Transient stability constraint optimal power flow acquisition method for power system containing wind power

Abstract

The invention relates to a transient stability constraint optimal power flow acquisition method for a power system containing wind power. The method comprises the following steps: 1, representing the uncertainty of wind power generation through Rayleigh distribution; 2, on the basis of the opportunity constraint theory, a transient stability constraint optimal power flow model containing wind power generation is constructed, and the model comprises an objective function, equality constraints and inequality constraints; 3, processing the opportunity constraint by adopting an improved robust optimization method; and 4, solving the transient stability constraint optimal power flow through a biogeography optimization algorithm. The invention provides a transient stability constraint optimal power flow acquisition method for a power system containing wind power in order to positively respond to problems caused by access of new energy to a power grid under a dual-carbon target and ensure safe and stable operation of the power system containing wind power generation while ensuring economical efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to power system transient stability analysis and optimal power flow acquisition technology, and specifically to a method for acquiring optimal power flow with transient stability constraints for a power system containing wind power. Background Art

[0002] At present, the uncertainty of wind power generation has a huge impact on the original power system. In order to meet this challenge and ensure the safety of the power system while achieving economic operation, a transient stability constrained optimal power flow is proposed. Considering the large penetration rate of wind power in the power system, the solution of the TSCOPF problem becomes more difficult because uncertainty modeling requires a large number of samples. How to develop and utilize wind power while ensuring the safe operation of the power system is the key to current research. Finding a safe and reliable transient stability constrained optimal power flow model and solution method, and applying it to the power system containing wind power generation, is of great significance to improving the stability of the power system.

[0003] The patent application with publication number CN109888788A proposes a method for solving the optimal power flow of an electric power system. The invention establishes an optimization model of the electric power system, converts the probabilistic constraints of the system state variables into deterministic constraints, and obtains the optimal solution of the objective function, thereby obtaining the optimal power flow of the electric power system. The patent application with publication number CN113394787A proposes a method for calculating the probabilistic optimal power flow of an electric power system taking into account the characteristics of thermoelectric coupling. The invention method has certain guiding significance for optimizing the dispatch of the electric power system, improving the safety margin of the electric power system operation, and realizing safe and economical operation. However, when the above method is used to deal with the transient stability constrained optimal power flow containing wind power generation, it has poor effect on new energy and the system is more prone to instability.

[0004] In summary, most of the current models of transient stability constrained optimal power flow do not consider the uncertainty of wind power generation. In order to achieve this goal, the present invention proposes a method for obtaining transient stability constrained optimal power flow for a power system containing wind power. Summary of the invention

[0005] The content of the present invention is to solve the technical problem that the transient stability constrained optimal power flow model has poor processing effect on new energy, to ensure that the proposed model can better handle the uncertainty of new energy to ensure the stable operation of the system, while taking into account the system economy. For this purpose, a method for obtaining the transient stability constrained optimal power flow for a power system containing wind power is proposed.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A method for obtaining an optimal power flow with transient stability constraints for a power system including wind power comprises the following steps:

[0008] Step 1: Represent the uncertainty of wind power generation through Rayleigh distribution;

[0009] Step 2: Based on the chance constraint theory, a transient stability constrained optimal power flow model (TSCOPF) with wind power generation is constructed. The model includes objective function, equality constraints, and inequality constraints.

[0010] Step 3: Use improved robust optimization method to deal with chance constraints;

[0011] Step 4: Solve the optimal power flow constrained by transient stability using the biogeography-based optimization (BBO) algorithm.

[0012] In step 1, the following sub-steps are included:

[0013] Determine the probability of wind speed using Rayleigh distribution:

[0014]

[0015] Where: u is wind speed; d is shape parameter; r is scale parameter. The relationship between power and wind speed is shown in the following formula:

[0016]

[0017] Where: P fdx (u) is the actual output power of the x-th wind turbine; P ed is the rated output power of the wind turbine; u is the wind speed; u out is the cut-out speed of the wind turbine; u in is the cut-in speed of the wind turbine; u ed is the rated speed of the wind turbine.

[0018] In step 2, the details are as follows:

[0019] (1) Objective function:

[0020]

[0021] Where: minE[·] is the minimum expected value of the objective function; P gx is the active power generated by the x-th unit; a2, a1, a0 are the second-order coefficient, first-order coefficient, and constant coefficient of the fuel cost of the x-th unit respectively; Ω CT A collection of traditional units.

[0022] (2) Equality constraints:

[0023]

[0024] Where: P gx and Q gx are respectively the active output of the x-th traditional unit and the reactive output of the x-th traditional unit; P fdx (u) and Q fdx (u) are the active output of the x-th wind turbine and the reactive output of the x-th wind turbine respectively; P fzx and Q fzx are respectively the active load of the x-th load bus and the reactive load of the x-th load bus; V x and V y are the voltage amplitude of the xth bus and the voltage amplitude of the yth bus respectively; xy is the admittance between busbar x and busbar y; β x and β y are the voltage phase angles of the xth bus and the yth bus respectively; α xy is the phase between the xth bus and the yth bus; Ω MX For the busbar group.

[0025] (3) Inequality constraints based on chance constraints:

[0026]

[0027] Where: P gx is the active output of the traditional unit at bus x; are respectively the upper and lower limits of active output of the traditional unit at busbar x; Q gx is the reactive output of the traditional unit at bus x; are the upper and lower limits of reactive power output of traditional generators at busbar x; V x is the voltage at node x; are the upper and lower limits of the node voltage at x respectively; S xy is the apparent power between busbar x and busbar y; are the maximum apparent power and minimum apparent power between busbar x and busbar y respectively; P r (·) is the probability of violating the constraint; η P , η Q , η V , η S are respectively the violation probabilities of traditional unit active output, traditional unit reactive output, wind turbine reactive output, bus voltage, and apparent power constraints; Ω CT is the collection of traditional units; Ω MX For the busbar group.

[0028] (4) If the relative rotor angle of the synchronous generator exceeds the threshold, the transient stability constraint will be violated. Therefore, the transient stability constraint can be constructed by the relationship between the relative rotor angle and the threshold. The probability form of the transient stability constraint is:

[0029]

[0030] Where: δ' x is the rotor angle of the conventional unit at busbar x; δ COI is the position of the center of inertia; δ yz is the threshold value of the relative rotor angle; η δ is the violation probability of transient stability constraint; Ω CT A collection of traditional units.

[0031] In step 3, the following sub-steps are included:

[0032] Step 3-1: Simplify the probability form of the inequality constraint;

[0033] Step 3-2: Assuming the reliability level under chance constraints, determine the uncertainty set through the distribution of uncertainty;

[0034] Step 3-3: Based on the prior probability theory, optimize the range of the uncertainty set, specifically:

[0035]

[0036] Where: x is a vector consisting of the active power, reactive power and apparent power of the traditional unit; y is the bus voltage; z is the transient stability constraint; x max , x m i n ,y max ,y m i n , z max , z min are the upper and lower limits of different variables respectively; α is the corresponding violation probability; is the prior probability; ε is the uncertainty set.

[0037] In step 4, the following sub-steps are specifically included:

[0038] Step 4-1: First, use the control variable u to initialize the possible solutions to the problem;

[0039] Step 4-2: Initialize the parameters and verify whether the initialized data meets the constraints. If not, modify the solution. If the variable is not within the limit, fix the solution using the following formula:

[0040] If P gx ≥Pgxmax , then P gx =P gxmax ;

[0041] If P gx ≤P gxmin , then P gx =P gxmin .

[0042] Step 4-3: Define the fitness function of the BBO algorithm and find the best solution.

[0043] Compared with the prior art, the present invention has the following technical effects:

[0044] 1) The present invention proposes a method for obtaining the optimal power flow with transient stability constraints for a power system containing wind power, which meets the transient stability constraint requirements of the power system containing wind power generation;

[0045] 2) The present invention proposes a BBO algorithm for solving the TSCOPF problem, which can effectively reduce the operating cost and also reduce the operating risk;

[0046] 3) The present invention proposes a method for obtaining the optimal power flow with transient stability constraints for a power system containing wind power. The uncertainty of wind power generation is represented by Rayleigh distribution, and a TSCOPF model containing wind power generation is constructed based on the chance constraint theory. After that, an improved robust optimization method is used to process the chance constraints, and finally the BBO algorithm is used to solve the optimal power flow with transient stability constraints. The present invention can ensure that the power system can operate safely and stably after large-scale wind power generation is connected to the grid. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0048] Figure 1 is a flow chart of the method of the present invention;

[0049] Figure 2 It is a flowchart for solving the problem using the BBO algorithm;

[0050] Figure 3 is a schematic diagram of an IEEE 68-node system in an example of the present invention;

[0051] Figure 4 It is a power angle diagram of the system when the IEEE 68-node system fails in the example of the present invention;

[0052] Figure 5 is a power angle diagram of the IEEE 68-node system in the example of the present invention after being solved by the optimization algorithm of the present invention;

[0053] Figure 6It is the fuel cost graph of BBO algorithm and GSA algorithm in the case of IEEE 39-node system. DETAILED DESCRIPTION

[0054] The present invention proposes a method for obtaining the optimal power flow under transient stability constraints for a power system containing wind power. Figure 1 As shown, the method comprises the following steps:

[0055] Step 1: Represent the uncertainty of wind power generation through Rayleigh distribution. Compared with the Weibull distribution, the Rayleigh distribution can be applied to more wind speed scenarios and can obtain better results for different climate conditions. The specific steps are as follows:

[0056] Determine the probability of wind speed using Rayleigh distribution:

[0057]

[0058] Where: u is wind speed; d is shape parameter; r is scale parameter. The relationship between power and wind speed is shown in the following formula:

[0059]

[0060] Where: P fd (u) is the actual output power of the x-th wind turbine; P ed is the rated output power of the wind turbine; u is the wind speed; u out is the cut-out speed of the wind turbine; u in is the cut-in speed of the wind turbine; u ed is the rated speed of the wind turbine.

[0061] Step 2: Based on the opportunity constraint theory, construct a TSCOPF model with wind power generation, which includes objective function, equality constraints, and inequality constraints. Specifically, it includes the following steps:

[0062] (1) Objective function:

[0063]

[0064] Where: minE[·] is the minimum expected value of the objective function; P gx is the active power generated by the x-th unit; a2, a1, a0 are the second-order coefficient, first-order coefficient, and constant coefficient of the fuel cost of the x-th unit respectively; Ω CT A collection of traditional units.

[0065] (2) Equality constraints:

[0066]

[0067] Where: P gx and Q gx are respectively the active output of the x-th traditional unit and the reactive output of the x-th traditional unit; P fdx (u) and Q fdx (u) are the active output of the x-th wind turbine and the reactive output of the x-th wind turbine respectively; P fzx and Q fzx are respectively the active load of the x-th load bus and the reactive load of the x-th load bus; V x and V y are the voltage amplitude of the xth bus and the voltage amplitude of the yth bus respectively; xy is the admittance between busbar x and busbar y; β x and β y are the voltage phase angles of the xth bus and the yth bus respectively; α xy is the phase between the xth bus and the yth bus; Ω MX For the busbar group.

[0068] (3) Inequality constraints based on chance constraints:

[0069]

[0070] Where: P gx is the active output of the traditional unit at bus x; are respectively the upper and lower limits of active output of the traditional unit at busbar x; Q gx is the reactive output of the traditional unit at bus x; are the upper and lower limits of reactive power output of traditional generators at busbar x; V x is the voltage at node x; are the upper and lower limits of the node voltage at x respectively; S xy is the apparent power between busbar x and busbar y; are the maximum apparent power and minimum apparent power between busbar x and busbar y respectively; P r (·) is the probability of violating the constraint; η P , η Q , η V , η S are respectively the violation probabilities of traditional unit active output, traditional unit reactive output, wind turbine reactive output, bus voltage, and apparent power constraints; Ω CT is the collection of traditional units; Ω MX For the busbar group.

[0071] (4) If the relative rotor angle of the synchronous generator exceeds the threshold, the transient stability constraint will be violated. Therefore, the transient stability constraint can be constructed by the relationship between the relative rotor angle and the threshold. The probability form of the transient stability constraint is:

[0072]

[0073] Where: x ' is the rotor angle of the traditional unit at busbar x; δ COI is the position of the center of inertia; δ yz is the threshold value of the relative rotor angle; η δ is the violation probability of transient stability constraint; Ω CT A collection of traditional units.

[0074] Step 3: Use the improved robust optimization method to deal with chance constraints. Specifically, it includes the following steps:

[0075] Step 3-1: Simplify the probability form of the inequality constraint;

[0076] Step 3-2: Assuming the reliability level ε under the chance constraint, determine the uncertainty set through the distribution of uncertainty;

[0077] Step 3-3: Based on prior probability theory, optimize the range of the uncertainty set:

[0078]

[0079] Where: x is a vector consisting of the active power, reactive power and apparent power of the traditional unit; y is the bus voltage; z is the transient stability constraint; x max , x min ,y max ,y min , z max , z min are the upper and lower limits of different variables respectively; α is the corresponding violation probability; is the prior probability; ε is the uncertainty set.

[0080] Step 4: Solve the transient stability constrained optimal power flow through the BBO algorithm. Specifically, it includes the following steps:

[0081] Step 4-1: First, use the control variable u to initialize the possible solutions to the problem;

[0082] Step 4-2: Initialize the parameters and verify whether the initialized data meets the constraints. If not, modify the solution. If the variable is not within the limit, fix the solution using the following formula:

[0083] If P gx ≥Pgxmax , then P gx =P gxmax ;

[0084] If P gx ≤P gxmin , then P gx =P gxmin .

[0085] Step 4-3: Define the fitness function of the BBO algorithm and find the best solution.

[0086] The above formula explains how to construct a transient stability constrained optimal power flow model with wind power generation based on the chance constraint theory, and use an improved robust optimization method to deal with the chance constraints. Finally, the transient stability constrained optimal power flow is solved by the BBO algorithm.

[0087] Example:

[0088] In order to verify the feasibility of the present invention, Figure 3 The simulation is performed on the IEEE 39-bus system shown in FIG. 1 , and a wind turbine generator set is added to the system: it is assumed that two wind turbine generator sets replace the synchronous generators G5 and G9, and the power generation of the wind turbine generator is the same as that of the original generator.

[0089] A three-phase short circuit fault occurs on line 5-6 of the IEEE 39-bus system. The fault duration is 0.25s. The power angle diagram of the system is as follows: Figure 4 As shown in the figure, it can be seen that the system loses stability at this time, and the BBO algorithm is used for processing. After the BBO algorithm is iterated, the system gradually recovers to a stable state. Figure 5 is the optimized generator power angle.

[0090] In addition, if Figure 6 As shown in the figure, under the IEEE 39-node system, the proposed BBO algorithm requires less fuel cost and fewer iterations to stabilize the power system than the Gravitational Search Algorithm (GSA) when reaching stability. It can be seen that the proposed BBO algorithm has the characteristics of fast convergence and reduced fuel cost.

[0091] The present invention proposes a method for obtaining the optimal power flow with transient stability constraints for a power system containing wind power. The uncertainty of wind power generation is represented by Rayleigh distribution. A TSCOPF model containing wind power generation is constructed based on the chance constraint theory. After that, an improved robust optimization method is used to process the chance constraint. Finally, the BBO algorithm is used to solve the optimal power flow with transient stability constraints. The present invention can ensure that the power system can operate safely and stably after large-scale wind power generation is connected to the grid.

Claims

1. A method for obtaining the optimal power flow with transient stability constraints for a power system containing wind power, characterized in that: The following steps are involved: Step 1: Represent the uncertainty of wind power generation through Rayleigh distribution; Step 2: Based on the chance constraint theory, a transient stability constrained optimal power flow model with wind power generation is constructed. The model includes objective function, equality constraints, and inequality constraints. Step 3: Use improved robust optimization method to deal with chance constraints; Step 4: Solve the optimal power flow constrained by transient stability through the biogeographic optimization algorithm.

2. The method according to claim 1, characterized in that In step 1, the following sub-steps are included: Determine the probability of wind speed using Rayleigh distribution: Where: u is wind speed; d is shape parameter; r is scale parameter. The relationship between power and wind speed is shown as follows: Where: P fdx (u) is the actual output power of the x-th wind turbine; P ed is the rated output power of the wind turbine; u is the wind speed; u out is the cut-out speed of the wind turbine; u in is the cut-in speed of the wind turbine; u ed is the rated speed of the wind turbine.

3. The method according to claim 1, characterized in that In step 2, the details are as follows: (1) Objective function: Where: minE[·] is the minimum expected value of the objective function; P gx is the active power generated by the x-th unit; a2, a1, a0 are the second-order coefficient, first-order coefficient, and constant coefficient of the fuel cost of the x-th unit respectively; Ω CT It is a collection of traditional units; (2) Equality constraints: Where: P gx and Q gx are respectively the active output of the x-th traditional unit and the reactive output of the x-th traditional unit; P fdx (u) and Q fdx (u) are the active output of the x-th wind turbine and the reactive output of the x-th wind turbine respectively; P fzx and Q fzx are respectively the active load of the x-th load bus and the reactive load of the x-th load bus; V x and V y are the voltage amplitude of the xth bus and the voltage amplitude of the yth bus respectively; xy is the admittance between busbar x and busbar y; β x and β y are the voltage phase angles of the xth bus and the yth bus respectively; α xy is the phase between the xth bus and the yth bus; Ω MX For the busbar group; (3) Inequality constraints based on chance constraints: Where: P gx is the active output of the traditional unit at bus x; are respectively the upper and lower limits of active output of the traditional unit at busbar x; Q gx is the reactive output of the traditional unit at bus x; are the upper and lower limits of reactive power output of traditional generators at busbar x; V x is the voltage at node x; are the upper and lower limits of the node voltage at x respectively; S xy is the apparent power between busbar x and busbar y; are the maximum apparent power and minimum apparent power between busbar x and busbar y respectively; P r (·) is the probability of violating the constraint; η P , η Q , η V , η S are respectively the violation probabilities of traditional unit active output, traditional unit reactive output, wind turbine reactive output, bus voltage, and apparent power constraints; Ω CT is the collection of traditional units; Ω MX For the busbar group; (4) If the relative rotor angle of the synchronous generator exceeds the threshold, the transient stability constraint will be violated. Therefore, the transient stability constraint is constructed based on the relationship between the relative rotor angle and the threshold. The probability form of the transient stability constraint is: Where: x ' is the rotor angle of the traditional unit at busbar x; δ COI is the position of the center of inertia; δ yz is the threshold value of the relative rotor angle; η δ is the violation probability of transient stability constraint; Ω CT A collection of traditional units.

4. The method according to claim 1, characterized in that In step 3, the following sub-steps are included: Step 3-1: Simplify the probability form of the inequality constraint; Step 3-2: Assuming the reliability level under chance constraints, determine the uncertainty set through the distribution of uncertainty; Step 3-3: Based on the prior probability theory, optimize the range of the uncertainty set, specifically: Where: x is a vector consisting of the active power, reactive power and apparent power of the traditional unit; y is the bus voltage; z is the transient stability constraint; x max , x min ,y max ,y min , z max , z min are the upper and lower limits of different variables respectively; α is the corresponding violation probability; is the prior probability; ε is the uncertainty set.

5. The method according to claim 1, characterized in that In step 4, the following sub-steps are specifically included: Step 4-1: First, use the control variable u to initialize the possible solutions to the problem; Step 4-2: Initialize the parameters and verify whether the initialized data meets the constraints. If not, modify the solution. If the variables are not within the restricted range, fix the solution using the following formula: If P gx ≥P gxmax , then P gx =P gxmax ; If P gx ≤P gxmin , then P gx =P gxmin ; Step 4-3: Define the fitness function of the BBO algorithm and find the best solution.

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