A transient stability constrained optimal power flow solution considering photovoltaic output uncertainty

Abstract

A method for solving transient stability-constrained optimal power flow that takes into account photovoltaic output uncertainty includes the following steps: Step 1: Establish a probability distribution model for photovoltaic power station output; Step 2: Establish a traditional transient stability-constrained optimal power flow model; Step 3: Perform equivalent analysis on the transient stability constraints of the traditional TSCOPF model; Step 4: Introduce the photovoltaic power station into the equivalent TSCOPF model to establish a probabilistic TSCOPF model that takes into account photovoltaic output uncertainty; Step 5: Use the probability distribution model of photovoltaic output to calculate its numerical characteristics and perform deterministic transformation on the chance constraints in the model; Step 6: Use the augmented Lagrangian method to solve the deterministically transformed probabilistic TSCOPF model. The present invention discloses a method for solving transient stability-constrained optimal power flow that takes into account photovoltaic output uncertainty. The generator output strategy obtained by the present invention fully considers the impact of photovoltaic output uncertainty while maintaining transient stability of the power system.

Description

Technical Field

[0001] The present invention belongs to the technical field of power systems, and specifically relates to the technical fields related to photovoltaic output uncertainty analysis and optimal power flow solution of power systems, and in particular to a transient stability constrained optimal power flow solution method taking into account photovoltaic output uncertainty. Background Art

[0002] However, as conventional generators in power systems are replaced in large numbers with photovoltaic power plants, the system's stability will deteriorate due to the uncertainty of photovoltaics, significantly weakening its ability to withstand faults. The overall anti-interference capability of the power system needs to be further improved. Transient Stability Constrained Optimal Power Flow (TSCOPF) can improve the transient stability of power systems, ensuring that the system maintains sufficient safety margin to maintain its transient stability in the event of a fault.

[0003] Patent publication number CN109599872B discloses a method for calculating probabilistic optimal power flow for power systems based on a stacked denoising autoencoder. This method establishes an optimal power flow model using a stacked denoising autoencoder and trains the stacked denoising autoencoder using power system operating data, enabling rapid calculation of the probabilistic optimal power flow. However, this method does not specifically analyze the uncertainty of renewable energy sources, particularly the uncertainty of photovoltaic output. Furthermore, this method lacks consideration of system transients caused by faults, and therefore cannot provide optimal power flow calculation results that maintain transient power angle stability. Patent publication number CN104766142B discloses a transient stability constrained optimal power flow calculation method based on EEAC and trajectory sensitivity. This method uses trajectory sensitivity to determine the margin sensitivity of various fault types and incorporates transient stability constraints into the optimal power flow model, resulting in calculation results that meet the transient power angle stability requirements of the power system. This method improves computational efficiency and resolves convergence difficulties. However, this method does not consider the impact of renewable energy sources, which are increasingly becoming a significant component of power systems, making it potentially unsuitable for today's power systems. None of the above methods can provide an optimal power flow solution that takes into account the uncertainty of photovoltaic output and satisfies the stability of the system transient power angle.

[0004] Therefore, the applicant proposed a TSCOPF solution method that takes into account the uncertainty of photovoltaic output, providing the optimal output strategy of generator sets for the power system with large-scale grid-connected photovoltaic power stations, while ensuring the transient stability of the power system operation. Summary of the Invention

[0005] The purpose of the present invention is to solve the problem that the existing technology recorded in the background technology is unable to analyze the transient process of the power system under the expected fault when establishing the optimal power flow model for power flow calculation, and obtain the calculation results that meet the transient stable operation of the system, and at the same time specifically consider the impact of photovoltaic output uncertainty on the stable operation of the power system, and take this impact into account in the solution process. Therefore, in order to consider the transient process of the power system and the uncertainty of photovoltaic output at the same time in the optimal power flow solution process, a transient stability constrained optimal power flow solution method taking into account the uncertainty of photovoltaic output is proposed.

[0006] The transient stability constrained optimal power flow solution method taking into account the uncertainty of photovoltaic output includes the following steps:

[0007] Step 1: Obtain historical output data of photovoltaic power stations and establish a probability distribution model for photovoltaic power station output;

[0008] Step 2: Obtain various operating parameters of the power system after PV grid connection and establish a transient stability constrained optimal power flow (TSCOPF) model;

[0009] Step 3: Based on the trajectory sensitivity method, perform equivalent analysis on the transient stability constraints of the transient stability constrained optimal power flow TSCOPF model and establish an equivalent transient stability constrained optimal power flow TSCOPF model;

[0010] Step 4: Introduce the PV power plant into the equivalent transient stability constrained optimal power flow TSCOPF model to establish a probabilistic transient stability constrained optimal power flow TSCOPF model that takes into account the uncertainty of PV output;

[0011] Step 5: Use the PV power station output probability distribution model to calculate the digital characteristics of PV output and perform a second-order cone transformation on the chance constraints in the probabilistic transient stability constrained optimal power flow (TSCOPF) model.

[0012] Step 6: Use the augmented Lagrangian method (ALM) to solve the probabilistic transient stability constrained optimal power flow (TSCOPF) model after the second-order cone transformation, and obtain the calculation results that take into account the impact of PV output uncertainty and meet the transient stability of the system under fault conditions.

[0013] In step 1, photovoltaic power generation output is affected by one or more factors including light intensity, ambient temperature, and photovoltaic module conversion efficiency. The output data of photovoltaic power stations over the years are obtained from the data published by the power grid company. The probability density of the photovoltaic power station output is estimated based on the Gaussian mixture model, and a probability distribution model of the photovoltaic power station output is established.

[0014] In step 2, various operating parameters of the power system change after the photovoltaic grid is connected. The parameters such as the active and reactive output of the generator sets, active and reactive loads, photovoltaic power station output, node voltage amplitude and phase angle, and number of nodes at the power system nodes are re-determined, and the transient stability constrained optimal power flow TSCOPF model is established based on this.

[0015] In step 2, the objective function and constraints of the transient stability constrained optimal power flow TSCOPF model are as follows:

[0016] 1) Objective function for generator fuel cost and grid loss:

[0017]

[0018] Where: c i represents the cost function of the i-th group of generators; N represents the set of generators; p Gi Indicates the active output of the generator set at node i.

[0019] 2) The tidal current balance equation for steady-state operation:

[0020]

[0021] Where: p Di represents the active load at node i; v i ,θ i represents the node voltage amplitude and phase angle of the system node i; q Gi represents the reactive output of the generator set at node i; q Di represents the reactive load at node i; Y ij , α ij Represents the amplitude and phase angle of the elements in the node admittance matrix of the line from node i to node j.

[0022] 3) Steady-state operation constraints;

[0023]

[0024] Where: Respectively represent the minimum and maximum active output of the generator set at node i; Respectively represent the minimum and maximum reactive output of the generator set at node i; They represent the minimum and maximum voltage amplitudes of node j respectively; represents the minimum and maximum transmission power of line ij; N represents the set of generator sets; B represents the set of system nodes; L represents the set of lines.

[0025] 4) Transient stability constraints, which consist of differential algebraic equations describing the dynamic process of the power system and the dynamic differential characteristics of generators and loads, and transient stability criteria:

[0026]

[0027] G(x(t),y(t),z)=0,t∈T (5)

[0028] h(x(t),y(t),z)≤0,t∈T (6)

[0029] Where: x represents the system state variables, including generator power angle, speed, and internal potential; y represents algebraic variables, including node voltage and phase; z represents the control variables, including the active and reactive output of the unit; T represents the total time from the fault moment to the end of the transient process considered; Equations (4) and (5) constitute a set of differential equations and algebraic equations to describe the dynamic operation process of the power system; D(·) represents the function describing the dynamic differential characteristics of the generator, load, and controller; G(·) represents the function describing the network current balance equation and the internal static characteristics of the passive equipment; Equation (6) represents the transient stability criterion in the dynamic process that must be met to solve the optimal power flow with transient stability constraints.

[0030] In step 3, based on the trajectory sensitivity method, the transient stability constraints of the transient stability constrained optimal power flow TSCOPF model are analyzed equivalently. The dynamic differential equations in the transient stability constraints are converted into low-order algebraic inequality constraints. In this way, the equivalent transient stability constrained optimal power flow TSCOPF model is established. The converted transient stability constraints are shown as follows:

[0031]

[0032] Where: H d Represents the dynamic trajectory of the system after the fault; Indicates the critical reference power angle value when the system maintains transient stability; δ CT (t u ) refers to the power angle value at the time of fault clearing; t u ∈T.

[0033] In step 4, the PV power station output variable is introduced into the equivalent transient stability constrained optimal power flow TSCOPF model, and the objective function in the model is modified to take into account the cost of the PV power station output. The modified objective function is as follows:

[0034]

[0035] Where: f j represents the cost function of the j-th photovoltaic power station output; N represents the set of active power output nodes of the system; p UIndicates the active power output of the photovoltaic power station.

[0036] At this point, the net node injection power of the system is as follows:

[0037]

[0038] Where: p represents the net active power injected into the system node; q represents the net reactive power injected into the system node.

[0039] After considering the influence of photovoltaic output uncertainty on various variables in the power system, a probabilistic transient stability constrained optimal power flow TSCOPF model taking into account photovoltaic output uncertainty can be established.

[0040] The established probabilistic transient stability constrained optimal power flow TSCOPF model taking into account the uncertainty of photovoltaic output is specifically as follows:

[0041] 1) Objective function:

[0042]

[0043] Where: E(·) represents the expected value.

[0044] 2) Stochastic power flow balance equation:

[0045]

[0046] Where: ω represents the probability distribution model of photovoltaic power station output; p Gi (ω),q Gi (ω), v j (ω) represents the active and reactive outputs of the generator sets, the node voltage amplitude, and the random variables generated by the conversion after the output of the photovoltaic power station is introduced.

[0047] 3) Steady-state operation constraints in the form of opportunity constraints:

[0048]

[0049] Where: p ij (ω) represents the random variable generated by the power conversion of the transmission line after the output of the photovoltaic power station is introduced; P(·) represents the probability that the conditions in the brackets are met; They represent the probability of violation of the active and reactive output of the generator set, the node voltage amplitude, and the line transmission power, respectively. They are generally selected by weighing the system risk level and the dispatch cost.

[0050] 4) Transient stability constraints in the form of chance constraints:

[0051]

[0052] Where: εδ It represents the probability of violation of the chance constraint corresponding to the system equivalent power angle.

[0053] In step 5,

[0054] First, the numerical characteristics of the photovoltaic power station output probability distribution model including expectation and standard deviation are calculated;

[0055] Then, the chance constraint is transformed into a second-order cone constraint based on the expectation, standard deviation and inverse cumulative distribution function of the probability distribution model of the photovoltaic power station output, and the voltage amplitude v is used as the constraint. i As an example, its chance constraint formula can be re-expressed as a second-order cone constraint:

[0056]

[0057] Where: Φ -1 is the inverse Gaussian cumulative distribution function; E[v i (ω)]、Stdev[v i (ω)] are the expectation and standard deviation of vi(ω), respectively;

[0058] Finally, Taylor expansion is used to expand Equation (11) at a certain operating point of the system to realize the linearization of the power flow equilibrium equation, and then the deterministic transformation in the probabilistic transient stability constrained optimal power flow TSCOPF model is realized.

[0059] The augmented Lagrangian method (ALM) is used to transform the constraints in the deterministically transformed probabilistic transient stability constrained optimal power flow (TSCOPF) model into penalty terms of the objective function. This simplifies the calculation process and allows the probabilistic transient stability constrained optimal power flow (TSCOPF) model to be solved quickly and accurately. The calculation results are obtained that take into account the uncertainty of photovoltaic output and satisfy the requirement that the system maintains transient stability under faults.

[0060] Compared with the prior art, the present invention has the following technical effects:

[0061] 1) This paper proposes a transient stability constrained optimal power flow modeling method that considers the impact of photovoltaic output uncertainty. Combined with the chance-constrained programming method, it solves the problem that existing power system transient stability analysis cannot consider the randomness and intermittency of photovoltaic output;

[0062] 2) The present invention proposes a transient stability constrained optimal power flow solution method that takes into account the uncertainty of photovoltaic output. Its calculation results effectively consider the impact of uncertain variables on the formulation of the optimal dispatching strategy of the power system. To a certain extent, it can support the stable operation of the system after the photovoltaic power station is further expanded and integrated into the power grid, and improve the clean energy absorption capacity. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] The present invention will be further described below with reference to the accompanying drawings and examples:

[0064] Figure 1 This is a flowchart for solving the transient stability constrained optimal power flow taking into account the uncertainty of photovoltaic output;

[0065] Figure 2 This is the test result of the TSCOPF solution method when the photovoltaic penetration rate is about 10%;

[0066] Figure 3 is a test result diagram of the solution method of the present invention when the photovoltaic penetration rate is about 10%;

[0067] Figure 4 This is the test result of the TSCOPF solution method when the photovoltaic penetration rate is about 20%;

[0068] Figure 5 This is a test result diagram of the solution method of the present invention when the photovoltaic penetration rate is about 20%. DETAILED DESCRIPTION

[0069] The transient stability constrained optimal power flow solution method considering the uncertainty of photovoltaic output is as follows: Figure 1 As shown, the following steps are included:

[0070] Step 1: Obtain historical output data of photovoltaic power stations and establish a probability distribution model for photovoltaic power station output;

[0071] Step 2: Obtain various operating parameters of the power system after PV grid connection and establish a transient stability constrained optimal power flow (TSCOPF) model;

[0072] Step 3: Based on the trajectory sensitivity method, perform equivalent analysis on the transient stability constraints of the TSCOPF model and establish an equivalent TSCOPF model;

[0073] Step 4: Introduce the PV power station into the equivalent TSCOPF model and establish a probabilistic TSCOPF model that takes into account the uncertainty of PV output;

[0074] Step 5: Use the PV power station output probability distribution model to calculate the digital characteristics of PV output and perform a second-order cone transformation on the chance constraints in the probabilistic TSCOPF model;

[0075] Step 6: Use the augmented Lagrangian method (ALM) to solve the probabilistic TSCOPF model after the second-order cone transformation, and obtain the calculation results that take into account the impact of PV output uncertainty and meet the transient stability of the system under fault conditions.

[0076] In step 1: Specifically, photovoltaic power generation output is affected by multiple factors, including light intensity, ambient temperature, and photovoltaic module conversion efficiency, and is characterized by strong random fluctuations. Using data published by the power grid company, we obtained historical output data for photovoltaic power stations. Using a Gaussian mixture model, we estimated the probability density of photovoltaic power station output and established a probability distribution model for photovoltaic power station output.

[0077] In step 2: Specifically, various operating parameters of the power system change after photovoltaic grid connection. It is necessary to re-determine the active and reactive output of the generator sets, active and reactive loads, photovoltaic power station output, node voltage amplitude, phase angle, number of nodes and other parameters of the power system nodes, and establish the TSCOPF model based on this.

[0078] The TSCOPF model consists of the following objective function and related constraints:

[0079] 1) Objective function for generator fuel cost and grid loss:

[0080]

[0081] Where: c i represents the cost function of the i-th group of generators; N represents the set of generators; p Gi Indicates the active output of the generator set at node i.

[0082] 2) The tidal current balance equation for steady-state operation:

[0083]

[0084] Where: p Di represents the active load at node i; v i ,θ i represents the node voltage amplitude and phase angle of the system node i; q Gi represents the reactive output of the generator set at node i; q Di represents the reactive load at node i; Y ij , α ij Represents the amplitude and phase angle of the elements in the node admittance matrix of the line from node i to node j.

[0085] 3) Steady-state operation constraints;

[0086]

[0087] Where: Respectively represent the minimum and maximum active output of the generator set at node i; Respectively represent the minimum and maximum reactive output of the generator set at node i; They represent the minimum and maximum voltage amplitudes of node j respectively; represents the minimum and maximum transmission power of line ij; N represents the set of generator sets; B represents the set of system nodes; L represents the set of lines.

[0088] 4) Transient stability constraints, which consist of differential algebraic equations describing the dynamic process of the power system and the dynamic differential characteristics of generators and loads, and transient stability criteria:

[0089]

[0090] G(x(t),y(t),z)=0,t∈T (5)

[0091] h(x(t),y(t),z)≤0,t∈T (6)

[0092] Where: x represents the system state variables, including generator power angle, speed, and internal potential; y represents algebraic variables, including node voltage and phase; z represents the control variables, including the active and reactive output of the unit; T represents the total time from the fault moment to the end moment of the transient process considered; Equations (4) and (5) constitute a set of differential equations and algebraic equations to describe the dynamic operation process of the power system; D(·) represents the function describing the dynamic differential characteristics of the generator, load, and controller; G(·) represents the function describing the network current balance equation and the internal static characteristics of the passive equipment; Equation (6) represents the transient stability criterion in the dynamic process that must be met to solve the optimal power flow with transient stability constraints, and the transient power angle criterion is usually used.

[0093] The establishment of the TSCOPF model is a necessary prerequisite for the subsequent transient stability constraint equivalent analysis, and is also the basis for considering the impact of photovoltaic output uncertainty in the process of solving the transient stability constraint optimal power flow.

[0094] In step 3: Specifically, based on the trajectory sensitivity method, the transient stability constraints of the TSCOPF model are analyzed equivalently. The dynamic differential equations in the transient stability constraints are converted into low-order algebraic inequality constraints. This is used to establish the equivalent TSCOPF model. The converted transient stability constraints are shown below:

[0095]

[0096] Where: H d Represents the dynamic trajectory of the system after the fault; Indicates the critical reference power angle value when the system maintains transient stability; δ CT (t u ) refers to the power angle value at the time of fault clearing; t u ∈T.

[0097] In step 4: Specifically, the PV power station output variable is introduced into the equivalent TSCOPF model, and the objective function in the model is modified to take into account the cost of the PV power station output. The modified objective function is as follows:

[0098]

[0099] Where: f j represents the cost function of the j-th photovoltaic power station output; N represents the set of active power output nodes of the system; p U Indicates the active power output of the photovoltaic power station.

[0100] At this point, the net node injection power of the system is as follows:

[0101]

[0102] Where: p represents the net active power injected into the system node; q represents the net reactive power injected into the system node.

[0103] After considering the influence of photovoltaic output uncertainty on various variables in the power system, a probabilistic TSCOPF model taking into account photovoltaic output uncertainty can be established:

[0104] 1) Objective function:

[0105]

[0106] Where: E(·) represents the expected value.

[0107] 2) Stochastic power flow balance equation:

[0108]

[0109] Where: ω represents the probability distribution model of photovoltaic power station output; p Gi (ω),q Gi (ω), v j (ω) represents the active and reactive outputs of the generator sets, the node voltage amplitude, and the random variables generated by the conversion after the output of the photovoltaic power station is introduced.

[0110] 3) Steady-state operation constraints in the form of opportunity constraints:

[0111]

[0112] Where: p ij (ω) represents the random variable generated by the power conversion of the transmission line after the output of the photovoltaic power station is introduced; P(·) represents the probability that the conditions in the brackets are met; They represent the probability of violation of the active and reactive output of the generator set, the node voltage amplitude, and the line transmission power, respectively. They are generally selected by weighing the system risk level and the dispatch cost.

[0113] 4) Transient stability constraints in the form of chance constraints:

[0114]

[0115] Where: ε δ It represents the probability of violation of the chance constraint corresponding to the system equivalent power angle.

[0116] In step 5: Specifically, firstly, the numerical characteristics of the photovoltaic power station output probability distribution model including expectation, standard deviation, etc. are calculated.

[0117] Then, the chance constraint is transformed into a second-order cone constraint based on the expectation, standard deviation and inverse cumulative distribution function of the probability distribution model of the photovoltaic power station output, and the voltage amplitude v is used as the constraint. i As an example, its chance constraint formula can be re-expressed as a second-order cone constraint:

[0118]

[0119] Where: Φ -1 is the inverse Gaussian cumulative distribution function; E[v i (ω)]、Stdev[v i (ω)] are the expectation and standard deviation of vi(ω), respectively.

[0120] Finally, Taylor expansion is used to expand Equation (11) at a certain operating point of the system to realize the linearization of the power flow balance equation and thus achieve the deterministic transformation in the probabilistic TSCOPF model.

[0121] In step 6: Specifically, the ALM algorithm is used to convert each constraint in the deterministically transformed probabilistic TSCOPF model into a penalty term of the objective function, simplifying the calculation process and quickly and accurately solving the probabilistic TSCOPF model to obtain a calculation result that takes into account the impact of PV output uncertainty and satisfies the system's requirement to maintain transient stability under fault conditions.

[0122] Example 1: Example 1 of the present invention is based on the IEEE 140-node system. To test the effectiveness of the present invention in ensuring transient stability in a photovoltaic grid-connected power system under anticipated accidents, the following modifications were made to the IEEE 140-node system: five photovoltaic power plants were installed to replace synchronous generators G1, G5, G8, G15, and G20, with a photovoltaic penetration rate of approximately 10%.

[0123] The active output of the five photovoltaic power stations in the system fluctuates randomly due to weather conditions. The expected fault is set as a three-phase short circuit fault that has a serious impact on the power system. The fault location is line 85-112, the fault duration is 0.1s, and the system experiences transient instability. Figure 2 At this time, the system generator output strategy is formulated by the TSCOPF solution method. Figure 2 is the relative rotor angle trajectory diagram of the system. If the relative rotor angle between any two generators exceeds 180 degrees, it means that the system loses stability.

[0124] The transient stability constrained optimal power flow solution method taking into account the uncertainty of photovoltaic output proposed in this invention is used to re-derive the system's generator output strategy, as shown in Table 1. At this time, when a three-phase short circuit fault occurs in the system, the system power angle still maintains transient stability, as shown in Table 1. Figure 3 It can be seen from the test results that the present invention meets the actual needs and is in line with the purpose to be achieved by the present invention.

[0125] Table 1

[0126]

[0127] Example 2: Example 2, used in this invention, is also based on the IEEE 140-node system. To test the effectiveness of this invention at higher PV penetration rates, the following modifications were made to the IEEE 140-node system: 10 PV power plants were installed, replacing synchronous generators G1, G5, G8, G15, G20, G21, G25, G27, G28, and G32. The PV penetration rate was approximately 20%. The anticipated fault settings were the same as in Example 1.

[0128] like Figure 4 As shown in Figure 1, the power system generator output strategy formulated by the TSCOPF solution method. The active output of the 10 photovoltaic power stations in the system is random due to weather conditions. If a three-phase short circuit fault occurs in the system, the system will experience transient instability. Figure 5 As shown in the figure, the calculation results of the method proposed by the present invention show that the system maintains transient stability. From the test results, it can be seen that the present invention meets practical needs and is still effective under high photovoltaic penetration rates, which meets the purpose of the present invention.

Claims

1. A transient stability constrained optimal power flow solution method taking into account the uncertainty of photovoltaic output, characterized by: It includes the following steps: Step 1: Obtain historical output data of photovoltaic power stations and establish a probability distribution model for photovoltaic power station output; Step 2: Obtain various operating parameters of the power system after PV grid connection and establish a transient stability constrained optimal power flow (TSCOPF) model; Step 3: Based on the trajectory sensitivity method, perform equivalent analysis on the transient stability constraints of the transient stability constrained optimal power flow TSCOPF model and establish an equivalent transient stability constrained optimal power flow TSCOPF model; Step 4: Introduce the PV power plant into the equivalent transient stability constrained optimal power flow TSCOPF model to establish a probabilistic transient stability constrained optimal power flow TSCOPF model that takes into account the uncertainty of PV output; Step 5: Use the PV power station output probability distribution model to calculate the digital characteristics of PV output and perform a second-order cone transformation on the chance constraints in the probabilistic transient stability constrained optimal power flow (TSCOPF) model. Step 6: Use the augmented Lagrangian method (ALM) to solve the probabilistic transient stability constrained optimal power flow (TSCOPF) model after the second-order cone transformation, and obtain the calculation results that take into account the impact of PV output uncertainty and meet the transient stability requirements of the system under fault conditions. In step 2, the objective function and constraints of the transient stability constrained optimal power flow TSCOPF model are as follows: 1) Objective function for generator fuel cost and grid loss: （1）； Where: Indicates the i Cost function of group generator sets; N represents a collection of generator sets; express i Active power output of the node's generator set; 2) Flow balance equation for steady-state operation: （2）； Where: express i Active load at the node; 、 Representation System i Nodal voltage amplitude and phase angle of the node; express i Reactive output of the node's generator set; express i Reactive load at the node; 、 Representation node i To Node j The amplitude and phase angle of the elements in the line node admittance matrix; 3) Steady-state operation constraints; （3）； Where: 、 Respectively i The minimum and maximum active output of the node's generator set; 、 Respectively i The minimum and maximum reactive output values ​​of the node's generator set; 、 Respectively j The minimum and maximum voltage amplitudes of the nodes; 、 express ij The minimum and maximum values ​​of the line transmission power of the line; N represents a collection of generator sets; Represents a collection of system nodes; Represents a collection of lines; 4) Transient stability constraints, which consist of differential algebraic equations describing the dynamic process of the power system and the dynamic differential characteristics of generators and loads, and transient stability criteria: （4）； （5）； （6）； Where: x Represents the system state variables, including generator power angle, speed, and internal potential; y Represents algebraic variables, including node voltage, phase, etc.; z Represents the control variables, including the active and reactive output of the unit; T represents the sum of the duration from the moment of fault to the end of the transient process considered; Equations (4) and (5) constitute a set of differential equations and algebraic equations to describe the dynamic operation process of the power system; represents the function describing the dynamic differential characteristics of power system equipment; represents the function describing the network current balance equation and the internal static characteristics of the passive device; Equation (6) represents the transient stability criterion in the dynamic process that must be satisfied in solving the optimal power flow with transient stability constraints.

2. The method according to claim 1, characterized in that In step 1, photovoltaic power generation output is affected by one or more factors including light intensity, ambient temperature, and photovoltaic module conversion efficiency. The output data of photovoltaic power stations over the years are obtained from the data published by the power grid company. The probability density of the photovoltaic power station output is estimated based on the Gaussian mixture model, and a probability distribution model of the photovoltaic power station output is established.

3. The method according to claim 1, characterized in that In step 2, various operating parameters of the power system change after the photovoltaic grid is connected. The parameters such as the active and reactive output of the generator sets, active and reactive loads, photovoltaic power station output, node voltage amplitude and phase angle, and number of nodes at the power system nodes are re-determined, and the transient stability constrained optimal power flow TSCOPF model is established based on this.

4. The method according to claim 1, wherein In step 3, based on the trajectory sensitivity method, the transient stability constraints of the transient stability constrained optimal power flow TSCOPF model are analyzed equivalently. The dynamic differential equations in the transient stability constraints are converted into low-order algebraic inequality constraints. In this way, the equivalent transient stability constrained optimal power flow TSCOPF model is established. The converted transient stability constraints are shown as follows: （7）； Where: Represents the dynamic trajectory of the system after the fault; Indicates the critical reference power angle value when the system maintains transient stability; Refers to the power angle value at the moment the fault is cleared; .

5. The method according to claim 1, wherein In step 4, the PV power station output variable is introduced into the equivalent transient stability constrained optimal power flow TSCOPF model, and the objective function in the model is modified to take into account the cost of the PV power station output. The modified objective function is as follows: （8）； Where: Indicates the j Cost function of the output of a photovoltaic power station; N Represents the set of active output nodes of the system; Indicates the active power output of the photovoltaic power station; At this point, the net node injection power of the system is as follows: （9）； Where: Represents the net active power injected into the system node; It represents the net reactive power injected into the system node; After considering the influence of photovoltaic output uncertainty on various variables in the power system, a probabilistic transient stability constrained optimal power flow TSCOPF model taking into account photovoltaic output uncertainty can be established.

6. The method according to claim 5, characterized in that The established probabilistic transient stability constrained optimal power flow TSCOPF model taking into account the uncertainty of photovoltaic output is specifically as follows: 1) Objective function: （10）； Where: Indicates expected value; 2) Stochastic power flow equilibrium equation: （11）； Where: Represents the probability distribution model of photovoltaic power station output; 、 、 They represent the active and reactive outputs of the generator sets, node voltage amplitudes, and random variables generated by transformation after the output of the photovoltaic power station is introduced; 3) Steady-state operation constraints in the form of opportunity constraints: （12）； in: They represent the random variables generated by the power conversion of the transmission line after the output of the photovoltaic power station is introduced; Indicates the probability that the conditions in the brackets are true; They represent the probability of violation of the opportunity constraints of the active and reactive output of the generator set, the node voltage amplitude, and the line transmission power, respectively. They are generally selected by weighing the system risk level and the dispatch cost; 4) Transient stability constraints in the form of chance constraints: （13）； Where: It represents the probability of violation of the chance constraint corresponding to the system equivalent power angle.

7. The method according to claim 6, characterized in that In step 5, First, the numerical characteristics of the photovoltaic power station output probability distribution model including expectation and standard deviation are calculated; Then, the chance constraint is transformed into a second-order cone constraint based on the expectation, standard deviation and inverse cumulative distribution function of the probability distribution model of the photovoltaic power station output, and the voltage amplitude is used as the As an example, its chance constraint formula can be re-expressed as a second-order cone constraint: （14）； Where: is the inverse Gaussian cumulative distribution function; 、 They are The expectation and standard deviation of Finally, Taylor expansion is used to expand Equation (11) at a certain operating point of the system to realize the linearization of the power flow equilibrium equation, and then the deterministic transformation in the probabilistic transient stability constrained optimal power flow TSCOPF model is realized.

8. The method according to any one of claims 1 to 7, characterized in that The augmented Lagrangian method (ALM) is used to transform the constraints in the deterministically transformed probabilistic transient stability constrained optimal power flow (TSCOPF) model into penalty terms of the objective function. This simplifies the calculation process and allows the probabilistic transient stability constrained optimal power flow (TSCOPF) model to be solved quickly and accurately. The calculation results are obtained that take into account the uncertainty of photovoltaic output and satisfy the requirement that the system maintains transient stability under faults.

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