Transient stability constraint optimal power flow model construction method based on wind power uncertainty

Abstract

The invention discloses a transient stability constraint optimal power flow model construction method based on wind power uncertainty. The method comprises the following steps: step 1, establishing an uncertainty output model of wind power generation according to an uncertainty standard; step 2, constructing transient stability constraints by using a single-machine equivalent SME method; 3, describing inequality constraints and transient stability constraints based on a joint opportunity constraint (JCC) theory, and constructing a transient stability constraint optimal power flow TSCOPF model; 4, converting the joint opportunity constraint into a deterministic sample constraint by adopting sample average approximation SAA; and 5, solving the constructed TSCOPF model by using a collective decision optimization (CDO) algorithm. The invention discloses a transient stability constraint optimal power flow model construction method based on wind power generation uncertainty, which is suitable for a power system accessed by wind power generation and has important significance for improving the stable operation of the power system.

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 calculation technology, and specifically to a method for constructing a transient stability constrained optimal power flow model based on wind power uncertainty. Background Art

[0002] In recent years, new energy generation represented by wind power has been strongly advocated by national policies. However, wind power generation has uncertainty, and its large-scale access to the power system will inevitably reduce the stability of the power system operation. Therefore, under the condition of large-scale wind power access to the power system, considering the uncertainty of wind power generation has certain practical significance and application value for the transient stability analysis and optimal power flow calculation method of the power system.

[0003] The patent document with the publication number CN111525556A discloses a multi-objective optimal power flow calculation method taking into account the confidence risk of wind power. The method proposes a quantitative calculation method for the power deviation of wind power overestimation and underestimation confidence risk based on the probability density of wind power random distribution and chance constraints. By taking into account the confidence risk of wind power overestimation and underestimation, and introducing transformer ratio adjustment and reactive compensation capacity optimization in the decision variables, a multi-objective optimal power flow calculation model for source-grid coordinated operation is constructed. The patent document with the publication number CN111668828A discloses a method and device for calculating the probability optimal power flow of a power system, including obtaining an independent standard Gaussian domain sample matrix corresponding to a probabilistic uncertain source in the power system, converting the standard Gaussian domain sample matrix with correlation into a sample matrix of a probabilistic uncertain source with correlation in the original distribution domain using the principle of equal probability, and performing a probabilistic optimal power flow calculation based on the sample matrix of the probabilistic uncertain source with correlation in the original distribution domain to obtain the probabilistic optimal power flow calculation result. None of the above methods simultaneously considers the influence of the uncertainty of the wind power generation system and the transient stability constraint on the stable operation of the system, which may cause the calculation results to deviate from the actual operation requirements.

[0004] In summary, the current optimal power flow model of the power system rarely considers the uncertainty of wind power generation and the influence of transient stability constraints at the same time. The method proposed in the present invention studies the uncertainty of wind power generation on the basis of TSCOPF and enhances the accuracy of calculation. Summary of the invention

[0005] The purpose of the present invention is to take into account the uncertainty of wind power generation and the influence of transient stability constraints in the traditional optimal power flow model of the power system, so as to adapt to the current situation of large-scale access of wind power generation to the power system, and provide a method for constructing an optimal power flow model with transient stability constraints based on wind power uncertainty.

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

[0007] The method for constructing a transient stability constrained optimal power flow model based on wind power uncertainty includes the following steps:

[0008] Step 1: Establish an uncertainty output model for wind power generation;

[0009] Step 2: Use the single machine equivalent method to construct transient stability constraints;

[0010] Step 3: Based on the joint chance constraint theory, the inequality constraints and transient stability constraints are described, and the transient stability constraint optimal power flow model is constructed;

[0011] Step 4: Use sample average approximation to transform the joint chance constraint into a deterministic sample constraint;

[0012] Step 5: Use the collective decision-making optimization algorithm to solve the transient stability constrained optimal power flow model constructed above.

[0013] In step 1, the uncertainty output model of wind power generation is established as follows:

[0014]

[0015] Where: P t F is the available predicted value of wind power generation; a is the uncertainty standard.

[0016] In step 2, in the unstable case, the transient stability margin λ is the residual dynamic energy when the system is unstable; in the stable case, the system stops deflecting at the return angle and swings in the opposite direction; the transient stability margin λ is expressed as follows:

[0017]

[0018] Where: H e is the equivalent inertia coefficient of the infinite busbar of a single machine; ω(T u ) is the angular velocity of the single-machine wireless bus when it becomes unstable; T u is the time of instability; θ μ is the angle between the active power and mechanical power of the generator under instability; θ r is the return angle at the return time; P is the unbalanced power of the system; the transient stability margin λ is used to predict the transient stability of the power system;

[0019] The transient stability margin of the above situation is converted into a probability form, and the probabilistic transient stability constraint is constructed, which is expressed as follows:

[0020] P{λ<0}≥1-η z (3)

[0021] Where: ηz is the risk parameter of transient stability constraint.

[0022] The constructed optimal power flow model of power system transient stability constraints is as follows:

[0023] 1) Objective function

[0024] Taking the total cost of power generation as the objective function of the TSCOPF model, the expression is as follows:

[0025]

[0026] Where: a i 、b i 、c i are the cost coefficients of the i-th generator; P Gi is the output power of the i-th generator; N G is the number of generators;

[0027] 2) Equality constraints

[0028]

[0029] Where: P Gi , Q Gi are the active power and reactive power of the generator respectively; P Li , Q Li are the active power demand and reactive power demand respectively; N is the number of buses; G i,j , B i,j are the conductance and susceptance between busbars i and j respectively; U i and U j are the voltage amplitudes at nodes i and j respectively; θ ij is the phase angle difference of the voltage between nodes i and j;

[0030] 3) Inequality constraints and transient stability constraints based on JCC theory

[0031]

[0032] Where: P Gi,max , P Gi,min They are the upper and lower limits of the active output of the generator respectively; Q Gi,max , Q Gi,min are the upper and lower limits of the reactive power output of the generator respectively; U bi,max , U bi,min are the upper and lower limits of the node voltage respectively; P Gi , Q Gi are the active output and reactive output of the generator respectively; U bi is the node voltage; N b is the set of nodes; η is the risk parameter of JCC.

[0033] In step 4, the probability inequality constraint and transient stability constraint based on JCC theory in equation (6) are transformed into deterministic sample constraints using sample average approximation. The specific steps are as follows:

[0034] Step 4-1: Convert the intractable JCC into a simple probability expression, and then approximate it into a form containing an indicator function;

[0035] In step 4-1, the linear constraints in equation (6) are written in general form, and the function G(x,a) is defined as the maximum difference between the state variable and the control variable containing the uncertainty standard. The difficult JCC problem is converted into a simple probability expression form, which is then approximated into a form containing an indicator function, and its expression is as follows:

[0036]

[0037] Where: x is the decision variable; a is the uncertainty standard; η is the risk parameter of JCC; D is the number of historical samples; Z(G(x,a)≥0) is the indicator function, when the internal equation is established, its result is 1, otherwise it is 0;

[0038] Step 4-2: Use the Big-M method to transform the difficult-to-solve form containing indicator functions into a mixed integer form containing binary variables, that is, to transform the difficult-to-solve JCC into an easily-solved deterministic sample constraint;

[0039] In step 4-2, introduce the binary variable y d , converting the form containing the indicator function into a mixed integer form containing binary variables, the expression is as follows:

[0040]

[0041] Where: y d is a binary variable;

[0042] Introduce a large constant M, construct the function G(x,a) and the binary variable y d The inequality relationship between them is expressed as follows:

[0043] G(x,a (d) )≤My d (9)

[0044] Where: M is a large constant; when y d When it is 1, G(x,a)≤0 is violated; when y d When it is 0, G(x,a)≤0 is satisfied;

[0045] Furthermore, since the mixed integer form introduces binary variables that are difficult to calculate, a class of support vector clustering methods is used to train the model and cluster the samples; after the model training is completed, the model is used to predict the binary variables.

[0046] In step 5, the TSCOPF model constructed above is solved using a collective decision optimization algorithm, including the following steps:

[0047] Step 5-1: Initialize algorithm parameters and agents, each agent represents a possible power system dispatch scheme;

[0048] Step 5-2: Perform power flow calculation for each agent and calculate the fitness value of each agent;

[0049] Step 5-3: Update each group of agents and obtain the fitness function of the updated population;

[0050] Step 5-4: Evaluate the minimum value of the best fitness to obtain the best fitness value and the best group;

[0051] Step 5-5: Determine whether the maximum number of iterations has been reached. If so, output the optimal solution; otherwise, jump to step 5-3.

[0052] Compared with the prior art, the present invention has the following technical effects:

[0053] 1) The proposed TSCOPF model takes into account the uncertainty of wind turbine output and better improves the transient stability of the power system;

[0054] 2) The present invention adopts the CDO algorithm to solve the proposed TSCOPF model. The CDO algorithm works by imitating social behaviors affected by human decision-making ability and can perform global search in the decision space, which helps to find better solutions in the hidden decision space and avoids the limitations that may be brought about by local search. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0056] Figure 1 is a flow chart of the system of the present invention;

[0057] Figure 2 is a flow chart of the solution algorithm of the present invention;

[0058] Figure 3 It is a schematic diagram of an improved IEEE 39-node system in an example of the present invention;

[0059] Figure 4It is a power angle curve diagram of the system generator before the method of the present invention is adopted in the improved IEEE 39-node system in the example of the present invention;

[0060] Figure 5 It is a power angle curve diagram of the system generator after the method of the present invention is adopted in the improved IEEE 39-node system in the example of the present invention. DETAILED DESCRIPTION

[0061] The present invention provides a method for constructing a transient stability constrained optimal power flow model based on wind power uncertainty, such as Figure 1 As shown, the method comprises the following steps:

[0062] Step 1: Establish an uncertainty output model of wind power generation based on uncertainty criteria;

[0063] In step 1, the uncertainty output model of wind power generation is established as follows:

[0064]

[0065] Where: P t F is the available predicted value of wind power generation; a is the uncertainty standard.

[0066] Step 2: Use the Single Machine Equivalent (SME) method to construct the probabilistic transient stability constraints;

[0067] In step 2, the probabilistic transient stability constraint is constructed using the SME method, in which the transient stability margin λ is used to predict the transient stability of the power system.

[0068] Further, in step 2, in an unstable situation, the transient stability margin λ is the residual dynamic energy when the system is unstable; in a stable situation, the system stops deflecting at the return angle and swings in the opposite direction. The transient stability margin λ is expressed as follows:

[0069]

[0070] Where: H e is the equivalent inertia coefficient of the infinite busbar of a single machine; ω(T u ) is the angular velocity of the single-machine wireless bus when it becomes unstable; T u is the time of instability; θ μ is the angle between the active power and mechanical power of the generator under instability; θ r is the return angle at the return time; P is the unbalanced power of the system.

[0071] The transient stability margin of the above situation is converted into a probability form, and the probabilistic transient stability constraint is constructed, which is expressed as follows:

[0072] P{λ<0}≥1-η z (3)

[0073] Where: η z is the risk parameter of transient stability constraint.

[0074] Step 3: Based on the Joint Chance Constraints (JCC) theory, the inequality constraints and transient stability constraints are described, and the Transient Stability Constrained Optimal Power Flow (TSCOPF) model is constructed;

[0075] 1) Objective function

[0076] Taking the total cost of power generation as the objective function of the TSCOPF model, the expression is as follows:

[0077]

[0078] Where: a i , b i 、c i are the cost coefficients of the i-th generator; P Gi is the output power of the i-th generator; N G is the number of generators.

[0079] 2) Equality constraints

[0080]

[0081] Where: P Gi , Q Gi are the active power and reactive power of the generator respectively; P Li , Q Li are the active power demand and reactive power demand respectively; N is the number of buses; G i,j , B i,j are the conductance and susceptance between busbars i and j respectively; U i and U j are the voltage amplitudes at nodes i and j respectively; θ ij is the phase angle difference between the voltages at nodes i and j.

[0082] 3) Inequality constraints and transient stability constraints based on JCC theory

[0083]

[0084] Where: P Gi,max , P Gi,min They are the upper and lower limits of the active output of the generator respectively; QGi,max , Q Gi,min are the upper and lower limits of the reactive power output of the generator respectively; U bi,max , U bi,min are the upper and lower limits of the node voltage respectively; P Gi , Q Gi are the active output and reactive output of the generator respectively; U bi is the node voltage; N b is the set of nodes; η is the risk parameter of JCC.

[0085] Step 4: Use Sample Average Approximation (SAA) to transform the inequality constraints and transient stability constraints based on the JCC theory into deterministic sample constraints. The specific steps are as follows:

[0086] Step 4-1: Convert the intractable JCC into a simple probability expression, and then approximate it into a form containing an indicator function;

[0087] Furthermore, in step 4-1, the linear constraints in equation (6) are written in a general form, and the function G(x,a) is defined as the maximum difference between the state variable and the control variable containing the uncertainty standard. The difficult JCC problem is converted into a simple probability expression form, which is then approximated into a form containing an indicator function, and its expression is as follows:

[0088]

[0089] Where: x is the decision variable; a is the uncertainty standard; η is the risk parameter of JCC; D is the number of historical samples; Z(G(x,a)≥0) is the indicator function, and its result is 1 when the internal equation holds, otherwise it is 0.

[0090] Step 4-2: Use the Big-M method to transform the difficult-to-solve form containing indicator functions into a mixed integer form containing binary variables, that is, to transform the difficult-to-handle JCC into an easily solvable deterministic sample constraint.

[0091] In step 4-2, introduce the binary variable y d , converting the form containing the indicator function into a mixed integer form containing binary variables, the expression is as follows:

[0092]

[0093] Where: y d is a binary variable.

[0094] Introduce a large constant M, construct the function G(x,a) and the binary variable y dThe inequality relationship between them is expressed as follows:

[0095] G(x,a (d) )≤My d (9)

[0096] Where: M is a large constant; when y d When it is 1, G(x,a)≤0 is violated; when y d When is 0, G(x,a)≤0.

[0097] Furthermore, since the mixed integer form introduces binary variables that are difficult to calculate, a class of support vector clustering methods is used to train the model and cluster the samples. After the model training is completed, we can use the model to predict the binary variables.

[0098] Step 5: Use the Collective Decision Optimization (CDO) algorithm to solve the TSCOPF model constructed above;

[0099] The specific steps are as follows:

[0100] Step 5-1: Initialize algorithm parameters and agents, each agent represents a possible power system dispatch scheme;

[0101] Step 5-2: Perform power flow calculation for each agent and calculate the fitness value of each agent;

[0102] Step 5-3: Update each group of agents and obtain the fitness function of the updated population;

[0103] Step 5-4: Evaluate the minimum value of the best fitness to obtain the best fitness value and the best group;

[0104] Step 5-5: Determine whether the maximum number of iterations has been reached. If so, output the optimal solution; otherwise, jump to step 5-3.

[0105] Example:

[0106] The method proposed by the present invention is as follows Figure 3 The simulation is performed on the IEEE 39-bus system shown in the figure, with the following modifications: It is assumed that two wind turbines replace the synchronous generators G5 and G9, and their power generation is the same as the original generators.

[0107] In a certain wind power scenario, a three-phase short circuit occurs in the transmission line between lines 10 and 13.

[0108] Without considering transient stability constraints, that is, in the case of OPF optimization, the system cost is 30151.12$ / h. The power angle diagram of the system generator is as follows: Figure 4 As shown in the figure, it can be seen that the power angle between the generators continues to increase and the system is transiently unstable.

[0109] The TSCOPF method based on wind power generation uncertainty proposed in this invention is adopted. By considering the uncertainty of wind power output, a probabilistic transient stability constrained optimal power flow model is constructed based on the JCC theory, and finally the CDO algorithm is used for solution. The system cost is 30658.6$ / h. The generator power angle is obtained as follows Figure 5 As shown, the power angle trajectory does not continue to increase and the system is transiently stable.

[0110] From the example results, it can be concluded that the system cost under TSCOPF optimization considering transient stability is slightly higher than the system cost under OPF optimization. This is because a certain sacrifice is made to the economy of the system in order to ensure the transient stability of the entire system.

Claims

1. A method for constructing a transient stability constrained optimal power flow model based on wind power uncertainty, characterized in that: The following steps are involved: Step 1: Establish an uncertainty output model for wind power generation; Step 2: Use the single machine equivalent method to construct transient stability constraints; Step 3: Based on the joint chance constraint theory, the inequality constraints and transient stability constraints are described, and the transient stability constraint optimal power flow model is constructed; Step 4: Use sample average approximation to transform the joint chance constraint into a deterministic sample constraint; Step 5: Use the collective decision-making optimization algorithm to solve the transient stability constrained optimal power flow model constructed above.

2. The method according to claim 1, characterized in that In step 1, the uncertainty output model of wind power generation is established as follows: Where: P t F is the available predicted value of wind power generation; a is the uncertainty standard.

3. The method according to claim 1, characterized in that In step 2, in the unstable case, the transient stability margin λ is the residual dynamic energy when the system is unstable; in the stable case, the system stops deflecting at the return angle and swings in the opposite direction; the transient stability margin λ is expressed as follows: Where: H e is the equivalent inertia coefficient of the infinite busbar of a single machine; ω(T u ) is the angular velocity of the single-machine wireless bus when it becomes unstable; T u is the time of instability; θ μ is the angle between the active power and mechanical power of the generator under instability; θ r is the return angle at the return time; P is the unbalanced power of the system; the transient stability margin λ is used to predict the transient stability of the power system; The transient stability margin of the above situation is converted into a probability form, and the probabilistic transient stability constraint is constructed, which is expressed as follows: P{λ<0}≥1-η z (3) Where: η z is the risk parameter of transient stability constraint.

4. The method according to any one of claims 1 to 3, characterized in that: The constructed optimal power flow model of power system transient stability constraints is as follows: 1) Objective function Taking the total cost of power generation as the objective function of the TSCOPF model, the expression is as follows: Where: a i 、b i 、c i are the cost coefficients of the i-th generator; P Gi is the output power of the i-th generator; N G is the number of generators; 2) Equality constraints Where: P Gi , Q Gi are the active power and reactive power of the generator respectively; P Li , Q Li are the active power demand and reactive power demand respectively; N is the number of buses; G i,j , B i,j are the conductance and susceptance between busbars i and j respectively; U i and U j are the voltage amplitudes at nodes i and j respectively; θ ij is the phase angle difference of the voltage between nodes i and j; 3) Inequality constraints and transient stability constraints based on JCC theory Where: P Gi,max , P Gi,min They are the upper and lower limits of the active output of the generator respectively; Q Gi,max , Q Gi,min are the upper and lower limits of the reactive power output of the generator respectively; U bi,max , U bi,min are the upper and lower limits of the node voltage respectively; P Gi , Q Gi are the active output and reactive output of the generator respectively; U bi is the node voltage; N b is the set of nodes; η is the risk parameter of JCC.

5. The method according to claim 4, characterized in that In step 4, the probability inequality constraint and transient stability constraint based on JCC theory in equation (6) are transformed into deterministic sample constraints using sample average approximation. The specific steps are as follows: Step 4-1: Convert the intractable JCC into a simple probability expression, and then approximate it into a form containing an indicator function; In step 4-1, the linear constraints in equation (6) are written in general form, and the function G(x,a) is defined as the maximum difference between the state variable and the control variable containing the uncertainty standard. The difficult JCC problem is converted into a simple probability expression form, which is then approximated into a form containing an indicator function, and its expression is as follows: Where: x is the decision variable; a is the uncertainty standard; η is the risk parameter of JCC; D is the number of historical samples; Z(G(x,a)≥0) is the indicator function, when the internal equation is established, its result is 1, otherwise it is 0; Step 4-2: Use the Big-M method to transform the difficult-to-solve form containing indicator functions into a mixed integer form containing binary variables, that is, to transform the difficult-to-solve JCC into an easily-solved deterministic sample constraint; In step 4-2, introduce the binary variable y d , converting the form containing the indicator function into a mixed integer form containing binary variables, the expression is as follows: Where: y d is a binary variable; Introduce a large constant M, construct the function G(x,a) and the binary variable y d The inequality relationship between them is expressed as follows: G(x,a (d) )≤My d (9) Where: M is a large constant; when y d When it is 1, G(x,a)≤0 is violated; when y d When it is 0, G(x,a)≤0 is satisfied; Furthermore, since the mixed integer form introduces binary variables that are difficult to calculate, a class of support vector clustering methods is used to train the model and cluster the samples; after the model training is completed, the model is used to predict the binary variables.

6. The method according to claim 1, characterized in that In step 5, the TSCOPF model constructed above is solved using a collective decision optimization algorithm, including the following steps: Step 5-1: Initialize algorithm parameters and agents, each agent represents a possible power system dispatch scheme; Step 5-2: Perform power flow calculation for each agent and calculate the fitness value of each agent; Step 5-3: Update each group of agents and obtain the fitness function of the updated population; Step 5-4: Evaluate the minimum value of the best fitness to obtain the best fitness value and the best group; Step 5-5: Determine whether the maximum number of iterations has been reached. If so, output the optimal solution; otherwise, jump to step 5-3.

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