A method for obtaining transient stability constraint optimal power flow considering wind power uncertainty

Abstract

A transient stability constraint optimal power flow acquisition method considering wind power uncertainty, step 1: taking the power system optimal power flow solution as the initial operation state and setting the expected fault set; step 2: using a typical wind power scene to describe the uncertainty of wind power output; step 3: for a series of expected faults under each typical wind power scene, time domain simulation is carried out, and for the case that the power system is transiently unstable, the process constraint of the transient stability of the power system is converted into an algebraic form of the transient stability constraint through constraint conversion; step 4: the obtained transient stability constraint is added to the power system optimal power flow model, and the equivalent power system transient stability constraint optimal power flow (TSCOPF) model containing wind turbines is constructed, and the model solution is recalculated. The purpose of the application is to expand the power system transient stability constraint optimal power flow model solving method to adapt to the uncertainty of wind power generation and guarantee the transient stability of the power system.

Description

Technical Field

[0001] This invention belongs to the field of power system technology, specifically to the field of power system transient stability analysis and optimal power flow calculation technology, and particularly to a method for obtaining optimal power flow under transient stability constraints considering wind power uncertainty. Background Technology

[0002] Because wind turbines are connected to converters and their power output is uncertain, the operation and dynamic behavior of the power system become highly complex, affecting its security. Therefore, under stochastic wind power generation conditions, employing practical and efficient methods for power system transient stability analysis and optimal power flow calculation is of practical significance and value for further maintaining the transient stability of the power system.

[0003] Patent application CN104638644A discloses a method for obtaining dynamic stochastic optimal power flow in a power system containing a wind farm, solving the problem of dynamic optimal power flow under the randomness and spatiotemporal correlation of wind speed and load. However, this method does not consider the transient stability of the power system operation in the presence of wind power. Patent application CN107437811A discloses a parallel calculation method for optimal power flow constrained by transient stability in a power system. This parallel calculation method ensures that the main parameters of the optimized power flow are within the standard range while maintaining accuracy in solving the optimal power flow problem. However, for new energy power systems that are significantly affected by the uncertainty of wind power, this method is inefficient and has large errors.

[0004] Therefore, the applicant proposes a transient stability constraint-based optimal power flow acquisition method that considers the uncertainties of wind power. Summary of the Invention

[0005] The purpose of this invention is to solve the technical problem that the optimal power flow acquisition method mentioned in the background art does not simultaneously consider the transient stability of modern power systems and the uncertainty of wind power, resulting in low solution efficiency and large errors.

[0006] A method for obtaining transient stability-constrained optimal power flow considering wind power uncertainties includes the following steps:

[0007] Step 1: Use the solution of the optimal power flow of the power system as the initial operating state and set the expected fault set;

[0008] Step 2: Use typical wind power scenarios to describe the uncertainty of wind power output;

[0009] Step 3: Perform time-domain simulations for a series of anticipated faults under each typical wind power scenario. For the case of power system transient instability, transform the process constraints of power system transient stability into algebraic transient stability constraints through constraint transformation.

[0010] Step 4: Add the obtained transient stability constraints to the optimal power flow model of the power system, construct the equivalent power system TSCOPF model with wind turbines, and recalculate the model solution.

[0011] In step 2, generating a typical wind power scenario includes the following steps:

[0012] Step 2-1: Complete the optimization process based on the improved artificial bee colony algorithm;

[0013] The bee colony is initialized using the minimum-maximum distance product method to ensure that the initial point selection represents the distribution characteristics of the wind power output dataset as much as possible. To overcome the drawback of the original artificial bee colony algorithm being prone to getting trapped in local optima, a fitness function adapted to the KMC algorithm and a globally guided position update formula are constructed. During the iteration process, the new fitness function and position update formula are used to complete the optimization and evolution.

[0014] Step 2-2: Perform clustering based on the improved artificial bee colony algorithm and KMC algorithm, and select typical wind power scenarios;

[0015] Process the data from different scenarios, transforming the original... n The scenarios were reduced and merged into k A typical wind power scenario, in which... t The data at each time point retains its original time series, using a matrix. k × t This indicates that the optimal typical wind power scenario can be obtained.

[0016] In step 3, the constraints for the transient stability process of the power system before constraint transformation are:

[0017] (1);

[0018] (2);

[0019] (3);

[0020] In the formula: x ( t )and y ( t () is a transient period T State variables and algebraic variables; u denoted as control variables with lower and upper limits; D is the differential equation describing the generator's dynamic process; G is the algebraic equation describing the generator's dynamic process; and H is the transient stability criterion.

[0021] In step 3, generating the algebraic form of transient stability constraints includes the following steps:

[0022] Step 3-1: Based on the time-domain simulation results of a series of anticipated faults under each typical wind power scenario, the system is divided into critical units (CMs) and non-critical units (NMs) to obtain the trajectory of the single-unit infinite OMIB system.

[0023] Step 3-2: Calculate the stability characteristics and evaluate the transient stability level based on the EEAC method;

[0024] Step 3-3: Establish or update the unstable single-machine infinite U-OMIB system, and calculate the trajectory sensitivity of each synchronous generator in the unstable single-machine infinite U-OMIB system at the instability time;

[0025] Steps 3-4: Estimate the critical cut-off time, construct the critical single-machine infinite C-OMIB system, and calculate the power angle of the critical single-machine infinite C-OMIB system at the instability time;

[0026] Steps 3-5: Based on the target power angle of the unstable single-machine infinite U-OMIB system at the instability time and the power angle of the critical single-machine infinite C-OMIB system at the instability time, construct algebraic transient stability constraints.

[0027] In step 3-2, specifically:

[0028] Stability characteristics include instability time T u Time to stabilize during the first oscillation T r Transient stability margin η .

[0029] instability time T u This determines the time when the generator loses synchronization. In this case, the mechanical and electromagnetic power of a single-unit infinite bus (OMIB) system satisfies the following relationship:

[0030] (4);

[0031] In the formula: , and The instability time of a single-machine infinite OMIB system is as follows. T u The unbalanced power, mechanical power, and electromagnetic power at the point.

[0032] Time to stabilize during the first oscillation T r This determines the time it takes for the system to stabilize during the first oscillation. In this case, the mechanical and electromagnetic power of the single-machine infinite bus OMIB system satisfies the following relationship:

[0033] (5);

[0034] In the formula: , and The first oscillation settling time for a single-machine infinite OMIB system are respectively... T r The unbalanced power, mechanical power, and electromagnetic power at the point; For a single-machine infinite OMIB system, the first oscillation stabilization time T r The rotational speed at that point.

[0035] Transient stability margin η This is a quantified value of transient stability. It is based on the power of a single-machine infinite OMIB system. From the angle plane, we can obtain:

[0036] (6);

[0037] In the formula: A dec The deceleration area; A acc To accelerate the area; M The inertia coefficient; For a single-machine infinite OMIB system in the instability time T u Rotational speed at that point; and The instability time of a single-machine infinite OMIB system is as follows. T u and the first oscillation settling time T r The angle of attack at that location. η ≥0 indicates stability; otherwise, it is unstable.

[0038] In steps 3-5, the transient stability constraint is:

[0039] (7);

[0040] In the formula: For the critical single-machine infinite C-OMIB system at the instability time T u The angle of attack at the location; For the system during instability time T u The target angle of attack at a given location is defined as:

[0041] (8);

[0042] In the formula: For an unstable single-machine infinite U-OMIB system, the instability timeT u The angle of attack at the location; In order to make Less than The required reduction amount.

[0043] Based on trajectory sensitivity, it is possible to... Transform it into the following form:

[0044] (9);

[0045] In the formula: S + and S These represent generator sets with positive and negative sensitivity, respectively. and The instability time of the unstable single-machine infinite U-OMIB system is as follows. T u The work angle at the first The generator and the first Sensitivity of the active power of the generator; and For the first The generator and the first The initial active power of the generator; and For the first The generator and the first The active power of the generator.

[0046] In step 4, an equivalent TSCOPF model including wind turbines is constructed, and the particle swarm optimization algorithm is used to solve the equivalent TSCOPF model including wind turbines. The equivalent TSCOPF model of the power system including wind turbines is as follows:

[0047] 1) Objective function:

[0048] (10);

[0049] In the formula: N G This represents the total number of synchronous generators; , , For the first l The power generation cost coefficient of a generator; For the first l The active power of the generator.

[0050] 2) Power flow equations:

[0051] (11);

[0052] In the formula: For the first l The reactive power of the generator; and The first l Active and reactive power of a typhoon generator; and The first l Active and reactive power of the load at each node; and It is a node l and nodes n The voltage amplitude; It is a node l and nodes n The phase angle difference between them; and They are nodes l and nodes n The line conductance and susceptance; N B This represents the total number of nodes.

[0053] 3) Stable operation constraints:

[0054] (12);

[0055] In the formula: and These are the lower and upper limits of the generator's active power output; and These are the lower and upper limits of the generator's reactive power output; and These are the lower and upper limits of the node voltage; and These are the lower and upper limits of the thermal stability constraints for the line.

[0056] 4) Transient stability constraints:

[0057] (13);

[0058] Compared with the prior art, the present invention has the following technical effects:

[0059] 1) The transient stability of the power system is considered and the stability constraints in the original differential algebraic form are transformed into algebraic form based on EEAC and trajectory sensitivity, which greatly reduces the size of the optimization problem;

[0060] 2) A transient stability constraint optimal power flow acquisition method considering wind power uncertainty is proposed, which optimizes the system operation state and can adapt to the transient stability requirements under the uncertainty of wind power generation. Attached Figure Description

[0061] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0062] Figure 1 This is a system flowchart of the present invention;

[0063] Figure 2 This is a flowchart of the algebraic form of transient stability constraints generated by the present invention;

[0064] Figure 3 This is a schematic diagram of the IEEE 39-node system in an example of the present invention;

[0065] Figure 4 This is a schematic diagram of the relative rotor angle trajectory curve before optimization at node 4 in an example of the present invention;

[0066] Figure 5 This is a schematic diagram of the optimized relative rotor angle trajectory curve at node 4 in an example of the present invention. Detailed Implementation

[0067] A method for obtaining the optimal power flow under transient stability constraints considering wind power uncertainties, such as... Figure 1 As shown, it includes the following steps:

[0068] Step 1: Use the solution of the optimal power flow of the power system as the initial operating state and set the expected fault set;

[0069] The optimal power flow model of the power system takes the state variable parameters of the power system as input, and solves them using the particle swarm optimization algorithm to obtain the initial operating point and set the set of anticipated faults.

[0070] Step 2: Use typical wind power scenarios to describe the uncertainty of wind power output;

[0071] The intermittent and fluctuating nature of wind energy leads to uncertainty in wind power output. To describe this uncertainty, typical wind power output scenarios are selected; accurate wind power output scenarios are crucial for grid security and economic efficiency. Generating typical wind power scenarios involves the following steps:

[0072] Step 2-1: Complete the optimization process based on the improved artificial bee colony algorithm;

[0073] The bee colony is initialized using the minimum-maximum distance product method to ensure that the initial point selection represents the distribution characteristics of the wind power output dataset as much as possible. To overcome the drawback of the original artificial bee colony algorithm being prone to getting trapped in local optima, a fitness function adapted to the KMC algorithm and a globally guided position update formula are constructed. During the iteration process, the new fitness function and position update formula are used to complete the optimization and evolution.

[0074] Step 2-2: Perform clustering based on the improved artificial bee colony algorithm and KMC algorithm, and select typical wind power scenarios.

[0075] Process the data from different scenarios, transforming the original... n The scenarios were reduced and merged into k A typical wind power scenario, in which... t The data at each time point retains its original time series, using a matrix. k × t This indicates that the optimal typical wind power scenario can be obtained.

[0076] Step 3: Perform time-domain simulations for a series of anticipated faults under each typical wind power scenario. For the case of power system transient instability, transform the process constraints of power system transient stability into algebraic transient stability constraints through constraint transformation.

[0077] The constraints for the transient stability process of the power system before the constraint transformation are:

[0078] (1);

[0079] (2);

[0080] (3);

[0081] In the formula: x ( t )and y ( t () is a transient period T State variables and algebraic variables; u denoted as control variables with lower and upper limits; D is the differential equation describing the generator's dynamic process; G is the algebraic equation describing the generator's dynamic process; and H is the transient stability criterion.

[0082] Figure 2 To generate a flowchart of transient stability constraints in algebraic form, the following steps are included.

[0083] Step 3-1: Based on the time-domain simulation results of a series of anticipated faults under each typical wind power scenario, the system is divided into critical units (CMs) and non-critical units (NMs) to obtain the trajectory of the single-unit infinite OMIB system.

[0084] Step 3-2: Calculate the stability characteristics and evaluate the transient stability level based on the EEAC method;

[0085] Stability characteristics include instability time T u Time to stabilize during the first oscillation T r Transient stability margin η.

[0086] instability time T u This determines the time when the generator loses synchronization. In this case, the mechanical and electromagnetic power of a single-unit infinite bus (OMIB) system satisfies the following relationship:

[0087] (4);

[0088] In the formula: , and The instability time of a single-machine infinite OMIB system is as follows. T u The unbalanced power, mechanical power, and electromagnetic power at the point.

[0089] Time to stabilize during the first oscillation T r This determines the time it takes for the system to stabilize during the first oscillation. In this case, the mechanical and electromagnetic power of the single-machine infinite bus OMIB system satisfies the following relationship:

[0090] (5);

[0091] In the formula: , and The first oscillation settling time for a single-machine infinite OMIB system are respectively... T r The unbalanced power, mechanical power, and electromagnetic power at the point; For a single-machine infinite OMIB system, the first oscillation stabilization time T r The rotational speed at that point.

[0092] Transient stability margin η This is a quantified value of transient stability. It is based on the power of a single-machine infinite OMIB system. From the angle plane, we can obtain:

[0093] (6);

[0094] In the formula: A dec The deceleration area; A acc To accelerate the area; M The inertia coefficient; For a single-machine infinite OMIB system in the instability time T u Rotational speed at that point; and The instability time of a single-machine infinite OMIB system is as follows.T u and the first oscillation settling time T r The angle of attack at that location. η ≥0 indicates stability; otherwise, it is unstable.

[0095] Step 3-3: Establish or update the unstable single-machine infinite U-OMIB system, and calculate the trajectory sensitivity of each synchronous generator in the unstable single-machine infinite U-OMIB system at the instability time;

[0096] Steps 3-4: Estimate the critical cut-off time, construct the critical single-machine infinite C-OMIB system, and calculate the power angle of the critical single-machine infinite C-OMIB system at the instability time;

[0097] Steps 3-5: Based on the target power angle of the unstable single-machine infinite U-OMIB system at the instability time and the power angle of the critical single-machine infinite C-OMIB system at the instability time, construct algebraic transient stability constraints.

[0098] The transient stability constraint is:

[0099] (7);

[0100] In the formula: For the critical single-machine infinite C-OMIB system at the instability time T u The angle of attack at the location; For the system during instability time T u The target angle of attack at a given location is defined as:

[0101] (8);

[0102] In the formula: For an unstable single-machine infinite U-OMIB system, the instability time T u The angle of attack at the location; In order to make Less than The required reduction amount.

[0103] Based on trajectory sensitivity, it is possible to... Transform it into the following form:

[0104] (9);

[0105] In the formula: S + and S These represent generator sets with positive and negative sensitivity, respectively. and The instability time of the unstable single-machine infinite U-OMIB system is as follows. T u The work angle at the first The generator and the first Sensitivity of the active power of the generator; and For the first The generator and the first The initial active power of the generator; and For the first The generator and the first The active power of the generator.

[0106] Step 4: Add the obtained transient stability constraints to the optimal power flow model of the power system, construct the equivalent power system TSCOPF model with wind turbines, and recalculate the model solution.

[0107] An equivalent TSCOPF model incorporating wind turbines is constructed, and the particle swarm optimization algorithm is used to solve the equivalent TSCOPF model. The equivalent TSCOPF model incorporating wind turbines is as follows:

[0108] 1) Objective function:

[0109] (10);

[0110] In the formula: N G This represents the total number of synchronous generators; , , For the first l The power generation cost coefficient of a generator; For the first l The active power of the generator.

[0111] 2) Power flow equations:

[0112] (11);

[0113] In the formula: For the first l The reactive power of the generator; and The first l Active and reactive power of a typhoon generator; and The first l Active and reactive power of the load at each node; and It is a node l and nodes nThe voltage amplitude; It is a node l and nodes n The phase angle difference between them; and They are nodes l and nodes n The line conductance and susceptance; N B This represents the total number of nodes.

[0114] 3) Stable operation constraints:

[0115] (12);

[0116] In the formula: and These are the lower and upper limits of the generator's active power output; and These are the lower and upper limits of the generator's reactive power output; and These are the lower and upper limits of the node voltage; and These are the lower and upper limits of the thermal stability constraints for the line.

[0117] 4) Transient stability constraints:

[0118] (13);

[0119] Example:

[0120] The method proposed in this invention is as follows: Figure 3 The simulation was performed on the IEEE 39-node system shown, with the following modifications: it was assumed that three wind turbines replaced synchronous generators G1, G3, and G8, with the same power output as the original generators.

[0121] In a typical wind power scenario, a three-phase short-circuit fault occurs at node 4. Under these conditions, the stability margin becomes negative, indicating that the power system is unstable, relative to the rotor angle as shown below. Figure 4 As shown. After one iteration, the system becomes stable in this typical wind power scenario. The calculation process is repeated until a series of fault conditions in all typical wind power scenarios are stable. After using the method proposed in this invention, the power system becomes transiently stable. Figure 5 This is the optimized relative rotor angle.

[0122] Compared with existing technologies, this invention proposes a transient stability-constrained optimal power flow acquisition method that considers the uncertainties of wind power. It utilizes an improved artificial bee colony algorithm and the KMC algorithm to select typical wind power scenarios to describe the uncertainties in wind power output, and transforms the difficult-to-process differential-algebraic equations into algebraic forms based on EEAC and trajectory sensitivity. This invention enables the TSCOPF calculation method to adapt to the uncertainties of wind power generation and ensure the transient stability of the power system.

Claims

1. A method for obtaining optimal power flow under transient stability constraints considering wind power uncertainties, characterized in that, Includes the following steps: Step 1: Use the solution of the optimal power flow model of the power system as the initial operating state and set the expected fault set; Step 2: Use typical wind power scenarios to describe the uncertainty of wind power output; Step 3: Perform time-domain simulations for a series of anticipated faults under each typical wind power scenario. For the case of power system transient instability, transform the process constraints of power system transient stability into algebraic transient stability constraints through constraint transformation. Step 4: Add the obtained transient stability constraints to the optimal power flow model of the power system, construct the equivalent power system TSCOPF model including wind turbines, and recalculate the model solution; In step 3, generating the algebraic form of transient stability constraints includes the following steps: Step 3-1: Based on the time-domain simulation results of a series of anticipated faults under each typical wind power scenario, the system is divided into critical units (CMs) and non-critical units (NMs) to obtain the trajectory of the single-unit infinite OMIB system. Step 3-2: Calculate the stability characteristics and evaluate the transient stability level based on the EEAC method; Step 3-3: Establish or update the unstable single-machine infinite U-OMIB system, and calculate the trajectory sensitivity of each synchronous generator in the unstable single-machine infinite U-OMIB system at the instability time; Steps 3-4: Estimate the critical cut-off time, construct the critical single-machine infinite C-OMIB system, and calculate the power angle of the critical single-machine infinite C-OMIB system at the instability time; Steps 3-5: Based on the target power angle of the unstable single-machine infinite U-OMIB system at the instability time and the power angle of the critical single-machine infinite C-OMIB system at the instability time, construct algebraic transient stability constraints.

2. The method according to claim 1, characterized in that, In step 2, generating a typical wind power scenario includes the following steps: Step 2-1: Complete the optimization process based on the improved artificial bee colony algorithm; The bee colony is initialized using the maximum-minimum distance product method to ensure that the selection of the initial point can represent the distribution characteristics of the wind power output dataset as much as possible. In order to overcome the shortcomings of the original artificial bee colony algorithm, which is prone to getting trapped in local optima, a fitness function adapted to the KMC algorithm and a position update formula based on global guidance are constructed. During the iteration process, the new fitness function and position update formula are used to complete the optimization and evolution. Step 2-2: Perform clustering based on the improved artificial bee colony algorithm and KMC algorithm, and select typical wind power scenarios; Process the data from different scenarios, transforming the original... c The scenarios were reduced and merged into k A typical wind power scenario, in which... t The data at each time point retains its original time series, using a matrix. k × t This indicates that the optimal typical wind power scenario can be obtained.

3. The method according to claim 1, characterized in that, In step 3, the constraints for the transient stability process of the power system before constraint transformation are: (1) ； (2) ； (3) ； In the formula: x ( t )and y ( t () is a transient period T State variables and algebraic variables; u denoted as control variables with lower and upper limits; D is the differential equation describing the generator's dynamic process; G is the algebraic equation describing the generator's dynamic process; and H is the transient stability criterion.

4. The method according to claim 1, characterized in that, In step 3-2, specifically: Stability characteristics include instability time T u Time to stabilize during the first oscillation T r Transient stability margin η ; instability time T u This determines the time when the generator loses synchronization; in this case, the mechanical power and electromagnetic power of a single-unit infinite bus (OMIB) system satisfy the following relationship: (4) ； In the formula: , and The instability time of a single-machine infinite OMIB system is as follows. T u The unbalanced power, mechanical power, and electromagnetic power at the point; First oscillation settling time T r This determines the time it takes for the system to stabilize during the first oscillation; in this case, the mechanical power and electromagnetic power of the single-machine infinite bus OMIB system satisfy the following relationship: (5) ； In the formula: , and The first oscillation settling time for a single-machine infinite OMIB system are respectively... T r The unbalanced power, mechanical power, and electromagnetic power at the point; For a single-machine infinite OMIB system, the first oscillation stabilization time T r Rotational speed at that point; Transient stability margin η It is a quantified value of transient stability; based on the single-machine infinite bus OMIB system. From the plane, we can obtain: (6) ； In the formula: A dec The deceleration area; A acc To accelerate the area; M The inertia coefficient; For a single-machine infinite OMIB system in the instability time T u Rotational speed at that point; and The instability time of a single-machine infinite OMIB system is as follows. T u and the first oscillation settling time T r The angle of attack at the location; η ≥0 indicates stability; otherwise, it is unstable.

5. The method according to claim 1, characterized in that, In steps 3-5, the transient stability constraint is: (7) ； In the formula: For the critical single-machine infinite C-OMIB system at the instability time T u The angle of attack at the location; For the system during instability time T u The target angle of attack at a given location is defined as: (8) ； In the formula: For an unstable single-machine infinite U-OMIB system, the instability time T u The angle of attack at the location; In order to make Less than The required reduction amount; Based on trajectory sensitivity, it is possible to... Transform it into the following form: (9) ； In the formula: S + and These represent generator sets with positive and negative sensitivity, respectively. and The instability time of the unstable single-machine infinite U-OMIB system is as follows. T u The work angle at the first The generator and the first Sensitivity of the active power of the generator; and For the first The generator and the first The initial active power of the generator; and For the first The generator and the first The active power of the generator.

6. The method according to claim 1, characterized in that, In step 4, an equivalent TSCOPF model including wind turbines is constructed, and the particle swarm optimization algorithm is used to solve the equivalent TSCOPF model including wind turbines; the equivalent power system TSCOPF model including wind turbines is as follows: 1) Objective function: (10) ； In the formula: N G This represents the total number of synchronous generators; , , For the first l The power generation cost coefficient of a generator; For the first l The active power of the generator; 2) Power flow equations: (11) ； In the formula: For the first l The reactive power of the generator; and The first l Active and reactive power of a typhoon generator; and The first l Active and reactive power of the load at each node; and It is a node l and nodes n The voltage amplitude; It is a node l and nodes n The phase angle difference between them; and They are nodes l and nodes n The line conductance and susceptance; N B The total number of nodes; 3) Stable operation constraints: (12) ； In the formula: and These are the lower and upper limits of the generator's active power output; and These are the lower and upper limits of the generator's reactive power output; and These are the lower and upper limits of the node voltage; and The lower and upper limits of the line thermal stability constraints; 4) Transient stability constraints: (13)。

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