Spacecraft Power System Controller Based on Neural Network

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1 Proceedings of the 4 th International Middle East Power Systems Conference (MEPCON ), Cairo University, Egyt, December 9-2, 2, Paer ID 242. Sacecraft Power System Controller Based on Neural Network Hanaa T. El-madany, Faten H. Fahmy, Ninet M. A. El-rahman, and Hassen T. Dorrah 2 Electronics Research Institute, National Research Center Building, Cairo, Egyt 2 Electrical Power & Machines Det., Cairo University, Egyt Abstract- Neural control is a branch of the general field of intelligent control, which is based on the concet of artificial intelligence. This work resents the sacecraft orbit determination, dimensioning of the renewable ower system, and mathematical modeling of sacecraft ower system which are required for simulating the system. The comlete system is simulated using MATLAB SIMULINK. The NN controller out erform PID in the extreme range of non-linearity. Well trained neural controller can oerate at different conditions of load current at different orbital eriods without any tuning such in case of PID controller. So an artificial neural network (ANN) based model has been develoed for the otimum oeration of sacecraft ower system. An ANN is trained using a back roagation with Levenberg Marquardt algorithm. The best validation erformance is obtained for mean square error is equal to at eoch 637. The regression between the network outut and the corresonding target is equal to % which means a high accuracy. NNC architecture gives satisfactory results with small number of neurons, hence better in terms of memory and time are required for NNC imlementation. The results indicate that the roosed control unit using ANN can be successfully used for controlling the sacecraft ower system in low earth orbit (LEO). Therefore, this technique is going to be a very useful tool for the interested designers in sace field. I. INTRODUCTION Provision of electrical ower for sace vehicles is the most fundamental requirement for the satellite ayload. Power system failure necessarily results in the loss of a sace mission, and it is interesting to note that many of the early satellite systems failed due to such a loss []. In general a sacecraft ower system consists of three main elements: rimary and secondary energy sources and a ower control/distribution network. The rimary energy source converts a fuel into electrical ower. On early sace flights and on launch vehicles, batteries have rovided this. Strictly these systems do not have a fuel element, in that a battery is a device that stores energy rather than erforming a direct energy conversion rocess. The majority of resent-day sacecraft use a solar array as the rimary energy source. The fuel in this case is solar radiant energy, which is converted via the hotovoltaic effect. The secondary energy source is required to store energy and subsequently deliver electrical ower to the satellite system and its ayload, when the rimary system's energy is not available. The most usual situation when this condition arises is during an eclise eriod when the rimary system is a solar array. The ower control unit controls the voltage levels on the buses and turns ower on and off to a secific items of the equiment. In recent years it has been shown that ANN have been successfully emloyed in solving comlex roblems in various fields of alications including attern recognition, identification, classification, seech, vision, rediction and control systems [2]. Today ANNs can be trained to solve roblems that are difficult for conventional comuters or human beings. ANNs, overcome the limitations of the conventional aroaches by extracting the desired information directly from the exerimental (measured) data. In this aer, a simulation study has been carried out to the electrical ower system. ANN is used to control the sacecraft ower system. Also this adjustment is carried out by using the back-roagation ANN. The erformance of the global system has been develoed using MATLAB SIMULINK. II. ORBITAL DETERMINATION The choice of orbit for a LEO remote sensing is governed by the mission objectives and ayload oerational requirements. For remote sensing satellite, the orbit must be circular and synchronous to ermit easy comarison between satially or temorally distinct data. This reduces the imact of atmoshere drag which can be considered as a major erturbation of artificial satellite orbits caused by the resistance of atmoshere. Also the choice of orbit limits the radiation dosage and kees the satellite close to the ground. Synchronous orbit kees the angle between the sun s direction and orbital lane are constant and always sees the sun at the same angle. The inclination angle can be determined for sun dω synchronous orbit from earth s orbital rotation rate ( ) dt (deg/day) as follows [3]: dω h R = 9.95 dt RE E 3.5 cos ( i ) Where i s is the inclination angle (degree), R E is the earth radius (6378 Km), and h is the orbital height (Km). For a satellite following a circular orbit, the orbital eriod (T) in minuets is given by the third keler s law [4]:.5 s () ( RE + h) T = 2Π (2) GM 584

2 Where: G is the earth s gravitation constant (6.67* m 3 Kg s 2 ), M is the mass of the earth (5.9* 24 Kg). The eclise duration is deendant on the orbit altitude, inclination angle, and the sunlight incidence angle on the orbit lane. For circular orbit, the eclise eriod is given by (4), [4]: 2 R E R + E h Te =.5 + sin Π cos β.5 (3) Power Dissiation Solar Panels Radiator Shunt Regulator Batteries Charger Loads Where: ß (in Radian) is the angle between the sunlight incidence on the lane, i.e., the angle between the sun-earth line and the local normal of the orbit lane. Orbital height is chosen to be 8 Km for remote sensing satellite. The inclination angle is nearly equal to degree. The orbital eriod, the eclise duration, and the sun duration are equal to min, 38 min, and 65 min resectively. III. SPACECRAFT POWER SYSTEM Photovoltaic conversion of the sun s energy is the most common source of electrical ower in sace. A tyical solar anel-battery ower system is shown in Fig. [5, 6]. When the sacecraft is in the shade, the ower from the solar anels dros to zero and the ower is taken from the batteries to sacecraft loads [5]. IV. SPACECRAFT POWER SYSTEM SIZING AND MODELING A. Solar Array and Dimensioning The size of PV-system is a general concet including the sizing of PV array subsystem and the energy storage subsystem. The PV array area (A a ) can be calculated as follows [5]: Pa Aa = (4) P f BOL( ) L Fig.. Tyical solar anel- battery system architecture Where: P a is the solar array ower, P BOL is the beginning of life ower, f is the array degradation factor, L is the sacecraft life, N is the number of arallel strings, I a, V a are array current and voltage resectively, I c, V c are cell current and voltage resectively, C is the total cell caacity, V B is the battery voltage, E B is the energy density. The calculated sizing arameters of ower sources are shown in Table I. B. Solar Array and Mathematical Modeling Using the equivalent circuit of a solar cell, the non-linear I V characteristics of a solar array are extracted, neglecting the series resistance [7]: qv kta V o / o Io = I h Irs( e ) (9) R Where: I is the PV array outut current (A), V is the PV array outut voltage (V), q is the charge of an electron, k is the Boltzmann s constant in J/K, A the n junction ideality factor, T is the cell temerature (K), and I rs is the cell reverse saturation current (A). sh TABLE I Solar array and battery dimensioning The number of cells in series (N s ) required for roducing a certain voltage is [4]: V = N V (5) a s The number of arallel string required for a given current is: a c I = N I (6) The total battery caacity (C B ) in Wh and the battery mass (m B ) can be estimated as follows: C = C (7) c B V B CB m B = (8) E B Solar Array Ni-cd Dimensioning Solar array ower W End of life ower W/m 2 Area.499 m 2 Mass 7.76 Kg The number of cells in series 2 cell The number of strings in arallel 9 The number of cells in the 22 cell battery The total cell caacity 2 Ah The battery mass 22.2 Kg 585

3 The hotocurrent I h deends on the solar radiation and the cell temerature as described in the following equation [7]: s I = ( I + k T T ) () h scr i ( r ) 353 Where: I scr is the PV array short circuit current at reference temerature and radiation (A), T r is the cell reference temerature, k i the short circuit current temerature coefficient (A/K) and S is the solar radiation (W/m 2 ). A generic model to most oular tyes of rechargeable batteries is reresented as follows [8]: Q E = Eo K + C ex ( D idt) () Q idt Where: E is no load voltage (V), E is constant voltage (V), K is olarization voltage (V), Q is battery caacity (Ah), C is exonential voltage (V), and D is exonential caacity (Ah ). All the arameters of the equivalent circuit can be modified to reresent a articular battery tye, based on its discharge characteristics. The state of charge (SOC) of the battery can be calculated as: Q.5 SOC = idt V. CONTROL METHODOLOGY (2) Artificial intelligence (AI) techniques are becoming useful as alternate aroaches to conventional techniques or as comonents of integrated systems. They have been used to solve comlicated ractical roblems in various areas and are becoming more and more oular nowadays. Nowadays, considerable attention has been focused on use of ANN on system modeling and control alications. A. Proerties & Benefits of Neural Networks The main advantages of the neural network technique are:- Nonlinearity. Maing inut signals to desired resonse. Adativity. Evidential resonse: confidence level imroves classification. Contextual information: Knowledge is reresented by the very structure and activation. Fault tolerent: graceful degradation of erformance if damaged. Uniformity of analysis and design. Neurobiological analogy. B. Back Proagation Algorithm Back roagation is a form of suervised learning for multilayer nets, also known as the generalized delta rule. Error data at the outut layer is back roagated to earlier ones, allowing incoming weights to these layers to be udated. It is most often used as training algorithm in current neural network alications [9-]. The weighted sum of the inuts calculates the total weighted inut x j, using the formula: x = y W (3) j i The outut of each basic rocessing element can be determined by different activation functions. A convenient choice for the activation function (y j ) is the sigmoidal function given below: y j = xj (4) + e The network comutes the error E, which is defined by the exression: E ( ) 2 2 y j d j (5) = j Where y j is the activity level of the i th unit in the to layer and d j is the desired outut of the i th unit. C. Proosed Multi-Layer Percetron (Ml) Network Fig. 2 shows the block diagram of the control subsystem using NN. In this diagram, the NNC controls whether the system is in eak ower or in eclise conditions comaring the solar array current with the load current, the change in battery charge current is considered as the difference between them. Fig. 3 indicates the roosed architecture of NNC. The inuts of this controller are the load current (I L ) and the error signal (E) while the outut is the change in battery charge current ( I BC ). The inut and the outut are fixed initially however the number of hidden layers and the neurons within these layers are otimized during the learning rocess based on the good erformance of root mean square error (RMSE). A two layer feed-forward network with "logsig" hidden neurons and "urlin" outut neurons are be used. The network will be trained with Levenberg-Marquardt back roagation algorithm. I L I BD I PV E I L NN controller Fig. 2. Block diagram of NN controller i ij subsystem 586

4 Inut layer Hidden layer 4 2 Error Load current Outut layer IB Sun Intensity (W /m 2) Fig. 3. The architecture of the NN controller model VI. SIMULATION RESULTS The ower control unit controls whether the system is in eak ower or in eclise conditions comaring the solar array current with the load current, the difference between them is the change in battery charge current. Neural network is used to control the ower system. NNC is deicted in Fig. 4. Fig. 5 indicates the weight block diagram of layer. The solar insolation and the temerature rofile in LEO indicated in Fig. 6 and Fig. 7 [2]. It is noticed that during sun eriods, the sun intensity is constant. In the contrary, its values remaining zero during eclise eriod. The temerature in sun eriod is higher than that in eclise eriod. Tem (oc) Fig. 6. Solar Radiation in LEO x {} a{} x{} Process Inut Layer a{} Fig. 7. Temerature in LEO a{} d {,} a{} a{2} Layer 2 a y Process Outut Fig. 4. Neural network controller weights w z IW{,}(,:)' dotrod weights w z IW{,}(2,:)' Mux dotrod 2 Mux weights w z IW{,}(3,:)' dotrod 3 Fig. 5. Weight block diagram of layer y{} iz{,} The tyical current behavior of the PV array system is shown in Fig. 8. From figure, it is indicated that the variations of PV current follows the variations of the sun intensity. There will be time eriods when the PV system is unable to meet the load demand (eclise eriod). This imlies the PV systems will need a storage system that will be able to rovide enough energy during such eriod. Another imortant element of sacecraft ower system is the energy storage subsystem. The battery is necessary in such a system because of the fluctuating nature of the outut delivered by the PV arrays. Thus, during the sun eriod, the PV system is directly feeding the load, the excess electrical energy being stored in the battery. During the eclise eriod, or during a eriod of low solar intensity, energy is sulied to the load from the battery. Fig. 9 shows the battery current. The ositive values of the battery current refer to the charge mode. In the contrary, the negative values indicate the discharge mode. The ercentage of rated caacity remaining in the battery is called the State of Charge (SOC). The battery fractional SOC versus time is indicated in Fig.. 587

5 Fig. shows the PV outut ower, the battery ower, and the load ower rofile. It is clear from figure that during sun eriods, the generated ower from PV feeds the load and the excess ower charges the battery. In the contrary, during eclise eriods, the PV array unable to suly the load demand so the battery feeds the sacecraft subsystems. 8 6 Pow er (W ) PV Load PV Current (A) Fig.. The PV, battery, and load ower rofile S O C ( % ) B attery C harge C urrent (A ) Fig. 8. The tyical PV current Fig. 9. charge current VII. ANN TESTING AND VALIDATION RESULTS The results of ANN are comared to actual results. The trained model is assumed to be successful if the model gives good results for that test set. To insure that ANN models rovide correct rediction or classifications, the rediction results roduced by ANN models can be validated against exert redictions for the same cases or it can be validated against the results of other comuter rograms. Having trained the network successfully, the next ste is to test the network in order to judge its erformance and to determine whether the redicted results confirm with the actual results. Fig. 2 deicts the mean square error which can be defined as the average squared difference between oututs and targets. It is clear from the figure that the results is reasonable because of small mean square error can be obtained from NNC, the test set error and the validation set error have similar characteristics. The best validation erformance is equal to at eoch 637. The network resonse analysis is indicated in Fig. 3. It indicates the regression (R) which measures the correlation between oututs and targets. The value of (R) is equal to one which means that the outut tracks the targets very well for training, testing, and validation. An ANN is trained using a back roagation with Levenberg Marquardt algorithm. The weights of the hidden layer are W {, } = [ ; ; ]. The weights of the hidden layer 2 are W {2, } = [ ]. The bias to layer is b {} = [ ; 3.623;.9558]. The bias to layer 2 is b {2} = [.55] Fig.. The battery state of charge 588

Mean squared Error (mse) Best validation Performance is 9.9962e at eoch 637 637 Eoch Fig. 2. Mean square error VIII.

6 Mean squared Error (mse) Best validation Performance is e at eoch Eoch Fig. 2. Mean square error VIII. CONCLUSION The obvious functions of a sacecraft ower system are to generate and store electric ower for use by the other sacecraft subsystems. This work resents the design, dimensioning, and simulation of the sacecraft ower system. Also ANN is used to control the oeration of the system as a result of its ability to handle large and comlex systems with many interrelated arameters. Also it can ma nonlinearity and it has generalization caability, therefore it can interolate data. ANN is trained using a back roagation with Levenberg Marquardt algorithm using MATLAB SIMULINK. Results obtained clearly demonstrate that an ANN can be used with high degree of confidence for control strategy. The results show that the roosed ANN introduces a good accurate rediction for the change in the battery charge current. REFERENCES [] Peter Fortescue, John Stark, and Graham Swinerd, Sacecraft Systems Engineering, John Wiley & Sons Ltd., England, 23. [2] James A. Freeman, David M. Skaura, Neural Networks Algorithms, Alications, And Programming Techniques, Addison-Wesley Publishing Comany, Inc., Paris,99. [3] Andrea Milani and Giovanni F. Gronchi, Theory of Orbit Determination, Cambridge University Press, New York, 2. [4] Mukund R. Patel, Sacecraft Power Systems, CRC Press, Boca Raton, Florida, 25. [5] Wiley J. Larson, and James R. Wertz, Sacecraft Mission Analysis and Design, Micrcosm Press, Elo, Segrund, California, 28. [6] Sung-Soo Jang, and Jaeho Choi," Energy balance analysis of small satellite in low earth orbit (LEO)," Proc. of 2 nd IEEE International Conference on Power and Energy (PECon 8), Johor Baharu, Malaysia. PP , 28. [7] C. Hua, C. Shen, Study of maximum ower tracking techniques and control of DC/DC converters for hotovoltaic ower system, Proc. of the 29 th Annual IEEE Power Electronics Secialists Conference, 998. [8] Patrick Bailey, Roger Hollandsworth, Jon Armantrout, Advanced battery models from test data for secific satellite EPS alications, Proc. of 4th International Energy Conversion Engineering Conference and Exhibit (IECEC), San Diego, California, 26. [9] Ali Al-Alawi, Saleh M Al-Alawi, and Syed M Islam, Predictive control of an integrated PV-diesel water and ower suly system using an artificial neural network, Renewable Energy, vol. 32, , 27. [] B. Chuco Paucar, J.L. Roel Ortiz, K.S. Collazos L., L.C.Leite, and J.O.P Pinto, Power oeration otimization of hotovoltaic stand alone system with variable loads using fuzzy voltage estimator and neural network controller, IEEEPowerTech, 27. [] Adel Mellita*, Mohamed Benghanemb, Sizing of stand-alone hotovoltaic systems using neural network adative model, Desalination,Vol. 29, PP , 27. [2] G. Colombo, U. Grasselli, A. De Luca, A. Sizzichino, And S. Falzinis, Satellite ower system simulation, Acra Asmnautica, Vol. 4, No. I, PP. 449, 997. Fig. 3. Regression between the network outut and target 589

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