Improved whale optimization algorithm-based power distribution network distributed power supply bearing capacity assessment method

Abstract

The invention discloses a power distribution network distributed power supply bearing capacity assessment method based on an improved whale optimization algorithm. The method comprises the following steps: step 1, constructing a total optimization objective function; 2, determining constraint conditions; and step 3, solving the model based on the improved whale optimization algorithm. According to the method, the proper access capacity and position of the distributed power supply can be determined, and reasonable resource configuration and layout planning are realized; the overload problem caused by exceeding the power grid bearing capacity can be avoided, and the risks of power grid faults and power failure are reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of power systems, and specifically discloses a method for evaluating the carrying capacity of distributed power sources in a distribution network based on an improved whale optimization algorithm. Background Art

[0002] The large-scale access of distributed power sources has brought many problems to the operation of the distribution network, mainly including node voltage exceeding the limit, reverse flow, etc., which seriously affect the safety of the distribution network. At the same time, the traditional passive management mode is difficult to adapt to the operation of the power grid under the influence of uncertain factors such as light and load. In order to further improve the carrying capacity of the distribution network economically and reasonably, it is necessary to take into account certain economic efficiency and consider active management measures for comprehensive control. In order to make more efficient use of distributed power sources on the basis of ensuring the safe and stable operation of the distribution network, this patent has carried out research on the evaluation method of the carrying capacity of distributed power sources in the distribution network.

[0003] In response to the above problems, domestic and foreign scholars have proposed to evaluate the carrying capacity of distributed power sources with multiple indicators, under the premise that the access of distributed power sources does not cause the current in the grid equipment and lines to exceed their thermal stability limits. The basic carrying capacity evaluation problem is mainly the optimal configuration of distributed power sources, that is, the determination of the optimal access location and access capacity of distributed power sources. At the same time, considering different planning purposes, it is also necessary to select the required objective function, operation constraints and analysis methods. The objective function is the ultimate goal of accessing distributed power sources, and the constraints are the main factors that limit the improvement of the carrying capacity of distributed power sources in the distribution network. The unreasonable grid connection of distributed power sources will cause the relevant constraints to reach the limit value, thereby limiting the improvement of carrying capacity. Therefore, in order to avoid the above situation, feasible and efficient analysis methods need to be considered. It can be seen that the carrying capacity evaluation problem is a complex mixed integer nonlinear optimization problem.

[0004] In terms of engineering practice, according to the Chinese power industry standard "Guidelines for Assessment of Distributed Generation Connected to the Grid Carrying Capacity", in general, the quantitative assessment of distributed generation connected to the grid carrying capacity refers to the assessment of all equipment in the same power supply area under the existing grid structure, with the premise of ensuring the safe and stable operation of the grid and the full absorption of distributed generation, so as to determine the assessment level of distributed generation connected to the grid carrying capacity; in the assessment process, the five factors of thermal stability of power system equipment, node voltage deviation, short-circuit current of each node of the system, harmonics of each node of the grid and power abandonment rate are mainly calculated and analyzed. In the distribution network containing distributed generation, the distribution network itself has various control equipment and measures. The active control equipment and measures of the distribution network are mainly divided into two categories: the distribution network's own regulation and control means and energy storage technology. The distribution network's own regulation means mainly include: on-load tap-changing transformer tap adjustment, reactive power regulation equipment and network reconstruction. As a flexible resource, energy storage technology mainly participates in regulating the power supply and demand balance of the distribution network, and can be regarded as a means of regulating power balance after the distribution network is connected to DG (distributed generation). Taking into account the control equipment and measures, the distribution network's carrying capacity for DG will also change as the control equipment parameters or measures change. Energy storage is a flexible resource that can participate in the balance of power supply and demand in the distribution network. When analyzing energy storage from a planning perspective, we should seek the optimal location and capacity of energy storage, that is, the optimal configuration method of energy storage.

[0005] Research has shown that the above control equipment and measures can actively participate in the regulation of distribution network operating parameters, and improve the stable operation margin of the distribution network to a certain extent. It is necessary to consider the above control measures and make a quantitative assessment of the DG carrying capacity of the distribution network. The current solution method has problems such as complex constraints, large amount of calculation, and difficult solution. Summary of the invention

[0006] The purpose of the present invention is to provide a method for evaluating the carrying capacity of distributed power sources in a distribution network based on an improved whale optimization algorithm, which can determine the appropriate access capacity and location of distributed power sources, achieve reasonable resource allocation and layout planning; avoid overload problems caused by exceeding the carrying capacity of the power grid, and reduce the risk of power grid failures and power outages.

[0007] The technical solution adopted by the present invention is a method for evaluating the carrying capacity of distributed power sources in a distribution network based on an improved whale optimization algorithm, comprising the following steps:

[0008] Step 1: construct the overall optimization objective function;

[0009] Step 2: Determine the constraints;

[0010] Step 3: Solve the model based on the improved whale optimization algorithm.

[0011] The present invention is also characterized in that:

[0012] Step 1 is as follows:

[0013] Step 1.1, determine the maximum distributed generation installed capacity maxC, as shown in the following formula:

[0014]

[0015] Where P DG.i is the active power of distributed generation connected to node i, and n is the number of nodes.

[0016] Step 1.2, find the minimum total cost minF;

[0017] Step 1.3: Find the total optimization objective function maxF0.

[0018] Step 1.2 is as follows:

[0019] 1) Determine the investment cost F1 as shown below:

[0020]

[0021] In the formula, K DG is the unit capacity investment cost, S DGi is the capacity of distributed power generation connected to node i, and N is the number of nodes;

[0022] 2) Determine the operation and maintenance cost F2, as shown below:

[0023]

[0024] Where t is the service life of distributed power; r is the discount rate; T DG It is the operation and maintenance cost per unit capacity;

[0025] 3) Add the two cost sub-objective functions of investment cost F1 and operation and maintenance cost F2 to obtain the minimum total cost minF, as shown in the following formula:

[0026] minF=min(F1+F2) (4).

[0027] Step 1.3 is as follows:

[0028] By linearly weighting the combination of equations (1) and (4), the overall optimization objective function is obtained as follows:

[0029] maxF0=ω1C-ω2F (5)

[0030] Where: ω1, ω2 are the weight coefficients of the two sub-objective functions.

[0031] The constraints determined in step 2 are as follows:

[0032] 1) Distribution network flow constraints:

[0033]

[0034] Where: P DG,i , Q DG,i is the active and reactive output of the distributed power source connected to the i node; P i , Q i is the active and reactive loads of node i; G ij , B ij is the conductance and susceptance in the node admittance matrix; θ ij is the phase angle difference with the voltage at nodes i and j;

[0035] 2) Voltage constraint:

[0036] U N (1-ε)≤U i ≤U N (1+ε) (7)

[0037] Where U i is the voltage at node i, U N is the nominal voltage; ε is the voltage deviation rate limit under a specific voltage level;

[0038] The requirements for voltage fluctuation are as follows:

[0039] d i ≤d max (8)

[0040] Where, d i is the system voltage fluctuation value caused by distributed power generation at node i; d max It is the maximum voltage fluctuation value specified by the national standard;

[0041] The voltage fluctuation value of any node is estimated by the following formula:

[0042]

[0043] Where, d is the voltage fluctuation value; R L , X L are the line resistance and reactance at the load, respectively; ΔP and ΔQ are the changes in active and reactive power of the load, respectively;

[0044] DG (distributed generation) usually has a higher power factor. Assuming that the reactive power output of DG is zero and all active power is generated, the voltage fluctuation value caused by DG at node i is expressed as:

[0045]

[0046] Where PDG.i is the output power of distributed power generation, U N is the nominal voltage, R i is the resistance of node i.

[0047] 3) Current Constraint:

[0048] |I k |≤I k.max (11)

[0049] In the formula, I k is the current on branch k; I k.max is the maximum current allowed to flow through branch k;

[0050] The short-circuit current comparison should be based on the principle that the short-circuit current of each bus node of the system after the distributed power supply is connected does not exceed the breaking current limit of the corresponding circuit breaker; the national standard "Short-circuit current calculation of three-phase AC system" (GB / T15544-1995) is used for verification:

[0051] I xz <I m (12)

[0052] In the formula, I xz is the system bus short-circuit current, I m is the allowable short-circuit current limit;

[0053] 4) Harmonic constraints:

[0054] In order to ensure the effectiveness of the harmonic current constraint conditions, the injection current under the condition of maximum harmonic output of DG is taken to determine its access capacity. The constraint conditions determined by the harmonic current are:

[0055]

[0056] In the formula, S DG is the DG access amount; U N is the nominal voltage; μ k It is the content rate limit of each harmonic output of DG specified in the national standard; I k These are the harmonic currents allowed to be connected to the power grid as specified in the national standard.

[0057] In order to ensure the validity of the harmonic voltage content constraint condition, the injection current of DG under the condition of maximum harmonic output is taken to determine its access capacity;

[0058]

[0059] U k =HRU k ×U N (16)

[0060]

[0061] In the formula, I k is the kth harmonic current of the distributed power source; HRU k is the kth harmonic voltage content rate; S k is the short-circuit capacity; U k is the kth harmonic voltage; THD U is the total harmonic voltage distortion rate;

[0062] 5) Energy storage operation constraints:

[0063] Energy storage power constraints:

[0064] u_dch+u_ch≤1 (18)

[0065] 0≤p_dch≤u_dch*α (19)

[0066] 0≤p_ch≤u_ch*β (20)

[0067] In the formula, u_dch and u_ch are the energy storage discharge and charge states respectively, u_dch, u_ch∈{0,1}, u_dch = 1 means discharge, u_ch = 1 means charge, the above formula means there are three energy storage states, charge, discharge and neither charge nor discharge. p_dch is the discharge power, p_ch is the charge power, α and β are the discharge and charge limit coefficients;

[0068] Energy storage capacity constraints:

[0069] E_ess t+1 =E_ess t +λ*p_ch t -μ*p_dch t (twenty one)

[0070] In the formula, λ and μ are the charge and discharge coefficients, E_ess t+1 is the energy storage capacity at time t+1, E_ess t is the energy storage capacity at time t; p_ch t 、p_dch t are the charging and discharging powers at time t respectively.

[0071] 6) Other constraints, including constraints on set temperature range and electric vehicle battery SOC constraints.

[0072] In step 2, other constraints, including the constraints of setting the temperature range and the SOC constraints of the electric vehicle battery, are as follows:

[0073] For air conditioners with temperature adjustment authority, set temperature range constraints to ensure user comfort:

[0074]

[0075] Where: T i Set,Min and T i Set,Max are the lower and upper bounds of the operating temperature of the i-th air conditioner respectively;

[0076] Electric vehicle battery SOC constraints:

[0077] S min ≤S EV (t)≤S max (twenty three)

[0078] In the formula, S max , S min They are the upper and lower limits of the car battery SOC respectively.

[0079] Step 3 is as follows:

[0080] Step 3.1: Improvement of the whale optimization algorithm;

[0081] Step 3.2, the distribution network parameters, the original power output and load power scenario data, and the total optimization objective function and constraints are used as inputs of the improved whale optimization algorithm;

[0082] Step 3.3: Set the power access capacity range and initialize the population, including the population size num and the maximum number of iterations T. max ;

[0083] Step 3.4: Calculate the fitness of each whale, select the position of the best whale and keep it as the initial target prey, that is, X * (t);

[0084] Step 3.5, calculate the nonlinear convergence factor a and coefficient vectors A and C;

[0085] Step 3.6, determine whether the random probability p is less than the probability P, if yes, directly go to step 3.7, otherwise update the spiral position after adding the adaptive weight;

[0086] Step 3.7, determine whether the absolute value of the coefficient vector A is greater than or equal to 1, if so, adopt a random search mechanism to update the position; if not, adopt a shrinking and surrounding mechanism to update the position after increasing the adaptive weight;

[0087] Step 3.8: Determine whether the termination condition of the algorithm is met. If not, return to step 3.4 to continue the calculation; otherwise, proceed to step 3.9.

[0088] Step 3.9: Output the optimal value and the optimal individual position.

[0089] Step 3.1 is as follows:

[0090] The cosine curve is applied to change the way the convergence factor changes, and the adaptive weight adjustment method is adopted to improve the convergence performance of the whale optimization algorithm. Specifically:

[0091] The cosine curve is used to improve the change process of the convergence factor. The specific expression is as follows:

[0092]

[0093] The adaptive weight coefficient ω is derived, and the corresponding expression is as follows:

[0094]

[0095] In the formula, ω max ,ω min are the upper and lower limits of the weight coefficient respectively;

[0096] In the whale optimization algorithm, the mathematical model of whales using echolocation to determine the location of target prey and surround them is improved, that is, the improved mathematical model is as follows:

[0097] X(t+1)=ωX * (t)-A·D (30)

[0098] Where D is the distance between the whale and the target prey; t is the number of iterations; X * (t) is the global optimal whale position; X(t) and X(t+1) represent the position vectors before and after the whale update, respectively; A and C represent the coefficient vectors.

[0099] The beneficial effects of the present invention are:

[0100] (1) In order to promote the high-quality development of distributed power sources under the dual carbon goals and guide more access to distributed power sources, the present invention proposes a method for evaluating the maximum carrying capacity of the distribution network taking into account the access status of the power source. By understanding the potential capacity and limitations of the power grid, the appropriate access capacity and location of distributed power sources can be determined to achieve reasonable resource allocation and layout planning; understanding the access capacity of distributed power sources can avoid overload problems caused by exceeding the grid carrying capacity and reduce the risk of grid failures and power outages; reasonable planning and management of the access of distributed power sources can reduce system operating costs, reduce transmission losses, and promote the utilization and development of renewable energy; accurately evaluating the access capacity of distributed power sources can better manage and dispatch the power system, achieve the optimal configuration and operation regulation of distributed power sources, so as to adapt to the ever-changing energy demand and supply situation, and provide theoretical guidance for my country to achieve large-scale access to distributed power sources.

[0101] (2) The method of the present invention takes the evaluation of the carrying capacity of distributed power sources in the distribution network as the starting point, considers the uncertainty of power output and load power, and conducts qualitative and quantitative analysis of the carrying capacity from two aspects: energy storage and variable load; and evaluates the maximum carrying capacity of the distribution network for distributed power sources while taking into account certain economic costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] Figure 1 A distributed power supply carrying capacity evaluation model in the method of the present invention;

[0103] Figure 2 The figure is a flow chart of the improved whale algorithm in the method of the present invention. DETAILED DESCRIPTION

[0104] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0105] The present invention provides a method for evaluating the carrying capacity of distributed power sources in a distribution network based on an improved whale optimization algorithm. First, an output model of a typical distributed power source is established and the impact of the access of distributed power sources on the voltage level, branch current, system network loss, short-circuit current and network harmonics of the distribution network is analyzed; secondly, a DG output and new load uncertainty model is established, and the grid-accessible capacity of distributed power sources is modeled based on uncertainty and energy storage configuration, with maximizing the new energy absorption capacity and minimizing the cost as the optimization goal, and taking into account the uncertainty of power and load and the active-reactive power of energy storage as important constraints, a distribution network new energy carrying capacity evaluation model is established; finally, the whale algorithm is used to solve the problem by using the whale optimization algorithm, which has the characteristics of fast convergence speed and high accuracy; the specific implementation is carried out according to the following steps, such as Figure 1 As shown:

[0106] Step 1: construct the overall optimization objective function;

[0107] Step 1 is as follows:

[0108] Step 1.1, determine the maximum distributed generation installed capacity maxC, as shown in the following formula:

[0109]

[0110] Where P DG.i is the active power of distributed generation connected to node i, and n is the number of nodes.

[0111] Step 1.2, find the minimum total cost minF;

[0112] Step 1.2 is as follows:

[0113] 1) Determine the investment cost F1 as shown below:

[0114]

[0115] In the formula, K DG is the unit capacity investment cost, S DGi is the capacity of distributed power generation connected to node i, and N is the number of nodes;

[0116] 2) Determine the operation and maintenance cost F2, as shown below:

[0117]

[0118] Where t is the service life of distributed power; r is the discount rate; T DG It is the operation and maintenance cost per unit capacity;

[0119] 3) Add the two cost sub-objective functions of investment cost F1 and operation and maintenance cost F2 to obtain the minimum total cost minF, as shown in the following formula:

[0120] minF=min(F1+F2) (4);

[0121] Step 1.3, find the total optimization objective function maxF0, specifically:

[0122] By linearly weighting the combination of equations (1) and (4), the overall optimization objective function is obtained as follows:

[0123] maxF0=ω1C-ω2F (5)

[0124] Where: ω1, ω2 are the weight coefficients of the two sub-objective functions.

[0125] Step 2: Determine the constraints;

[0126] The constraints determined in step 2 are as follows:

[0127] 1) Distribution network flow constraints:

[0128]

[0129] Where: P DG,i , Q DG,i is the active and reactive output of the distributed power source connected to the i node; P i , Q i is the active and reactive loads of node i; G ij , B ij is the conductance and susceptance in the node admittance matrix; θ ij is the phase angle difference with the voltage at nodes i and j;

[0130] 2) Voltage constraint:

[0131] UN (1-ε)≤U i ≤U N (1+ε) (7)

[0132] Where U i is the voltage at node i, U N is the nominal voltage; ε is the voltage deviation rate limit under a specific voltage level;

[0133] The requirements for voltage fluctuation are as follows:

[0134] d i ≤d max (8)

[0135] Where, d i is the system voltage fluctuation value caused by distributed power generation at node i; d max It is the maximum voltage fluctuation value specified by the national standard;

[0136] The voltage fluctuation value of any node is estimated by the following formula:

[0137]

[0138] Where, d is the voltage fluctuation value; R L , X L are the line resistance and reactance at the load, respectively; ΔP and ΔQ are the changes in active and reactive power of the load, respectively;

[0139] DG (distributed generation) usually has a higher power factor. Assuming that the reactive power output of DG is zero and all active power is generated, the voltage fluctuation value caused by DG at node i is expressed as:

[0140]

[0141] Where P DG.i is the output power of distributed power generation, U N is the nominal voltage, R i is the resistance of node i.

[0142] 3) Current Constraint:

[0143] |I k |≤I k.max (11)

[0144] In the formula, I k is the current on branch k; I k.max is the maximum current allowed to flow through branch k;

[0145] The short-circuit current comparison should be based on the principle that the short-circuit current of each bus node of the system after the distributed power supply is connected does not exceed the breaking current limit of the corresponding circuit breaker; the national standard "Short-circuit current calculation of three-phase AC system" (GB / T15544-1995) is used for verification:

[0146] I xz <I m (12)

[0147] In the formula, I xz is the system bus short-circuit current, I m is the allowable short-circuit current limit;

[0148] 4) Harmonic constraints:

[0149] In order to ensure the effectiveness of the harmonic current constraint conditions, the injection current under the condition of maximum harmonic output of DG is taken to determine its access capacity. The constraint conditions determined by the harmonic current are:

[0150]

[0151] In the formula, S DG is the DG access amount; U N is the nominal voltage; μ k It is the content rate limit of each harmonic output of DG specified in the national standard; I k These are the harmonic currents allowed to be connected to the power grid as specified in the national standard.

[0152] In order to ensure the validity of the harmonic voltage content constraint condition, the injection current of DG under the condition of maximum harmonic output is taken to determine its access capacity;

[0153]

[0154] U k =HRU k ×U N (16)

[0155]

[0156] In the formula, I k is the kth harmonic current of the distributed power source; HRU k is the kth harmonic voltage content rate; S k is the short-circuit capacity; U k is the kth harmonic voltage; THD U is the total harmonic voltage distortion rate;

[0157] 5) Energy storage operation constraints:

[0158] Energy storage power constraints:

[0159] u_dch+u_ch≤1(u_dch, u_ch∈{0,1}) (18)

[0160] 0≤p_dch≤u_dch*α (19)

[0161] 0≤p_ch≤u_ch*β (20) In the formula, u_dch and u_ch are the energy storage discharge and charge states respectively. When u_dch is 1, it means discharge, and when u_ch is 1, it means charge. The above formula means that there are three energy storage states, charge, discharge and neither charge nor discharge. p_dch is the discharge power, p_ch is the charge power, α and β are the discharge and charge limit coefficients;

[0162] Energy storage capacity constraints:

[0163] E_ess t+1 =E_ess t +λ*p_ch t -μ*p_dch t (twenty one)

[0164] In the formula, λ and μ are the charge and discharge coefficients, E_ess t+1 is the energy storage capacity at time t+1, E_ess t is the energy storage capacity at time t; p_ch t 、p_dch t are the charging and discharging powers at time t respectively.

[0165] 6) Other constraints:

[0166] For air conditioners with temperature adjustment authority, set temperature range constraints to ensure user comfort:

[0167]

[0168] Where: T i Set,Min and T i Set,Max are the middle and upper bounds of the operating temperature of the i-th air conditioner respectively.

[0169] Electric vehicle battery SOC constraints:

[0170] S min ≤S EV (t)≤S max (twenty three)

[0171] In the formula, S max , S min They are the upper and lower limits of the car battery SOC respectively.

[0172] The evaluation model of distributed power generation capacity in distribution network is as follows: Figure 1 shown.

[0173] Step 3: Model solution based on improved whale optimization algorithm;

[0174] Whale optimization algorithm, the specific process is as follows:

[0175] 1) Shrink surround

[0176] Whales use echolocation to determine the location of target prey and surround them. The mathematical model is as follows:

[0177]

[0178] Where D is the distance between the whale and the target prey; t is the number of iterations; X * (t) is the global optimal whale position; X(t) and X(t+1) represent the position vectors before and after the whale update, respectively; A and C represent the coefficient vectors;

[0179] 2) Spiral Update

[0180] The individual whales calculate the distance to their prey and then move around it in a spiral, using the following mathematical model:

[0181]

[0182] In the formula, b is a constant describing the shape of the spiral; l is a random number between [-1,1];

[0183] 3) Random Search

[0184] This process can avoid falling into local optimality and achieve global search. The corresponding mathematical model is as follows:

[0185]

[0186] In the formula, X rand is a randomly selected whale position vector;

[0187]

[0188] Where a is the convergence coefficient; r1 is a random number between [0,1]; T max is the maximum number of iterations.

[0189] The specific implementation plan of step 3 is as follows: Figure 2 As shown:

[0190] Step 3.1: Improvement of the whale optimization algorithm:

[0191] The cosine curve is applied to change the way the convergence factor changes, and the adaptive weight adjustment method is adopted to improve the convergence performance of the whale optimization algorithm. Specifically:

[0192] In order to avoid falling into the local optimum too early and improve the convergence ability, it is necessary to change the way the convergence factor changes. This paper applies the cosine curve to improve the change process of the convergence factor. The specific expression is as follows:

[0193]

[0194] When the number of iterations is small, a larger a value can effectively improve the global exploration ability; when the number of iterations is close to the maximum value, a smaller a value can enhance the local optimization ability.

[0195] In addition, the adaptive weight adjustment method is adopted to improve the convergence performance of the whale optimization algorithm. When the whale performs local optimization according to formula (24), it is likely to fall into the local optimal solution. Therefore, the adaptive weight coefficient ω is introduced, and the corresponding expression is as follows:

[0196]

[0197] In the formula, ω max ,ω min are the upper and lower limits of the weight coefficient respectively;

[0198] In the whale optimization algorithm, the mathematical model of whales using echolocation to determine the location of target prey and surround them is improved, that is, the improved formula (24) is as follows:

[0199] X(t+1)=ωX * (t)-A·D (30)

[0200] Where D is the distance between the whale and the target prey; t is the number of iterations; X * (t) is the global optimal whale position; X(t) and X(t+1) represent the position vectors before and after the whale update, respectively; A and C represent the coefficient vectors;

[0201] Moreover, the aforementioned shrinking and surrounding and spiral updating behaviors exist simultaneously, and individual whales will randomly choose one of them to approach the prey. This simultaneous behavior is represented by probability P, that is, there is a probability of P to choose shrinking and surrounding and a probability of 1-P to choose spiral updating;

[0202] Step 3.2, the distribution network parameters, the original power output and load power scenario data, and the total optimization objective function and constraints are used as inputs of the improved whale optimization algorithm;

[0203] Step 3.3: Set the power access capacity range and initialize the population, including the population size num and the maximum number of iterations T. max ;

[0204] Step 3.4: Calculate the fitness of each whale, select the position of the best whale and keep it as the initial target prey, that is, X * (t);

[0205] Step 3.5, calculate the nonlinear convergence factor a and coefficient vectors A and C;

[0206] Step 3.6, determine whether the random probability p is less than the probability P, if yes, directly go to step 3.7, otherwise update the spiral position after adding the adaptive weight;

[0207] Step 3.7, determine whether the absolute value of the coefficient vector A is greater than or equal to 1, if so, adopt a random search mechanism to update the position; if not, adopt a shrinking and surrounding mechanism to update the position after increasing the adaptive weight;

[0208] Step 3.8: Determine whether the termination condition of the algorithm is met. If not, return to step 3.4 to continue the calculation; otherwise, proceed to step 3.9.

[0209] Step 3.9: Output the optimal value and the optimal individual position.

[0210] The iterative process of improving the whale algorithm is as follows Figure 1 shown.

[0211] Compared with the single-objective model that only considers the carrying capacity, the multi-objective optimization model that considers the optimal total cost proposed in the present invention is more comprehensive and can optimize each sub-objective as much as possible, taking into account the economy while reasonably evaluating the carrying capacity.

[0212] When the coefficient of the whale optimization algorithm is |A|≤1, it means that the whale is shrinking and surrounding the prey, and the corresponding algorithm chooses the local optimal solution. When |A|>1, it means that the whale is performing random search, and the corresponding algorithm is searching globally. Therefore, |A| is crucial to the balance of the algorithm's search ability. In this algorithm, the convergence factor a related to the size of A decreases linearly to 0 with the increase of the number of iterations, which makes the algorithm easy to fall into the local optimum in the later stage. The change of the convergence factor a directly determines the development and exploration capabilities of the algorithm. The larger the convergence factor, the stronger the corresponding algorithm has the global search ability and the stronger the ability to jump out of the local optimal value; the smaller the convergence factor, the stronger the local development ability of the algorithm and the faster the convergence speed. However, in the basic whale optimization algorithm, the convergence coefficient decreases linearly from 2 to 0 after the number of iterations increases. This linear decrease strategy will make the algorithm have a strong global exploration ability but a slow convergence speed in the early stage, and will make the algorithm converge faster in the later stage but it is easy to cause the algorithm to fall into the local optimum. This phenomenon will be more obvious when solving the optimal value problem of multi-peak functions.

[0213] The improved whale optimization algorithm uses the cosine curve to optimize the convergence factor, which enhances the convergence speed and exploration level of the algorithm in the early stage, and keeps the convergence speed of the algorithm stable in the later stage, improving the shortcomings of the optimization algorithm itself, such as slow convergence speed and easy to fall into the local optimal solution, and has better global optimization ability. The adaptive weight can make the algorithm mainly search globally in the early stage of iteration and mainly search locally in the later stage of iteration, further improving the search ability of the algorithm.

[0214] By understanding the potential capacity and limitations of the power grid, we can determine the appropriate access capacity and location of distributed power sources and achieve reasonable resource allocation and layout planning; understanding the access capacity of distributed power sources can avoid overload problems caused by exceeding the grid's carrying capacity and reduce the risk of grid failures and power outages; reasonable planning and management of the access of distributed power sources can reduce system operating costs, reduce transmission losses, and promote the utilization and development of renewable energy; accurately assessing the access capacity of distributed power sources can better manage and dispatch power systems, achieve optimal configuration and operation regulation of distributed power sources, so as to adapt to the ever-changing energy demand and supply situation, and provide theoretical guidance for my country to achieve large-scale access to distributed power sources.

[0215] Example 1

[0216] The distributed power generation capacity evaluation method of the distribution network based on the improved whale optimization algorithm includes the following steps:

[0217] Step 1: construct the overall optimization objective function;

[0218] Step 2: Determine the constraints;

[0219] Step 3: Solve the model based on the improved whale optimization algorithm.

[0220] Example 2

[0221] The distributed power generation capacity evaluation method of the distribution network based on the improved whale optimization algorithm includes the following steps:

[0222] Step 1: construct the overall optimization objective function;

[0223] Step 1 is as follows:

[0224] Step 1.1, determine the maximum distributed generation installed capacity maxC, as shown in the following formula:

[0225]

[0226] Where P DG.i is the active power of distributed generation connected to node i, and n is the number of nodes.

[0227] Step 1.2, find the minimum total cost minF;

[0228] Step 1.3: Find the total optimization objective function maxF0.

[0229] Step 2: Determine the constraints;

[0230] Step 3: Solve the model based on the improved whale optimization algorithm.

[0231] Example 3

[0232] The distributed power generation capacity evaluation method of the distribution network based on the improved whale optimization algorithm includes the following steps:

[0233] Step 1: construct the overall optimization objective function;

[0234] Step 1 is as follows:

[0235] Step 1.1, determine the maximum distributed generation installed capacity maxC, as shown in the following formula:

[0236]

[0237] Where P DG.i is the active power of distributed generation connected to node i, and n is the number of nodes.

[0238] Step 1.2, find the minimum total cost minF;

[0239] Step 1.2 is as follows:

[0240] 1) Determine the investment cost F1 as shown below:

[0241]

[0242] In the formula, K DG is the unit capacity investment cost, S DGi is the capacity of distributed power generation connected to node i, and N is the number of nodes;

[0243] 2) Determine the operation and maintenance cost F2, as shown below:

[0244]

[0245] Where t is the service life of distributed power; r is the discount rate; T DG It is the operation and maintenance cost per unit capacity;

[0246] 3) Add the two cost sub-objective functions of investment cost F1 and operation and maintenance cost F2 to obtain the minimum total cost minF, as shown in the following formula:

[0247] minF=min(F1+F2) (4).

[0248] Step 1.3: Find the total optimization objective function maxF0.

[0249] Step 2: Determine the constraints;

[0250] Step 3: Solve the model based on the improved whale optimization algorithm.

[0251] Example 4

[0252] The distributed power generation capacity evaluation method of the distribution network based on the improved whale optimization algorithm includes the following steps:

[0253] Step 1: construct the overall optimization objective function;

[0254] Step 1 is as follows:

[0255] Step 1.1, determine the maximum distributed generation installed capacity maxC, as shown in the following formula:

[0256]

[0257] Where P DG.i is the active power of distributed generation connected to node i, and n is the number of nodes.

[0258] Step 1.2, find the minimum total cost minF;

[0259] Step 1.2 is as follows:

[0260] 1) Determine the investment cost F1 as shown below:

[0261]

[0262] In the formula, K DG is the unit capacity investment cost, S DGi is the capacity of distributed power generation connected to node i, and N is the number of nodes;

[0263] 2) Determine the operation and maintenance cost F2, as shown below:

[0264]

[0265] Where t is the service life of distributed power; r is the discount rate; T DG It is the operation and maintenance cost per unit capacity;

[0266] 3) Add the two cost sub-objective functions of investment cost F1 and operation and maintenance cost F2 to obtain the minimum total cost minF, as shown in the following formula:

[0267] minF=min(F1+F2) (4).

[0268] Step 1.3: Find the total optimization objective function maxF0.

[0269] Step 1.3 is as follows:

[0270] By linearly weighting the combination of equations (1) and (4), the overall optimization objective function is obtained as follows:

[0271] maxF0=ω1C-ω2F (5)

[0272] Where: ω1, ω2 are the weight coefficients of the two sub-objective functions.

[0273] Step 2: Determine the constraints;

[0274] Step 3: Solve the model based on the improved whale optimization algorithm.

[0275] Example 5

[0276] The distributed power generation capacity evaluation method of the distribution network based on the improved whale optimization algorithm includes the following steps:

[0277] Step 1: construct the overall optimization objective function;

[0278] Step 1 is as follows:

[0279] Step 1.1, determine the maximum distributed generation installed capacity maxC, as shown in the following formula:

[0280]

[0281] Where P DG.i is the active power of distributed generation connected to node i, and n is the number of nodes.

[0282] Step 1.2, find the minimum total cost minF;

[0283] Step 1.2 is as follows:

[0284] 1) Determine the investment cost F1 as shown below:

[0285]

[0286] In the formula, K DG is the unit capacity investment cost, S DGi is the capacity of distributed power generation connected to node i, and N is the number of nodes;

[0287] 2) Determine the operation and maintenance cost F2, as shown below:

[0288]

[0289] Where t is the service life of distributed power; r is the discount rate; T DGIt is the operation and maintenance cost per unit capacity;

[0290] 3) Add the two cost sub-objective functions of investment cost F1 and operation and maintenance cost F2 to obtain the minimum total cost minF, as shown in the following formula:

[0291] minF=min(F1+F2) (4).

[0292] Step 1.3: Find the total optimization objective function maxF0.

[0293] Step 1.3 is as follows:

[0294] By linearly weighting the combination of equations (1) and (4), the overall optimization objective function is obtained as follows:

[0295] maxF0=ω1C-ω2F (5)

[0296] Where: ω1, ω2 are the weight coefficients of the two sub-objective functions.

[0297] Step 2: Determine the constraints;

[0298] The constraints determined in step 2 are as follows:

[0299] 1) Distribution network flow constraints:

[0300]

[0301] Where: P DG,i , Q DG,i is the active and reactive output of the distributed power source connected to the i node; P i , Q i is the active and reactive loads of node i; G ij , B ij is the conductance and susceptance in the node admittance matrix; θ ij is the phase angle difference with the voltage at nodes i and j;

[0302] 2) Voltage constraint:

[0303] U N (1-ε)≤U i ≤U N (1+ε) (7)

[0304] Where U i is the voltage at node i, U N is the nominal voltage; ε is the voltage deviation rate limit under a specific voltage level;

[0305] The requirements for voltage fluctuation are as follows:

[0306] d i ≤d max(8)

[0307] Where, d i is the system voltage fluctuation value caused by distributed power generation at node i; d max It is the maximum voltage fluctuation value specified by the national standard;

[0308] The voltage fluctuation value of any node is estimated by the following formula:

[0309]

[0310] Where, d is the voltage fluctuation value; R L , X L are the line resistance and reactance at the load, respectively; ΔP and ΔQ are the changes in active and reactive power of the load, respectively;

[0311] DG usually has a higher power factor. Assuming that the reactive power output of DG is zero and all active power is generated, the voltage fluctuation value caused by DG at node i is expressed as:

[0312]

[0313] Where P DG.i is the output power of distributed power generation, U N is the nominal voltage, R i is the resistance of node i.

[0314] 3) Current Constraint:

[0315] |I k |≤I k.max (11)

[0316] In the formula, I k is the current on branch k; I k.max is the maximum current allowed to flow through branch k;

[0317] Verify according to the national standard "Calculation of short-circuit current in three-phase AC system":

[0318] I xz <I m (12)

[0319] In the formula, I xz is the system bus short-circuit current, I m is the allowable short-circuit current limit;

[0320] 4) Harmonic constraints:

[0321] In order to ensure the effectiveness of the harmonic current constraint conditions, the injection current under the condition of maximum harmonic output of DG is taken to determine its access capacity. The constraint conditions determined by the harmonic current are:

[0322]

[0323] In the formula, S DG is the DG access amount; U N is the nominal voltage; μ k It is the content rate limit of each harmonic output of DG specified in the national standard; I k These are the harmonic currents allowed to be connected to the power grid as specified in the national standard.

[0324] In order to ensure the validity of the harmonic voltage content constraint condition, the injection current of DG under the condition of maximum harmonic output is taken to determine its access capacity;

[0325]

[0326] U k =HRU k ×U N (16)

[0327]

[0328] In the formula, I k is the kth harmonic current of the distributed power source; HRU k is the kth harmonic voltage content rate; S k is the short-circuit capacity; U k is the kth harmonic voltage; THD U is the total harmonic voltage distortion rate;

[0329] 5) Energy storage operation constraints:

[0330] Energy storage power constraints:

[0331] u_dch+u_ch≤1 (18)

[0332] 0≤p_dch≤u_dch*α (19)

[0333] 0≤p_ch≤u_ch*β (20)

[0334] In the formula, u_dch and u_ch are the energy storage discharge and charge states respectively, u_dch, u_ch∈{0,1}, u_dch = 1 means discharge, u_ch = 1 means charge, the above formula means there are three energy storage states, charge, discharge and neither charge nor discharge. p_dch is the discharge power, p_ch is the charge power, α and β are the discharge and charge limit coefficients;

[0335] Energy storage capacity constraints:

[0336] E_ess t+1 =E_ess t +λ*p_ch t-μ*p_dch t (twenty one)

[0337] In the formula, λ and μ are the charge and discharge coefficients, E_ess t+1 is the energy storage capacity at time t+1, E_ess t is the energy storage capacity at time t; p_ch t 、p_dch t are the charging and discharging powers at time t respectively.

[0338] 6) Other constraints, including constraints on set temperature range and electric vehicle battery SOC constraints.

[0339] Step 3: Solve the model based on the improved whale optimization algorithm.

[0340] Example 6

[0341] The distributed power generation capacity evaluation method of the distribution network based on the improved whale optimization algorithm includes the following steps:

[0342] Step 1: construct the overall optimization objective function;

[0343] Step 1 is as follows:

[0344] Step 1.1, determine the maximum distributed generation installed capacity maxC, as shown in the following formula:

[0345]

[0346] Where P DG.i is the active power of distributed generation connected to node i, and n is the number of nodes.

[0347] Step 1.2, find the minimum total cost minF;

[0348] Step 1.2 is as follows:

[0349] 1) Determine the investment cost F1 as shown below:

[0350]

[0351] In the formula, K DG is the unit capacity investment cost, S DGi is the capacity of distributed power generation connected to node i, and N is the number of nodes;

[0352] 2) Determine the operation and maintenance cost F2, as shown below:

[0353]

[0354] Where t is the service life of distributed power; r is the discount rate; T DGIt is the operation and maintenance cost per unit capacity;

[0355] 3) Add the two cost sub-objective functions of investment cost F1 and operation and maintenance cost F2 to obtain the minimum total cost minF, as shown in the following formula:

[0356] minF=min(F1+F2) (4).

[0357] Step 1.3: Find the total optimization objective function maxF0.

[0358] Step 1.3 is as follows:

[0359] By linearly weighting the combination of equations (1) and (4), the overall optimization objective function is obtained as follows:

[0360] maxF0=ω1C-ω2F (5)

[0361] Where: ω1, ω2 are the weight coefficients of the two sub-objective functions.

[0362] Step 2: Determine the constraints;

[0363] The constraints determined in step 2 are as follows:

[0364] 1) Distribution network flow constraints:

[0365]

[0366] Where: P DG,i , Q DG,i is the active and reactive output of the distributed power source connected to the i node; P i , Q i is the active and reactive loads of node i; G ij , B ij is the conductance and susceptance in the node admittance matrix; θ ij is the phase angle difference with the voltage at nodes i and j;

[0367] 2) Voltage constraint:

[0368] U N (1-ε)≤U i ≤U N (1+ε) (7)

[0369] Where U i is the voltage at node i, U N is the nominal voltage; ε is the voltage deviation rate limit under a specific voltage level;

[0370] The requirements for voltage fluctuation are as follows:

[0371] d i ≤d max(8)

[0372] Where, d i is the system voltage fluctuation value caused by distributed power generation at node i; d max It is the maximum voltage fluctuation value specified by the national standard;

[0373] The voltage fluctuation value of any node is estimated by the following formula:

[0374]

[0375] Where, d is the voltage fluctuation value; R L , X L are the line resistance and reactance at the load, respectively; ΔP and ΔQ are the changes in active and reactive power of the load, respectively;

[0376] DG usually has a higher power factor. Assuming that the reactive power output of DG is zero and all active power is generated, the voltage fluctuation value caused by DG at node i is expressed as:

[0377]

[0378] Where P DG.i is the output power of distributed power generation, U N is the nominal voltage, R i is the resistance of node i.

[0379] 3) Current Constraint:

[0380] |I k |≤I k.max (11)

[0381] In the formula, I k is the current on branch k; I k.max is the maximum current allowed to flow through branch k;

[0382] Verify according to the national standard "Calculation of short-circuit current in three-phase AC system":

[0383] I xz <I m (12)

[0384] In the formula, I xz is the system bus short-circuit current, I m is the allowable short-circuit current limit;

[0385] 4) Harmonic constraints:

[0386] In order to ensure the effectiveness of the harmonic current constraint conditions, the injection current under the condition of maximum harmonic output of DG is taken to determine its access capacity. The constraint conditions determined by the harmonic current are:

[0387]

[0388] In the formula, S DG is the DG access amount; U N is the nominal voltage; μ k It is the content rate limit of each harmonic output of DG specified in the national standard; I k These are the harmonic currents allowed to be connected to the power grid as specified in the national standard.

[0389] In order to ensure the validity of the harmonic voltage content constraint condition, the injection current of DG under the condition of maximum harmonic output is taken to determine its access capacity;

[0390]

[0391] U k =HRU k ×U N (16)

[0392]

[0393] In the formula, I k is the kth harmonic current of the distributed power source; HRU k is the kth harmonic voltage content rate; S k is the short-circuit capacity; U k is the kth harmonic voltage; THD U is the total harmonic voltage distortion rate;

[0394] 5) Energy storage operation constraints:

[0395] Energy storage power constraints:

[0396] u_dch+u_ch≤1 (18)

[0397] 0≤p_dch≤u_dch*α (19)

[0398] 0≤p_ch≤u_ch*β (20)

[0399] In the formula, u_dch and u_ch are the energy storage discharge and charge states respectively, u_dch, u_ch∈{0,1}, u_dch = 1 means discharge, u_ch = 1 means charge, the above formula means there are three energy storage states, charge, discharge and neither charge nor discharge. p_dch is the discharge power, p_ch is the charge power, α and β are the discharge and charge limit coefficients;

[0400] Energy storage capacity constraints:

[0401] E_ess t+1 =E_ess t +λ*p_ch t-μ*p_dch t (twenty one)

[0402] In the formula, λ and μ are the charge and discharge coefficients, E_ess t+1 is the energy storage capacity at time t+1, E_ess t is the energy storage capacity at time t; p_ch t 、p_dch t are the charging and discharging powers at time t respectively.

[0403] 6) Other constraints, including constraints on set temperature range and electric vehicle battery SOC constraints.

[0404] In step 2, other constraints, including the constraints of setting the temperature range and the SOC constraints of the electric vehicle battery, are as follows:

[0405] For air conditioners with temperature adjustment authority, set temperature range constraints to ensure user comfort:

[0406]

[0407] Where: T i Set,Min and T i Set,Max are the lower and upper bounds of the operating temperature of the i-th air conditioner respectively;

[0408] Electric vehicle battery SOC constraints:

[0409] S min ≤S EV (t)≤S max (twenty three)

[0410] In the formula, S max , S min They are the upper and lower limits of the car battery SOC respectively.

[0411] Step 3: Solve the model based on the improved whale optimization algorithm.

Claims

1. A method for evaluating the carrying capacity of distributed power sources in distribution networks based on an improved whale optimization algorithm is characterized in that: The following steps are involved: Step 1: construct the overall optimization objective function; Step 2: Determine the constraints; Step 3: Solve the model based on the improved whale optimization algorithm.

2. According to the method for evaluating the carrying capacity of distributed power sources in distribution network based on improved whale optimization algorithm according to claim 1, it is characterized in that: Step 1 is as follows: Step 1.1, determine the maximum distributed generation installed capacity maxC, as shown in the following formula: Where P DG.i is the active power of distributed generation connected to node i, and n is the number of nodes; Step 1.2, find the minimum total cost minF; Step 1.3: Find the total optimization objective function max F0.

3. The method for evaluating the carrying capacity of distributed power sources in a distribution network based on an improved whale optimization algorithm according to claim 2 is characterized in that: Step 1.2 is as follows: 1) Determine the investment cost F1 as shown below: In the formula, K DG is the unit capacity investment cost, S DGi is the capacity of distributed power generation connected to node i, and N is the number of nodes; 2) Determine the operation and maintenance cost F2, as shown below: Where t is the service life of distributed power; r is the discount rate; T DG It is the operation and maintenance cost per unit capacity; 3) Add the two cost sub-objective functions of investment cost F1 and operation and maintenance cost F2 to obtain the minimum total cost minF, as shown in the following formula: minF=min(F1+F2) (4).

4. The method for evaluating the carrying capacity of distributed power sources in a distribution network based on an improved whale optimization algorithm according to claim 3 is characterized in that: Step 1.3 is as follows: By linearly weighting the combination of equations (1) and (4), the overall optimization objective function is obtained as follows: maxF0=ω1C-ω2F (5) Where: ω1, ω2 are the weight coefficients of the two sub-objective functions.

5. The method for evaluating the carrying capacity of distributed power sources in a distribution network based on an improved whale optimization algorithm according to claim 3 is characterized in that: The constraints determined in step 2 are as follows: 1) Distribution network flow constraints: Where: P DG,i , Q DG,i is the active and reactive output of the distributed power source connected to the i node; P i , Q i is the active and reactive loads of node i; G ij , B ij is the conductance and susceptance in the node admittance matrix; θ ij is the phase angle difference with the voltage at nodes i and j; 2) Voltage constraint: U N (1-ε)≤U i ≤U N (1+e) (7) Where U i is the voltage at node i, U N is the nominal voltage; ε is the voltage deviation rate limit under a specific voltage level; The requirements for voltage fluctuation are as follows: d i ≤d max (8) Where, d i is the system voltage fluctuation value caused by distributed power generation at node i; d max It is the maximum voltage fluctuation value specified by the national standard; The voltage fluctuation value of any node is estimated by the following formula: Where, d is the voltage fluctuation value; R L , X L are the line resistance and reactance at the load, respectively; ΔP and ΔQ are the changes in active and reactive power of the load respectively; DG usually has a higher power factor. Assuming that the reactive power output of DG is zero and all active power is generated, the voltage fluctuation value caused by DG at node i is expressed as: Where P DG.i is the output power of distributed power generation, U N is the nominal voltage, R i is the resistance of node i; 3) Current Constraint: |I k |≤I k.max (11) In the formula, I k is the current on branch k; I k.max is the maximum current allowed to flow through branch k; Verify according to the national standard "Calculation of short-circuit current in three-phase AC system": I xz <I m (12) In the formula, I xz is the system bus short-circuit current, I m is the allowable short-circuit current limit; 4) Harmonic constraints: In order to ensure the effectiveness of the harmonic current constraint conditions, the injection current under the condition of maximum harmonic output of DG is taken to determine its access capacity. The constraint conditions determined by the harmonic current are: In the formula, S DG is the DG access amount; U N is the nominal voltage; μ k It is the content rate limit of each harmonic output of DG specified in the national standard; I k It is the harmonic currents allowed to be connected to the power grid as specified in the national standard; In order to ensure the validity of the harmonic voltage content constraint condition, the injection current of DG under the condition of maximum harmonic output is taken to determine its access capacity; IN k =HRU k ×U N (16) In the formula, I k is the kth harmonic current of the distributed power source; HRU k is the kth harmonic voltage content rate; S k is the short-circuit capacity; U k is the kth harmonic voltage; THD U is the total harmonic voltage distortion rate; 5) Energy storage operation constraints: Energy storage power constraints: u_dch+u_ch≤1 (18) 0≤p_dch≤u_dch*α (19) 0≤p_ch≤u_ch*β (20) In the formula, u_dch and u_ch are the energy storage discharge and charge states respectively, u_dch, u_ch∈{0,1}, u_dch is 1 for discharge, u_ch is 1 for charge, the above formula means that there are three energy storage states, charge, discharge and neither charge nor discharge; p_dch is the discharge power, p_ch is the charge power, α and β are the discharge and charge limit coefficients; Energy storage capacity constraints: E_ess t+1 =E_ess t +λ*p_ch t -μ*p_dch t (21) In the formula, λ and μ are the charge and discharge coefficients, E_ess t+1 is the energy storage capacity at time t+1, E_ess t is the energy storage capacity at time t; p_ch t 、p_dch t are the charging and discharging powers at time t respectively; 6) Other constraints, including constraints on set temperature range and electric vehicle battery SOC constraints.

6. The method for evaluating the carrying capacity of distributed power sources in a distribution network based on an improved whale optimization algorithm according to claim 5 is characterized in that: In step 2, other constraints, including the constraints of setting the temperature range and the SOC constraints of the electric vehicle battery, are as follows: For air conditioners with temperature adjustment authority, set temperature range constraints to ensure user comfort: Where: are the lower and upper bounds of the operating temperature of the i-th air conditioner respectively; Electric vehicle battery SOC constraints: S min ≤S EV (t)≤S max (23) In the formula, S max , S min They are the upper and lower limits of the car battery SOC respectively.

7. The method for evaluating the carrying capacity of distributed power sources in a distribution network based on an improved whale optimization algorithm according to claim 6 is characterized in that: Step 3 is as follows: Step 3.1: Improvement of the whale optimization algorithm; Step 3.2, the distribution network parameters, the original power output and load power scenario data, and the total optimization objective function and constraints are used as inputs of the improved whale optimization algorithm; Step 3.3: Set the power access capacity range and initialize the population, including the population size num and the maximum number of iterations T. max ; Step 3.4: Calculate the fitness of each whale, select the position of the best whale and keep it as the initial target prey, that is, X * (t); Step 3.5, calculate the nonlinear convergence factor a and coefficient vectors A and C; Step 3.6, determine whether the random probability p is less than the probability P, if yes, directly go to step 3.7, otherwise update the spiral position after adding the adaptive weight; Step 3.7, determine whether the absolute value of the coefficient vector A is greater than or equal to 1, if so, adopt a random search mechanism to update the position; if not, adopt a shrinking and surrounding mechanism to update the position after increasing the adaptive weight; Step 3.8: Determine whether the termination condition of the algorithm is met. If not, return to step 3.4 to continue the calculation; otherwise, proceed to step 3.

9. Step 3.9: Output the optimal value and the optimal individual position.

8. The method for evaluating the carrying capacity of distributed power sources in a distribution network based on an improved whale optimization algorithm according to claim 7 is characterized in that: Step 3.1 is as follows: The cosine curve is applied to change the way the convergence factor changes, and the adaptive weight adjustment method is adopted to improve the convergence performance of the whale optimization algorithm. Specifically: The cosine curve is used to improve the change process of the convergence factor. The specific expression is as follows: The adaptive weight coefficient ω is derived, and the corresponding expression is as follows: In the formula, ω max ,ω min are the upper and lower limits of the weight coefficient respectively; In the whale optimization algorithm, the mathematical model of whales using echolocation to determine the location of target prey and surround them is improved, that is, the improved mathematical model is as follows: X(t+1)=ωX * (t)-A·D (30) Where D is the distance between the whale and the target prey; t is the number of iterations; X * (t) is the global optimal whale position; X(t) and X(t+1) represent the position vectors before and after the whale update, respectively; A and C represent the coefficient vectors.

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