A Reactive Power Optimization Method for Distribution Networks Based on Improved Whale Algorithm

Abstract

The present invention discloses a reactive power optimization method for a distribution network based on an improved whale algorithm, which includes: taking the minimum of active power loss and voltage violation penalty as the objective function, and establishing a reactive power optimization model for the distribution network by considering the constraint conditions of wind turbines and the static var generator (SVG) of the reactive power compensation device; processing the load of each node by multiplying it with a load change coefficient to obtain the processed power load data; obtaining the power flow calculation results of the distribution network system based on the processed power load data; and performing reactive power optimization on the distribution network with wind turbines and SVG based on the improved whale algorithm to obtain the reactive power output of the wind turbines and SVG. By establishing a reactive power optimization model for the distribution network, introducing a non-linear time-varying factor, a stochastic learning strategy and a Cauchy mutation strategy to improve the convergence speed and calculation accuracy of the whale algorithm, the present invention obtains a reactive power optimization strategy for the IEEE 33-node system with wind turbines and SVG, reasonably coordinates the reactive power output of the wind turbines and SVG, reduces the system power loss, and improves the economic benefits of system operation.

Description

Technical Field

[0001] The present invention relates to a reactive power optimization method for a distribution network based on an improved whale algorithm, belonging to the field of reactive power optimization. Background Art

[0002] With the continuous expansion of the scale of wind power grid connection, the voltage reactive power problem of the wind power grid-connected system has become increasingly prominent. Maintaining the reactive power balance of the system is an important means to ensure the stable and economic operation of the power system. Wind turbines have a certain reactive power support ability. After being connected to the system, they lack unified coordination with reactive power compensation devices, and the reactive power capacity cannot be fully utilized, resulting in poor economic performance of the system operation.

[0003] The traditional whale algorithm is prone to falling into local optimum and has weak global search ability, resulting in problems such as slow convergence speed and low calculation accuracy of the algorithm. Summary of the Invention

[0004] The present invention provides a reactive power optimization method for a distribution network based on an improved whale algorithm, which is used to optimize the reactive power output of the distribution network system.

[0005] The technical solution of the present invention is: a reactive power optimization method for a distribution network based on an improved whale algorithm, including:

[0006] Taking the minimum of active power loss and voltage violation penalty as the objective function, and establishing a reactive power optimization model for the distribution network considering the constraint conditions of wind turbines and the static var generator (SVG) of reactive power compensation devices;

[0007] Processing the load of each node, multiplying it by a load change coefficient as the processed power load data; obtaining the power flow calculation result of the distribution network system according to the processed power load data.

[0008] Based on the improved whale algorithm, performing reactive power optimization on the distribution network containing wind turbines and SVG to obtain the reactive power output of wind turbines and SVG.

[0009] The established reactive power optimization model for the distribution network is specifically:

[0010] Active power loss P loss :

[0011]

[0012] Voltage violation penalty Δf:

[0013]

[0014] In summary, the comprehensive objective function F of the reactive power optimization model for the distribution network is:

[0015] minF = Δf + P loss

[0016] Where: i and j are node numbers; n is the total number of nodes in the distribution network system; G ij is the conductance of branch ij; U i and U j are the voltage amplitudes of nodes i and j; δ i and δ j are the phase angles of the node voltages; λ is the penalty coefficient; U is the reference voltage.

[0017] The constraint conditions include equality constraints and inequality constraints.

[0018] The equality constraints:

[0019]

[0020] Where: P Gi and P Di are the active power injected by node i and the active power of the load respectively; Q Gi and Q Di are the reactive power injected by node i and the reactive power of the load respectively; P W and Q W are the active power and reactive power injected by the installed doubly-fed wind turbine respectively; G ij is the conductance of branch ij; U i and U j are the voltage amplitudes of nodes i and j; Q S is the reactive power injected by the reactive power compensation device SVG; B ij is the susceptance of branch ij; δ ij is the voltage phase angle difference between nodes i and j;

[0021] The inequality constraints:

[0022]

[0023] Where: U i,max and U i,min are the upper and lower limits of the voltage of node i respectively; Q S,max and Q S,min are the upper and lower limits of the reactive power output of the reactive power compensation device SVG respectively; Q W,max and Q W,min are the upper and lower limits of the reactive power output of the doubly-fed wind turbine respectively.

[0024] Based on the traditional whale algorithm, a nonlinear time-varying factor, an adaptive weight strategy, a random learning strategy, and a Cauchy mutation strategy are introduced to obtain an improved whale algorithm.

[0025] The position update is carried out according to the introduced nonlinear time-varying factor, adaptive weight strategy, random learning strategy, and Cauchy mutation strategy. The specific formula is:

[0026] x(t + 1) = x rand (t) × ω(t) - A × D rand , p < 0.5, |A| > 1

[0027] x(t + 1) = x new (t) × ω(t) - A × D1, p < 0.5, |A| ≤ 1

[0028] x(t + 1) = D2e bl cos(2πl) + x new (t) × (1 - ω(t)), p ≥ 0.5

[0029] A = 2ar - a, r ∈ rand[0, 1]

[0030] Where: x(t + 1) is the position of the whale after update, x rand (t) is any position of the whale, ω(t) is the adaptive weight, A is an important parameter for adjusting the global survey and local optimization of the algorithm; D rand = |c · x rand (t) - x new1 (t)|, c = 2r, r is a random number between 0 and 1, x(t) is the current position of the whale, x new1 (t) is the optimal individual after the random learning strategy; p is the random probability; x new (t) is the current optimal individual / the new value of the current optimal individual after Cauchy mutation; D1 = |c · x * (t) - x(t)|, x * (t) is the current optimal individual, D2 = |x * (t) - x(t)|, b = 1 is a constant coefficient, l is a random number between -1 and 1; a represents the non - linear time - varying factor.

[0031] The non - linear time - varying factor is introduced as:

[0032]

[0033] Where: a represents the non - linear time - varying factor, t is the current iteration number, T is the maximum iteration number.

[0034] The adaptive weight strategy is introduced as:

[0035]

[0036] Where: ω(t) represents the adaptive weight; t is the current iteration number, T is the maximum iteration number.

[0037] If the optimal fitness values of an individual are the same after multiple iterations, Cauchy mutation is performed on the individual. The position update formula of the Cauchy mutation strategy for the current optimal individual is as follows:

[0038] x new (t) = x * (t) × (1 + cauchy(0, 1))

[0039] Where: x new (t) is the new value of the current optimal individual after Cauchy mutation, x * (t) is the current optimal individual, and cauchy(0, 1) is the Cauchy operator.

[0040] The random learning strategy selects a better individual by comparing the fitness values of two individuals. For the current individual x(t), a different individual x(t1) is randomly selected from the population to generate a new individual:

[0041]

[0042] Where: x new1 (t) is the optimal individual after the random learning strategy, and f(x(t)) and f(x(t1)) are the fitness values of individuals x(t) and x(t1) respectively; if f(x new1 (t)) < f(x(t)), then the individual x new1 (t) replaces the individual x(t), otherwise x new1 (t) is directly the individual x(t).

[0043] The beneficial effects of the present invention are as follows: By establishing a reactive power optimization model for the distribution network, introducing non - linear time - varying factors, random learning strategies, and Cauchy mutation strategies, the convergence speed and calculation accuracy of the whale algorithm are improved, and a reactive power optimization strategy for the IEEE33 - node system with wind turbines and SVG is obtained, which reasonably coordinates the reactive power output of wind turbines and SVG, reduces the system network loss, and improves the economic benefits of system operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is the flowchart of the method of the present invention;

[0045] Figure 2 is the flowchart of the improved whale algorithm;

[0046] Figure 3 is the topological diagram of the IEEE33 - node system with wind turbines and SVG;

[0047] Figure 4 is the active power output of the doubly - fed wind turbine;

[0048] Figure 5Voltage change before and after optimization for Scenario 1;

[0049] Figure 6 Fitness function value for Scenario 1;

[0050] Figure 7 Reactive power output of SVG and wind turbines under Scenario 1;

[0051] Figure 8 Voltage change before and after optimization for Scenario 2;

[0052] Figure 9 Fitness function value for Scenario 2;

[0053] Figure 10 Reactive power output of SVG and wind turbines under Scenario 2. Detailed implementation manners

[0054] The following further describes the invention with reference to the accompanying drawings and embodiments, but the content of the present invention is not limited to the described scope.

[0055] Embodiment 1: As Figure 1-10 shown, according to one aspect of the embodiments of the present invention, a reactive power optimization method for a distribution network based on an improved whale algorithm is provided, including: taking the minimum of active power loss and voltage violation penalty as the objective function, establishing a reactive power optimization model for the distribution network by considering the constraint conditions of wind turbines and reactive power compensation devices SVG; processing the load of each node by multiplying it by a load change coefficient as the processed power load data; obtaining the power flow calculation results of the distribution network system based on the processed power load data; and performing reactive power optimization on the distribution network with wind turbines and SVG based on the improved whale algorithm to obtain the reactive power output of the wind turbines and SVG.

[0056] Further, the established reactive power optimization model for the distribution network is specifically:

[0057] Active power loss P loss :

[0058]

[0059] Voltage violation penalty Δf:

[0060]

[0061] In summary, the comprehensive objective function F of the reactive power optimization model for the distribution network is:

[0062] minF = Δf + P loss

[0063] where: i and j are node numbers; n is the total number of nodes in the distribution network system; G ijis the conductance of branch ij; U i and U j are the voltage amplitudes of nodes i and j; δ i and δ j are the phase angles of the node voltages; λ is the penalty coefficient; U is the base voltage.

[0064] Furthermore, the constraint conditions include equality constraints and inequality constraints.

[0065] The equality constraints:

[0066]

[0067] In the formula: P Gi and P Di are the active power injected by node i and the active power of the load respectively; Q Gi and Q Di are the reactive power injected by node i and the reactive power of the load respectively; P W and Q W are the active power and reactive power injected by the installed doubly-fed wind turbine respectively; Q S is the reactive power injected by the reactive power compensation device SVG; B ij is the susceptance of branch ij; δ ij is the voltage phase angle difference between nodes i and j;

[0068] The inequality constraints:

[0069]

[0070] In the formula: U i,max and U i,min are the upper and lower limits of the voltage of node i respectively; Q S,max and Q S,min are the upper and lower limits of the reactive power output of the reactive power compensation device SVG respectively; Q W,max and Q W,min are the upper and lower limits of the reactive power output of the doubly-fed wind turbine respectively.

[0071] Furthermore, to simulate the load fluctuation within 24 hours of a day, the load of each node is processed by multiplying it by a load change coefficient to obtain the processed power load data; based on the processed power load data, the power flow calculation results of the distribution network system are obtained.

[0072] Furthermore, based on the traditional whale algorithm, a nonlinear time-varying factor, an adaptive weight strategy, a random learning strategy, and a Cauchy mutation strategy are introduced to obtain an improved whale algorithm.

[0073] As Figure 2 shown, the steps of the improved whale algorithm are described as follows:

[0074] S1. Set the algorithm-related parameters;

[0075] S2. Initialize the whale population;

[0076] S3. Calculate the individual fitness value, find the optimal individual, determine whether the individual mutates, and perform Cauchy mutation on the individual if it mutates;

[0077] S4. Update the algorithm parameters a, A, c, p, ω(t);

[0078] S5. When p < 0.5 and |A| > 1, optimize the position of the individual through stochastic learning and enter step S6; when |A| ≤ 1, enter step 7; when p ≥ 0.5, enter step S8;

[0079] S6. Perform a global search on the whale population, optimize the individuals with poor positions according to the stochastic learning strategy, and further update the whale positions;

[0080] S7. Encircle the prey and update the whale positions according to the corresponding formula;

[0081] S8. Perform predation and update the whale positions according to the corresponding formula;

[0082] S9. Determine whether the algorithm termination condition is satisfied. If not, enter step 3 to continue the iteration; otherwise, output the result.

[0083] Furthermore, the position update is performed based on the introduced non-linear time-varying factor, adaptive weight strategy, stochastic learning strategy, and Cauchy mutation strategy. The specific formula is as follows:

[0084] x(t + 1) = x rand (t) × ω(t) - A × D rand , p < 0.5, |A| > 1

[0085] x(t + 1) = x new (t) × ω(t) - A × D1, p < 0.5, |A| ≤ 1

[0086] x(t + 1) = D2e bl cos(2πl) + x new (t) × (1 - ω(t)), p ≥ 0.5

[0087] A = 2ar - a, r ∈ rand[0, 1]

[0088] Where: x(t + 1) is the updated position of the whale, x rand (t) is any position of the whale, ω(t) is the adaptive weight, A is an important parameter for adjusting the global survey and local optimization of the algorithm; D rand = |c · x rand(t)-x new1 (t)|, where c = 2r, r is a random number between 0 and 1, x(t) is the current position of the whale, and x new1 (t) is the optimal individual after the random learning strategy; p is the random probability; x new (t) is the current optimal individual / the new value of the current optimal individual after Cauchy mutation; D1 = |c · x * (t)-x(t)|, x * (t) is the current optimal individual, D2 = |x * (t)-x(t)|, b = 1 is a constant coefficient, l is a random number between -1 and 1; a represents the non - linear time - varying factor.

[0089] Furthermore, the non - linear time - varying factor is introduced as:

[0090]

[0091] In the formula: a represents the non - linear time - varying factor, t is the current iteration number, and T is the maximum iteration number.

[0092] Furthermore, the adaptive weight strategy is introduced as:

[0093]

[0094] In the formula: ω(t) represents the adaptive weight; t is the current iteration number, and T is the maximum iteration number.

[0095] If the optimal fitness values of an individual are the same after multiple iterations, then Cauchy mutation is performed on the individual. The position update formula of the Cauchy mutation strategy for the current optimal individual is as follows:

[0096] x new (t) = x * (t)×(1 + cauchy(0, 1))

[0097] In the formula: x new (t) is the new value of the current optimal individual after Cauchy mutation, x * (t) is the current optimal individual, and cauchy(0, 1) is the Cauchy operator.

[0098] Furthermore, the random learning strategy selects a better individual by comparing the fitness values of two individuals. For the current individual x(t), a different individual x(t1) is randomly selected from the population to generate a new individual:

[0099]

[0100] In the formula: x new1(t) is the optimal individual after the random learning strategy, and f(x(t)) and f(x(t1)) are the fitness values of individuals x(t) and x(t1) respectively; if f(x new1 (t)) < f(x(t)), then individual x new1 (t) replaces individual x(t), otherwise x new1 (t) is directly individual x(t).

[0101] Furthermore, combined with the experimental data, the present invention gives the following optional specific implementation manners:

[0102] Based on the IEEE33 node system, the effectiveness of the algorithm is verified. The structure diagram of the IEEE33 node system of the wind turbine and SVG is as Figure 3 shown, where the reactive power compensation device SVG is connected to nodes 20, 24 and node 30, the doubly-fed wind turbines are connected to nodes 3 and 11, the reactive power output range of the reactive power compensation device is [0, 0.8] MW, the reactive power output range of unit 1 is [0, 0.3] MW, and the reactive power output range of unit 2 is [0, 0.3] MW. The population size of the improved whale algorithm is set to 40, the space dimension is 5, the searchable space of the whale population is [-40 40], and the number of iterations is 100 times.

[0103] To simulate the load volatility within 24 hours of a day, the loads of each node are processed by multiplying a load change coefficient (as shown in Table 1) to obtain the processed power load data of each node; based on the processed power load data and the active power output of the wind turbines, the power flow calculation of the distribution network system is carried out based on matpower; among them, the active power output of the wind turbines is as Figure 4 shown.

[0104] Table 1 Load change coefficients of each node in each time period.

[0105]

[0106] Based on the improved whale algorithm, the reactive power of the system is optimized to obtain the reasonable reactive power output of SVG and the wind turbines, reduce the active power loss of the system. The changes in the node voltages of the system before and after optimization, the fitness function, and the reactive power output of SVG and the wind turbines are as Figure 5 、 6 、7 shown.

[0107] In the same way as the above steps, the wind turbines are connected to nodes 8 and 16 to obtain the corresponding reactive power optimization strategy. The changes in the node voltages of the system before and after optimization, the fitness function, and the reactive power output of SVG and the wind turbines are as Figure 8 、 9 、10 shown.

[0108] Table 2 System network loss and average voltage deviation before and after optimization under different scenarios

[0109]

[0110] Applying the above technical solution, it can be seen that by introducing non - linear time - varying factors, adaptive value strategies, stochastic learning strategies and Cauchy mutation strategies, the search and convergence performance of the traditional whale algorithm is improved, and the ability of the algorithm to find the global optimum and avoid falling into the local optimum is enhanced; further, based on the improved algorithm, the reactive power optimization of the distribution network with wind power and SVG is carried out to obtain the reasonable output of wind turbines and SVG, reduce the system network loss and improve the node voltage.

[0111] According to another aspect of the embodiments of the present invention, a reactive power optimization system for a distribution network based on an improved whale algorithm is provided, including: a building module, configured to establish a reactive power optimization model for the distribution network with the minimum active power loss and voltage violation penalty as the objective function, taking into account the constraint conditions of wind turbines and reactive power compensation devices SVG; an acquisition module, configured to process the load of each node, multiply it by a load change coefficient as the processed power load data, and obtain the power flow calculation result of the distribution network system based on the processed power load data; an obtaining module, configured to perform reactive power optimization on the distribution network with wind turbines and SVG based on the improved whale algorithm to obtain the reactive power output of wind turbines and SVG.

[0112] The specific embodiments of the present invention have been described in detail above in conjunction with the accompanying drawings. However, the present invention is not limited to the above - mentioned embodiments. Within the scope of knowledge possessed by those of ordinary skill in the art, various changes can be made without departing from the gist of the present invention.

Claims

1. A reactive power optimization method for distribution network based on improved whale algorithm, characterized in that, Including: Taking the minimum of active power loss and voltage violation penalty as the objective function, and considering the constraint conditions of wind turbines and static var generators (SVG) to establish a reactive power optimization model for the distribution network; Process the load of each node by multiplying it with a load change coefficient as the processed power load data; obtain the power flow calculation results of the distribution network system based on the processed power load data; Perform reactive power optimization on the distribution network with wind turbines and SVG based on the improved whale algorithm to obtain the reactive power outputs of wind turbines and SVG; Based on the traditional whale algorithm, introduce a non-linear time-varying factor, an adaptive weight strategy, a stochastic learning strategy, and a Cauchy mutation strategy to obtain the improved whale algorithm; Update the position according to the introduced non-linear time-varying factor, adaptive weight strategy, stochastic learning strategy, and Cauchy mutation strategy. The specific formula is: x(t + 1)=x rand (t)×ω(t)-A×D rand , p < 0.5, |A| > 1 x(t + 1) = x new (t)×ω(t) - A×D1,p < 0.5, |A| ≤ 1 x(t + 1) = D2e bl cos(2πl) + x new (t)×(1 - ω(t)), p ≥ 0.5 A = 2ar - a, r ∈ rand[0, 1] where: x(t + 1) is the updated position of the whale, x rand (t) is the arbitrary position of the whale, ω(t) is the adaptive weight, A is an important parameter for adjusting the global survey and local optimization of the algorithm; D rand = |c · x rand (t) - x new1 (t)|, c = 2r, r is a random number between 0 and 1, x(t) is the current position of the whale, x new1 (t) is the optimal individual after the random learning strategy; p is the random probability; x new (t) is the current optimal individual / the new value of the current optimal individual after Cauchy mutation; D1 = |c · x * (t) - x(t)|, x * (t) is the current optimal individual, D2 = |x * (t) - x(t)|, b = 1 is a constant coefficient, l is a random number between -1 and 1; a represents the non-linear time-varying factor.

2. The reactive power optimization method for a distribution network based on an improved whale algorithm according to claim 1, characterized in that The established reactive power optimization model for the distribution network is specifically: Active power loss P loss : Voltage violation penalty Δf: In summary, the comprehensive objective function F of the reactive power optimization model for the distribution network is: minF = Δf + P loss Where: i and j are node numbers; n is the total number of nodes in the distribution network system; G ij is the conductance of branch ij; U i , U j and U i are the voltage amplitudes of nodes i and j; δ j and δ are the phase angles of the node voltages; λ is the penalty coefficient; U is the reference voltage.

3. The reactive power optimization method for a distribution network based on an improved whale algorithm according to claim 1, characterized in that, The said constraint conditions include equality constraints and inequality constraints.

4. The reactive power optimization method for a distribution network based on an improved whale algorithm according to claim 3, characterized in that, The said equality constraints: Where: P Gi and P Di are the active power injected at node i and the active power of the load respectively; Q Gi and Q Di are the reactive power injected at node i and the reactive power of the load respectively; P W and Q W are the active power and reactive power injected by the installed doubly-fed wind turbine respectively; G ij is the conductance of branch ij; U i and U j are the voltage amplitudes of nodes i and j; Q S is the reactive power injected by the reactive power compensation device SVG; B ij is the susceptance of branch ij; δ ij is the voltage phase angle difference between nodes i and j; The said inequality constraints: Where: U i,max and U i,min are respectively the upper and lower limits of the voltage of node i; Q S,max and Q S,min are respectively the upper and lower limits of the reactive power output of the static var generator (SVG) of the reactive power compensation device; Q W,max and Q W,min are respectively the upper and lower limits of the reactive power output of the doubly-fed wind turbine generator set.

5. The reactive power optimization method for a distribution network based on an improved whale algorithm according to claim 1, characterized in that The introduced non-linear time-varying factor is: In the formula: a represents the non-linear time-varying factor, t is the current iteration number, and T is the maximum iteration number.

6. The reactive power optimization method for a distribution network based on an improved whale algorithm according to claim 1, wherein, The introduced adaptive weight strategy is: In the formula: ω(t) represents the adaptive weight; t is the current iteration number, and T is the maximum iteration number.

7. The reactive power optimization method for a distribution network based on an improved whale algorithm according to claim 1, characterized in that If the optimal fitness values of an individual are the same after multiple iterations, perform Cauchy mutation on the individual. The position update formula of the Cauchy mutation strategy for the current optimal individual is as follows: x new x(t) = x * x(t) × (1 + cauchy(0, 1)) Where: x new (t) is the new value after Cauchy mutation of the current optimal individual, x * (t) is the current optimal individual, and cauchy(0, 1) is the Cauchy operator.

8. The reactive power optimization method for a distribution network based on an improved whale algorithm according to claim 1, characterized in that The stochastic learning strategy selects a better individual by comparing the fitness values of two individuals. For the current individual x(t), randomly select a different individual x(t1) from the population to generate a new individual: where: x new1 (t) is the optimal individual after the stochastic learning strategy, and f(x(t)) and f(x(t1)) are the fitness values of individuals x(t) and x(t1) respectively; if f(x new1 (t)) < f(x(t)), then the individual x new1 (t) replaces the individual x(t), otherwise x new1 (t) is directly the individual x(t).

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