Research on dynamic PI parameter tuning of double-fed wind turbine based on ant colony algorithm

Considering the drawbacks of flexible adjustment of PI controller control parameters in the constant pressure control system of doubly fed fans, a PI controller control parameter flexible adjustment method considering ant colony optimization algorithm (ACO) is proposed. This method uses the proportional coefficient and integration time parameters in the PI controller as the ants in the ant colony optimization algorithm, and the ultimate optimization goal is to control the absolute error integration function. During the control process, the parameters of the PI controller are dynamically adjusted. When the electrified wire netting IR-drop and wind velocity changes, a comparative analysis of the dynamic tuning PI controller parameters and the non-dynamic tuning method was conducted. At last, the simulation studies have shown that the constant voltage control system using the PI parameter Flexible adjustment control method found on ACO can rapidly improve the grid voltage stability of double-fed wind turbines and reduce response time.


Introduction
At present, the main clean energy sources that are vigorously developing are wind energy and photovoltaic.Especially in today's increasingly serious global energy problems, considering some of the drawbacks of photovoltaic, how to efficiently utilize wind energy is increasingly receiving attention from scholars [1][2].The size of wind power generation power is mainly affected by wind speed and weather.Considering the characteristics of wind power generation and the instability of output power, its grid connection will seriously affect the safe operation of the power grid.Especially in areas with a high proportion of wind power grid connection, changes in grid connection voltage can have serious consequences for the safe operation of the power grid [3] .Therefore, when wind power is connected to the grid, the voltage fluctuation range of the grid connection point should be controlled within a certain range.
The double-fed generator unit has independent and flexible reactive power regulation capabilities, which can be used to control the grid-connected voltage of the double-fed wind farm [4][5] .The doubly fed power generation unit mainly operates in two modes: constant power factor and constant voltage control.The control mode that can provide stable support for grid voltage is the constant voltage control mode [6][7] .However, in recent years, although many experts in the wind power field have conducted in-depth research on PI controllers for constant voltage control systems, the research direction is how to obtain the optimal PI parameter values [8] .However, there is relatively little research on how to flexibly adjust the parameters of PI controllers in the context of wind velocity changes and fluctuations in the power grid.
Based on the existing research on constant voltage control technology for doubly fed wind turbine, this article proposes a dynamic parameter tuning strategy for PI controllers found on ACO.The method uses the two-argument of the PI controller as ants in the ant colony, and adopts the control absolute error integral function as the optimization objective.During the control process, the arguments of the PI regulator are dynamically adjusted, and a comparative analysis is conducted between dynamically tuned PI parameters and non-dynamically tuned parameters under two states: wind speed variation and grid voltage drop.

Selection of path points in ant colony algorithm
Let the ant colony move to line segment   at time t, the number of ants at node j a at time t is  ( = 0~8) ,m = ∑   () From the above equation, it can be seen thatα is the Info inspire factor, indicating that the greater the accumulated information during the ant colony movement, the greater the probability of the ant colony choosing the path it has traveled.β is the expected heuristic factor, and its value plays an important role in ant colony optimization.δ(  ,  , t) is the heuristic function on node kont(  ,  , , j), that is, In equation ( 2), , * ( = 1~5,  = 0~8) is taken as follows.When the ant colony first traverses the path,  , * is the initial PI controller parameter 0 , and  0 represents the values of the corresponding ordinates of each node mapped on the weighted graph.In each subsequent path traversal,  , * is the PI controller parameter   * in the optimal path obtained during the last iterationand the value of   * is mapped to the corresponding ordinate value of each point on the weight graph.
To avoid the overabundance of residual pheromone causing the residual information to overwhelm the inspired information, after every ant completes the first path traversal, it must update the pheromones on the nodes in the traversed path.Therefore, the information amount of node kont(  ,  , ) at time t+n is as follows: In the above equation, ρ is the pheromone volatilization factor, which shows the pheromone remain factor 1 − ρ.To maintain a reasonable range of pheromones, the size of this value ρ is ρ ∈ [0,1).∆τ(  ,  , , t)is to add pheromones to node kont(  ,  , ) during this path traversal.Among them, the value of the pheromone left by the k-th ant on node kont(  ,  , ) during this path traversal is ∆τ(  ,  , ) ∆τ(  ,  , ) = {    ,   kont(  ,  , ) 0,  −   kont(  ,  , ) (5) In the above equation, the value of pheromone intensity is Q, which is the total amount of pheromones released on the ant traversal path.The larger Q, the faster the ant accumulates pheromone on the path it has already traversed, which helps accelerate convergence.The target value of the k-th ant in this path traversal is Fk.

Steps for optimizing PI parameters using ACO
From the above analysis, it can be seen that the steps for optimizing PI parameters using ACO are as follows: 1) Calculate the parameters Kp0 and Ki0 of the PI controller mentioned above using the Ziegler Nichols method; 2) Let the total number of ants m in the algorithm and assign a one-dimensional group Pathk to each ant k(k=1~m)., which has 6 elements.The array Pathk is used to record the ordinate values of ants passing through nodes.This value represents the path of ants crawling; 3) All ants are at the starting point O, and then define the values for each initialization.t represents timing, N represents the number of cycles, Ncmax represents the maximum number of cycles, and c represents the amount of node information at the starting time; 4) Let the value of variable i in the above equation be 1; 5) Firstly, calculate the probability of ants transitioning on each node according to formula (1).Then, select the next node for each ant based on the calculated result, and place the calculated value of the node in the corresponding i -th element in Pathk; 6) Start the loop calculation, increasing by 1 for each iteration.If the number of iterations is not greater than 6, return to step 4. If it is greater than 6, directly skip to step 7.
7) Calculate the two key parameters    and    based on the array Pathk and formula, and store the results in the corresponding positions.
8) Let t ← t + 6,  ←   + 1, update the amount of information on each node in the light of formulas (3) to (5), and clear all elements in Pathk to zero; 9) During the calculation process, the number of cycles of the entire ant colony is less than the set maximum number of cycles.If the path of the ant colony does not converge, it needs to be adjusted to step 4 and recalculated; If the path of the ant colony converges, two optimal parameters   * and   * are output.

Simulation analysis
Based on the above theoretical construction of the model, the capacity of the wind turbine unit in the model is set to 1.5MW, the terminal voltage is 575V, and then it rises to 25kV.After passing through a 30km transmission line, the voltage is raised to 120kV through a secondary step-up transformer, and then connected to the grid for power supply; In the constructed model, the reference voltage at the fan outlet remains unchanged at 1pu.This article will use the ant colony optimization algorithm model to analyze the PI parameter control when wind speed changes and voltage drop occurs in the 120kV power grid.The values of algorithm parameters are shown in Table 1: As shown in Figure 1, the dynamic change diagram of the rotor shaft current at a certain moment when the wind speed increases from 8m/s to 10m/s.The blue line represents the dynamic overall parameters of the ACO, with values of   = 5.45 and   = 404;, The red dashed line represents the traditional PI control algorithm, with values of   = 1.24 and   = 301.From the simulation calculation results in Figure 1, it can be seen that at a certain moment, during the process of wind speed change, compared with traditional control algorithms, the dynamic tuning of PI parameters founded on ACO advances the response time of rotor shaft current by 7.46 seconds.From the simulation calculation results in Figure 2, it can be seen that at a certain moment, during the process of wind speed change, compared with traditional control algorithms, the response time of the PI parameter dynamic tuning of the terminal voltage Us founded on ACO is seconds earlier.
As shown in Figure 3, at a certain moment, the voltage of the party power grid drops by 0.   The simulation results show that at t=5s, during the process of voltage drop of 0.1pu, compared with traditional control algorithms, the dynamic tuning of PI parameters founded on ACO improves the dynamic response characteristics of rotor d-axis current Idr and reduces the response time.
At a certain moment，Figure 4   The simulation results show that when t=5s, during the process of grid voltage drop of 0.1pu, compared with the traditional control algorithms, the dynamic tuning of PI parameters founded on ACO improves the dynamic response characteristics of the terminal voltage Us of the double-fed wind turbine unit, and reduces the response time.

Conclusion
his article proposes a flexible adjustment method for PI controller parameters founded on ACO to solve the problem of PI parameters being unable to be flexibly adjusted in the constant pressure control system of doubly fed fans.This article compares and analyzes the dynamic and non dynamic adjustment of the parameters of the PI controller under the conditions of wind speed changes and voltage drops.The simulation results show that the algorithm proposed in this paper can improve the stability of grid connected voltage and compress the corresponding time

Figure 1
Figure 1 Dynamic change diagram of Idr when wind speed changes from 8m/s to 10m/s.

Figure 2
is a dynamic variation diagram of the terminal voltage Us of a double-fed wind turbine unit when the wind speed increases from 8m/s to 10m/s.The bule line represents the dynamic overall parameters of the ACO, with values of   = 5.46 and   = 405; The red dashed line represents the traditional PI control algorithm, with values of   = 1.25 and   = 300.

Figure 2
Figure 2 Dynamic change diagram of Us when wind speed changes from 8m/s to 10m/s.
1 pu, and the dynamic change diagram of the rotor shaft current is shown.The blue line represents the dynamic overall parameters of the ACO, with values of   = 1.35 and   = 152.The red dashed line represents the traditional PI control algorithm, with values of   = 1.24 and   = 301.

Figure 3
Figure 3 Dynamic change diagram of Idr when the grid voltage drops by 0.1 pu.
is a dynamic variation diagram of the terminal voltage Us of the double-fed wind turbine unit when the grid voltage drops by 0.1 pu; The blue line represents the dynamic overall parameters of the ant colony optimization algorithm, with values of   = 1.35 and   = 152.The red dashed line represents the traditional PI control algorithm, with values of   = 1.24 and   = 301.

Figure 4
Figure 4 Dynamic change diagram of Us when the grid voltage drops by 0.1 pu.

Table 1
The values of each parameter in the ACO