Cuckoo search algorithm-based grid-connected inverter multi-objective optimization control method

Abstract

The invention discloses a Cuckoo search algorithm-based grid-connected inverter multi-objective optimization control method, which comprises the following steps of: constructing a three-level grid-connected inverter mathematical model, and calculating to obtain an inverter side current reference value; constructing a current prediction model of the inverter side; constructing a value function control item of the inverter side current by adopting a value function in a square error form; constructing a cost function by taking the neutral-point potential balance and the switching frequency as control items; and iteratively calculating a weight factor by adopting an improved self-adaptive cuckoo retrieval algorithm to realize multi-objective optimization control of the grid-connected inverter. According to the multi-objective optimization control method for the grid-connected inverter based on the cuckoo search algorithm, the problem that the control performance is limited due to the fact that weight factors are difficult to set in multi-objective optimization of the grid-connected inverter in the prior art is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of new energy inverter control, and in particular relates to a multi-objective optimization control method for a grid-connected inverter based on a cuckoo search algorithm. Background Art

[0002] Distributed generation, as a new power supply method, is gaining increasing popularity due to its advantages, such as high utilization, low environmental pollution, and flexible power generation methods. Among various types of three-phase, three-level inverters, the T-type three-level inverter stands out due to its simple topology, low conduction losses, and the highest economic efficiency at a specific switching frequency. As a result, it is gaining increasing popularity in distributed generation grid-connected systems.

[0003] With the rapid development of digital signal processing technology and microprocessors, finite control set model predictive control (FCS-MPC), as a nonlinear control strategy, has attracted increasing attention from researchers. Traditional linear control strategies cannot meet the high-performance control requirements of inverter systems. FCS-MPC offers advantages such as fast dynamic response, simple and easy-to-implement control algorithms, no modulation steps, and ease of multi-objective and constraint synchronization. Consequently, FCS-MPC is increasingly being used in inverter systems.

[0004] However, traditional FCS-MPC also has some problems. The simultaneous processing of multiple objectives and constraints is achieved by introducing relevant weight factor control terms in the cost function. In the model predictive control (MPC) of three-level inverters, the weight factor is a key parameter for coordinating multi-objective optimization problems. MPC usually needs to optimize multiple objectives (such as current tracking, neutral point voltage balance, switching frequency reduction, etc.) at the same time, and these objectives may be contradictory. Strict current tracking may increase the switching frequency, resulting in increased losses; neutral point voltage balance may require sacrificing current tracking accuracy. By adjusting the weight factor, the relative importance of each objective can be clarified. Due to the lack of theoretical guidance on weight factor adjustment, the value of the weight factor is generally determined by "trial and error", which increases the complexity of controller design and makes weight factor adjustment difficult. Summary of the Invention

[0005] The purpose of the present invention is to provide a multi-objective optimization control method for a grid-connected inverter based on a cuckoo search algorithm, which solves the problem in the prior art that the control performance is limited due to the difficulty in setting the weight factors in the multi-objective optimization of the grid-connected inverter.

[0006] The technical solution adopted by the present invention is a multi-objective optimization control method for a grid-connected inverter based on a cuckoo search algorithm, which specifically includes the following steps:

[0007] Step 1: Construct a mathematical model of a three-level grid-connected inverter and calculate the inverter-side current reference value;

[0008] Step 2: Build a current prediction model on the inverter side;

[0009] Step 3: Use the cost function in the form of square error to construct the cost function control term of the inverter side current;

[0010] Step 4: Take the midpoint potential balance and switching frequency as control items and construct the cost function;

[0011] Step 5: Use the improved adaptive cuckoo retrieval algorithm to iteratively calculate the weight factors to achieve multi-objective optimization control of the grid-connected inverter.

[0012] The present invention is also characterized in that:

[0013] Step 1 specifically includes the following steps:

[0014] Step 1.1: Construct a mathematical model of a three-level grid-connected inverter, which includes the following steps:

[0015] Step 1.1.1: Define the midpoint of the upper and lower capacitors as the zero potential reference point of the inverter output voltage;

[0016] Step 1.1.2: Define a switch function, that is, the switch variable S x ,x=a,b,c, which is expressed as follows:

[0017]

[0018] Where a, b, and c represent phases a, b, and c in a T-type three-level topology.

[0019] Step 1.1.3: Combine the KCL and KVL formulas to derive the inverter output voltage in matrix form, as shown below:

[0020]

[0021] Where u a 、u b 、u c Indicates the output voltage of the inverter, U dc Indicates the bus voltage on the DC side of the inverter;

[0022] Step 1.1.4: In the abc three-phase coordinate system, the relationship between the inverter-side current, the grid-side current, and the filter capacitor C is expressed as follows:

[0023]

[0024] Where i 1a 、i 1b 、i 1cIndicates the output current on the inverter side, i 2a 、i 2b 、i 2c Indicates the output current on the grid side, u ca 、u cb 、u cc Indicates the voltage drop across the filter capacitor;

[0025] Step 1.2: Transform the mathematical model in the abc three-phase coordinate system to the mathematical model in the αβ two-phase coordinate system, specifically:

[0026] In the αβ two-phase coordinate system, the inverter side loop equation is expressed as follows:

[0027]

[0028] Where L1 represents the three-phase equivalent inductance on the inverter side, R1 represents the equivalent resistance on the inverter side, and u αβ represents the output voltage of the inverter in the αβ coordinate system, u cαβ Indicates the voltage drop on the filter capacitor in the αβ coordinate system, i 1αβ represents the output current of the inverter side in the αβ coordinate system;

[0029] The grid side loop equation is expressed as follows:

[0030]

[0031] Where L2 represents the three-phase equivalent inductance on the grid side; R2 represents the equivalent resistance on the grid side, e αβ represents the grid voltage in the αβ coordinate system, i 2αβ represents the output current on the grid side in the αβ two-phase coordinate system;

[0032] The relationship between the inverter-side current, grid-side current and filter capacitor C is as follows:

[0033]

[0034] Step 1.3: Convert equations (4), (5), and (6) into complex vectors in the αβ two-phase coordinate system and integrate them to obtain:

[0035]

[0036] Where, e αβ represents the grid voltage in the αβ two-phase coordinate system;

[0037] The variables in formula (7) in the αβ two-phase coordinate system are Park transformed and rewritten into complex vector form to obtain the mathematical model in the dq rotating coordinate system, which is expressed as:

[0038]

[0039] Where, e dq represents the grid voltage in the dq rotating coordinate system, i 1dq represents the output current of the inverter side in the dq rotating coordinate system, i 2dq represents the output current of the grid side in the dq rotating coordinate system, u cdq represents the voltage drop on the filter capacitor in the dq rotating coordinate system, j represents the imaginary unit, and ω represents the angular frequency;

[0040] Without considering the impact of high frequency harmonics under power frequency conditions, i 2dq and u cdq can be regarded as a constant, then the relevant terms in formula (8) are expressed as follows:

[0041]

[0042] According to the grid-connected control requirement that the grid voltage and current are in opposite phase, the grid-side current reference value is set to be the components of the two coordinate axes in the dq rotating coordinate system. Then replace i in formula (8) 2dq Use the set reference value Instead, the reference value of the voltage drop on the filter capacitor is obtained by transposition transformation. and the inverter side current reference value when connected to the grid Expressed as:

[0043]

[0044] Finally, the final inverter side current reference value obtained in formulas (10) and (11) is converted into the reference current value in the αβ two-phase coordinate system through inverse Park transformation. For subsequent analysis and algorithm implementation.

[0045] Step 2 is as follows:

[0046] Discretize some terms in the inverter measurement loop equation in the αβ two-phase coordinate system and obtain:

[0047]

[0048] The differential term in formula (7) is discretized using the forward difference formula to obtain:

[0049]

[0050] Where i 1αβ (k) represents the sampling value of the inverter side current at time k, i 1αβ (k+1) represents the predicted value of the inverter side current at time k+1;

[0051] Substituting the discretized inverter side current differential term expression (13) into formula (12) yields the fully discretized discrete control model, which is expressed as follows:

[0052]

[0053] The current prediction model of the inverter side is further sorted out and expressed as follows:

[0054]

[0055] Where, T s is the sampling period, u αβ (k) is the output voltage vector of the inverter at time k, u cαβ (k) is the voltage drop on the filter capacitor at time k.

[0056] The value function control term of the inverter side current constructed in step 3 is expressed as follows:

[0057]

[0058] In step 4, the midpoint potential balance is used as a control item, specifically:

[0059] The voltage difference between the upper and lower capacitors on the DC side is used as a control item to control the midpoint potential balance, and the voltage difference between the upper and lower capacitors is set to Δu=u C1 -u C2 ,get:

[0060]

[0061] The forward difference formula is used to discretize the predicted value model of the voltage difference between the upper and lower capacitors on the DC side, which is expressed as follows:

[0062]

[0063] When the three phases are balanced, i la +i lb +i lc =0, simplify formula (18) to express it as follows:

[0064]

[0065] In step 4, the switching frequency is used as the control term, which is expressed as follows:

[0066] f s =|S a (k)-S a (k-1)|+|S b (k)-S b (k-1)|+|Sc (k)-S c (k-1)| (20)

[0067] Where, f s Represents the number of times all switching devices of the inverter are turned on and off during the current control cycle.

[0068] In step 4, the cost function constructed is expressed as follows:

[0069] G=g+λ1|Δu(k+1)|+λ2f s (twenty one)

[0070] Where G represents the cost function, λ1 and λ2 represent the weight coefficients of midpoint potential balance and switching frequency constraints, respectively.

[0071] In step 5, the traditional cuckoo search algorithm is expressed as follows:

[0072]

[0073] Where, is the position of the i-th nest in the t-th iteration, α is the step scale factor, s is the step size, p a is the probability of discovery, H is the unit step function, ε is a random number drawn from a uniform distribution, is the element-wise multiplication symbol, is the position of the jth nest in the tth iteration, is the position of the kth nest in the tth iteration;

[0074] The improvements to the traditional cuckoo search algorithm are as follows:

[0075] In the iterative process of the cuckoo search algorithm, the population diversity index D is introduced to adaptively adjust the discovery probability P according to the distribution state of the solution. a , to balance global exploration and local development capabilities, specifically:

[0076] Define population diversity indicators:

[0077] Calculate the Euclidean distance variance of the solution in the current population as the population diversity indicator, which is expressed as follows:

[0078]

[0079] Where λ i represents the i-th weight factor combination; λ avg represents the population average weight vector; λ range represents the value range of the weight factor, and N represents the total number of weight factors;

[0080] Adaptively adjust the discovery probability Pa The process is expressed as follows:

[0081]

[0082] Where D th represents the diversity threshold; γ d represents the diversity regulator;

[0083] Introduce the attenuation coefficient η(t) and dynamically adjust the discovery probability P together with the number of iterations a , which is expressed as follows:

[0084]

[0085] Where, T max Indicates the maximum number of iterations.

[0086] Step 5 is as follows:

[0087] Step 5.1: Initialize the number of bird nests, step size, number of iterations, and the initial probability of finding a bird nest P a (0), define the diversity threshold D th , diversity regulator γ d , weight factor range λ range ;

[0088] Step 5.2: Normalize the value function, calculate the fitness value of each individual, and calculate the current population diversity index D(t);

[0089] Step 5.3: Add diversity feedback and adjust the discovery probability P according to D(t) a (t+1), joint iterative decay, applying the decay coefficient η(t) to stabilize the late search;

[0090] Step 5.4: Perform Levy flight on each individual to generate a new solution. If the new solution is better than the previous solution, replace the previous solution and proceed to the next iteration. a (t+1) Randomly eliminate inferior solutions and generate new bird nests;

[0091] Step 5.5: Record the weight factor value under the optimal solution and repeat steps 5.1 to 5.4 until the maximum number of iterations is reached.

[0092] The beneficial effects of the present invention are:

[0093] The present invention proposes a multi-objective optimization control method for grid-connected inverters based on a cuckoo search algorithm. The method first constructs a multi-objective optimization function including current tracking, neutral point voltage balance, and switching frequency reduction, wherein the current tracking model is related to the dynamic performance and control accuracy of the system, the switching frequency index is used to evaluate device losses, and the midpoint potential balance index ensures the balance of the DC side capacitor voltage. In response to the problem of limited control performance caused by the difficulty in adjusting the weight factors in traditional multi-objective optimization, the present invention adopts an improved cuckoo algorithm to dynamically optimize the weight factors. During the iterative process of the cuckoo algorithm, a population diversity index is introduced, and the discovery probability is adaptively adjusted according to the distribution state of the solution to balance the global exploration and local exploration capabilities. The weight factors are adaptively adjusted during the iterative process. The present invention improves the convergence speed and optimization accuracy of the algorithm, effectively realizes multi-objective collaborative optimization, and achieves the goals of current tracking, neutral point voltage balance, and switching frequency reduction. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 It is a flowchart of a multi-objective optimization control method for a grid-connected inverter based on a cuckoo search algorithm according to the present invention;

[0095] Figure 2 It is a T-type three-level LCL filter grid-connected inverter topology. DETAILED DESCRIPTION

[0096] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0097] The present invention is based on the multi-objective optimization control method of the grid-connected inverter of the cuckoo search algorithm, such as Figure 1 As shown, the specific steps include:

[0098] Step 1: Construct a mathematical model of a three-level grid-connected inverter and calculate the inverter-side current reference value.

[0099] The specific steps include:

[0100] Step 1.1: Construct a mathematical model of a three-level grid-connected inverter to describe the dynamic behavior and electrical characteristics of the inverter, using a T-type three-level topology. Figure 2 As shown in the figure: the three-phase equivalent inductance on the inverter side is represented by L1, and the three-phase equivalent inductance on the grid side is represented by L2; the filter capacitor is represented by C; the upper and lower capacitors on the DC side are represented by C1 and C2 respectively. The voltage midpoint of the upper and lower capacitors on the DC side of the inverter is selected as point O, the common node of the grid voltage is marked as point n, and the voltage U is used as the reference voltage. dc Indicates the bus voltage on the DC side of the inverter, with u a 、u b 、u c Indicates the output voltage of the inverter, with u ca 、ucb 、u cc Indicates the voltage drop on the filter capacitor, using e a 、e b 、e c Indicates the grid voltage, i 1a 、i 1b 、i 1c Indicates the output current of the inverter side, i 2c 、i 2b 、i 2c Represents the output current on the grid side, R1 represents the equivalent resistance on the inverter side, and R2 represents the equivalent resistance on the grid side.

[0101] Step 1.1.1: Define the midpoint O between the upper and lower capacitors as the zero potential reference point of the inverter output voltage;

[0102] Step 1.1.2: Define a switch function, that is, the switch variable S x ,x=a,b,c, which is expressed as follows:

[0103]

[0104] Where a, b, and c represent phases a, b, and c in a T-type three-level topology.

[0105] Step 1.1.3: Combine the KCL (Kirchhoff's Current Law) and KVL (Kirchhoff's Voltage Law) formulas to derive the inverter output voltage in matrix form, as shown below:

[0106]

[0107] Where u a 、u b 、u c Indicates the output voltage of the inverter, U dc Indicates the bus voltage on the DC side of the inverter;

[0108] Step 1.1.4: In the abc three-phase coordinate system, the relationship between the inverter-side current, the grid-side current, and the filter capacitor C is expressed as follows:

[0109]

[0110] Where i 1a 、i 1b 、i 1c Indicates the output current on the inverter side, i 2a 、i 2b 、i 2c Indicates the output current on the grid side, u ca 、u cb 、u ccIndicates the voltage drop across the filter capacitor;

[0111] Step 1.2: Transform the mathematical model in the abc three-phase coordinate system to the mathematical model in the αβ two-phase coordinate system, specifically:

[0112] In the αβ two-phase coordinate system, the KVL loop equation on the inverter side is expressed as follows:

[0113]

[0114] Where L1 represents the three-phase equivalent inductance on the inverter side, R1 represents the equivalent resistance on the inverter side, and u αβ represents the output voltage of the inverter in the αβ coordinate system, u cαβ Indicates the voltage drop on the filter capacitor in the αβ coordinate system, i 1αβ represents the output current of the inverter side in the αβ coordinate system;

[0115] The grid side loop equation is expressed as follows:

[0116]

[0117] Where L2 represents the three-phase equivalent inductance on the grid side; R2 represents the equivalent resistance on the grid side, e αβ represents the grid voltage in the αβ coordinate system, i 2αβ represents the output current on the grid side in the αβ two-phase coordinate system;

[0118] The relationship between the inverter-side current, grid-side current and filter capacitor C is as follows:

[0119]

[0120] Step 1.3: Convert equations (4), (5), and (6) into complex vectors in the αβ two-phase coordinate system and integrate them to obtain:

[0121]

[0122] Where, e αβ represents the grid voltage in the αβ two-phase coordinate system;

[0123] The variables in formula (7) in the αβ two-phase coordinate system are Park transformed and rewritten into complex vector form to obtain the mathematical model in the dq rotating coordinate system, which is expressed as:

[0124]

[0125] Where, e dq represents the grid voltage in the dq rotating coordinate system, i 1dq represents the output current of the inverter side in the dq rotating coordinate system, i2dq represents the output current of the grid side in the dq rotating coordinate system, u cdq represents the voltage drop on the filter capacitor in the dq rotating coordinate system, j represents the imaginary unit, and ω represents the angular frequency;

[0126] Without considering the impact of high frequency harmonics under power frequency conditions, i 2dq and u cdq can be regarded as a constant, then the relevant terms in formula (8) are expressed as follows:

[0127]

[0128] According to the grid-connected control requirement that the grid voltage and current are in opposite phase, the grid-side current reference value is set to be the components of the two coordinate axes in the dq rotating coordinate system. Then replace i in formula (8) 2dq Use the set reference value Instead, the reference value of the voltage drop on the filter capacitor is obtained by transposition transformation. and the inverter side current reference value when connected to the grid Expressed as:

[0129]

[0130] Finally, the final inverter side current reference value obtained in formulas (10) and (11) is converted into the reference current value in the αβ two-phase coordinate system through inverse Park transformation. For subsequent analysis and algorithm implementation.

[0131] Step 2: Build a current prediction model on the inverter side.

[0132] Specifically, discretize some terms in the inverter measurement loop equation in the αβ two-phase coordinate system to obtain:

[0133]

[0134] The differential term in formula (7) is discretized using the forward difference formula to obtain:

[0135]

[0136] Where i 1αβ (k) represents the sampling value of the inverter side current at time k, i 1αβ (k+1) represents the predicted value of the inverter side current at time k+1;

[0137] Substituting the discretized inverter side current differential term expression (13) into formula (12) yields the fully discretized discrete control model, which is expressed as follows:

[0138]

[0139] The current prediction model of the inverter side is further sorted out and expressed as follows:

[0140]

[0141] Where, T s is the sampling period, u αβ (k) is the output voltage vector of the inverter at time k, u cαβ (k) is the voltage drop on the filter capacitor at time k.

[0142] Step 3: Use the cost function in the form of square error to construct the cost function control term of the inverter side current, which is expressed as follows:

[0143]

[0144] Step 4: Take the midpoint potential balance and switching frequency as control items and construct the cost function.

[0145] In order to control the midpoint potential balance, the voltage difference between the upper and lower capacitors on the DC side is used as a control item to control the midpoint potential balance, and the voltage difference between the upper and lower capacitors is set to Δu = u C1 -u C2 ,get:

[0146]

[0147] The forward difference formula is used to discretize the predicted value model of the voltage difference between the upper and lower capacitors on the DC side, which is expressed as follows:

[0148]

[0149] When the three phases are balanced, i la +i lb +i lc =0, simplify formula (18) to express it as follows:

[0150]

[0151] Switching loss is also an important metric for grid-connected inverters. Excessively high switching frequency increases losses and reduces the life of switching devices. However, due to the lack of a modulator in the control scheme, the switching frequency is variable. To limit the average switching frequency of each device—that is, to reduce the number of commutations between two consecutive sampling periods—an additional objective is added to the cost function. To reduce the switching frequency of the inverter, the switching frequency is used as a control term, expressed as follows:

[0152] f s =|S a(k)-S a (k-1)|+|S b (k)-S b (k-1)|+|S c (k)-S c (k-1)| (20)

[0153] Where, f s Represents the number of times all switching devices of the inverter are turned on and off during the current control cycle.

[0154] The main control item in the cost function of the model predictive control strategy in the present invention is the grid current. To make it closely follow the given reference value, the control items are the voltage difference between the upper and lower capacitors on the DC side and the number of switching times, which can be expressed as follows:

[0155] G=g+λ1|Δu(k+1)|+λ2f s (twenty one)

[0156] In the formula, G represents the cost function, and λ1 and λ2 represent the weight coefficients for the midpoint potential balance and switching frequency constraints, respectively. By varying the weight coefficients, the strength of the constraints on the control objective can be adjusted. The cost function is analyzed based on the system's control objectives: of the three control objectives, inverter-side current and midpoint potential balance are primarily controlled, with average switching frequency as a secondary objective. Traditionally, when debugging the system's weight factors, one would first set λ2 = 0, adjust λ1, and then adjust λ2 once the system meets the control requirements. This complicates controller design.

[0157] Step 5: Use the improved adaptive cuckoo retrieval algorithm to iteratively calculate the weight factors to achieve multi-objective optimization control of the grid-connected inverter.

[0158] After building the predictive model, the cost function is constructed based on the control objective. Then, through rolling optimization, the cost function values corresponding to all switching vectors are traversed, and the switching vector that minimizes the cost function value is converted into a control signal output. The primary control term in the cost function of the model predictive control strategy is the grid current, which must closely follow the given reference value. The secondary control term is the voltage difference between the upper and lower capacitors on the DC side, which must be as close to zero as possible.

[0159] The Cuckoo Search Algorithm is a heuristic optimization algorithm based on foraging behavior, inspired by the breeding behavior of cuckoos. This algorithm has simple parameters and is easy to implement, making it widely used in multi-objective optimization. The details are as follows:

[0160]

[0161] Where, is the position of the i-th nest in the t-th iteration, α is the step scale factor, s is the step size, p a is the probability of discovery, H is the unit step function, ε is a random number drawn from a uniform distribution, is the element-wise multiplication symbol, is the position of the jth nest in the tth iteration, is the position of the kth nest in the tth iteration;

[0162] The present invention improves the traditional cuckoo search algorithm as follows:

[0163] In the iterative process of the cuckoo search algorithm, the population diversity index D is introduced to adaptively adjust the discovery probability P according to the distribution state of the solution. a , to balance global exploration and local development capabilities. When the population diversity is insufficient, increase P a To eliminate similar solutions and promote the generation of new solutions; when diversity is sufficient, reduce P a To retain high-quality solutions and improve convergence efficiency. Specifically:

[0164] Define population diversity indicators:

[0165] Calculate the Euclidean distance variance of the solution in the current population as the population diversity indicator, which is expressed as follows:

[0166]

[0167] Where λ i represents the i-th weight factor combination; λ avg represents the population average weight vector; λ range represents the value range of the weight factor, and N represents the total number of weight factors;

[0168] Adaptively adjust the discovery probability P a The process is expressed as follows:

[0169]

[0170] Where D th represents the diversity threshold; γ d represents the diversity regulator;

[0171] Introduce the attenuation coefficient η(t) and dynamically adjust the discovery probability P together with the number of iterations a , which is expressed as follows:

[0172]

[0173] Where, T max Indicates the maximum number of iterations.

[0174] The introduction of the attenuation coefficient η(t) makes the discovery probability gradually converge with the number of iterations: in the early stage (t is small): a larger adjustment range is allowed to enhance the global search; in the later stage (t is close to T max ): Gradually stabilize P a , improving local optimization accuracy.

[0175] The weight factor is iteratively calculated using the improved cuckoo search algorithm, which includes the following steps:

[0176] Step 5.1: Initialize the number of bird nests, step size, number of iterations, and the initial probability of finding a bird nest P a (0), define the diversity threshold D th , diversity regulator γ d , weight factor range λ range ;

[0177] Step 5.2: Normalize the value function, calculate the fitness value of each individual, and calculate the current population diversity index D(t);

[0178] Step 5.3: Add diversity feedback and adjust the discovery probability P according to D(t) a (t+1), joint iterative decay, applying the decay coefficient η(t) to stabilize the late search;

[0179] Step 5.4: Perform Levy flight on each individual to generate a new solution. If the new solution is better than the previous solution, replace the previous solution and proceed to the next iteration. a (t+1) Randomly eliminate inferior solutions and generate new bird nests;

[0180] Step 5.5: Record the weight factor value of the optimal solution and repeat steps 5.1 to 5.4 until the maximum number of iterations is reached. The maximum number of iterations in the present invention is set to 100.

[0181] Example 1

[0182] The multi-objective optimization control method for a grid-connected inverter based on a cuckoo search algorithm of the present invention specifically comprises the following steps:

[0183] Step 1: Construct a mathematical model of a three-level grid-connected inverter and calculate the inverter-side current reference value;

[0184] Step 2: Build a current prediction model on the inverter side;

[0185] Step 3: Use the cost function in the form of square error to construct the cost function control term of the inverter side current;

[0186] Step 4: Take the midpoint potential balance and switching frequency as control items and construct the cost function;

[0187] Step 5: Use the improved adaptive cuckoo retrieval algorithm to iteratively calculate the weight factors to achieve multi-objective optimization control of the grid-connected inverter.

[0188] Example 2

[0189] Based on Example 1, step 1 specifically includes the following steps:

[0190] Step 1.1: Construct a mathematical model of a three-level grid-connected inverter, which includes the following steps:

[0191] Step 1.1.1: Define the midpoint of the upper and lower capacitors as the zero potential reference point of the inverter output voltage;

[0192] Step 1.1.2: Define a switch function, that is, the switch variable S x ,x=a,b,c, which is expressed as follows:

[0193]

[0194] Where a, b, and c represent phases a, b, and c in a T-type three-level topology.

[0195] Step 1.1.3: Combine the KCL and KVL formulas to derive the inverter output voltage in matrix form, as shown below:

[0196]

[0197] Where u a 、u b 、u c Indicates the output voltage of the inverter, U dc Indicates the bus voltage on the DC side of the inverter;

[0198] Step 1.1.4: In the abc three-phase coordinate system, the relationship between the inverter-side current, the grid-side current, and the filter capacitor C is expressed as follows:

[0199]

[0200] Where i 1a 、i 1b 、i 1c Indicates the output current on the inverter side, i 2a 、i 2b 、i 2c Indicates the output current on the grid side, u ca 、u cb 、u cc Indicates the voltage drop across the filter capacitor;

[0201] Step 1.2: Transform the mathematical model in the abc three-phase coordinate system to the mathematical model in the αβ two-phase coordinate system, specifically:

[0202] In the αβ two-phase coordinate system, the inverter side loop equation is expressed as follows:

[0203]

[0204] Where L1 represents the three-phase equivalent inductance on the inverter side, R1 represents the equivalent resistance on the inverter side, and u αβ represents the output voltage of the inverter in the αβ coordinate system, u cαβ Indicates the voltage drop on the filter capacitor in the αβ coordinate system, i 1αβ represents the output current of the inverter side in the αβ coordinate system;

[0205] The grid side loop equation is expressed as follows:

[0206]

[0207] Where L2 represents the three-phase equivalent inductance on the grid side; R2 represents the equivalent resistance on the grid side, e αβ represents the grid voltage in the αβ coordinate system, i 2αβ represents the output current on the grid side in the αβ two-phase coordinate system;

[0208] The relationship between the inverter-side current, grid-side current and filter capacitor C is as follows:

[0209]

[0210] Step 1.3: Convert equations (4), (5), and (6) into complex vectors in the αβ two-phase coordinate system and integrate them to obtain:

[0211]

[0212] Where, e αβ represents the grid voltage in the αβ two-phase coordinate system;

[0213] The variables in formula (7) in the αβ two-phase coordinate system are Park transformed and rewritten into complex vector form to obtain the mathematical model in the dq rotating coordinate system, which is expressed as:

[0214]

[0215] Where, e dq represents the grid voltage in the dq rotating coordinate system, i 1dq represents the output current of the inverter side in the dq rotating coordinate system, i 2dq represents the output current of the grid side in the dq rotating coordinate system, u cdqrepresents the voltage drop on the filter capacitor in the dq rotating coordinate system, j represents the imaginary unit, and ω represents the angular frequency;

[0216] Without considering the impact of high frequency harmonics under power frequency conditions, i 2dq and u cdq can be regarded as a constant, then the relevant terms in formula (8) are expressed as follows:

[0217]

[0218] According to the grid-connected control requirement that the grid voltage and current are in opposite phase, the grid-side current reference value is set to be the components of the two coordinate axes in the dq rotating coordinate system. Then replace i in formula (8) 2dq Use the set reference value Instead, the reference value of the voltage drop on the filter capacitor is obtained by transposition transformation. and the inverter side current reference value when connected to the grid Expressed as:

[0219]

[0220] Finally, the final inverter side current reference value obtained in formulas (10) and (11) is converted into the reference current value in the αβ two-phase coordinate system through inverse Park transformation. For subsequent analysis and algorithm implementation.

[0221] Example 3

[0222] Based on Example 2, step 2 is specifically as follows:

[0223] Discretize some terms in the inverter measurement loop equation in the αβ two-phase coordinate system and obtain:

[0224]

[0225] The differential term in formula (7) is discretized using the forward difference formula to obtain:

[0226]

[0227] Where i 1αβ (k) represents the sampling value of the inverter side current at time k, i 1αβ (k+1) represents the predicted value of the inverter side current at time k+1;

[0228] Substituting the discretized inverter side current differential term expression (13) into formula (12) yields the fully discretized discrete control model, which is expressed as follows:

[0229]

[0230] The current prediction model of the inverter side is further sorted out and expressed as follows:

[0231]

[0232] Where, T s is the sampling period, u αβ (k) is the output voltage vector of the inverter at time k, u cαβ (k) is the voltage drop on the filter capacitor at time k.

[0233] Example 4

[0234] Based on Example 3, the value function control term of the inverter side current is constructed as follows:

[0235]

[0236] In step 4, the midpoint potential balance is used as a control item, specifically:

[0237] The voltage difference between the upper and lower capacitors on the DC side is used as a control item to control the midpoint potential balance, and the voltage difference between the upper and lower capacitors is set to Δu=u C1 -u C2 ,get:

[0238]

[0239] The forward difference formula is used to discretize the predicted value model of the voltage difference between the upper and lower capacitors on the DC side, which is expressed as follows:

[0240]

[0241] When the three phases are balanced, i la +i lb +i lc =0, simplify formula (18) to express it as follows:

[0242]

[0243] In step 4, the switching frequency is used as the control term, which is expressed as follows:

[0244] f s =|S a (k)-S a (k-1)|+|S b (k)-S b (k-1)|+|S c (k)-S c (k-1)| (20)

[0245] Where, fs Represents the number of times all switching devices of the inverter are turned on and off during the current control cycle.

[0246] In step 4, the cost function constructed is expressed as follows:

[0247] G=g+λ1|Δu(k+1)|+λ2f s (twenty one)

[0248] Where G represents the cost function, λ1 and λ2 represent the weight coefficients of midpoint potential balance and switching frequency constraints, respectively.

[0249] Example 5

[0250] Based on Example 4, the traditional cuckoo search algorithm is expressed as follows:

[0251]

[0252] Where, is the position of the i-th nest in the t-th iteration, α is the step scale factor, s is the step size, p a is the probability of discovery, H is the unit step function, ε is a random number drawn from a uniform distribution, is the element-wise multiplication symbol, is the position of the jth nest in the tth iteration, is the position of the kth nest in the tth iteration;

[0253] The improvements to the traditional cuckoo search algorithm are as follows:

[0254] In the iterative process of the cuckoo search algorithm, the population diversity index D is introduced to adaptively adjust the discovery probability P according to the distribution state of the solution. a , to balance global exploration and local development capabilities, specifically:

[0255] Define population diversity indicators:

[0256] Calculate the Euclidean distance variance of the solution in the current population as the population diversity indicator, which is expressed as follows:

[0257]

[0258] Where λ i represents the i-th weight factor combination; λ avg represents the population average weight vector; λ range represents the value range of the weight factor, and N represents the total number of weight factors;

[0259] Adaptively adjust the discovery probability P a The process is expressed as follows:

[0260]

[0261] Where D th represents the diversity threshold; γ d represents the diversity regulator;

[0262] Introduce the attenuation coefficient η(t) and dynamically adjust the discovery probability P together with the number of iterations a , which is expressed as follows:

[0263]

[0264] Where, T max Indicates the maximum number of iterations.

[0265] Example 6

[0266] Based on Example 5, step 5 is specifically as follows:

[0267] Step 5.1: Initialize the number of bird nests, step size, number of iterations, and the initial probability of finding a bird nest P a (0), define the diversity threshold D th , diversity regulator γ d , weight factor range λ range ;

[0268] Step 5.2: Normalize the value function, calculate the fitness value of each individual, and calculate the current population diversity index D(t);

[0269] Step 5.3: Add diversity feedback and adjust the discovery probability P according to D(t) a (t+1), joint iterative decay, applying the decay coefficient η(t) to stabilize the late search;

[0270] Step 5.4: Perform Levy flight on each individual to generate a new solution. If the new solution is better than the previous solution, replace the previous solution and proceed to the next iteration. a (t+1) Randomly eliminate inferior solutions and generate new bird nests;

[0271] Step 5.5: Record the weight factor value of the optimal solution and repeat steps 5.1 to 5.4 until the maximum number of iterations is reached. The maximum number of iterations in the present invention is set to 100.

Claims

1. A multi-objective optimization control method for grid-connected inverters based on a cuckoo search algorithm, characterized in that: The specific steps include: Step 1: Construct a mathematical model of a three-level grid-connected inverter and calculate the inverter-side current reference value; Step 2: Build a current prediction model on the inverter side; Step 3: Use the cost function in the form of square error to construct the cost function control term of the inverter side current; Step 4: Take the midpoint potential balance and switching frequency as control items and construct the cost function; Step 5: Use the improved adaptive cuckoo retrieval algorithm to iteratively calculate the weight factors to achieve multi-objective optimization control of the grid-connected inverter.

2. The multi-objective optimization control method for grid-connected inverters based on the cuckoo search algorithm according to claim 1, characterized in that: Step 1 specifically includes the following steps: Step 1.1: Construct a mathematical model of a three-level grid-connected inverter, which includes the following steps: Step 1.1.1: Define the midpoint of the upper and lower capacitors as the zero potential reference point of the inverter output voltage; Step 1.1.2: Define a switch function, that is, the switch variable S x ,x=a,b,c, which is expressed as follows: Where a, b, and c represent phases a, b, and c in a T-type three-level topology. Step 1.1.3: Combine the KCL and KVL formulas to derive the inverter output voltage in matrix form, as shown below: Where u a 、u b 、u c Indicates the output voltage of the inverter, U dc Indicates the bus voltage on the DC side of the inverter; Step 1.1.4: In the abc three-phase coordinate system, the relationship between the inverter-side current, the grid-side current, and the filter capacitor C is expressed as follows: Where i 1a 、i 1b 、i 1c Indicates the output current on the inverter side, i 2a 、i 2b 、i 2c Indicates the output current on the grid side, u ca 、u cb 、u cc Indicates the voltage drop across the filter capacitor; Step 1.2: Transform the mathematical model in the abc three-phase coordinate system to the mathematical model in the αβ two-phase coordinate system, specifically: In the αβ two-phase coordinate system, the inverter side loop equation is expressed as follows: Where L1 represents the three-phase equivalent inductance on the inverter side, R1 represents the equivalent resistance on the inverter side, and u αβ represents the output voltage of the inverter in the αβ coordinate system, u cαβ Indicates the voltage drop on the filter capacitor in the αβ coordinate system, i 1αβ represents the output current of the inverter side in the αβ coordinate system; The grid side loop equation is expressed as follows: Where L2 represents the three-phase equivalent inductance on the grid side; R2 represents the equivalent resistance on the grid side, e αβ represents the grid voltage in the αβ coordinate system, i 2αβ represents the output current on the grid side in the αβ two-phase coordinate system; The relationship between the inverter-side current, grid-side current and filter capacitor C is as follows: Step 1.3: Convert equations (4), (5), and (6) into complex vectors in the αβ two-phase coordinate system and integrate them to obtain: Where, e αβ represents the grid voltage in the αβ two-phase coordinate system; The variables in formula (7) in the αβ two-phase coordinate system are Park transformed and rewritten into complex vector form to obtain the mathematical model in the dq rotating coordinate system, which is expressed as: Where, e dq represents the grid voltage in the dq rotating coordinate system, i 1dq represents the output current of the inverter side in the dq rotating coordinate system, i 2dq represents the output current of the grid side in the dq rotating coordinate system, u cdq represents the voltage drop on the filter capacitor in the dq rotating coordinate system, j represents the imaginary unit, and ω represents the angular frequency; Without considering the impact of high frequency harmonics under power frequency conditions, i 2dq and u cdq can be regarded as a constant, then the relevant terms in formula (8) are expressed as follows: According to the grid-connected control requirement that the grid voltage and current are in opposite phase, the grid-side current reference value is set to be the components of the two coordinate axes in the dq rotating coordinate system. Then replace i in formula (8) 2dq Use the set reference value Instead, the reference value of the voltage drop on the filter capacitor is obtained by transposition transformation. and the inverter side current reference value when connected to the grid Expressed as: Finally, the final inverter side current reference value obtained in formulas (10) and (11) is converted into the reference current value in the αβ two-phase coordinate system through inverse Park transformation. For subsequent analysis and algorithm implementation.

3. The multi-objective optimization control method for grid-connected inverter based on cuckoo search algorithm according to claim 2, characterized in that: Step 2 is as follows: Discretize some terms in the inverter measurement loop equation in the αβ two-phase coordinate system and obtain: The differential term in formula (7) is discretized using the forward difference formula to obtain: Where i 1αβ (k) represents the sampling value of the inverter side current at time k, i 1αβ (k+1) represents the predicted value of the inverter side current at time k+1; Substituting the discretized inverter side current differential term expression (13) into formula (12) yields the fully discretized discrete control model, which is expressed as follows: The current prediction model of the inverter side is further sorted out and expressed as follows: Where, T s is the sampling period, u αβ (k) is the output voltage vector of the inverter at time k, u cαβ (k) is the voltage drop on the filter capacitor at time k.

4. The multi-objective optimization control method for grid-connected inverter based on cuckoo search algorithm according to claim 3, characterized in that: The value function control term of the inverter side current constructed in step 3 is expressed as follows:

5. The multi-objective optimization control method for grid-connected inverter based on cuckoo search algorithm according to claim 4, characterized in that: In step 4, the midpoint potential balance is used as a control item, specifically: The voltage difference between the upper and lower capacitors on the DC side is used as a control item to control the midpoint potential balance, and the voltage difference between the upper and lower capacitors is set to Δu=u C1 -u C2 ,get: The forward difference formula is used to discretize the predicted value model of the voltage difference between the upper and lower capacitors on the DC side, which is expressed as follows: When the three phases are balanced, i la +i lb +i lc =0, simplify formula (18) to express it as follows:

6. The multi-objective optimization control method for grid-connected inverter based on cuckoo search algorithm according to claim 5, characterized in that: In step 4, the switching frequency is used as the control term, which is expressed as follows: f s =|S a (k)-S a (k-1)|+|S b (k)-S b (k-1)|+|S c (k)-S c (k-1)| (20) Where, f s Represents the number of times all switching devices of the inverter are turned on and off during the current control cycle.

7. The multi-objective optimization control method for grid-connected inverter based on cuckoo search algorithm according to claim 6, characterized in that: In step 4, the cost function constructed is expressed as follows: G=g+λ1|Δu(k+1)|+λ2f s (21) Where G represents the cost function, λ1 and λ2 represent the weight coefficients of midpoint potential balance and switching frequency constraints, respectively.

8. The multi-objective optimization control method for grid-connected inverter based on cuckoo search algorithm according to claim 7, characterized in that: In step 5, the traditional cuckoo search algorithm is expressed as follows: Where, is the position of the i-th nest in the t-th iteration, α is the step scale factor, s is the step size, p a is the probability of discovery, H is the unit step function, ε is a random number drawn from a uniform distribution, is the element-wise multiplication symbol, is the position of the jth nest in the tth iteration, is the position of the kth nest in the tth iteration; The improvements to the traditional cuckoo search algorithm are as follows: In the iterative process of the cuckoo search algorithm, the population diversity index D is introduced to adaptively adjust the discovery probability P according to the distribution state of the solution. a , to balance global exploration and local development capabilities, specifically: Define population diversity indicators: Calculate the Euclidean distance variance of the solution in the current population as the population diversity indicator, which is expressed as follows: Where λ i represents the i-th weight factor combination; λ avg represents the population average weight vector; λ range represents the value range of the weight factor, and N represents the total number of weight factors; Adaptively adjust the discovery probability P a The process is expressed as follows: Where D th represents the diversity threshold; γ d represents the diversity regulator; Introduce the attenuation coefficient η(t) and dynamically adjust the discovery probability P together with the number of iterations a , which is expressed as follows: Where, T max Indicates the maximum number of iterations.

9. The multi-objective optimization control method for grid-connected inverter based on cuckoo search algorithm according to claim 8, characterized in that: Step 5 is as follows: Step 5.1: Initialize the number of bird nests, step size, number of iterations, and the initial probability of finding a bird nest P a (0), define the diversity threshold D th , diversity regulator γ d , weight factor range λ range ; Step 5.2: Normalize the value function, calculate the fitness value of each individual, and calculate the current population diversity index D(t); Step 5.3: Add diversity feedback and adjust the discovery probability P according to D(t) a (t+1), joint iterative decay, applying the decay coefficient η(t) to stabilize the late search; Step 5.4: Perform Levy flight on each individual to generate a new solution. If the new solution is better than the previous solution, replace the previous solution and proceed to the next iteration. a (t+1) Randomly eliminate inferior solutions and generate new bird nests; Step 5.5: Record the weight factor value under the optimal solution and repeat steps 5.1 to 5.4 until the maximum number of iterations is reached.

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