Power system robust optimal power flow method considering photovoltaic output uncertainty and transient stability constraint

Abstract

The invention provides a power system robust optimal power flow method considering photovoltaic output uncertainty and transient stability constraint, and belongs to the field of power system operation control methods, and the method comprises the following steps: S1, considering the stable operation and transient stability constraint of a power system, and building a target function with the minimum operation cost of the power system; s2, based on the model in the step S1, establishing a double-layer robust optimization model integrating TSA and transient stability constraint; and S3, solving the double-layer robust optimization model integrating the TSA and the transient stability constraint in the step S2, and obtaining the load reduction quantity of each node of the power system. The method can describe the operation state of the generator, and reduces the load of the power system when transient disturbance occurs, so that the power system is kept stable.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system optimization methods, and specifically relates to a robust optimal power flow method for power systems considering the uncertainty of photovoltaic output and transient stability constraints. Background Art

[0002] With the continuous increase in the penetration rate of new energy sources such as photovoltaics in the power system, the inertia in the power grid decreases and the volatility increases. Once a disturbance occurs (such as a line fault, node disconnection, etc.), the power system will exhibit transient instability phenomena, resulting in severe fluctuations or even collapse of frequency and voltage.

[0003] Existing power system control methods, such as the grid two-stage robust optimization operation control method proposed in a Chinese application (application number 202410599567.9), in this existing technology, a robust configuration of generation plans and reserve capacity is achieved by constructing an uncertain output set. This method is only a comprehensive optimization that takes into account energy storage and distributed power sources under the condition of stable operation of the power system. Specifically, the optimization process in this method only relies on static-level constraint conditions and can only handle steady-state disturbances, such as slow changes and continuous deviations of electrical quantities in the power system over a long time. When dealing with transient disturbances, such as short-circuit faults and large-power fluctuations, it cannot optimize them, further leading to the instability of the power system.

[0004] Although adding a transient stability assessment model to the existing control method can solve the above problems, it is not easy to implement in actual situations. This is because the two-stage robust optimization model (TSRO optimization model) in the existing method is mainly based on linear modeling, while the transient stability assessment model is based on a non-linear dynamic model. There are serious mismatches in their expression forms, time scales, and variable definitions. Therefore, the transient stability assessment model cannot be applied to the traditional TSRO optimization model currently. Summary of the Invention

[0005] To solve the above problems, the present solution proposes a robust optimal power flow method for power systems considering the uncertainty of photovoltaic output and transient stability constraints.

[0006] To achieve the above object, the present invention proposes the following technical content:

[0007] A robust optimal power flow method for power systems considering the uncertainty of photovoltaic output and transient stability constraints, comprising the following steps:

[0008] S1: Considering the stable operation of the power system and transient stability constraints, establish an objective function with the minimum operation cost of the power system;

[0009] S2: Based on the model in step S1, establish a two-layer robust optimization model integrating TSA and transient stability constraints;

[0010] S3: Solve the bi-level robust optimization model integrating TSA and transient stability constraints in S2 to obtain the load shedding amounts of each node in the power system.

[0011] Furthermore, S1 specifically includes the following steps:

[0012] S1.1: Establish an objective function for minimizing the cost of the power system; the power system cost includes: preventive dispatch cost and emergency control cost;

[0013]

[0014] In formula (1), x represents the load amount of preventive dispatch; u represents the output of uncertain photovoltaic power; U s represents the set of uncertain outputs of photovoltaic power; y represents the output of the power system after emergency load shedding; φ k (k, u) represents the output of the power system under the k-th transient disturbance; C G (x) represents the preventive dispatch cost of the power system; C LS (y) represents the emergency control cost;

[0015] In formula (2), i represents the i-th generator in the power system; N G represents the number of generators in the power system, i ∈ [1, N G ; a i , b i , c i all represent the generation cost coefficients of the i-th generator; P Gi is the generation power of the i-th generator in the power system corresponding to the load amount x of preventive dispatch;

[0016] In formula (3), r represents the r-th branch of the power system, N D represents the number of branches in the power system, r ∈ [1, N D ; P Lr represents the line power corresponding to the emergency load shedding of the r-th branch; p k represents the occurrence probability of the k-th transient disturbance; C LS，O represents the load shedding cost;

[0017] S1.2: Constraints for the stable operation model of the power system; used to ensure the stable operation of the power system when no transient disturbance occurs;

[0018]

[0019] In formula (4), t represents the moment when the transient disturbance occurs; and respectively represent the active power and reactive power of the i-th generator at time t; and respectively represent the active and reactive power outputs of the i-th generator's photovoltaic system at time t; and represent the active and reactive power of the m-th bus at time t; and respectively represent the voltages of the m-th and n-th buses; G mn represents the conductance between the m-th and n-th buses; B mn represents the susceptance between the m-th and n-th buses; represents the phase angle difference between the m-th and n-th buses at time t;

[0020] In Equation (5), and respectively represent the upper and lower limits of the active power output of the i-th generator; N G represents the number of generators;

[0021] In Equation (6), and respectively represent the upper and lower limits of the reactive power output of the i-th generator;

[0022] In Equation (7), and respectively represent the upper and lower limits of the voltage of the m-th bus;

[0023] In Equation (8), and respectively represent the upper and lower limits of the apparent power of the m-th bus; N B represents the number of buses;

[0024] In Equation (9), and respectively represent the upper and lower limits of the reactive power output of the d-th photovoltaic; represents the reactive power output of the d-th photovoltaic in the power system at time t; N S represents the number of photovoltaics;

[0025] In Equations (10) and (11), represents the active power of the m-th bus at time t; represents the active power of the m-th bus at the initial time; P Lm represents the active power reduction of the m-th bus; represents the reactive power of the m-th bus at time t; represents the reactive power of the m-th bus at the initial time; Q Lm represents the reactive power reduction of the m-th bus;

[0026] S1.3: Transient stability quantitative evaluation model constraints;

[0027] Define the set \(U\) of the uncertain output of the photovoltaic s :

[0028]

[0029] Expand the response of the non - linear dynamic system using the first - order Taylor expansion:

[0030]

[0031] Neglect the high - order terms in Equation (13), then Equation (13) is transformed into:

[0032]

[0033]

[0034] Introduce the photovoltaic perturbation and propose a transient evaluation index to evaluate whether the power system is stable;

[0035]

[0036] In Equation (12), \(U\) s represents the set of uncertain outputs of the photovoltaic; represents the set of active power outputs of the photovoltaic; represents the minimum active power output of the \(d\) - th photovoltaic; represents the active power output of the \(d\) - th photovoltaic at time \(t\); represents the maximum active power output of the \(d\) - th photovoltaic; \(\mu\) s.u and \(\mu\) s.l represent the upper and lower limits of the uncertainty of the photovoltaic output; represents the predicted output of the \(d\) - th photovoltaic;

[0037] In Equation (13), \(\varphi(x_0,t,\beta)\) represents the trajectory sensitivity matrix of the power system at time \(t\); \(\varphi_1(x_0,t,\beta+\Delta\beta)\) represents the trajectory sensitivity matrix of the transformed power system; \(\Delta\beta\) represents the change in the uncertain output of the photovoltaic; \(\beta\) represents the uncertain output of the photovoltaic; \(x_0\) represents the load of the preventive dispatch at the initial time;

[0038] In Equations (14) and (15), \(\varPhi(x_0,t,\beta)\) represents the trajectory sensitivity of the power system at time \(t\);

[0039] In Equation (16), \(\Delta\eta\) represents the change in the stability margin after the generation change; \(\varPhi_1(\eta,\beta)\) represents the system trajectory sensitivity after the generation change. If \(\Delta\beta\leq0.3\), it indicates that the power system is in a stable state;

[0040] In Equation (17), \(\eta\) k (PC,EC,\(\Delta P\)s ) represents the stability margin during the k-th transient disturbance; represents the initial stability margin; represents the change in the stability margin after the change in PV output; represents the change in the stability margin after load shedding under the k-th transient disturbance condition; σ represents the minimum stability margin;

[0041] In equations (18) and (19), is the disturbance mapping function of PV output; f2(P Lm ) represents the disturbance mapping function of the bus;

[0042] In equations (20), (21) and (22), Φ i (η, P Li ) represents the root locus of the i-th generator; Φ r (η, P Lr ) represents the root locus of the r-th branch; k i represents the automatic generation control participation factor of the i-th generator.

[0043] Furthermore, the transient energy margin is evaluated, and the formula is:

[0044]

[0045] E current = P m - P e

[0046] E critical = 2 * max(P e )(23)

[0047] In equation (23), E current is the energy state of the current power system; E critical is the energy at the critical unstable point of the power system; H eq is the equivalent inertia constant of the power system; P m is the mechanical power of the system; P e is the electromagnetic power of the system.

[0048] Furthermore, the integrated TSA and transient stability constraint-based two-layer robust optimization model is:

[0049]

[0050] s.t. Ax + Bu = b

[0051] Fx ≤ f

[0052] G ≤ g

[0053] U + Vu ≤ e

[0054] y ≥ 0 (24)

[0055] This equation (24) is divided into a main problem and a sub - problem;

[0056] Main problem:

[0057]

[0058]

[0059] Fx ≤ f

[0060] θ ≥ d T y l

[0061] G ≤ g

[0062]

[0063] y l ≥ 0 (25)

[0064] In the formula, x represents the load amount of preventive scheduling;

[0065] θ represents the upper limit of emergency load curtailment cost;

[0066] a, b, and c all represent cost coefficients;

[0067] is the PV output at the most extreme case;

[0068] F is the preventive scheduling coefficient; f is the upper limit of preventive scheduling power;

[0069] d is a coefficient vector representing the unit cost of load curtailment; y l represents the output after load curtailment; d T y l represents the total cost of load curtailment.

[0070] G represents a coefficient matrix; the coefficients in G are linearly related to y l ; g is a constant vector representing the set upper limit.

[0071] U and V represent the system sensitivity matrix and the PV sensitivity matrix respectively; e represents the constraint vector value;

[0072] Sub - problem:

[0073]

[0074] U(x * )y + V(x * )u ≤ e

[0075] y ≥ 0

[0076] u ∈ U s

[0077] In the formula, S(u, x * ) is the objective function of the sub-problem;

[0078] Using the strong duality method, the max-min problem in Equation (26) is transformed into a max problem, simplifying the solution process of Equation (26);

[0079] The formula is:

[0080]

[0081] s.t. d T + G T λ + U s T ρ ≥ 0

[0082] In the formula, λ and ρ are Lagrange multipliers, both non-negative numbers, corresponding to the dual variables of the load shedding constraint and the transient stability constraint respectively.

[0083] Adopting the above technical content, the beneficial effects that can be achieved are:

[0084] It is possible to shed the load of the power system after a transient disturbance, thereby reducing the power demand of the system and keeping the system within the normal range, and improving the power balance of the power system after a transient disturbance.

[0085] Introducing the root locus analysis method, the root locus is a graphical method that can intuitively depict the dynamic behavior during the operation of the generator. Description of the Drawings

[0086] Figure 1 is the flow chart of this method;

[0087] Figure 2 is the example diagram of the 32-node power system;

[0088] Figure 3 is the power flow under linear factors and the power flow under non-linear factors;

[0089] Figure 4 is the optimal active power output of the power system at steady state;

[0090] Figure 5 is the optimal reactive power output of the power system at steady state;

[0091] Figure 6 is the optimal load shedding scheme after a transient disturbance. Detailed Implementation Modes

[0092] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0093] Embodiment 1: A robust optimal power flow method for a power system considering the uncertainty of photovoltaic output and transient stability constraints, specifically including the following steps:

[0094] S1: Considering the stable operation of the power system and transient stability constraints, establish an objective function with the minimum operating cost of the power system.

[0095] S1 specifically includes the following steps:

[0096] S1.1: Establish an objective function with the minimum cost of the power system. This belongs to the prior art.

[0097] The objective function is:

[0098]

[0099] In formula (1), C G (x) represents the preventive dispatching cost of the power system; x represents the load amount of preventive dispatching; C LS (y) represents the emergency control cost; u represents the output of the uncertain photovoltaic; U s represents the set of uncertain outputs of the photovoltaic; y represents the output of the power system after emergency load shedding; φ k (k, u) represents the output of the power system under the kth transient disturbance;

[0100] i represents the ith generator in the power system, N G represents the number of generators in the power system, i ∈ [1, N G ; a i , b i , c i all represent the generation cost coefficients of the ith generator; P Gi is the generation power of the ith generator in the power system corresponding to the load amount x of preventive dispatching;

[0101] r represents the rth branch of the power system, N D represents the number of branches in the power system, r ∈ [1, N D ; P Lr represents the line power of the rth branch corresponding to emergency load shedding; p k represents the occurrence probability of the kth transient disturbance; C LS，OIndicates the load reduction cost.

[0102] S1.2: Power system stable operation model constraints. Used to ensure the stable operation of the power system when no transient disturbances occur, which belongs to the prior art.

[0103]

[0104] In the formula, t represents the moment when the transient disturbance occurs; among them, the meaning of the transient disturbance is: the evolution process of the system's dynamic state within a short time after the system undergoes a sudden disturbance (such as: photovoltaic output fluctuation, line fault); and respectively represent the active power and reactive power of the i-th generator at time t; and respectively represent the active power output and reactive power output of the i-th generator's photovoltaic at time t; and represent the active power and reactive power on the m-th bus at time t;

[0105] and respectively represent the voltages on the m-th bus and the n-th bus; G mn represents the conductance between the m-th bus and the n-th bus; B mn represents the admittance between the m-th bus and the n-th bus; represents the phase angle difference between the m-th bus and the n-th bus at time t;

[0106] and respectively represent the upper and lower limits of the active power output of the i-th generator; represents the active power output of the i-th generator at time t; and respectively represent the upper and lower limits of the reactive power output of the i-th generator; represents the reactive power output of the i-th generator at time t; N G represents the number of generators;

[0107] and respectively represent the upper and lower limits of the voltage of the m-th bus; and respectively represent the upper and lower limits of the apparent power of the m-th bus; N B represents the number of buses; represents the active power of the m-th bus at time t; represents the reactive power of the m-th bus at time t; represents the active power of the m-th bus at the initial moment; represents the reactive power of the m-th bus at the initial moment; PLm Denote the active power shedding of the m-th busbar; Q Lm Denote the reactive power shedding of the m-th busbar.

[0108] and Denote the upper and lower limits of the reactive power output of the d-th photovoltaic respectively; Denote the reactive power output of the d-th photovoltaic in the power system at time t; N S Denote the number of photovoltaics.

[0109] S1.3: Transient stability quantitative evaluation model constraints. This is the core design of this solution.

[0110] The existing technologies mentioned in the background art are difficult to quantitatively model the dynamic process. When a severe transient disturbance occurs, they cannot accurately depict the dynamic behavior of the generator, nor can they fundamentally evaluate the risk of system instability. Therefore, it is necessary to embed a transient stability quantitative evaluation model. However, the existing TSRO optimization models are mainly based on linear / convex optimization modeling, while the transient stability quantitative evaluation models are often based on differential equations or non-linear dynamic models. There are serious mismatches between them in terms of expression form, time scale, variable definition, etc.

[0111] In order to incorporate the transient stability quantitative evaluation model into the TSRO optimization model for analysis, this solution introduces the root locus analysis method to depict the dynamic behavior of the generator, and linearizes the non-linear transient stability analysis through the first-order Taylor expansion into a linear constraint form that can be embedded in the optimization model, obtaining the sensitivity matrix φ(x0,t,β), thus solving the problem that the transient stability quantitative evaluation model is difficult to model, and linearly expressing the influence of photovoltaic output fluctuations and load shedding on the margin through sensitivity analysis, solving the problem that the constraint form cannot be embedded.

[0112] The specific expression is:

[0113]

[0114] In Equation (3), U s Denote the set of uncertain outputs of the photovoltaics; Denote the set of active power outputs of the photovoltaics; μ s.u and μ s.l Denote the upper and lower bounds of the uncertainty of the photovoltaic output; Denote the minimum active power output of the d-th photovoltaic; Denote the maximum active power output of the d-th photovoltaic; Denote the active power output of the d-th photovoltaic at time t; Denote the predicted output of the d-th photovoltaic;

[0115] In Equation (4), ε φis the high-order term of the Taylor series expansion; φ(x0,t,β) represents the trajectory sensitivity matrix of the power system at time t; Δβ represents the change in the uncertain PV output; β represents the uncertain PV output; φ1(x0,t,β+Δβ) represents the transformed trajectory sensitivity matrix;

[0116] In Equation (5), Δx(t) represents the load change of preventive dispatch at time t; Φ(x0,t,β) represents the trajectory sensitivity of the power system at time t.

[0117] In Equation (6), Φ(x0,t,β) represents the trajectory sensitivity of the power system at time t;

[0118] In Equation (7), Δη represents the change in the stability margin after the generation change (after load shedding); Φ1(η,β) represents the system trajectory sensitivity after the generation change.

[0119] In Equation (8), represents the initial stability margin; represents the change in the stability margin after the PV output change; represents the change in the stability margin after load shedding under the k-th transient disturbance; σ represents the minimum stability margin; η k (PC,EC,ΔP s ) represents the stability margin at the k-th transient disturbance;

[0120] In Equation (9), the change in the stability margin after the PV output change; is the disturbance mapping function of the PV output; represents the change in the PV output;

[0121] In Equation (10), f2(P Lm ) represents the disturbance mapping function of the bus;

[0122] In Equation (11), ΔP Gi represents the change in the output of the i-th generator; N S represents the number of PVs, represents the change in the active power output of the d-th PV; represents the change in the PV output;

[0123] In Equation (12), k i represents the automatic generation control participation coefficient of the i-th generator; represents the change in the PV output;

[0124] In Equation (13), Φ i (η,P Li) represents the root locus of the i-th generator; according to the value of the root locus, the stability and dynamic response characteristics of the i-th generator can be reflected.

[0125] In Equation (14), Φ r (η, P Lr ) represents the root locus of the r-th branch; according to the value of the root locus, the stability and dynamic response characteristics of the r branches can be reflected.

[0126] Equation (3) is used to define the set U of uncertain output of photovoltaic power generation s , which is used to represent the range of photovoltaic power fluctuation in actual operation; Equation (4) linearizes the response of the nonlinear dynamic system by using the first-order Taylor expansion of the input parameters with respect to the system state variables (x0, t, β), which serves as the basis for subsequent root locus analysis; Equation (5) ignores the high-order term ε φ on the basis of Equation (4) to obtain the sensitivity mapping relationship of the state variables to the perturbation parameters and ensure the solvability of the model; Equations (6)-(9) jointly construct a transient stability sensitivity evaluation framework based on the root locus method; specifically:

[0127] Equation (6) quantifies the partial derivative effect of the perturbation on the system state trajectory; Equation (7) proposes a transient stability evaluation index, that is, to measure whether the system can remain within the stable domain after the perturbation; Equations (7)-(9) introduce the photovoltaic perturbation expression into the sensitivity expression to measure the influence direction and amplitude of the perturbation on the offset of the system root locus, so as to judge whether the system remains within the stable domain. If Δβ is less than or equal to 0.3, it is within the stable domain and the power system remains stable; Equations (10) and (15) are the stability criterion and feasibility condition after the system is perturbed;

[0128] S1.4: Evaluate the transient energy margin. It belongs to the prior art. It is used to know the ability to resist the perturbation after determining the transient perturbation in S1.3; the formula is:

[0129]

[0130] E current = P m - P e

[0131] E critical = 2 * max(P e )

[0132] In the formula, E current is the energy state of the current power system; E critical is the energy at the critical unstable point of the power system, which can be understood as the energy possessed by the power system in the critical state; H eq is the equivalent inertia constant of the power system; P mis the mechanical power of the system; P e is the electromagnetic power of the system;

[0133] Equation (7) can intuitively show the impact of system parameter changes (Δβ) on stability and help determine the parameter range for system stability. The energy margin index in S1.4 focuses more on reflecting the energy balance and reserve during the transient process after the system is disturbed, and can quantitatively give the magnitude of the system's ability to resist disturbances. The two together constitute the index for evaluating the stability of the power system.

[0134] S2: Based on the model in step S1, establish a two-layer robust optimization model integrating TSA (Trajectory Sensitivity Analysis) and transient stability constraints.

[0135] Since the traditional C&CG (Column and Constraint Generation algorithm, an algorithm for solving two-stage robust optimization problems) cannot be directly used in the TSA process and transient stability constraints, we propose the following improved algorithm to integrate TSA and transient stability constraints:

[0136] The formula is:

[0137]

[0138] Fx ≤ f

[0139] G ≤ g

[0140] U + Vu ≤ e

[0141] y ≥ 0

[0142] In the formula, A represents the first-stage decision coefficient matrix; B represents the uncertain photovoltaic output matrix;

[0143] S3: Divide the two-layer robust optimization model integrating TSA (Trajectory Sensitivity Analysis) and transient stability constraints in S2 into a master problem and a sub-problem, and solve them.

[0144] Divide Equation (16) into a master problem and a sub-problem:

[0145] Master problem:

[0146]

[0147] Fx ≤ f

[0148] θ ≥ d T y l

[0149] G ≤ g

[0150]

[0151] y l ≥ 0

[0152] Wherein, x represents the load amount of preventive scheduling;

[0153] θ represents the upper limit of emergency load shedding cost; a, b, and c all represent cost coefficients;

[0154] is the PV output at the most extreme case;

[0155] F is the preventive scheduling coefficient; f is the upper limit of preventive scheduling power;

[0156] d is a coefficient vector representing the unit cost of load shedding; y l represents the output after load shedding; d T y l represents the total cost of load shedding.

[0157] G represents a coefficient matrix; the coefficients in G have a linear relationship with y; g is a constant vector representing the set upper limit.

[0158] U and V respectively represent the system sensitivity matrix and the PV sensitivity matrix; e represents the constraint vector value.

[0159] Sub-problem:

[0160]

[0161] U(x * )y + V(x * )u ≤ e

[0162] y ≥ 0

[0163] u ∈ U s

[0164] Wherein, S(u, x * ) is the objective function of the sub-problem;

[0165] Using the strong duality method, the max-min problem in Equation (16) is transformed into a max problem, simplifying the solution process of Equation (16).

[0166] The formula is:

[0167]

[0168] s.t. d T + G T λ + U s T ρ ≥ 0 (19)

[0169] In the formula, λ and ρ are Lagrange multipliers, both of which are non - negative numbers and correspond to the dual variables of the load shedding constraint and the transient stability constraint respectively; the optimal solution x*(y) is solved using Equation (19) under the given y. Based on the optimal solution x*(y), the objective value at this time is solved using the objective function of the master problem, and then the objective value is substituted into the sub - problem to solve, obtaining the optimal solution y*. This optimal solution is the "node" output corresponding to the load in Example 2.

[0170] Example 2: The present invention uses a 32 - node power system example, and the node diagram is shown in Figures 2 - 6 , and the present invention is implemented through the MATLAB optimization platform, and the CPLEX solver is used to solve the TSC - OPF problem.

[0171] Based on this example, the method of the present invention is used to simulate the optimal power flow calculation and generation plan of the power system under high photovoltaic penetration, and to simulate the emergency load shedding plan and generator output plan with the lowest total system cost after the disturbance occurs. The results are shown in Table 1 and Table 2.

[0172] Table 1 Optimal power flow dispatch of the system before the transient occurs

[0173]

[0174]

[0175] Table 2 Optimal load shedding plan after the transient occurs

[0176]

[0177]

[0178] Figure 3 The red curve in shows the voltage conditions of each node under linear disturbance factors; the blue curve shows the voltage conditions of each node in this scheme under non - linear disturbance factors. From Figure 3 It can be seen that after this scheme considers non - linear disturbance factors, there is not much difference compared with only under linear disturbance factors, which indicates that this scheme is applicable to non - linear disturbances.

[0179] Figure 4 and Figure 5 respectively show the active power and reactive power of each node.

[0180] Figure 6 After the transient disturbance occurs, the scheme in Example 1 is used to solve the optimal load shedding amount of each node. According to the optimal load shedding amount, that is, reducing the load amount of the power system, when the transient disturbance occurs, the power demand of the power system is reduced, thus ensuring the stability of the power system.

[0181] Based on the above-mentioned ideal embodiments of the present invention as inspiration, through the above description, relevant staff can completely make various changes and modifications without departing from the technical idea of this invention. The technical scope of this invention is not limited to the content in the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A robust optimal power flow method for power systems considering the uncertainty of photovoltaic power output and transient stability constraints, characterized in that, It includes the following steps: S1: Considering the stable operation of the power system and transient stability constraints, establish an objective function with the minimum operating cost of the power system; S2: Based on the model in step S1, establish a two-layer robust optimization model integrating TSA and transient stability constraints; S3: Solve the two-layer robust optimization model integrating TSA and transient stability constraints in S2 to obtain the load shedding amounts of each node in the power system.

2. A robust optimal power flow method for a power system considering the uncertainty of photovoltaic output and transient stability constraints according to claim 1, characterized in that S1 specifically includes the following steps: S1.1: Establish an objective function with the minimum cost of the power system; the power system cost includes: preventive scheduling cost and emergency control cost; In Equation (1), x represents the load amount of preventive scheduling; u represents the output of uncertain photovoltaic power; U s represents the set of uncertain output of photovoltaic power; y represents the output of the power system after emergency load shedding; φ k (k, u) represents the output of the power system under the k-th transient disturbance; C G (x) represents the preventive scheduling cost of the power system; C LS (y) represents the emergency control cost; In formula (2), i represents the i-th generator in the power system; N G represents the number of generators in the power system, i ∈ [1, N G ; a i , b i , c i all represent the power generation cost coefficients of the i-th generator; P Gi is the power generation power of the i-th generator in the power system corresponding to the load amount x of the preventive dispatch; In formula (3), r represents the r-th branch of the power system, and N D represents the number of branches in the power system, r ∈ [1, N D ; P Lr represents the line power corresponding to the emergency load shedding of the r-th branch; p k represents the occurrence probability of the k-th transient disturbance; C LS，O represents the load shedding cost; S1.2: Constraints for the stable operation model of the power system; used to ensure the stable operation of the power system when no transient disturbance occurs; In formula (4), t represents the occurrence time of the transient disturbance; and respectively represent the active power and reactive power of the i-th generator at time t; and respectively represent the active power output and reactive power output of the photovoltaic of the i-th generator at time t; and represent the active power and reactive power of the m-th bus at time t; and respectively represent the voltages of the m-th bus and the n-th bus; G mn represents the conductance between the m-th bus and the n-th bus; B mn represents the admittance between the m-th bus and the n-th bus; represents the phase angle difference between the m-th bus and the n-th bus at time t; In formula (5), and respectively represent the upper and lower limits of the active power output of the i-th generator; N G represents the number of generators; In formula (6), and respectively represent the upper and lower limits of the reactive power output of the i-th generator; In formula (7), and respectively represent the upper and lower limits of the voltage of the m-th busbar; In formula (8), and respectively represent the upper and lower limits of the apparent power of the m-th bus; N B represents the number of buses. In Equation (9), and represent the upper and lower limits of the reactive power output of the d-th photovoltaic cell, respectively; represents the reactive power output of the d-th photovoltaic cell in the power system at time t; N S represents the number of photovoltaic cells; In formulas (10) and (11), represents the active power of the m-th bus at time t; represents the active power of the m-th bus at the initial time; P Lm represents the active power reduction of the m-th bus; represents the reactive power of the m-th bus at time t; represents the reactive power of the m-th bus at the initial time; Q Lm represents the reactive power reduction of the m-th bus; S1.3: Constraints for the quantitative evaluation model of transient stability; Define the set of uncertain output U of photovoltaic output s : Expand the response of the nonlinear dynamic system using the first-order Taylor expansion: Neglect the high-order terms in Equation (13), then Equation (13) is transformed into: Introduce photovoltaic disturbances and propose a transient evaluation index to evaluate whether the power system is stable; In formula (12), U s represents the uncertainty set of photovoltaic power; represents the set of active power outputs of photovoltaic power; represents the minimum active power output of the d-th photovoltaic power; represents the active power output of the d-th photovoltaic power at time t; represents the maximum active power output of the d-th photovoltaic power; μ s.u and μ s.l represent the upper and lower limits of the uncertainty of photovoltaic power output; represents the predicted power output of the d-th photovoltaic power; In Equation (13), φ(x0,t,β) represents the trajectory sensitivity matrix of the power system at time t; φ1(x0,t,β + Δβ) represents the trajectory sensitivity matrix of the transformed power system; Δβ represents the change in the uncertain photovoltaic output; β represents the uncertain photovoltaic output; x0 represents the load amount of preventive scheduling at the initial time; In Equations (14) and (15), Φ(x0,t,β) represents the trajectory sensitivity of the power system at time t; In Equation (16), Δη represents the change in the stability margin after the generation change; Φ1(η,β) represents the system trajectory sensitivity after the generation change; if Δβ is less than or equal to 0.3, it indicates that the power system is in a stable state; In Equation (17), η k (PC, EC, ΔP s ) represents the stability margin during the k-th transient disturbance; represents the initial stability margin; represents the change in the stability margin after the change in PV output; represents the change in the stability margin after load shedding under the k-th transient disturbance condition; σ represents the minimum stability margin; In formulas (18) and (19), is the disturbance mapping function of PV output; f2(P Lm ) represents the disturbance mapping function of the busbar; In equations (20), (21) and (22), Φ i (η, P Li ) represents the root locus of the i-th generator; Φ r (η, P Lr ) represents the root locus of the r-th branch; k i represents the automatic generation control participation factor of the i-th generator.

3. A robust optimal power flow method for a power system considering photovoltaic output uncertainty and transient stability constraints according to claim 2, characterized in that Evaluate the transient energy margin, and the formula is: E current = P m - P e E critical = 2 * max(P e )(23) In Equation (23), E current is the energy state of the current power system; E critical is the energy at the critical instability point of the power system; H eq is the equivalent inertia constant of the power system; P m is the mechanical power of the system; P e is the electromagnetic power of the system.

4. A robust optimal power flow method for a power system considering the uncertainty of photovoltaic output and transient stability constraints according to claim 2, characterized in that, In step S2, the two-layer robust optimization model integrating TSA and transient stability constraints is: s.t. Ax + Bu = b Fx ≤ f G ≤ g U + Vu ≤ e y≥0 (24) This Equation (24) is divided into a master problem and a sub-problem; Master problem: Fx ≤ f θ≥d T y l G ≤ g y l ≥0 (25) In the formula, x represents the load amount of preventive scheduling; θ represents the upper limit of the emergency load shedding cost; a, b, and c all represent cost coefficients; is the PV output at the most extreme case; F is the preventive scheduling coefficient; f is the upper limit of the preventive scheduling power; d is the coefficient vector, representing the unit cost of load shedding; y l represents the output after load shedding; d T y l represents the total cost of load shedding; G represents the coefficient matrix; the coefficients in G have a linear relationship with y l and g is a constant vector representing the set upper limit; U and V respectively represent the system sensitivity matrix and the photovoltaic sensitivity matrix; e represents the constraint vector value; Sub-problem: s.t. G ≤ g U(x * )y + V(x * )u ≤ e y≥0 u ∈ U s where S(u, x * ) is the objective function of the sub-problem; Using the strong duality method, transform the max-min problem in Equation (26) into a max problem to simplify the solution process of Equation (26); The formula is: s.t.d T +G T λ+U s T ρ≥0 In the formula, λ and ρ are Lagrange multipliers, both non-negative numbers, corresponding to the dual variables of the load shedding constraint and the transient stability constraint respectively.

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