A Differential Evolution Based Adaptive Neural Network Pitch Controller for a Doubly Fed Wind Turbine Generator System

Extraction of maximum energy from wind and transferring it to the grid with high efficiency are challenging problems. To this end, this study proposes a smart pitch controller for a wind turbine-doubly fed induction generator system using a Differential Evolution (DE) based adaptive neural network. The nominal weights for the back-propagation neural network controller are obtained from input-output training data generated by DE optimization method. These weights are then adaptively updated in time domain depending on the variation of the system outputs. The adaptive control strategy has been tested through simulation of complete system dynamics comprising of the turbine-generator system and its various components. It has been observed that the DE based smart pitch controller is able to achieve efficient energy transfer to the grid and at the same time provide a good damping profile. Locally collected wind data was used in the testing phase.


INTRODUCTION
Most modern wind turbines used in utility are the variable speed Doubly Fed Induction Generator (DFIG) or Permanent Magnet Synchronous Generator (PMSG) types. Although costly power electronics are required to convert power at varying frequency, the variable speed wind turbines are industry favorite because of their better energy capture capability, operation at higher efficiency and lower loading (Muljadi and Butterfield, 2001). When compared with the synchronous generator type, the DFIG wind turbine have additional advantage in terms of reduced converter losses, independent real and reactive power control, grid support through reactive control etc. (Lin et al., 2011a) The utility-scale turbines generally have three levels of control, the uppermost is supervisory control, mid-level turbine control and in the lowest level are the pitch actuator control, the generator and power electronics control (Johnson et al., 2006).
A major disadvantage of the induction type wind generators is their sensitivity to low voltage conditions at the grid. Fault ride of DFIG is a matter of intense research in the recent times. Various types of controls on the converter system have been attempted by several investigators. Reference (Vinothkumar and Selvan, 2011) presents an interesting strategy of low voltage ride using a circuit comprising of a rectifier and IGBT in the rotor side converter and inductor in parallel with it. Voltage source inverter with current controller was employed by Muyeen et al. (2011) for fault ride through. Hybrid current controllers in the converter circuit has been used for improving fault ride through capabilities which comprises of a standard PI controller in addition to hysteresis current controller (Mohseni et al., 2011). A voltage source converter connected between the generator and grid, termed a voltage restorer and a virtual resistance deactivating the normal crowbar has been employed for riding low voltages (Ibrahim et al., 2011;Hu et al., 2011). Use of FACTS (flexible ac transmission system) and energy storage devices which supply both real and reactive power have the additional advantage that they also provide damping to the system during the low voltage recovery. The devices which have been used to enhance the wind system performance vary from simple static VAR controller (Amaris and Alonso, 2011), battery energy storage (Mendis et al., 2012), supercapacitor with STATCOM (Qu and Qiao, 2011;Rahim and Nowicki, 2012), etc. Superconducting magnetic energy storage (SMES) units can be controlled to supply both real and reactive power and are shown to be effective in terms of leveling wind power fluctuations as well as low voltage ride through (Shi et al., 2011;Yunus et al., 2012).
The inertia of the turbine-generator rotor is large and hence the rotor speed control is relatively slow. The doubly fed generator based wind plants do not have good frequency response characteristics because of lack of coupling between grid frequency and output power. Also, the DFIG does not have reserve margin in maximum power tracking (Zhang et al., 2012). Since pitch control is relatively faster the aerodynamic power can be regulated to limit rotor speed (Muljadi and Butterfield, 2001). Generally, nonlinear strategies are involved for power maximization and also for frequency regulation analysis (Moutis et al., 2012). A PI (proportional integral) controller has been used for generator and pitch actuators using small-signal analysis in Riziotis et al. (2008). Maximum energy capture using PI and fuzzy logic controllers were proposed in Kamel et al. (2011) and Lin et al. (2011b). Reference (Kamel et al., 2011) uses PI controllers in battery storage system, while (Lin et al., 2011b) employs a fuzzy interface to estimate the wind speed fluctuations. Applications of intelligent techniques for maximizing energy capture have been reported in the literature in recent times. Pitch control to regulate the output power of squirrel cage type wind generator through neural network was reported in Yilmaz and Ozer (2009). The output power leveling by generalized pitch control has been used in Senjyu et al. (2006). Also, artificial neural network has been employed for achieving fast and stable response for a stand-alone hybrid system (Lin et al., 2011c).
Generally, in aerodynamic modeling and pitch control studies the relatively slower rotor dynamics is considered. Since the generator wheels the energy, its dynamics should be adequately modeled. Also, because of random nature of wind variation, the any control design should include the system nonlinearities. This makes the pitch controller design difficult. In this study a smart pitch control strategy for a turbine-generator system is obtained in time domain by using an adaptive Back-Propagation (BP) neural network. The backpropagation network is used because it is known that a three layered BP can approximate any nonlinear function under any precision (Xu et al., 2012). The starting weights for the back-propagation network are obtained through an optimum evolutionary algorithm.

SYSTEM MODEL
A block diagram of the wind turbine-generator is given in Fig. 1. The converter circuitry of the doubly fed induction generator (DFIG) is located between the generator stator and rotor terminals. The grid connects to the stator through transformer and line. A local load is located at the generator terminal bus. The turbine has a pitch control system shown in the block diagram. The system model includes the turbine dynamics and its pitch controller, the DFIG and converter circuitry, the line and the load.
The relationships between the flux linkages and currents of the stator and rotor circuits are: The slip (s) of the machine given in the above The input current to the converter on the grid side, written in terms of d-q components, is Rahim and Habiballah (2011): Here, I a = i da +ji qa , V s = v ds +jv qs and E a = e da +je qa , ω 0 is the base frequency. The DC ink capacitor is located between the two back to back converters. Neglecting the power loss in the capacitor, the power balance yields the following capacitor voltage equation: The modulation index and phase angle of the two converter voltages on grid and rotor sides, Aerodynamics and drive model: The rotor drive train model for the turbine-generator system in terms of torsional angle between the two masses and their speed are expressed as: The mechanical input power, which is the turbine output, is: Here, V w , γ, λ, C p , α are the wind velocity, tip speed ratio, density of air, power coefficient and pitch angle, respectively. C p depends ߣ and α through the highly non-linear relationship: The electrical power output term in (7) is given as: Plot of the turbine power output against generator speed for wind speed of 12m/s is given in Fig. 2 for different pitch angles.
Pitch controller: Figure 3 presents the block diagram of the pitch controller system. The pitch controller is actuated between the reference and actual output of the generator. From (8) and (9) it can be seen that the input power to the generator can be controlled through control of pitch angle α. The blade pitch angle depends on control of the pitch servos. The pitch servo system model includes a rate limiter, an angle limiter, delay elements, etc. Conventionally a pitch angle control system uses PI controllers to generate the appropriate α. While a more detailed servo modeling may be used, a first order servo system is sufficient in investigations of power system studies. In this study, all the components in the pitch control and servo system are included in the parameters of the PI controller, dynamic relationships of which are: Here, K P and K I are the controller gains to be determined; ∆P is the input to the controller and α is the pitch angle.
The composite model of the turbine-generator system which includes the pitch control device is expressed through the state model: [ , ] [ , ] x f x u y g x u The input u represents the pitch controller gains and y is the vector of selected output variables.

ADAPTIVE BPNN BASED PITCH CONTROLLER
A block diagram of the adaptive back-propagation neural network (BPNN) based pitch controller proposed in this work is shown in Fig. 4. The core of the controller consists of two BP networks, one which produces the nominal weight and nominal control (u nom ) through training of a large input-output data set. This part of the controller guarantees a stable nominal bounded-input bounded output system (Suresh, 2009). The other BP network is responsible to modify the network weights in time domain depending on the wind system transients and generates control ∆u. The pitch controller gains are adaptively tuned as ∆u changes. A differential evolution (DE) optimization technique is employed to create the input-output data for training the nominal BPNN network.
The DE optimization procedure, the back-propagation and adaptive backpropagation methods are presented briefly in the following.

Differential evolution:
In training the neural network the objective function used is, generally, multimodal. The gradient technique based algorithms for such problems may end up producing a local minimum. This can be avoided by employing a global optimization procedure based on evolutionary methods. Differential Evolution (DE) is such a procedure suitable for finding global minimum (Slowik, 2011). Although initially used for a single objective function, it has the capability of handling multi-objective functions and equality as well as inequality constraints (Qin et al., 2010). The major steps in a DE algorithm are mutation, crossover and selection of the population. The final retention is through a check of fitness on the population. The steps in the search for the pitch control parameters are summarized below (Lu et al., 2011). The various steps involved in the evolutionary progression are given below: • Initialization: In this step, it is required to specify the number of control variables or problem dimension with their corresponding constraints. For each control parameter, a population is generated within the search space using the relationship: In the above, N P is total number population and N G is the number of generations.

• Evaluation and location of the best solution:
The best solution among the initial population is obtained from the objective function: Here, ζ k is the damping ratio calculated from dominant eigenvalues of the linearized system obtained from (12) for each population k and ζ 0 is the desired damping ratio. The objective function in (14) is minimized to provide the optimal solution satisfying all the constraints.
• Mutation: The mutation process aims to produce a new generation of solutions. For every individual k, we build a donor vector V k from three random solutions Z r1 , z r2 and Z r3 among the population. The difference of any two solutions is added to the third through a mutation factor F given by the relation: The limit violation in the mutant vector is checked through (14): • Crossover: This is employed to have a second generation to enhance the diversity employing a binomial type crossover given by: CR represents the crossover factor.
• Selection: The selection process in DE involves determining survivor of a generation by comparing the trial vector with the parents based on fitness in terms of objective value (14): • Stopping criteria: The procedure is continued until a solution is reached within pre-specified precision or the maximum number of iteration is exceeded.
Back propagation neural network: Artificial neural networks are parallel and distributed information systems which are used to learn complex systems and generalize the information learned. The massive networks comprise of simple neurons and consist of interconnected elements called nodes. The Back-Propagation Neural Network (BPNN) considered in Fig. 4 has three layers-the Input (I), Hidden (H) and output (O) layer. The hidden layer comprises of L-1 sub-layers, the input layer being numbered 0 and output layer L. The data is transferred from input to the output node through the weight linked hidden neurons using an activation function. The activation function considered is a sigmoid having the characteristic: The back-propagation algorithm minimizes the error function E written as: Od j is the desired output corresponding to j th neuron and k represents the iteration count. The change in weight between the i th and j th node is computed by using the gradient descent and is written as: The gradient term can be evaluated through a chain rule and the recursive relationship for the weight updates can be shown to be (Lee, 2008): The computation is accelerated through the momentum constant α M is the learning rate parameter η 1 . Note that for i = 0, the weight w 0j corresponds to the bias at layer l j and H j (L) = O j . The back propagation algorithm has two different computational directions. In the forward direction the weights remain unchanged and the signals are computed at different nodes. The weights are updated in the backward pass from the error signal propagated backwards.

Adaptive back-propagation neural network:
The back-propagation network is trained through a large input-output data set which, in turn, is generated by DE algorithm. The trained weights are then used to calculate the nominal value of controller parameters (u nom ) for a certain operating condition. Depending on the variation of system outputs from their desired values, the control parameters are updated as time advances according to the relation: The weight adaptation process is carried out by minimizing the mean square error E c (t) at each instant of time expressed as: Here, y(t) is the output vector given in (12) and r(t) is the desired output. The gradient descent method gives the change in weight: The weight update is obtained by adding the change with the nominal value generated by training the input-output data set and is finally expressed by: The expression for γ j is similar to that given in (22). The output can be found from (12) or from online measurements. The nominal values of w ij are assumed to remain constant during the process time.

TESTING THE ADAPTIVE PITCH CONTROLLER
The proposed adaptive pitch controller strategy was tested on the turbine-generator system of Fig. 1. The ability of the pitch control strategy to transfer the wind power under varying wind speed condition was investigated considering different wind speed conditions. The nominal power output of the DFIG at a speed of 12 m/s is 0.9 pu. The parameter values of the various components are included in the Appendix. The nominal gains of the pitch controller are considered as K P = 1, K I = 0. Responses with two types of wind speed variation are reported here -a step change of wind speed and random speed change as recorded at a local site. Figure 5 to 7 show the plots of various responses for a step change in wind speed from 12 m/s to 11 m/s. The speed change is affected at t = 1s. In the absence of pitch control the wind power output at the new speed is 0.82 pu. Figure 5 shows the power input to the generator (solid line) and power output with and without adaptive pitch controller (dotted and dashed    damping profile. Figure 8 shows the variation of the controller gains during the adaptation period. Note that it is the variation of these parameters which contribute to the improved system performance. Figure 9 shows the wind speed data recorded at the local wind generator station for a period of 1000s. The actual wind data has been normalized and scaled around a nominal value of 11 m/s. The transient responses shown in Fig. 10 to 14 are for the interval of 1s to 10s of the record of Fig. 9, wind speed kept constant at 11m/s for the first 1s. A comparison of the power input to the generator (wind power), electrical power output with the proposed adaptive pitch control and also with nominal pitch control is presented in Fig. 10. From the response it can be seen that pitch controller makes the generator output track the wind power very well. Records of generator output power, speed and stator current, shown in Fig. 10 to 12, show that the adaptive control is very effective in damping the electrical transients even for this randomly varying wind speed changes. Figure 13 shows the variation of the controller gains over the 10s period. Figure 14 shows the variation of the pitch angle during this period. It can be observed that the pitch angle change is not large during the transient period.

CONCLUSION
This study proposes a novel adaptive pitch controller for a wind turbine-DFIG system for transferring wind power to the grid efficiently. Contrary to conventional offline neural network designs, the proposed controller adapts the network weights in time domain depending on system transients. In normal maximum power transfer problems only the turbine generator rotor dynamics is considered, while this study incorporates a detailed model of the generator and its converter circuitry along with the turbine aerodynamics. The simulation results show that the neural network based pitch controller enables the electric power to follows the mechanical power closely by varying the blade pitch angle adaptively. This is achieved with minimum transients in the generator system. The differential evolution technique used in training the neural network is an efficient method to find the global minimum. The proposed adaptive back-propagation algorithm is computationally simple.