Hybrid kernel search optimization reactive power scheduling method based on crown porcupine algorithm

Abstract

The invention relates to a hybrid kernel search optimization reactive power scheduling method based on a crown porcupine algorithm, and the method comprises the following steps: S1, converting active loss and voltage deviation into a single objective function through employing a weighted summation method, and building a reactive power scheduling model in combination with constraint conditions; s2, randomly initializing an active power scheduling matrix of the generator set; s3, randomly initializing another scheduling scheme, and sequentially taking out the output of a certain generator to replace the active power of the corresponding generator set in the scheduling matrix to form a new scheduling matrix; s4, according to Newton-Rafson power flow, solving the active power of the last group of generators by a power flow equation; s5, calculating the penalty function value of the last group of generator active power exceeding the constraint; s6, calculating the sum of the actual power loss and the voltage deviation of the generator set in the scheduling scheme, and adding a penalty function value for common normalization; s7, executing a hybrid kernel search optimization algorithm based on a crown porcupine algorithm to update the active power of the generator set; s8, if the maximum number of iterations is reached, outputting the optimal generator set output; otherwise, turning to S3.

Description

Technical Field

[0001] This invention relates to the field of reactive power dispatching in power systems, and in particular to a reactive power dispatching method based on the Crowned Porcupine algorithm and hybrid kernel search optimization. Background Technology

[0002] With the continuous advancement of industrialization, the power system has gradually become the core carrier of modern society, and electricity has become an indispensable energy source. Electricity is also applied in many key areas, such as edge computing technology, reinforcement learning, blockchain technology, biofuel cells, and joint economic emissions dispatch. The safety and stability of the power system are of great significance to human life; its stability not only affects economic trends but is also closely linked to social stability. However, the power system has undergone significant changes during its development. For example, renewable energy has become intermittent, making it impossible to guarantee the stability of power generation; the widespread distribution of power plants has led to an exponential increase in the difficulty of determining the system network topology and growth model; and the excessive geographical length of transmission lines has gradually reduced effective power transmission, making the system model more complex and variable. To address these issues, researchers have proposed the Optimal Reactive Power Dispatch (ORDP) dispatch model. This model determines the optimal operating state of control variables in the power system, including generator bus voltage, transformer tap settings, and reactive power compensators, while satisfying equality and inequality constraints. Since the ratio of parallel capacitors and transformer windings are discrete variables, while the voltage value is a continuous variable, ORPD is generally considered to be a nonlinear, nonconvex, and multi-constrained mixed integer problem.

[0003] The ORPD (Order of Power Displacement) problem has always been a hot topic in power systems, aiming to optimize power loss, voltage deviation, and stability index of power lines. Early solutions relied on traditional mathematical methods. These methods perform algebraic operations on the optimization problem, moving rapidly towards the optimal solution from an initial point with increasing iterations. However, traditional methods have significant limitations, such as susceptibility to local optima, sensitivity to initial points, low robustness, and high algorithm complexity. Compared to traditional mathematical methods, metaheuristic algorithms do not rely on the mathematical properties of the problem. By balancing exploration and mining, they can effectively avoid getting trapped in local optima. However, these algorithms require multiple input parameters, necessitating repeated parameter adjustments for other engineering problems, which greatly increases the difficulty of using them. Furthermore, their excessively fast convergence speed or susceptibility to local optima prevents them from achieving higher-precision solutions.

[0004] Therefore, to address the shortcomings of existing algorithms, a hybrid kernel search optimization algorithm based on the Crowned Porcupine algorithm is developed. This algorithm does not require setting any parameters and has excellent global search capabilities, and it is applied to the ORPD problem. Summary of the Invention:

[0005] The purpose of this invention is to provide a reactive power scheduling method that can simultaneously optimize active power loss (Ploss) and voltage deviation (VD), and comprehensively consider global exploration and local mining.

[0006] To achieve the above-mentioned objectives, this invention provides a reactive power scheduling method based on the Crowned Porcupine algorithm with hybrid kernel search optimization, comprising the following steps:

[0007] S1. The two optimization objective functions of active power loss and voltage deviation are transformed into a single objective optimization function by using the weighted summation method, and the available control variables are adjusted to find the optimal power flow allocation that can satisfy all operating constraints and achieve a certain performance index of the system, and a reactive power scheduling model is established together.

[0008] S2. Suppose there are N groups of generator sets whose active power needs to be dispatched. M dispatch schemes are randomly initialized. The active power P of N-1 groups is calculated according to formula (1). i , i = 1, 2, ..., N-1, together constitute the active power output scheme matrix A of the generator set;

[0009]

[0010] Where P min and P max are the upper and lower limits of the active power of the i-th generator set, respectively, and rand is a random number in [0,1].

[0011] S3. Randomly initialize another scheduling scheme, with N-1 groups of active power P′. Then, sequentially select a group of generator active power P′ from this scheduling scheme. i Replace the active power P of the generator set corresponding to each scheduling scheme in A. i This forms a new M*(N-1) scheduling scheme matrix A′, as shown in formula (2);

[0012]

[0013] S4. Based on the Newton-Raphson power flow, calculate the active power P of the Nth generator group from A and A′ using the power flow equation constraints. N ;

[0014] S5. Calculate the active power P of the Nth generator group. N The penalty function value that exceeds the generator set constraint range;

[0015] S6. Calculate the sum of the actual power loss and voltage deviation of N generator sets in scheduling schemes A and A′, and combine it with the penalty function value to form the fitness function value y. i With y i Then normalize to [0,1];

[0016] S7. Execute a hybrid kernel search optimization algorithm based on the porcupine algorithm to update the active power P of the generator set. i ;

[0017] S8. If the maximum number of iterations is reached, output the optimal generator output P. gbest Otherwise, switch to S3.

[0018] Specifically, in step S7, the hybrid kernel search optimization algorithm based on the hooded porcupine algorithm is executed as follows:

[0019] Step S7.1: Calculate the kernel vector a, the specific formula is shown in (3):

[0020]

[0021] Step S7.2: Calculate the approximate optimal scheduling scheme P best The specific formula is shown in (4);

[0022]

[0023] Step S7.3: Calculate the latest position (visual strategy and acoustic strategy) of the Crowned Porcupine optimization algorithm, where the specific formula for the visual strategy is as follows:

[0024]

[0025] in, For the best crowned porcupine position, This is the vector generated between the current hooded porcupine and a random hooded porcupine. γ1 and γ2 are random values ​​generated between 0 and 1.

[0026] The formula for the sound method is as follows:

[0027]

[0028] Where r1 and r2 are two random integers between [1, N], and γ3 is a random value generated between 0 and 1. U1 is a random individual.

[0029] Step S7.4: Then substitute it into formula (4) to get:

[0030]

[0031] Step S7.5: Calculate the active power output P of the generator set. best The specific formula is shown in (8);

[0032]

[0033] Compared with the prior art, the beneficial effects of the present invention are:

[0034] This invention improves the original kernel search algorithm by proposing a hybrid kernel search optimization algorithm based on the Crowned Porcupine algorithm, which avoids the influence of parameters on the algorithm and getting trapped in local optima. It can solve for reactive power scheduling that minimizes active power loss and voltage deviation. Attached image description:

[0035] Figure 1 Method framework flowchart; Detailed implementation method:

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0037] like Figure 1 As shown in the figure, a reactive power scheduling method based on the Crowned Porcupine algorithm and hybrid kernel search optimization proposed in this invention includes the following steps:

[0038] S1. The two objective functions of active power loss and voltage deviation are transformed into a single objective function using a weighted summation method. The available control variables are then adjusted to find the optimal power flow allocation that satisfies all operational constraints and achieves a certain performance index of the system. This forms the basis of the reactive power dispatch model, which is as follows:

[0039] Minimize f(s,a)

[0040]

[0041] Here, f(s,a) represents the objective function. s represents a vector consisting of dependent variables, and a represents a vector consisting of independent variables.

[0042] g(s,a)=0 and h(s,a)≤0 represent equality constraints and inequality constraints, respectively.

[0043] In ORPD, except for the idle bus, the actual output power of the generating bus remains constant, and all other controls are independent variables. Its mathematical form is expressed as:

[0044] a T =[V Gen1 …VGenNG Q C1 …Q CNC ,T1…T NT (10)

[0045] Among them, V Gen1 This indicates the voltage of the generating bus, and NG indicates the number of generating buses. Qc indicates the parallel capacitor reactive power compensator, and NC indicates the number of reactive power compensators. T indicates the tap ratio, and NT indicates the number of tap changers.

[0046] The dependent variable of the ORPD problem can be expressed mathematically as follows:

[0047] S T =[P1,V D1 ...V DNPQ Q Gen1 ...Q GenNG ,S L1 ...S LNL (11)

[0048] Where P1 represents the idle bus power. V D This represents the active and reactive power bus voltages, and NPQ represents the number of active and reactive power buses. Q Gen This indicates the reactive power output of the generating line, NG indicates the number of generating buses. SL indicates the line current through the transmission line, and NL indicates the number of line currents through the transmission line.

[0049] The formula for the minimum actual power loss (Ploss) in the objective function is as follows:

[0050]

[0051] Where gk represents the k-th conductance, V a and V b δ represents the voltage magnitudes of the ath and bth buses, respectively. a and δ b This indicates the voltage angle.

[0052] Minimizing the voltage deviation (VD) on the load bus can be expressed as:

[0053]

[0054] Where NPQ represents the number of load buses. V refa This represents a reference value for the amplitude of the ATH load bus voltage (1 P.U.).

[0055] In the ORPD problem, inequality constraints and equality constraints coexist, among which equality constraints include:

[0056]

[0057] Among them, P Gi Q Gi P Di Q Di These represent the active power injection, reactive power injection, active power demand, and reactive power demand at the i-th bus generator, respectively. NB represents the total number of buses in the system.

[0058] The inequality constraints defined in the ORPD problem are as follows:

[0059] V i min ≤V i ≤V i max ,i∈N B (15)

[0060]

[0061] Among them, T m For the transformer, m is the tap adjustment amount; N pv The number of PV buses in the power system under study is defined; N t The number of on-load tap-changing transformers is defined; N c The number of parallel reactive power compensation devices in the system is defined; N l P represents the total number of branches; s To balance the active power of the busbar; and These represent the minimum and maximum limits of the power output of the balancing bus, respectively; furthermore, S l The apparent power transmitted through branch l is defined.

[0062] S2. Suppose there are N groups of generator sets whose active power needs to be dispatched. M dispatch schemes are randomly initialized. The active power P of N-1 groups is calculated according to formula (21). i , i = 1, 2, ... N-1, together constitute the active power scheme matrix A of the generator set;

[0063]

[0064] Where P min and P max are the upper and lower limits of the active power of the i-th generator set, respectively, and rand is a random number in [0,1].

[0065] S3. Randomly initialize another scheduling scheme, with N-1 groups of active power output P', i = 1, 2, ... N-1. Sequentially select the active power P' of a certain group of generators from this scheduling scheme. i Replace ' with the corresponding active power output P of the generator set in each scheduling scheme in A.i This forms a new M*(N-1) scheduling scheme matrix A′, as shown in formula (22);

[0066]

[0067] S4. For each bus, two equality constraints are associated (as shown in Equation (14)), one related to active power balance and the other to reactive power balance. In power systems, these equality constraints are handled by power flow solving methods. This paper adopts the Newton-Raphson Load Flow (NRLF) method to solve the power flow problem.

[0068] S5. Inequality constraints on the independent variables can be generated randomly. If the generated independent variables contain violations, they can be fixed using upper or lower bounds on the violations. Furthermore, inequality constraints on the dependent variables can be handled by penalizing solutions that include violations in the dependent variable. The penal method is used to mathematically express the overall objective function for power system operation and safety constraints.

[0069]

[0070] Where Fn is the objective function to be minimized. and This indicates a violation of the limit related to the dependent variable. λ QGn , λ Ln and λ TL It is a penalty factor that can be selected through trial and error.

[0071] S6. Calculate the sum of the actual power loss and voltage deviation of N generator sets in scheduling schemes A and A′, and combine it with the penalty function value to form the fitness function value y. i and y′ i' Then normalize to [0,1];

[0072] The specific process is as follows:

[0073]

[0074] S7. Execute a hybrid kernel search optimization algorithm based on the porcupine algorithm to update the active power output P of the generator unit. i This includes the following sub-steps:

[0075] Step S7.1: Calculate the kernel vector a, the specific formula is shown in (25):

[0076]

[0077] Step S7.2: Calculate the approximate optimal scheduling scheme P best The specific formula is shown in (26);

[0078]

[0079] Step S7.3: Calculate the latest position (visual strategy and acoustic strategy) of the Crowned Porcupine optimization algorithm, where the specific formula for the visual strategy is as follows:

[0080]

[0081] in, For the best crowned porcupine position, This is the vector generated between the current hooded porcupine and a random hooded porcupine.

[0082] The formula for the sound method is as follows:

[0083]

[0084] Where r1 and r2 are two random integers between [1, N], and τ3 is a random value generated between 0 and 1. U1 is a random individual. Step S7.4: Then substitute it into formula (26) to get:

[0085] Step S7.5: Calculate the active power output P of the generator set. gbest The specific formula is shown in (30);

[0086]

[0087] S8. If the maximum number of iterations is reached, output the optimal generator set active power loss or voltage deviation; otherwise, go to S3.

[0088] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

[0089] Experimental results:

[0090] Case-1:IEEE 14bus Case-2:IEEE 30bus Case-3: IEEE 57bus; Case-4: IEEE 118bus; Case-1: Objective function: Power loss (Ploss)

[0091]

[0092] Case-1: Objective function: Voltage deviation (VD)

[0093]

[0094] Case-2: Objective function: Power loss (Ploss)

[0095]

[0096] Case-2: Objective function: Voltage deviation (VD)

[0097]

[0098] Case-3: Objective function: Power loss (Ploss)

[0099]

[0100] Case-3: Objective function: Voltage deviation (VD)

[0101] Case-4: Objective Function: Power Loss (Ploss)

[0102]

[0103] Case-4: Objective function: Voltage deviation (VD)

[0104]

Claims

1. A method for reactive power dispatch based on hybrid kernel search optimization of the Crown-Hoary Porcupine algorithm, characterized by, The steps include: S1. The active power loss (Ploss) and voltage deviation (VD) two optimization objective functions are converted into a single objective optimization function by using the weighted summation method, and the available control variables are adjusted to find the optimal power flow distribution that can meet all operating constraints and achieve a certain performance index of the system, and the optimal reactive power dispatch (ORPD) scheduling model is established together, which is specifically: Minimize f(s,a) Where f(s,a) represents the objective function. s represents a vector composed of dependent variables, and a represents a vector composed of independent variables. g(s,a) = 0 and h(s,a) ≤ 0 represent equality constraints and inequality constraints. In ORPD, the actual output power of the generating bus remains unchanged except for the idle bus, and the remaining control is the independent variable. Its mathematical form is represented as: a T = [V Gen1 …V GenNG , Q C1 …Q CNC , T1…T NT ] (2) where V Gen1 represents the number of generating busbars. Q C represents the active and reactive power compensator of the shunt capacitor, NC represents the number of active and reactive power compensators. T represents the tapping ratio, and NT represents the number of tapped transformers. The dependent variable of the ORPD problem can be mathematically represented as: S T = [P1, V D1 ...V DNPQ ,Q Gen1 ...Q GenNG ,S L1 ...S LNL ] (3) where P1 represents the idle bus power. V D represents the active and reactive bus voltage, NPQ represents the active and reactive bus number. Q Gen represents the generation bus reactive output, NG represents the generation bus number. SL represents the line flow through the transmission line, NL represents the line flow number. The formula for the minimum actual power loss (Ploss) in the objective function is: where gk represents the kth conductance, V a and V b represent the voltage amplitudes of ath and bth bus, respectively. δ a and δ b represent the voltage angles. The voltage deviation minimization (VD) on the load bus can be represented as: where NPQ is the number of the load buses. V refa represents the reference value of ath load bus voltage amplitude (1 pu). In the ORPD problem, both inequality constraints and equality constraints exist, where the equality constraints are: where P Gi , Q Gi , P Di , Q Di are the active power injection, the reactive power injection, the active power demand and the reactive power demand of the generator at the i-th bus, respectively. N Bis the total number of buses in the system. The inequality constraints defined in the ORPD problem are as follows: where T m is the tap adjustment of transformer m; N pv defines the number of PV buses in the studied power system; N t defines the number of on-load tap-changing transformers; N c defines the number of shunt reactive power compensation devices in the system; N l is the total number of branches; P s is the active power of the slack bus; and denote the minimum and maximum limits of the slack bus power, respectively; furthermore, S l defines the apparent power transmitted through branch l. S2. Set N groups of generator sets active power need to be scheduled, randomly initialize M scheduling schemes, initialize the calculation of N-1 groups of active power P i , i = 1, 2, … N-1, which together constitute the generator set active power output scheme matrix A; where P min and P max are the upper and lower limits of the active power of the ith group of generators, respectively, and randis a random number in [0, 1]; S3. Randomly initialize another dispatching scheme, N-1 groups of active power P' i , i = 1, 2, … N-1, sequentially take out a group of generator active power P' from the dispatching scheme i , replace the corresponding generator group active power P in each dispatching scheme in A i , form a new M*(N-1) dispatching scheme matrix A', as shown in formula (14); S4. For each bus, determine 2 equality constraints (as shown in formula (6)), one of which is related to active power balance, and the other is related to reactive power balance. In power systems, these equality constraints are handled by the load flow solution method. This paper uses the Newton-Raphson load flow (NRLF) solution method to solve the load flow problem. S5. The inequality constraints of the independent variable can be randomly generated. If the generated independent variable has a violation, it can be fixed with the upper or lower limit of the variable violation. In addition, the inequality constraints of the dependent variable can be handled by penalizing solutions that violate the dependent variable. The overall objective function of the power system operation and safety constraints is mathematically represented using the penalty method. where Fn is the minimization objective function. and denotes a limit violation related to the dependent variable λ. QGn , λ Ln and λ TL are penalty factors, which can be chosen by trial and error. S6. Calculate the sum of actual power loss and voltage deviation of N groups of generator sets in scheduling scheme A and A', and together with the penalty function value to form the fitness function value y i and y' i and then normalized to [0, 1]; The specific process is: S7. Perform hybrid kernel search optimization algorithm based on the crow search algorithm to update the active power P of the generator unit i including the following sub-steps: Step S7.1: Calculate the kernel vector a, the specific formula is as shown in (17): Step S7.2: Calculate the approximately optimal scheduling scheme P best , as shown in (18). Step S7.3: Calculate the latest position of the Chamois optimization algorithm (visual strategy and sound strategy), where the visual strategy is specifically as follows: wherein, is the optimal crown-hedgehog position, is the generated vector between the current crown-hedgehog and the random crown-hedgehog, γ1 and γ2 are random values generated between 0 and 1. And the formula of the sound method is as follows: Where r1 and r2 are two random integers between [1, N], and γ3 is a random value generated between 0 and 1. U1 is a random individual. Step S7.4: Then bring it into formula (18): Step S7.5: Calculate the generator set active power P gbest The specific formula is shown in (22). S8. If the maximum number of iterations is reached, output the optimal generator set P gbest ; otherwise go to S3.

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