Improved lead-acid battery modelling for photovoltaic ...

SPEEDAM 2008 International Symposium on Power Electronics, Electrical Drives, Automation and Motion

 Improved Lead -Acid Battery Modelling for Photovoltaic Application by Recurrent Neural Networks G. Tina*, G. Capizzi* * Department of Electric, Electronic & Systems Engineering University of Catania Viale A. Doria 6 -95125 Catania, Italy

performance and economics of PV. The application of energy management is based on State of Charge (SOC) monitoring aimed to minimize battery SOC stress, or supply the power by the batteries. Several models have been reported in the literature in order to simulate the performance of different kinds of batteries. Circuital model networks, linearized mathematical battery models are widely used to calculate and predict the complex battery discharge phenomena. Nowadays the contributions on battery modeling show different levels in accuracy so as in easily of parameters identification. Extensive comparisons and evaluations with some selected models, generally recognised as reliable have shown that further efforts are needed to make refinements on the single battery cell model [1]-[10]. The RNN based approach is proposed in order to obtain an improved discharge battery modelling by using our improved mathematical model in conjunction with the neuro-procedure processing of the experimental voltage data at constant current discharge regime. An RNN based SOC observer can be usefully exploited to improve the battery modeling especially at low rate discharge regime. In fact it was observed that the mathematical discharge battery models can provide terminal voltage behaviour with high level of accuracy only at fast and deep discharge regime. In some operating regimes underestimated and overestimated SOC values, depending on the simulated models, lead to failures in cell voltage prediction. It provides more accurate SOC values estimation with respect to the merely based mathematical battery cell model, so achieving an improved voltage modeling at low rate discharge regime. The main simulation results reported in the paper are compared with the experimental and model-calculated data. The battery modeling was made by using a 6x4x3x2 Real–Time Recurrent Neural Networks (R-T RNN) .

Abstract--The paper presents some multilayer Recurrent Neural Networks (RNNs) to improve the highly non linear behaviour modelling of lead acid cell battery. Dynamic RNNs, keeping into account the non-linear dynamic behavior of both input-output variables of the battery charge-discharge processes, provide a powerful tools in the above mentioned problem, despite the higher computational burden involved respect to the feed-forward networks. Since the electric current supplied by the battery is dependent upon the user application, it can be regarded as the only effective external input of the dynamic system described by the equations, and then of the RNNs. The basic variables of the discharge process are in fact both voltage and SOC. Index Terms-- Battery modelling, Neural network applications, Nonlinear circuits, Recurrent neural networks.

I. INTRODUCTION While extensive research has been carried out to develop new types of batteries and converters to convert appropriately the batteries’ output, very little work has been done in modeling the battery itself. The fact that most power converters are now switched at relatively very high frequencies (much higher than 50Hz) will require new model of the batteries to take into account the operation of the battery under this high switching mode (dynamic behavior). The State Of Charge (SOC) evaluation is a fundamental step, especially in energy flows management problems of stand alone Photovoltaic (PV) hybrid systems, in fact Lead-acid batteries are the dominant energy storage in the PV stand-alone systems. Nevertheless, uneconomical lifetime of the battery is one typical feature of such systems. During the last decade, the attention of system developers has concentrated on analysing the reasons for this premature battery failure. Sensitivity of the battery and severe operating conditions of the PV systems stimulate the battery ageing mechanisms and result in rapid degradation of its capacity. Therefore the battery always suffers from short life-cycle under stand alone PV systems. However, there is some technological development on the component level that allows to obtain special solar batteries, which have s relatively longer life cycle under PV operating conditions. These technologies are still expensive and rarely available in the current markets of developing countries. On the other hand, operation control plays an important role in the

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II. THE PROPOSED BATTERY MODELING The complex, nonlinear behavior of electrochemical batteries can be conveniently modeled using equivalent electric networks. Although these networks contain elements that are nonlinear and depend on battery stateof-charge and electrolyte temperature, they are very useful for the electric engineer, since they allow to think in terms of electric quantities, instead of internal battery 1170

The battery capacity model of CT has been tested by using data available from several lead-acid battery manufacturers. In fig. 2 is shown one of this test.

electrochemical reactions. There have been many electrical models of batteries, from lead-acid to polymer Li-ion batteries. Most of these electrical models fall under three basic categories: Thevenin [3]–[9], impedance [10], [11], and runtime-based models [12]. The Thevenin approach presented here belongs to the first category which allows us to reach the best result in terms of generality and accuracy. This category is commonly approached by an electric circuit with a voltage source E in series with an internal resistance ƒ0 as shown in fig. 1. The internal electrochemical electromotive force (emf ) E and the internal resistance ƒ0 are functions either of internal electric parameters or electric quantities observable at the terminals. Moreover the battery capacity CT (Ahour at a specified discharge time t ) must be carefully modeled in a consistent manner with the capacity drop at increasing discharge current, than related to the time history of the battery. The proposed dynamic discharge battery model takes into account the changing either in the internal resistance or in the internal electrochemical emf.

Fig. 2. Capacity versus Current (HOPPECKE 12V 20PzS100).

III. BATTERY CELL MODELING BY DINAMICAL RNNS APPROACH The analysis of a non linear electric circuit with a voltage source in series with an internal resistance related respectively to the internal electrochemical electromotive force (emf) E and the internal resistance R0 both functions either of internal electric parameters or electric observable quantities at the terminals, provides simple and powerful tool to evaluate the battery performance. At present the tuning procedure of the empirical coefficient needed to use the circuital model reported in the previous section is performed in a heuristic manner. The use of RNN leads to improvement in the battery discharge modeling, and the extraction of the parameters to be used in circuital models. As stated by some researchers RNN behaviour is similar to the IIR filter behaviour, whose output response depends on the previous outputs value. The weight vector of the network is WT =[aT bT ] and a e b are the weight vectors related respectively to the external input vector xi (the supplied electric current i) and the state vectors (SOC and voltage v) of a FIR filter. The basic block diagram of RNN is shown in fig.3 In order to estimate the unknown vectors a e b, a training procedure with a set of input-output data pattern is required and a recursive gradient type scheme has to be used for the training of the network [13]. The battery modeling was made by using a 6x10x10x8x2 real time RNN as depicted in fig 4. Relevant considerations and guidelines about choice, design and training of the selected RNN lie in. the accurate evaluation of the learning curves and output response by changing the learning rate value, so as the pattern data input choice and normalization [13 ].

Fig. 1. Equivalent circuit of the lead-acid battery model.

A. The proposed Mathematical battery model The basic dynamic battery discharge equations are the following:

E

E0  E e ln( SOC )

ƒ0

R0  R1 ln(J /(J  q / CT ))

CT

C0 

(1)

i

E

where: q is the so-called “extracted charge,” i.e., the charge that has been actually extracted from the battery starting from a completely full battery (battery is full when t=0 ); C0 is the nominal capacity; SOC = 1  q / C0 is the State Of Charge; CT is the battery capacity at current “i”; R0 is a constant parameter; Ee , R1 J, E are empirical coefficients.

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calculate the model parameters are established as follows. Let us consider the equation (1). If the no-load battery emf is measured, this equation provide also the ohmic resistance R0. This is an important calculation because at low discharge rate the value of R1 is lower than R0.. Reversely increasing the discharge rate, the value of R1 rise. up to 4*R0 due to the increasing non linearity. At the beginning of the discharge process by constant rated current, the calculation of Ee is performed exploiting the slope of the voltage curve and the SOC values evaluated by the RNN output traces. The proposed procedure to predict the battery discharge behaviour by RNN battery cell modeling and mathematical model leads to set some parameters in a systematic manner over a wide range of discharge operation. The effect of aging and operating temperature on the battery performance will be incorporate in the neural modeling by changing the value of thresholds and the parameters of activation function.

Fig. 3. Schematic of a basic RNN.

V. EXPERIMENTAL RESULT The validity of the proposed SOC evaluation model is based on and verified by means of a series of experimental tests In the test setup, battery voltage and battery current waveforms are taken from Hall-effect voltage and current transducers by means of the analog interface. The data are sampled at 5 Hz, and recorded on a PC, using a data acquisition system. The data acquisition system used consists of LabView software, a data acquisition card and a sample-and-hold card (DAQPad-6015) from National Instruments. The DAQPad-6015 converts analog inputs to digital data at 0.2 MS/s rate with 16-bit resolution. It has 16 singleended analog inputs . The collected data are processed by MATLAB software, and the time variations of battery voltage, battery current and SOC are obtained for different charge-discharge strategies. The test are conducted on 4x12 V, 100-Ah rated capacity HOPPECKE mod. 2OPzS100 open vase, lead-acid battery. The manufacturer’s data giving the necessary constant currents to be supplied to the tested batteries to discharge them to 1.75 V/cell level for different time durations. Four charge tests at 7 A, 10 A, 18 A constant currents, three discharge tests at 2A, 5A and 7A constant currents and two tests at cyclical current at 2A and 7A, with 15 and 20 minutes switching time respectively were carried out.

Fig. 4. The selected recurrent neural networks for lead –acid cell modeling.

The 36 neurons are arranged in five layers: an input layer, three hidden layers and an output layer. The number of processing recurrent neurons in the hidden layer is 28. Then the slots of the recurrent weights matrix of the network are filled by 256 weights. The four synaptic weights matrix were calculated according to the real time recurrent learning algorithm implemented in Matlab®. Training of the RNN was done under both current constant discharge rate and cycling behavior. A more detailed description of the training algorithm can be found in [13]. The learning curves showed that, by changing the learning rate in the range 0.01-0.9, with fixed momentum factor D, we get the target by the RNN outputs after 20000 iterations.

A. Charging tests Charging tests were carried out with constant current ensured by the power supply system throughout all the experiment, whose target was the upper voltage limit given by the manufacturer. In these conditions, nearly all the current does not tend to charge the battery, but rather causes a marked gasification of the electrolithic solution.

IV. MODEL PARAMETERS ESTIMATION BY RNN OUTPUTS EXPLOITATION Accurate model parameters determination and tuning is needed to avoid overestimated terminal voltages values. By a simple measurement of the no load battery voltage and by exploitation of the RNN output a procedure to

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B. Discharge tests In carrying out discharge tests, a constant current load was applied until a minimum voltage threshold was reached, depending both on the applied current and temperature, with the same law indicated for the charging process. During discharge it is important not to go down this threshold, so as to avoid precipitation phenomena that might badly damage the battery.

The use of RNN in photovoltaic application leads to significant improvement in battery discharge modelling problems, and in the extraction of the parameters to be used in circuital models. Simulation results show the improved lead-acid battery modeling also at low discharge rate and also the consistency of the proposed procedure of parameters calculation. The preliminary RNN training process can be obtained by simulated current profiles, voltage and SOC values evaluated by the tuned circuital models. The actual values of electric currents to provide as external input to the proposed RNN employed to model the dynamics of the battery discharge cycling behaviour, can be obtained from on board data acquisition systems. Simulation study is a very important tool both to investigate convenient discharge current profile, related to the selected trajectories, for increased available capacity, by analysis of battery SOC and voltage under cycling operation, and to design hardware devices implementing the circuital network battery model or RNN.

VI. SIMULATION RESULT In order to provide easy charge-discharge model simulation, by the several current profiles as input data pattern to the RNN, obtained from the available model simulation and experimental data, the developed simulation tool is split into two main Matlab routines. The first one provides processing of the available data to be used for further neural processing, while the second one is the basic program used to perform dynamic simulation. The effectiveness of the procedure described in the previous section relies on a proper handling of the experimental data by the neural net to be exploited for accurate parameters calculation. The simulation results of fig.5, fig.6 and fig.7 show that the experimental curve and. simulated traces, obtained with the recurrent neuroprocessing, are well matched, while the model provides overestimated values.. The model with the parameters tuned by exploiting the RNN traces (model improved) confirms the effectiveness of both the model and parameters calculation procedure presented in the previous sections. As shown by the voltage traces shown in fig.5, fig.6 and fig.7, the model prediction is improved compared with the already used model. A. Battery Cycling Behavior During cycling discharge behavior of the battery storage and at highly variable discharge currents, the SOC values change dynamically and so does the terminal voltage, strongly depending upon the time history of the SOC values, rated discharge currents and its rated change. Because the weights are expected to change, one more training of the selected RNN was performed providing as inputs the cycling current shown in fig. . The main aim of these investigations (looking for the maximum weights deviation) was to develop a single trained RNN to be used for lead acid battery at any discharge current shape. The simulation was performed for 36 cycles. In this case too it can be seen that the better agreement with experimental data is obtained through the proposed neural model.

Fig. 5. Battery voltage versus time at discharge current of 2A

VII. CONCLUSIONS Fig. 6. Battery voltage versus time at discharge current of 5A

The potential of RNNs with respect to other neural network approach is that they are able to take into account the earlier value of current, SOC and voltage when the battery discharge phenomenon is in progress.

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Fig. 7. Battery voltage versus time at discharge current of 7A

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