective coordination between system economy and safety in the formulation of optimized scheduling plans. Traditional point-by-point methods are extremely computationally burdensome and cannot meet the requirements of real-time online optimization. In contrast, the non-sampling approximation functional method proposed in this method can significantly improve computational efficiency, and its output results can meet the requirements of real-time online optimization of integrated energy microgrid systems.

[0112] In addition, existing technologies rarely consider the small-disturbance stability safety domain of integrated energy systems, and mostly consider the static safety domain. However, the randomness of renewable energy generation and load in integrated energy microgrids, as well as parameters such as the mechanical power of gas turbines, have become factors that must be considered in the analysis and calculation of integrated energy microgrids. The sparse Galerkin method introduced in this method can significantly improve computational efficiency.

[0113] This method, combined with the proposed bifurcation surface, constitutes a small-disturbance stability boundary, based on which it can directly determine whether the system remains stable under small-disturbance conditions after fluctuations and adjustments of parameters such as renewable energy, load, and gas turbine mechanical power. At the same time, this method can effectively improve computational efficiency, and the generated safety domain can be directly applied to the real-time online scheduling optimization of integrated energy microgrid systems.

[0114] Example 2

[0115] This embodiment provides a method for optimizing the scheduling of an integrated energy microgrid group based on a small disturbance stability safety region, including the following steps:

[0116] S1: Construct and linearize the algebraic-differential equations of the integrated energy microgrid group to further obtain the dynamic model of the integrated energy microgrid group;

[0117] S2: Construct the bifurcation equation of the integrated energy microgrid and its small perturbation stability domain, and select the dominant bifurcation parameters;

[0118] S3: Construct a set of polynomial basis functions and use linear combinations of polynomial basis functions to construct polynomial approximation expressions for each variable in the bifurcation equation;

[0119] S4: Substituting the polynomial approximation expression into the bifurcation equation, projecting the bifurcation equation onto each polynomial basis function by inner product calculation, and obtaining the Galerkin projection equation group;

[0120] S5: Obtain the initial values ​​of the approximation coefficients of each polynomial approximation expression, solve the Galerkin projection equations using the sparse Galerkin method based on the equation residual, and substitute the solution results into the polynomial approximation expression to obtain the safety domain of the integrated energy microgrid considering small disturbance stability;

[0121] Performing scheduling optimization according to the security domain of the integrated energy microgrid group;

[0122] In step S1, the algebraic-differential equations of the integrated energy microgrid group are expressed as:

[0123]

[0124] in, is the first-order derivative of the system dynamic state variable; x| t＝0 is the initial value of the system state variable; x is the dynamic state variable of the integrated energy microgrid; y is an algebraic variable; p is an independent variable parameter; f(x, y, p), g(x, y, p) and h(p) represent the initial values ​​of the differential equation, algebraic equation and dynamic system respectively;

[0125] When the independent parameter p is constant, the following equation is linearized at the equilibrium point (x0, y0):

[0126]

[0127] Where Δx and Δy are the increments of the differential and algebraic state variables relative to their equilibrium points, respectively;

[0128] when When it is non-singular, the state matrix A of the integrated energy microgrid group is further obtained:

[0129]

[0130] According to the first Lyapunov stability judgment method, when all eigenvalues ​​of the state matrix A have negative real parts, the integrated energy microgrid is small-disturbance stable.

[0131] In step S1, the integrated energy microgrid group includes a plurality of single integrated energy microgrids with the same structure, each of which includes: a distributed wind turbine generator set, a distributed photovoltaic generator set, a split-shaft gas turbine, a distributed energy storage device, a control center, and a power load;

[0132] The dynamic model of the integrated energy microgrid group includes several single integrated energy microgrid models; each of the single integrated energy microgrid models includes: a grid-type doubly-fed wind turbine generator model, a grid-type photovoltaic generator model, a split-shaft gas turbine generator model, and an energy storage device model;

[0133] The grid-type doubly-fed wind turbine generator model is specifically as follows:

[0134]

[0135] in, is the first-order derivative of the dynamic state variable of the grid-type doubly-fed wind turbine generator set; x WT is the dynamic state variable of the grid-type doubly-fed wind turbine generator set; WT is the algebraic variable of the grid-type doubly-fed wind turbine generator set; p WT is the independent variable parameter of the grid-type doubly-fed wind turbine generator set; f WT (x WT ,y WT ,p WT ) and g WT (x WT ,y WT ,p WT ) represent the differential equation and algebraic equation of the grid-type doubly-fed wind turbine generator model respectively;

[0136] The grid-type photovoltaic generator model is specifically as follows:

[0137]

[0138] in, is the first-order derivative of the grid-type photovoltaic generator configuration state variable; x PV is the dynamic state variable of the grid-type photovoltaic generator set; y PV is the algebraic variable of the grid-type photovoltaic generator set; p PV is the independent variable parameter of the grid-type photovoltaic generator set; f PV (x PV ,y PV ,p PV ) and g PV (x PV ,y PV ,p PV ) represent the differential equation and algebraic equation of the grid-type photovoltaic generator model respectively;

[0139] The energy storage device model is specifically:

[0140]

[0141] in, is the first-order derivative of the state variable of the energy storage device; x ESS is the dynamic state variable of the energy storage device; y ESS is the algebraic variable of the energy storage device; p ESS is the independent variable parameter of the energy storage device; f ESS (x ESS ,y ESS ,p ESS ) and g ESS (x ESS ,y ESS ,p ESS ) represent the differential equation and algebraic equation of the energy storage device model respectively;

[0142] The split-shaft gas turbine generator set model is specifically as follows:

[0143]

[0144] in, is the first-order derivative of the state variable of the split-shaft gas turbine generator set; x GT is the dynamic state variable of the split-shaft gas turbine generator set; y GT is the algebraic variable of the split-shaft gas turbine generator set; p GT is the independent variable parameter of the split-shaft gas turbine generator set; f GT (x GT ,y GT ,p GT ) and g GT (x GT ,y GT ,p GT ) represent the differential equation and algebraic equation of the split-shaft gas turbine generator model respectively;

[0145] The models of each feeder and tie line in the integrated energy microgrid system are:

[0146]

[0147] Where i TLi·D and i TLi·Q represents the current of the tie line connected to the i-th microgrid in the public DQ coordinate system; R TLi 、R TLi is the resistance and inductance of the i-th tie line; v pcci·D and v pcci·Q is the voltage at the common coupling point where all distributed generation sources in the i-th microgrid are connected in the common DQ coordinate system; v pcc·D and v pcc·Q is the voltage of the common coupling point to which all microgrids are connected under the common DQ coordinate;

[0148] The local load in the i-th integrated energy microgrid can be described as:

[0149]

[0150] Where i loadi·D and i loadi·Q represents the current of the local load in the i-th microgrid in the public DQ coordinate system; R loadi , L loadi is the resistance and inductance of the local load;

[0151] Each single integrated energy microgrid model is specifically:

[0152]

[0153] in, is the first-order derivative of the state variable of the single integrated energy microgrid; x IMG is the dynamic state variable of the single integrated energy microgrid; y IMG is the variable of single integrated energy microgrid number; p IMG is the independent variable parameter of the single integrated energy microgrid; f IMG (x IMG ,y IMG ,p IMG ) and g IMG (x IMG ,y IMG ,p IMG ) represent the differential equation and algebraic equation of the single integrated energy microgrid model respectively;

[0154] The comprehensive energy microgrid model is specifically as follows:

[0155]

[0156] in, is the first-order derivative of the state variable of the integrated energy microgrid group; x IMGC is the dynamic state variable of the integrated energy microgrid group; y IMGC is the algebraic variable of the integrated energy microgrid group; p IMGC is the independent variable parameter of the integrated energy microgrid group; f IMGC (x IMGC ,y IMGC ,p IMGC ) and g IMGC (x IMGC ,y IMGC ,p IMGC ) represent the differential equation and algebraic equation of the integrated energy microgrid model respectively;

[0157] In step S2, the bifurcation equation of the integrated energy microgrid is constructed, which is expressed as:

[0158] F class (x,y,x B ,p)=0

[0159] Among them, F class represents the value of the bifurcation equation with bifurcation type class, which includes any of Hopf bifurcation, saddle-node bifurcation, and singularity-induced bifurcation; x B is an additional variable;

[0160] The small perturbation stability region is expressed as:

[0161]

[0162] in, Represents the real number domain, Re(λ i ) represents the real part of the i-th eigenvalue;

[0163] The boundary of the small perturbation stability region is defined as:

[0164]

[0165] Among them, Σ SNB represents the set of all saddle bifurcation points; Σ Hopf represents the set of Hopf bifurcation points; Σ SIB represents the set of singularity-induced bifurcation points;

[0166] In step S2, the dominant bifurcation parameters selected include:

[0167] p={p load ,p wind ,p pv ,p GT ,p k}

[0168] Among them, p load is the load factor of each single integrated energy microgrid; p wind is the wind power factor of each single integrated energy microgrid wind turbine unit; p pv is the optical power factor of each single integrated energy microgrid photovoltaic unit; p GT is the mechanical power of each single integrated energy microgrid gas turbine; p k is the gas turbine excitation regulator gain coefficient;

[0169] In step S3, a set of polynomial basis functions is constructed for each dominant bifurcation parameter to build a polynomial basis function set. The polynomial basis function is expressed as:

[0170] Φ i,0 (q i ),Φ i,1 (q i),Φ i,2 (q i ),...,Φ i,N (q i )∈U,i=1,2,…,s

[0171] Among them, q i is the i-th dominant bifurcation parameter to be analyzed, s is the number of dominant bifurcation parameters to be analyzed; Φ i,N (q i ) is the basis function of degree N corresponding to the i-th dominant bifurcation parameter; U is the inner product space;

[0172] The sum of the tensor product of the basis function groups corresponding to each parameter is not higher than the preset value N b The function of is used as the basis function of the inner product space U subspace to obtain the complete polynomial basis function, which is expressed as:

[0173]

[0174] Among them, N b is the number of basis functions, satisfying is the experimental basis function; q is the dominant bifurcation parameter to be analyzed selected from p, and p≠q; is the tensor product;

[0175] The polynomial approximation expression of each variable in the bifurcation equation is expressed as:

[0176]

[0177] in, is the value of the polynomial approximation expression of the i-th variable; c ij is the coefficient of the jth basis function in the polynomial approximation expression of the i-th variable;

[0178] In step S4, the Galerkin projection equations are expressed as:

[0179]

[0180] Among them, B i is the approximation equation for the boundary criterion of the small disturbance stability security region of the i-th integrated energy microgrid group;

[0181] In step S5, an initial search direction vector is selected, and then the equations of Hopf bifurcation and saddle-node bifurcation are solved along the initial search direction to obtain the instability critical point on the boundary of the small perturbation stability region. and p * The corresponding state variable x * , algebraic variable y * With the eigenvector φ * ; If the calculated p* Not belonging to the preset parameter support domain Ω p , then update the search direction vector, adjust the search direction and calculate again;

[0182] The instability critical point p * The corresponding state variable x * , algebraic variable y * With the eigenvector φ * As the initial value of the constant coefficient in the polynomial approximation expression, and set the other non-constant coefficients to 0 to complete the initialization;

[0183] In step S5, the Galerkin projection equations are solved using a sparse Galerkin method based on equation residuals, including:

[0184] First-order approximation: Use the Newton-Raphson method to solve the Galerkin projection equations to obtain c ij The first-order approximation result of ;

[0185] Second-order and higher-order approximation: The importance of the second-order and higher-order terms of the Galerkin projection equation is quantified by using the weighted average of the absolute value of the residual equation and its inner product;

[0186] For each order of the second order and above, sort the items in each order according to their corresponding importance and take the top s τ Items, generate sparse bases of order 2 and above in turn;

[0187] The first-order approximation result and the sparse basis of the second order and above are used to replace each basis function in the polynomial approximation expression respectively to obtain the safety domain of the integrated energy microgrid considering small disturbance stability;

[0188] The importance of the second-order and higher-order terms is expressed as:

[0189]

[0190] Among them, G r,s ({c j,k}) is the nonlinear equation system after Galerkin projection, and the unknown coefficients can be obtained by solving it; c (1,1) are the undetermined coefficients solved by the first-order approximation equation; represents the total amount of inner products of the second-order Galerkin projection equation to be solved and all quadratic basis function terms, is the number of quadratic basis functions;

[0191] The s τ satisfy:

[0192]

[0193] Among them, τ is the preset threshold.

[0194] In the specific implementation process, this method includes the following steps:

[0195] Step 1): Construct a parameterized algebraic-differential equation system from the integrated energy microgrid and linearize it at its system equilibrium point;

[0196] In this embodiment, the algebraic-differential equations of the established integrated energy microgrid group can be expressed as:

[0197]

[0198] Where: is the first-order derivative of the system dynamic state variable; x| t＝0 is the initial value of the system state variable; x is the system state variable; y is the algebraic variable, and p is the disturbance parameter variable (independent parameter); f(x, y, p), g(x, y, p) and h(p) represent the initial values ​​of the differential equation, algebraic equation and dynamic system respectively;

[0199] When the independent variable p is constant, the system equilibrium point (x0, y0) will be Linearization;

[0200] Where: Δx and Δy are the increments of the differential and algebraic state variables relative to their equilibrium points, i.e., small perturbations of the dynamic state variable x and algebraic variable y near the equilibrium point; is the Jacobian matrix of the function f(.) with respect to x, which is a function of the equilibrium point, and the same applies to the others;

[0201] Then when When it is non-singular, we can further obtain:

[0202]

[0203] Linearizing the algebraic differential equation yields the matrix is the state matrix of the integrated energy microgrid. According to Lyapunov's first stability test, when all eigenvalues ​​of A have negative real parts, the system is asymptotically stable near the equilibrium point. If one eigenvalue of A has a positive real part, the equilibrium point is unstable. Both the equilibrium point and the state matrix depend on the independent variable parameter p, so the eigenvalue and small perturbation stability will also change with changes in p.

[0204] In this embodiment, the integrated energy microgrid group includes several single integrated energy microgrids with the same structure, each of which includes a split-shaft gas turbine, a distributed wind turbine generator set, a distributed photovoltaic generator set, a distributed energy storage device, a control center, and power loads;

[0205] The dynamic model of the integrated energy microgrid group includes several single integrated energy microgrid models; each single integrated energy microgrid model includes: a grid-type doubly-fed wind turbine generator model, a grid-type photovoltaic generator model, a split-shaft gas turbine generator model, and an energy storage device model;

[0206] The grid-type doubly-fed wind turbine generator model is specifically as follows:

[0207]

[0208] in, is the first-order derivative of the dynamic state variable of the grid-type doubly-fed wind turbine generator set; x WT is the dynamic state variable of the grid-type doubly-fed wind turbine generator set; WT is the algebraic variable of the grid-type doubly-fed wind turbine generator set; p WT is the independent variable parameter of the grid-type doubly-fed wind turbine generator set; f WT (x WT ,y WT ,p WT ) and g WT (x WT ,y WT ,p WT ) represent the differential equation and algebraic equation of the grid-type doubly-fed wind turbine generator model respectively;

[0209] The grid-type photovoltaic generator model is specifically as follows:

[0210]

[0211] in, is the first-order derivative of the grid-type photovoltaic generator configuration state variable; x PV is the dynamic state variable of the grid-type photovoltaic generator set; y PV is the algebraic variable of the grid-type photovoltaic generator set; p PV is the independent variable parameter of the grid-type photovoltaic generator set; f PV (x PV ,y PV ,p PV ) and g PV (x PV ,y PV ,p PV ) represent the differential equation and algebraic equation of the grid-type photovoltaic generator model respectively;

[0212] The energy storage device model is specifically as follows:

[0213]

[0214] in, is the first-order derivative of the state variable of the energy storage device; x ESS is the dynamic state variable of the energy storage device; y ESS is the algebraic variable of the energy storage device; p ESS is the independent variable parameter of the energy storage device; f ESS (x ESS ,y ESS ,p ESS ) and g ESS (x ESS ,y ESS ,p ESS ) represent the differential equation and algebraic equation of the energy storage device model respectively;

[0215] The split-shaft gas turbine generator model is as follows:

[0216]

[0217] in, is the first-order derivative of the state variable of the split-shaft gas turbine generator set; x GT is the dynamic state variable of the split-shaft gas turbine generator set; y GT is the algebraic variable of the split-shaft gas turbine generator set; p GT is the independent variable parameter of the split-shaft gas turbine generator set; f GT (x GT ,y GT ,p GT ) and g GT (x GT ,y GT ,p GT ) represent the differential equation and algebraic equation of the split-shaft gas turbine generator model respectively;

[0218] The models of each feeder and tie line in the integrated energy microgrid system are:

[0219]

[0220] Where i TLi·D and i TLi·Q represents the current of the tie line connected to the i-th microgrid in the public DQ coordinate system; R TLi , L TLi is the resistance and inductance of the i-th tie line; v pcci·D and v pcci·Q is the voltage at the common coupling point where all distributed generation sources in the i-th microgrid are connected in the common DQ coordinate system; v pcc·D and v pcc·Q is the voltage of the common coupling point to which all microgrids are connected under the common DQ coordinate;

[0221] The local load in the i-th integrated energy microgrid can be described as:

[0222]

[0223] Where i loadi·D and i loadi·Q represents the current of the local load in the i-th microgrid in the public DQ coordinate system; R loadi , L loadi is the resistance and inductance of the local load;

[0224] Each single integrated energy microgrid model is specifically:

[0225]

[0226] in, is the first-order derivative of the state variable of the single integrated energy microgrid; x IMG is the dynamic state variable of the single integrated energy microgrid; y IMG is the variable of single integrated energy microgrid number; p IMG is the independent variable parameter of the single integrated energy microgrid; f IMG (x IMG ,y IMG ,p IMG ) and g IMG (x IMG ,y IMG ,p IMG ) represent the differential equation and algebraic equation of the single integrated energy microgrid model respectively;

[0227] The integrated energy microgrid cluster model is as follows:

[0228]

[0229] in, is the first-order derivative of the state variable of the integrated energy microgrid group; x IMGC is the dynamic state variable of the integrated energy microgrid group; y IMGC is the algebraic variable of the integrated energy microgrid group; p IMGC is the independent variable parameter of the integrated energy microgrid group; f IMGC (x IMGC ,y IMGC ,p IMGC ) and g IMGC (x IMGC ,y IMGC ,p IMGC ) represent the differential equation and algebraic equation of the integrated energy microgrid model respectively;

[0230] Step 2): Based on the system dynamic model data, define the small perturbation stability region and the boundary of the small perturbation stability region and its boundary criterion approximation equation, and select the system's dominant bifurcation parameter;

[0231] Specifically, define the small perturbation stability region and the boundary of the small perturbation stability region and its boundary criterion approximation equation:

[0232] The small disturbance stability of integrated energy microgrid is mainly considered to be Hopf bifurcation (HB), saddle-node bifurcation (SNB) and singular induced bifurcation (SIB);

[0233] The equilibrium equations of the parameterized differential-algebraic equations and the three bifurcation criterion equations mentioned above together constitute the bifurcation equations:

[0234] F class (x,y,x B ,p)=0

[0235] Where, the subscript class refers to the bifurcation type, x B is an additional variable in the criterion equation;

[0236] The small perturbation stability region is defined as:

[0237]

[0238] in, Represents the real number domain, Re(λ i ) represents the real part of the i-th eigenvalue;

[0239] The boundary of the small perturbation stability region is defined as:

[0240]

[0241] Among them, Σ SNB represents the set of all saddle bifurcation points; Σ Hopf represents the set of Hopf bifurcation points; Σ SIB represents the set of singularity-induced bifurcation points;

[0242] In summary, the boundary criterion equation of the small disturbance stability safety region is unified into a vector form:

[0243] B(x B ,p)=0

[0244] The parameters on the boundary of the stable region form the following implicit function relationship:

[0245] 0=p(p1,p2,…,p n )

[0246] Select the parameter p1 to be analyzed as the dependent parameter and the other n-1 parameters as independent parameters. The implicit function expression can be approximated by the explicit analytical expression of the dependent parameter with respect to the other independent parameters. Specifically, define the extended variable vector Dimensionality reduction parameter vector The dependent variable parameters, state variables x, algebraic variables y, and eigenvectors can all be written as explicit approximate expressions about q: Will Substitute the approximate expression of the expanded variable vector Obtain the approximate equation for the boundary criterion of the small disturbance stability security region of the integrated energy microgrid Solving this set of equations can give us the approximate expression of the independent variable parameter to the dependent variable parameter of the small disturbance stability safety region of the integrated energy microgrid group we need.

[0247] Regarding the selection of the system's leading bifurcation parameters, in this embodiment, the selected parameters include:

[0248] p={p load ,p wind ,p pv ,p GT ,p k}

[0249] Where: p load is the load factor of each node; p wind is the wind power factor of each wind turbine unit; p pv is the optical power factor of each photovoltaic unit; p GT is the mechanical power of each gas turbine; p k is the gas turbine excitation regulator gain coefficient;

[0250] Step 3): Construct a set of polynomial basis functions and use their linear combinations to construct polynomial approximation expressions of dependent parameters and local bifurcation related variables;

[0251] Specifically, each independent parameter defines a set of polynomial basis functions:

[0252] Φ i,0 (q i ),Φ i,1 (q i ),Φ i,2 (q i ),...,Φ i,N (q i )∈U,i=1,2,…,s

[0253] Where: the subscript i of the basis function is the subscript of its corresponding independent variable parameter; the number after i is the approximation order N of the basis function, and the approximation order is selected as 3 in this paper; U is the inner product space defined below; n is the dimension of q;

[0254] The sum of the parameter degrees in the tensor product of the basis function groups corresponding to each parameter is not higher than N b The function of is used as the basis function of the inner product space U subspace, that is, the so-called complete polynomial basis function:

[0255]

[0256] Where: is the number of basis functions; is the basis function; k ranges from 0 to s; is the tensor product, which is used to construct multivariate basis functions;

[0257] The polynomial approximation expression of each extended state variable is a linear combination of the above-mentioned complete polynomial basis functions, where:

[0258]

[0259] Where: is the polynomial approximation expression of the i-th extended state variable; c ij The approximate expression is The j-th basis function coefficient;

[0260] Step 4): Substitute the polynomial approximation expression containing the undetermined approximation coefficient into the safety region boundary criterion approximation equation, and project it onto each basis function. The Galerkin projection equation group is obtained by inner product calculation;

[0261] Specifically, by setting the inner product of the boundary criterion equation and any set of basis functions to zero, we can obtain the Galerkin projection equation:

[0262]

[0263] Step 5): Obtain the initial values ​​of each approximation coefficient and construct an N-order sparse basis function based on the sparse Galerkin method of the equation residual to accelerate the solution of the corresponding Galerkin projection equation, and substitute the solved coefficients into the expression to obtain the polynomial approximation expression of the small perturbation stability region boundary and its state variables, algebraic variables and eigenvectors;

[0264] Specifically, first obtain the initial value of each approximation coefficient according to the following steps:

[0265] a) Parameter space search direction initialization:

[0266] Select the initial search direction vector in the l-dimensional parameter space:

[0267]

[0268] b) Solution and verification of bifurcation critical point:

[0269] Solve the bifurcation criterion equations for Hopf bifurcation and saddle-node bifurcation along the direction to obtain the instability critical point on the boundary of the small perturbation stability region And the state variable x corresponding to this point * , algebraic variable y * With the eigenvector φ * If the calculated (parameter support domain), then update the direction vector; adjust the initial parameter growth direction and calculate again;

[0270] c) Initialization of polynomial coefficients:

[0271] Initialize the constant coefficients in the polynomial approximation expression by setting them to the values ​​of the dependent parameters, system variables, eigenvectors, etc. corresponding to the critical instability point obtained in the previous step, and set the initial values ​​of the other non-constant approximation coefficients to 0 to complete the initialization.

[0272] Then, the projection equations are solved. In solving the projection equations, since solving the high-order Galerkin equations requires a huge amount of computation, this embodiment uses a sparse Galerkin method based on the equation residual to solve the equations.

[0273] First, use the Galerkin method to solve the equation B(w,q)=0 to obtain a first-order approximation where c (1 ,1) is the undetermined coefficient of the first-order basis function, and its number is the same as the first-order basis function N b1 are equal; for the second-order approximation, the residual of the equation The inner product of any component of and its second-order basis function forms the second-order Galerkin projection equation, and its 0-1 degree coefficient and the second-order coefficient c can be solved. (2,1) 、c (2,2) , whose numbers are N b1 、N b2 ;

[0274] The importance of each second-order basis function is quantified by defining the weighted average of the absolute value of the residual equation and its inner product, namely:

[0275]

[0276] Where: G r,s ({c j,k}) is the nonlinear equation system after Galerkin projection, and the unknown coefficients can be obtained by solving it; c (1,1) are the undetermined coefficients solved by the first-order approximation equation; represents the total amount of the inner product of the second-order Galerkin projection equation to be solved and all quadratic basis function terms, as a normalization constant, where is the number of quadratic basis functions; take the first s with the greatest importance τ The second-order sparse basis function can be obtained by combining the selected first-order basis function; and s τ satisfy:

[0277]

[0278] Where τ is the given threshold; and the above polynomial approximation expression The basis functions in are replaced with the proposed second-order sparse basis functions. After obtaining the second-order approximation results, the third-order sparse basis functions can be constructed by sorting them according to their importance and combining them with the second-order sparse basis functions.

[0279] In summary, the essence of the solution is to calculate the sparse Galerkin approximation of each order in turn; finally, the approximate expression of the boundary of the small disturbance stability safety region of the integrated energy microgrid group is obtained. At the same time, the polynomial approximation expression of the eigenvector of the system's reduced-order Jacobian matrix corresponding to the bifurcation type can be obtained, and the participation factors of each state variable of the system can be analyzed to analyze the physical information and main causes of its instability;

[0280] After obtaining the approximate expressions of the participation factors corresponding to each state variable on the boundary of the stability domain, the main instability modes corresponding to different points on the small-disturbance stability boundary of the integrated energy microgrid are identified. By adjusting the approximation order of the safety domain parameterization problem, an effective balance between the accuracy of the small-disturbance stability safety domain approximation and efficient calculation is achieved.

[0281] This method, combined with the proposed bifurcation surface, constitutes a small-disturbance stability boundary, based on which it can directly determine whether the system remains stable under small-disturbance conditions after fluctuations and adjustments of parameters such as renewable energy, load, and gas turbine mechanical power. At the same time, this method can effectively improve computational efficiency, and the generated safety domain can be directly applied to the real-time online scheduling optimization of integrated energy microgrid systems.

[0282] The same or similar reference numerals correspond to the same or similar components;

[0283] The terms used in the drawings to describe positional relationships are for illustrative purposes only and should not be construed as limiting this patent;

[0284] Obviously, the above embodiments of the present invention are merely examples for the purpose of clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the claims of the present invention.

Claims

1. A method for optimizing the scheduling of integrated energy microgrids based on a small disturbance stability safety region, characterized in that: The following steps are involved: S1: Construct and linearize the algebraic-differential equations of the integrated energy microgrid group to further obtain the dynamic model of the integrated energy microgrid group; S2: Construct the bifurcation equation of the integrated energy microgrid and its small perturbation stability domain, and select the dominant bifurcation parameters; S3: Construct a set of polynomial basis functions and use linear combinations of polynomial basis functions to construct polynomial approximation expressions for each variable in the bifurcation equation; S4: Substituting the polynomial approximation expression into the bifurcation equation, projecting the bifurcation equation onto each polynomial basis function by inner product calculation, and obtaining the Galerkin projection equation group; S5: Obtain the initial values ​​of the approximation coefficients of each polynomial approximation expression, solve the Galerkin projection equations using the sparse Galerkin method based on the equation residual, and substitute the solution results into the polynomial approximation expression to obtain the safety domain of the integrated energy microgrid considering small disturbance stability; Scheduling optimization is performed based on the security domain of the integrated energy microgrid group.

2. The method for optimizing the scheduling of integrated energy microgrids based on a small disturbance stability safety region according to claim 1, characterized in that: In step S1, the algebraic-differential equations of the integrated energy microgrid group can be expressed as: in, is the first-order derivative of the system dynamic state variable; x| t＝0 is the initial value of the system state variable; x is the dynamic state variable of the integrated energy microgrid; y is an algebraic variable; p is an independent variable parameter; f(x, y, p), g(x, y, p) and h(p) represent the initial values ​​of the differential equation, algebraic equation and dynamic system respectively; When the independent parameter p is constant, the following equation is linearized at the equilibrium point (x0, y0): Where Δx and Δy are the increments of the differential and algebraic state variables relative to their equilibrium points, respectively; when When it is non-singular, the state matrix A of the integrated energy microgrid group is further obtained: According to Lyapunov's first stability test, when all eigenvalues ​​of the state matrix A have negative real parts, the integrated energy microgrid group is small-disturbance stable.

3. The method for optimizing the scheduling of integrated energy microgrids based on a small disturbance stability safety region according to claim 2, characterized in that: In step S1, the integrated energy microgrid group includes a plurality of single integrated energy microgrids with the same structure, each of which includes: a distributed wind turbine generator set, a distributed photovoltaic generator set, a split-shaft gas turbine, a distributed energy storage device, a control center, and a power load; The dynamic model of the integrated energy microgrid group includes several single integrated energy microgrid models; each of the single integrated energy microgrid models includes: a grid-type doubly-fed wind turbine generator model, a grid-type photovoltaic generator model, a split-shaft gas turbine generator model, and an energy storage device model; The grid-type doubly-fed wind turbine generator model is specifically as follows: in, is the first-order derivative of the dynamic state variable of the grid-type doubly-fed wind turbine generator set; x WT is the dynamic state variable of the grid-type doubly-fed wind turbine generator set; WT is the algebraic variable of the grid-type doubly-fed wind turbine generator set; p WT is the independent variable parameter of the grid-type doubly-fed wind turbine generator set; f WT (x WT ,y WT ,p WT ) and g WT (x WT ,y WT ,p WT ) represent the differential equation and algebraic equation of the grid-type doubly-fed wind turbine generator model respectively; The grid-type photovoltaic generator model is specifically as follows: in, is the first-order derivative of the grid-type photovoltaic generator configuration state variable; x PV is the dynamic state variable of the grid-type photovoltaic generator set; y PV is the algebraic variable of the grid-type photovoltaic generator set; p PV is the independent variable parameter of the grid-type photovoltaic generator set; f PV (x PV ,y PV ,p PV ) and g PV (x PV ,y PV ,p PV ) represent the differential equation and algebraic equation of the grid-type photovoltaic generator model respectively; The energy storage device model is specifically: in, is the first-order derivative of the state variable of the energy storage device; x ESS is the dynamic state variable of the energy storage device; y ESS is the algebraic variable of the energy storage device; p ESS is the independent variable parameter of the energy storage device; f ESS (x ESS ,y ESS ,p ESS ) and g ESS (x ESS ,y ESS ,p ESS ) represent the differential equation and algebraic equation of the energy storage device model respectively; The split-shaft gas turbine generator set model is specifically as follows: in, is the first-order derivative of the state variable of the split-shaft gas turbine generator set; x GT is the dynamic state variable of the split-shaft gas turbine generator set; y GT is the algebraic variable of the split-shaft gas turbine generator set; p GT is the independent variable parameter of the split-shaft gas turbine generator set; f GT (x GT ,y GT ,p GT ) and g GT (x GT ,y GT ,p GT ) represent the differential equation and algebraic equation of the split-shaft gas turbine generator model respectively; The models of each feeder and tie line in the integrated energy microgrid system are: Where i TLi·D and i TLi·Q represents the current of the tie line connected to the i-th microgrid in the public DQ coordinate system; R TLi , L TLi is the resistance and inductance of the i-th tie line; v pcci·D and v pcci·Q is the voltage at the common coupling point where all distributed generation sources in the i-th microgrid are connected in the common DQ coordinate system; v pcc·D and v pcc·Q is the voltage of the common coupling point to which all microgrids are connected under the common DQ coordinate; The local load in the i-th integrated energy microgrid can be described as: Where i loadi·D and i loadi·Q represents the current of the local load in the i-th microgrid in the public DQ coordinate system; R loadi , L loadi is the resistance and inductance of the local load; Each single integrated energy microgrid model is specifically: in, is the first-order derivative of the state variable of the single integrated energy microgrid; x IMG is the dynamic state variable of the single integrated energy microgrid; y IMG is the variable of single integrated energy microgrid number; p IMG is the independent variable parameter of the single integrated energy microgrid; f IMG (x IMG ,y IMG ,p IMG ) and g IMG (x IMG ,y IMG ,p IMG ) represent the differential equation and algebraic equation of the single integrated energy microgrid model respectively; The comprehensive energy microgrid model is specifically as follows: in, is the first-order derivative of the state variable of the integrated energy microgrid group; x IMGC is the dynamic state variable of the integrated energy microgrid group; y IMGC is the algebraic variable of the integrated energy microgrid group; p IMGC is the independent variable parameter of the integrated energy microgrid group; f IMGC (x IMGC ,y IMGC ,p IMGC ) and g IMGC (x IMGC ,y IMGC ,p IMGC ) represent the differential equation and algebraic equation of the integrated energy microgrid model respectively.

4. The method for optimizing the scheduling of integrated energy microgrids based on a small disturbance stability safety region according to claim 3, characterized in that: In step S2, the bifurcation equation of the integrated energy microgrid is constructed, which is expressed as: F class (x,y,x B ,p)=0 Among them, F class represents the value of the bifurcation equation with bifurcation type class, which includes any of Hopf bifurcation, saddle-node bifurcation, and singularity-induced bifurcation; x B is an additional variable; The small perturbation stability region is expressed as: in, Represents the real number domain, Re(λ i ) represents the real part of the i-th eigenvalue; The boundary of the small perturbation stability region is defined as: Among them, Σ SNB represents the set of all saddle bifurcation points; Σ Hopf represents the set of Hopf bifurcation points; Σ SIB represents the set of singularity-induced bifurcation points.

5. The method for optimizing the scheduling of integrated energy microgrids based on a small disturbance stability safety region according to claim 4, characterized in that: In step S2, the dominant bifurcation parameters selected include: p={p load ,p wind ,p pv ,p GT ,p k } Among them, p load is the load factor of each single integrated energy microgrid; p wind is the wind power factor of each single integrated energy microgrid wind turbine unit; p pv is the optical power factor of each single integrated energy microgrid photovoltaic unit; p GT is the mechanical power of each single integrated energy microgrid gas turbine; p k is the gas turbine excitation regulator gain coefficient.

6. The method for optimizing the scheduling of integrated energy microgrids based on a small disturbance stability safety region according to claim 5, characterized in that: In step S3, a set of polynomial basis functions is constructed for each dominant bifurcation parameter to build a polynomial basis function set. The polynomial basis function is expressed as: Φ i,0 (q i ),Φ i,1 (q i ),Φ i,2 (q i ),...,Φ i,N (q i )∈U,i=1,2,…,s Among them, q i is the i-th dominant bifurcation parameter to be analyzed, s is the number of dominant bifurcation parameters to be analyzed; Φ i,N (q i ) is the basis function of degree N corresponding to the i-th dominant bifurcation parameter; U is the inner product space; The sum of the tensor product of the basis function groups corresponding to each parameter is not higher than the preset value N b The function of is used as the basis function of the inner product space U subspace to obtain the complete polynomial basis function, which is expressed as: Among them, N b is the number of basis functions, satisfying is the experimental basis function; q is the dominant bifurcation parameter to be analyzed selected from p, and p≠q; is the tensor product; The polynomial approximation expression of each variable in the bifurcation equation is expressed as: in, is the value of the polynomial approximation expression of the i-th variable; c ij is the coefficient of the jth basis function in the polynomial approximation expression of the i-th variable.

7. The method for optimizing the scheduling of integrated energy microgrids based on a small disturbance stability safety region according to claim 6, characterized in that: In step S4, the Galerkin projection equations are expressed as: Among them, B i It is the approximation equation of the boundary criterion of the small disturbance stability security region of the i-th integrated energy microgrid group.

8. The method for optimizing the scheduling of integrated energy microgrids based on a small disturbance stability safety region according to claim 7, characterized in that: In step S5, an initial search direction vector is selected, and then the equations of Hopf bifurcation and saddle-node bifurcation are solved along the initial search direction to obtain the instability critical point on the boundary of the small perturbation stability region. and p * The corresponding state variable x * , algebraic variable y c With the eigenvector φ * ; If the calculated p * Not belonging to the preset parameter support domain Ω p , then update the search direction vector, adjust the search direction and calculate again; The instability critical point p * The corresponding state variable x * , algebraic variable y * With the eigenvector φ * As the initial value of the constant coefficient in the polynomial approximation expression, and set the other non-constant coefficients to 0 to complete the initialization.

9. The method for optimizing the scheduling of integrated energy microgrids based on a small disturbance stability safety region according to claim 8, characterized in that: In step S5, the Galerkin projection equations are solved using a sparse Galerkin method based on equation residuals, including: First-order approximation: Use the Newton-Raphson method to iteratively solve the Galerkin projection equations to obtain c ij The first-order approximation result of ; Second-order and higher-order approximation: The importance of the second-order and higher-order terms of the Galerkin projection equation is quantified by using the weighted average of the absolute value of the residual equation and its inner product; For each order of the second order and above, sort the items in each order according to their corresponding importance and take the top s τ Items, generate sparse bases of order 2 and above in turn; The first-order approximation result and the sparse bases of the second order and above are used to replace the basis functions in the polynomial approximation expression respectively to obtain the safety domain of the integrated energy microgrid group considering small disturbance stability.

10. The method for optimizing the scheduling of integrated energy microgrids based on a small disturbance stability safety region according to claim 9, characterized in that: The importance of the second-order and higher-order terms is expressed as: Among them, G r,s ({c j,k }) is the nonlinear equation system after Galerkin projection, and the unknown coefficients can be obtained by solving it; c (1,1) are the undetermined coefficients solved by the first-order approximation equation; represents the total amount of inner products of the second-order Galerkin projection equation to be solved and all quadratic basis function terms, is the number of quadratic basis functions; The s τ satisfy: Among them, τ is the preset threshold.

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