NEURAL NETWORK BASED MAXIMUM POWER POINT TRACKING

Transcription

1 NEURAL NETWORK BASED MAXIMUM POWER POINT TRACKING 3.1 Introduction This chapter introduces concept of neural networks, it also deals with a novel approach to track the maximum power continuously from PV array using neural networks. A MPPT control algorithm is trained using neural networks and the simulation results are presented. 3.2 Introduction about neural networks What are Neural Networks? Neural Networks (NNs) are networks of neurons, for example, as found in real (i.e. biological) brains. Artificial Neurons are crude approximations of the neurons found in brains. They may be physical devices, or purely mathematical constructs. Artificial Neural Networks (ANNs) are networks of Artificial Neurons, and hence constitute crude approximations to parts of real brains. They may be physical devices, or simulated on conventional computers. From a practical point of view, an ANN is just a parallel computational system consisting of many simple processing elements connected together in a specific way in order to perform a particular task. One should never lose sight of how crude the approximations are, and how over-simplified our ANNs are compared to real brains. Why are Artificial Neural Networks worth studying? They are extremely powerful computational devices (universal computers). Massive parallelism makes them very efficient They can learn and generalize from training data so there is no need for enormous feats of programming. 30

2 They are particularly fault tolerant this is equivalent to the graceful degradation found in biological systems. They are very noise tolerant so they can cope with situations where normal symbolic systems would have difficulty. In principle, they can do anything a symbolic/logic system can do, and more. (In practice, getting them to do it can be rather difficult ). What are Artificial Neural Networks used for? As with the field of AI in general, there are two basic goals for neural network research: Brain modeling: The scientific goal of building models of how real brains work. This can potentially help us understand the nature of human intelligence, formulate better teaching strategies, or better remedial actions for brain damaged patients. Artificial System Building: The engineering goal of building efficient systems for real world applications. This may make machines more powerful, relieve humans of tedious tasks, and may even improve upon human performance. These should not be thought of as competing goals. We often use exactly the same networks and techniques for both. Frequently progress is made when the two approaches are allowed to feed into each other. There are fundamental differences though, e.g. the need for biological plausibility in brain modeling, and the need for computational efficiency in artificial system building. 3.3 A framework for distributed representation An artificial neural network consists of a pool of simple processing units which communicate by sending signals to each other over a large number of weighted connections. A set of major aspects of a parallel distributed model can be distinguished as follows: A set of processing units ('neurons,' 'cells'); A state of activation y k for every unit, which is equivalent to the output of the unit; Connections between the units. Generally each connection is defined by a weight w jk which determines the effect which the signal of unit j has on unit k; 31

3 A propagation rule, which determines the effective input s k of a unit from its external inputs; An activation function F k, which determines the new level of activation based on the effective input s k (t) and the current activation y k (t) (i.e., the update); An external input (bias, offset) θ k for each unit; A method for information gathering (the learning rule); An environment within which the system must operate, providing input signals andif necessary-error signals. Figure 3.1 illustrates these basics, some of which will be discussed in the next sections Processing units Fig. 3.1: The basic components of an artificial neural network Each unit performs a relatively simple job: receive input from neighbours or external sources and use this to compute an output signal which is propagated to other units. Apart from this processing, a second task is the adjustment of the weights. The system is inherently parallel in the sense that many units can carry out their computations at the same time. Within neural systems it is useful to distinguish three types of units: input units which receive data from outside the neural network, output units which send data out of the neural network, and hidden units whose input and output signals remain within the neural network. 32

4 During operation, units can be updated either synchronously or asynchronously. With synchronous updating, all units update their activation simultaneously; with asynchronous updating, each unit has a (usually fixed) probability of updating its activation at a time t, and usually only one unit will be able to do this at a time. In some cases the latter model has some advantages Connections between units In most cases we assume that each unit provides an additive contribution to the input of the unit with which it is connected. The total input to unit k is simply the weighted sum of the separate outputs from each of the connected units plus a bias or offset term θ k : (3.1) The contribution for positive w jk is considered as an excitation and for negative w jk as inhibition. In some cases more complex rules for combining inputs are used, in which a distinction is made between excitatory and inhibitory inputs Activation and output rules We also need a rule which gives the effect of the total input on the activation of the unit. We need a function F k which takes the total input s k (t) and the current activation y k (t) and produces a new value of the activation of the unit k: (3.2) Often, the activation function is a non-decreasing function of the total input of the unit: (3.3) although activation functions are not restricted to non-decreasing functions. Generally, some sort of threshold function is used: a hard limiting threshold function (a sgn function), or a linear or semi-linear function, or a smoothly limiting threshold (figure 3.2). For this smoothly limiting function often a sigmoid (S-shaped) function like: 33

5 (3.4) is used. In some applications a hyperbolic tangent is used, yielding output values in the range [-1, +1] Network topologies Fig. 3.2: Various activation functions for a unit. In the previous section we discussed the properties of the basic processing unit in an artificial neural network. This section focuses on the pattern of connections between the units and the propagation of data. As for this pattern of connections, the main distinction we can make is between: Feed-forward networks, where the data flow from input to output units is strictly feed forward. The data processing can extend over multiple (layers of) units, but no feedback connections are present, that is, connections extending from outputs of units to inputs of units in the same layer or previous layers. Recurrent networks that do contain feedback connections. Contrary to feed-forward networks, the dynamical properties of the network are important. In some cases, the activation values of the units undergo a relaxation process such that the network will evolve to a stable state in which these activations do not change anymore. In other applications, the changes of the activation values of the output neurons are significant, such that the dynamical behavior constitutes the output of the network. 34

6 3.3.5 Paradigms of learning We can categorize the learning situations in two distinct sorts. These are: Supervised learning or Associative learning in which the network is trained by providing it with input and matching output patterns. These input-output pairs can be provided by an external teacher, or by the system which contains the network (selfsupervised). Unsupervised learning or Self-organisation in which an (output) unit is trained to respond to clusters of pattern within the input. In this paradigm the system is supposed to discover statistically salient features of the input population. Unlike the supervised learning paradigm, there is no a priori set of categories into which the patterns are to be classified; rather the system must develop its own representation of the input stimuli Modifying patterns of connectivity Both learning paradigms discussed above result in an adjustment of the weights of the connections between units, according to some modification rule. Virtually all learning rules for models of this type can be considered as a variant of the Hebbian learning rule suggested by Hebb in his classic book Organization of Behaviour (1949) (Hebb, 1949). The basic idea is that if two units j and k are active simultaneously, their interconnection must be strengthened. If j receives input from k, the simplest version of Hebbian learning prescribes to modify the weight w jk with: (3.5) where γ is a positive constant of proportionality representing the learning rate. Another common rule uses not the actual activation of unit k but the difference between the actual and desired activation for adjusting the weights: (3.6) in which d k is the desired activation provided by a teacher. This is often called the Widrow- Hoff rule or the delta rule. 35

7 3.4 STRUCTURES OF ARTIFICIAL NEURAL NETWORK Network Models The interconnection of artificial neurons results in neural networks, NNW (often called neurocomputer or connectionist system in literature),and its objective is to emulate the function of a human brain in a certain domain to solve scientific, engineering, and many other real-life problems. The structure of biological neural network is not well-understood, and therefore, many NNW models have been proposed. A few NNW models can be listed from the literature as follows. 1) Perceptron 2) Adaline and Madaline 3) Backpropagation (BP) Network 4) Radial Basis Function Network (RBFN) 5) Modular Neural Network (MNN) 6) Learning Vector Quantization (LVQ) Network 7) Fuzzy Neural Network (FNN) 8) Kohonen s Self-Organizing Feature Map (SOFM) 9) Adaptive Resonance Theory (ART) Network 10) Real-Time Recurrent Network 11) Hopfield Network 12) Boltzmann Machine 13) Recirculation Network 14) Brain-State-In-A-Box (BSB) 15) Bi-Directional Associative Memory (BAM) Network For the training of the neural network in this thesis a backpropagation network is used. The introduction to the backpropagation network is explained as follows: Backpropagation Network The feed forward multilayer backpropagation topology, shown in Fig. 3.3, is most commonly used in power electronics and motor drives. The name backpropagation comes from the method of supervised training used for the NNW shown by the lower two blocks in 36

8 the figure. The network is normally called multilayer Perceptron (MLP) type, but its activation function(af) can be different from threshold function. The MLP type NNW is very powerful computationally compared with perceptron NNW. It uses error backpropagation supervised training algorithm which was first described by Paul Werbos in Subsequently, Rumelhart, Hinton, Williams, McClelland, Parker, LeCun, etc., further made contributions to this method. The example NNW shown in the figure has three input signals( X 1, X 2, X 3), and two output signals( Y andy 1 2). The circles represent the neurons which have associated AF (not shown), and the weights are indicated by dots. Fig.3.3: Three-layer back propagation network The network shown has three layers: (a) input layer, (b) hidden layer, and (c) output layer. With five neurons in the hidden layer as indicated, it is normally defined as network. The input layer is nothing but the nodes that distribute the signals to the middle layer. Therefore, the topology is often defined as two-layer network. The bias source is normally coupled to both hidden and output layer neurons, although it is shown here for the hidden 37

9 layer only for simplicity. Although the network handles continuous variables, the input and output signals can be continuous, logical, or discrete bidirectional. If the I/O signals are bipolar, the hidden layer neuron usually has hyperbolic tan AF and the output layer has bipolar linear TF. On the other hand, for unipolar signals, these AFs can be sigmoidal and unipolar linear, respectively. The signals within the NNW are processed in perunit (pu) magnitude, and therefore, input signals normalization and output signals descaling or denormalization are used as shown. Although, theoretically, three-layer NNW can solve all the mapping problems, occasionally more than three layers are used. Like a biological network, where the memory or intelligence is contributed in a distributed manner by the synaptic junctions of neurons, the NNW synaptic weights contribute similar distributed intelligence. This intelligence permits the basic input output mapping or pattern recognition property of NNW. This is also defined as associative memory by which when one signal pattern is impressed at the input, the corresponding pattern is generated at the output. This pattern generation or pattern recognition is possible by adequate training of the NNW. Because of parallel computation, the computation is faulttolerant, i.e., deterioration of a few weights and/or missing links will not significantly deteriorate the output signal quality. Besides, NNW has noise or harmonic filtering property Backpropagation Training A NNW requires supervised training by example data rather than the traditional programming in a computer system. This is similar to the training of a biological neural network. Backpropagation is the most popular training method for a multilayer feed forward network. In the beginning, input output example data patterns can be obtained from the experimental results or from simulation study if mathematical model of the plant is available. Analytical data patterns can also be used. An initial NNW configuration is created with the desired input and output layer neurons dictated by the number of respective signals, a hidden layer with a few neurons, and appropriate AFs. Small random weights are selected so that neuron outputs do not get saturated. With one input pattern, the output is calculated (defined as forward pass) and compared with the desired or target output pattern. With the calculated error (mean-squared-error (MSE)), the weights are then altered in the backward direction by backpropagation algorithm until the error between the output pattern and the 38

10 desired pattern is very small and acceptable (see Fig.3.3). A round trip (forward and reverse passes) of calculations is defined as an epoch. Similar training is repeated with all the patterns so that matching occurs for all the patterns. At this point, the network is said to have been trained satisfactorily to perform useful functions. If the error does not converge sufficiently, it may be necessary to increase number of neurons in the hidden layer, and/or add extra hidden layer(s). It has been explained that a three-layer NNW can solve practically all pattern matching problems. Instead of selecting one pattern at a time in sequence, batch method training can be used, where all the patterns are presented simultaneously and final weight updates are made after processing all the patterns. The weight adjustment for the minimization of error uses the standard gradient descent technique, where the weights are iterated one at a time starting backward from the output layer. Consider that a network is being trained with the input pattern number, and the squared output error for all the output layer neurons of the network is given by: (3.7) where = desired output of the j th neuron in the output layer, = corresponding actual output, Q= dimension of the output vector, actual network output vector, and = corresponding desired output vector. The total Mean Squared Error (MSE) for the P set of patterns is then given by MSE= (3.8) The weights of the neurons are altered to minimize the value of the objective function MSE by gradient descent method, as mentioned before. The weight update equation is then given as: (3.9) where η =learning rate, = new weight between i th and j th neurons, and = corresponding old weight. The weights are iteratively updated for all the P training patterns. 39

11 Sometimes mean square error is taken as the objective function. In order to be sure that the MSE converges to a global minimum (i.e., does not get locked up to a local minimum), a momentum term is added to the right of (3.9), where µ is a small value. Fig(3.4) illustrates the flowchart of the error back-propagation training algorithm for a basic two-layer network as shown in fig(3.3). Fig 3.4: Error backpropagation training algorithm Flowchart 40

12 The learning begins with the feed forward recall phase (step 2). After a single pattern vector Z is submitted at the input, the layers responses y and o are computed in this phase. Then the error signal computation phase (step 4) follows. Fist the error signal vector must be determined in the output layer first, and then it is propagated towards the input nodes. Then KXJ weights are subsequently adjusted within the matrix W in step 5. Finally, JXI weights are adjusted within the matrix V in step 6. The cumulative error of into output mapping is computed in step 3 as a sum over all continuous output errors in the entire training set. The final error for the entire training cycle is calculated after each completed pass through the training set. The learning procedure stops when the final error value the upper bound E max is obtained as shown in step Maximum Power Point Tracking of PV cell Using Neural Networks The block diagram for identifying the maximum power point of a PV cell using neural networks is shown in fig Fig.3.5: Block Diagram for the identification of optimal operating point 41

13 Fig.3.6: Configuration of a Neural Network The configuration of 3-layer feedforward neural network is in fig.3.6. The neural network is utilized to identify the maximum Imp of the pv module. The network has 3 layers: an input, a hidden, and an output layer. The number of neurons are 3,5,and 1 in the input, hidden and output layers respectively. The neuron in the input layer gets input solar irradiance (G) and cell temperature (T c ). These signals are directly passed to the neurons in the hidden layer. The neuron in the output layer provides the identified maximum I mp. For each neuron in the hidden and the output layer, the output O i (k) is given as follows: (3.10) The term I i (k) is the input signal given to the neuron I at the Kth sampling. The input I i (k) is given by the weighted sum from the previous nodes as follows: (3.11) In the above equation, W ij is the connection weight from the neuron j to the neuron i and O j (k) is the output from neuron j. The process of determining connection weights is referred to as training process. In the training process, we need a set of input-output patterns for the neural network. These computations are performed off-line during the training process. With the training patterns, the connection weights W ij recursively until the best fit is achieved for the input-output patterns in the training data. A commonly used approach is the generalized delta rule, where the sum of the squared error described below is minimized during the training process. (3.12) Where N is the total number of training patterns. T(k) is the target output from the output node and O(k) is the computed one. For all the training patterns, the error function E is evaluated, and the connection weights are updated to minimize the error function E. 42

14 3.5.1 Neural Network Model Development in MATLAB/Simulink The set of Input-Output patterns required for the training process of the neural network are calculated from the simulated model of PV array presented in the last section. In this training process for a step increase of every 5 C from 0 C to 75 C of Cell Temperature in combination with Irradiance for every step increase of 200W/m 2 from 0 to 2000W/m 2 Imp is calculated for different combinations of cell temperature and irradiance. The sample training data used to train the neural network is shown below for constant T C =25 C and varying Irradiance from 200 to 1000W/m 2. Table-3.1: Training data to train neural network T C G I mp (A) V mp (V) P(W) 25 C 200W/m W/m W/m W/m W/m W/m W/m W/m W/m

15 2000W/m Training of a Neural Network Fig 3.7 Training of neural network The training of a neural network consists of solar irradiance and cell temperature as the input patterns. The target pattern is given by measured I mp for training the neural network. The I mp is calculated for different values of irradiance and cell temperature w.r.t above modeled PV module. This calculated I mp values are given as a training data to the neural network. Fig.3.7, shows the simulation results convergence of error during training process. During the training process, the convergence error is taken as The graphs for the I mp of the neural network and the calculated values of the PV model, are combined to show the error between the two. The graphs are drawn for constant T c = 25 C and varying G from 200W/m 2 to 2000W/m 2. 44

16 Fig.3.8 (a): calculated I mp of a PV model Fig.3.8 (b): I mp of Neural Network Fig.3.8(c): Combined graph of I mp for both neural network and calculated From the above graph(fig 3.8c), it is to be noted that the accuracy of neural networks in finding the I mp of a PV array for MPPT is more. Therefore, for MPPT in this thesis a Neural Network based control algorithm is implemented. 45

17 3.6 Summary In this chapter, introduction about neural networks is explained and then the approach to track the maximum power continuously from PV array using neural networks are presented. A MPPT control algorithm is trained using neural networks and the simulation results are presented and the comparison of I mp of neural networks is compared with the data given to train the neural network. The efficiency of the proposed neural network has been presented for identifying the optimal operating point for the maximum power tracking control of the PV modules. Despite the small set of patterns utilized for the training of the neural network, the network gives accurate predictions over a wide variety of operating modes. The accuracy does not degrade following the seasonal variations of insolation and temperature. 46