Spacecraft power system controller based on neural network

Proceedings of the 14th International Middle East Power Systems Conference (MEPCON’10), Cairo University, Egypt, December 19-21, 2010, Paper ID 242.

Spacecraft Power System Controller Based on Neural Network Hanaa T. El-madany1, Faten H. Fahmy1, Ninet M. A. El-rahman1, and Hassen T. Dorrah2 1

Electronics Research Institute, National Research Center Building, Cairo, Egypt 2 Electrical Power & Machines Dept., Cairo University, Egypt is during an eclipse period when the primary system is a solar array. The power control unit controls the voltage levels on the buses and turns power on and off to a specific items of the equipment. In recent years it has been shown that ANN have been successfully employed in solving complex problems in various fields of applications including pattern recognition, identification, classification, speech, vision, prediction and control systems [2]. Today ANNs can be trained to solve problems that are difficult for conventional computers or human beings. ANNs, overcome the limitations of the conventional approaches by extracting the desired information directly from the experimental (measured) data. In this paper, a simulation study has been carried out to the electrical power system. ANN is used to control the spacecraft power system. Also this adjustment is carried out by using the back-propagation ANN. The performance of the global system has been developed using MATLAB – SIMULINK.

Abstract- Neural control is a branch of the general field of intelligent control, which is based on the concept of artificial intelligence. This work presents the spacecraft orbit determination, dimensioning of the renewable power system, and mathematical modeling of spacecraft power system which are required for simulating the system. The complete system is simulated using MATLAB–SIMULINK. The NN controller out perform PID in the extreme range of non-linearity. Well trained neural controller can operate at different conditions of load current at different orbital periods without any tuning such in case of PID controller. So an artificial neural network (ANN) based model has been developed for the optimum operation of spacecraft power system. An ANN is trained using a back propagation with Levenberg–Marquardt algorithm. The best validation performance is obtained for mean square error is equal to 9.9962 × 10–11 at epoch 637. The regression between the network output and the corresponding target is equal to 100% 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 implementation. The results indicate that the proposed control unit using ANN can be successfully used for controlling the spacecraft power system in low earth orbit (LEO). Therefore, this technique is going to be a very useful tool for the interested designers in space field.

II.

ORBITAL DETERMINATION

The choice of orbit for a LEO remote sensing is governed by the mission objectives and payload operational requirements. For remote sensing satellite, the orbit must be circular and synchronous to permit easy comparison between spatially or temporally distinct data. This reduces the impact of atmosphere drag which can be considered as a major perturbation of artificial satellite orbits caused by the resistance of atmosphere. Also the choice of orbit limits the radiation dosage and keeps the satellite close to the ground. Synchronous orbit keeps the angle between the sun’s direction and orbital plane 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]:

I. INTRODUCTION Provision of electrical power for space vehicles is the most fundamental requirement for the satellite payload. Power system failure necessarily results in the loss of a space mission, and it is interesting to note that many of the early satellite systems failed due to such a loss [1]. In general a spacecraft power system consists of three main elements: primary and secondary energy sources and a power control/distribution network. The primary energy source converts a fuel into electrical power. On early space flights and on launch vehicles, batteries have provided this. Strictly these systems do not have a fuel element, in that a battery is a device that stores energy rather than performing a direct energy conversion process. The majority of present-day spacecraft use a solar array as the primary energy source. The fuel in this case is solar radiant energy, which is converted via the photovoltaic effect. The secondary energy source is required to store energy and subsequently deliver electrical power to the satellite system and its payload, when the primary system's energy is not available. The most usual situation when this condition arises

⎡ h − RE ⎤ dΩ = 9.95⎢ ⎥ dt ⎣ RE ⎦

3.5

cos(i s )

(1)

Where is is the inclination angle (degree), RE is the earth radius (6378 Km), and h is the orbital height (Km). For a satellite following a circular orbit, the orbital period (T) in minuets is given by the third kepler’s law [4]: ⎡ ( R + h) ⎤ T = 2Π ⎢ E ⎥ ⎣ GM ⎦

584

0.5

(2)

Where: G is the earth’s gravitation constant (6.67*10–11 m3 Kg–1 s–2), M is the mass of the earth (5.9*1024 Kg). The eclipse duration is dependant on the orbit altitude, inclination angle, and the sunlight incidence angle on the orbit plane. For circular orbit, the eclipse period is given by (4), [4]: 0.5 ⎤ ⎡⎛ 2⎞ ⎢ ⎜ ⎛⎜ R E ⎞⎟ ⎟ ⎥ 1 − ⎢ ⎜⎜ ⎜ R + h ⎟ ⎟⎟ ⎥ ⎠ ⎠ ⎥ 1 ⎢⎝ ⎝ E Te = 0.5 + sin −1 ⎢ ⎥ cos β Π ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎦ ⎣

Solar Panels

Power Dissipation

(3)

Loads

Shunt Regulator

Battery Charger

Radiator Batteries Fig. 1. Typical solar panel- battery system architecture

Where: ß (in Radian) is the angle between the sunlight incidence on the plane, i.e., the angle between the sun-earth line and the local normal of the orbit plane. Orbital height is chosen to be 800 Km for remote sensing satellite. The inclination angle is nearly equal to 99.1144 degree. The orbital period, the eclipse duration, and the sun duration are equal to 102.436 min, 38 min, and 65 min respectively.

Where: Pa is the solar array power, PBOL is the beginning of life power, f is the array degradation factor, L is the spacecraft life , Np is the number of parallel strings, Ia, Va are array current and voltage respectively , Ic, Vc are cell current and voltage respectively , C is the total cell capacity, VB is the battery voltage, EB is the energy density . The calculated sizing parameters of power sources are shown in Table I.

III. SPACECRAFT POWER SYSTEM

B. Solar Array and Battery Mathematical Modeling

Photovoltaic conversion of the sun’s energy is the most common source of electrical power in space. A typical solar panel-battery power system is shown in Fig. 1 [5, 6]. When the spacecraft is in the shade, the power from the solar panels drops to zero and the power is taken from the batteries to spacecraft loads [5].

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]: V (9) I o = I ph − I rs eqVo / kTA − 1 − o Rsh

(

IV. SPACECRAFT POWER SYSTEM SIZING AND MODELING

Where: I0 is the PV array output current (A), V0 is the PV array output voltage (V), q is the charge of an electron, k is the Boltzmann’s constant in J/K, A the p–n junction ideality factor, T is the cell temperature (K), and Irs is the cell reverse saturation current (A).

A. Solar Array and Battery Dimensioning The size of PV-system is a general concept including the sizing of PV array subsystem and the energy storage subsystem. The PV array area (Aa) can be calculated as follows [5]: Aa =

Pa

PBOL (1 − f )L

(4)

TABLE I Solar array and battery dimensioning

The number of cells in series (Ns) required for producing a certain voltage is [4]: V a = N sV c (5)

Dimensioning

The number of parallel string required for a given current is:

Ia = N p Ic

(6)

The total battery capacity (CB) in Wh and the battery mass (mB) can be estimated as follows: (7) CB = C × VB

Solar array power

426.765 W

End of life power

284.533 W/m2

Solar

Area

1.499 m2

Array

Mass

17.0706 Kg

The number of cells in series

12 cell

The number of strings in parallel

9

The number of cells in the

22 cell

Ni-cd Battery

C mB = B EB

)

(8)

585

battery The total cell capacity

21 Ah

The battery mass

22.02 Kg

The photocurrent Iph depends on the solar radiation and the cell temperature as described in the following equation [7]: s (10) I ph = ( I scr + ki (T − Tr )) 1353

applications [9-11]. The weighted sum of the inputs calculates the total weighted input xj, using the formula:

xj =

∫

∫

1

yj =

(14)

1 + e − xj

The network computes the error E, which is defined by the expression:

(11)

E=

Where: E is no load voltage (V), E0 is constant voltage (V), K is polarization voltage (V), Q is battery capacity (Ah), C is exponential voltage (V), and D is exponential capacity (Ah–1). All the parameters of the equivalent circuit can be modified to represent a particular battery type, based on its discharge characteristics. The state of charge (SOC) of the battery can be calculated as: ⎛ ⎞ ⎜ Q ∗ 1.05 ⎟ SOC = 100⎜1 − ⎟ idt ⎟ ⎜ ⎝ ⎠

(13)

ij

The output of each basic processing element can be determined by different activation functions. A convenient choice for the activation function (yj) is the sigmoidal function given below:

A generic model to most popular types of rechargeable batteries is represented as follows [8]:

( ∫ )

i

i

Where: Iscr is the PV array short circuit current at reference temperature and radiation (A), Tr is the cell reference temperature, ki the short circuit current temperature coefficient (A/K) and S is the solar radiation (W/m2).

⎞ ⎛ ⎟ ⎜ Q E = Eo − K ⎜ ⎟ + C exp − D idt ⎜ Q − idt ⎟ ⎠ ⎝

∑yW

1 2

∑ (y

j

−dj

)2

(15)

j

Where yj is the activity level of the ith unit in the top layer and dj is the desired output of the ith unit. C. Proposed Multi-Layer Perceptron (Mlp) Network Fig. 2 shows the block diagram of the control subsystem using NN. In this diagram, the NNC controls whether the system is in peak power or in eclipse conditions comparing 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 proposed architecture of NNC. The inputs of this controller are the load current (IL) and the error signal (E) while the output is the change in battery charge current (∆IBC). The input and the output are fixed initially however the number of hidden layers and the neurons within these layers are optimized during the learning process based on the good performance of root mean square error (RMSE). A two layer feed-forward network with "logsig" hidden neurons and "purlin" output neurons are be used. The network will be trained with Levenberg-Marquardt back propagation algorithm.

(12)

V. CONTROL METHODOLOGY

Artificial intelligence (AI) techniques are becoming useful as alternate approaches to conventional techniques or as components of integrated systems. They have been used to solve complicated practical problems in various areas and are becoming more and more popular nowadays. Nowadays, considerable attention has been focused on use of ANN on system modeling and control applications. A. Properties & Benefits of Neural Networks The main advantages of the neural network technique are:• Nonlinearity. • Mapping input signals to desired response. • Adaptivity. • Evidential response: confidence level improves classification. • Contextual information: Knowledge is represented by the very structure and activation. • Fault tolerent: graceful degradation of performance if damaged. • Uniformity of analysis and design. • Neurobiological analogy.

IPV

IL

-

+

+ IBD

E NN controller

Battery subsystem

IL

Fig. 2. Block diagram of NN controller

B. Back Propagation Algorithm Back propagation is a form of supervised learning for multilayer nets, also known as the generalized delta rule. Error data at the output layer is back propagated to earlier ones, allowing incoming weights to these layers to be updated. It is most often used as training algorithm in current neural network

586

Hidden layer

Input layer

1400

S u n In te n s i ty ( W /m 2 )

1200

Output layer

Error

1000

∆IB

Load current

800 600 400 200 0

Fig. 3. The architecture of the NN controller model

0

10

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30

40

50

60

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100

Orbital Period (min) VI. SIMULATION RESULTS

Fig. 6. Solar Radiation in LEO 40

The power control unit controls whether the system is in peak power or in eclipse conditions comparing 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 power system. NNC is depicted in Fig. 4. Fig. 5 indicates the weight block diagram of layer1. The solar insolation and the temperature profile in LEO indicated in Fig. 6 and Fig. 7 [12]. It is noticed that during sun periods, the sun intensity is constant. In the contrary, its values remaining zero during eclipse period. The temperature in sun period is higher than that in eclipse period.

20

T e m p (o C )

0 -20 -40 -60 -80 -100 -120

1

x p

x{1}

Process Input 1

p{1}

Layer 1

a{1}

20

30

40

50

60

70

80

90

100

Fig. 7. Temperature in LEO

The typical 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 periods when the PV system is unable to meet the load demand (eclipse period). This implies the PV systems will need a storage system that will be able to provide enough energy during such period. Another important element of spacecraft power system is the energy storage subsystem. The battery is necessary in such a system because of the fluctuating nature of the output delivered by the PV arrays. Thus, during the sun period, the PV system is directly feeding the load, the excess electrical energy being stored in the battery. During the eclipse period, or during a period of low solar intensity, energy is supplied to the load from the battery. Fig. 9 shows the battery current. The positive values of the battery current refer to the charge mode. In the contrary, the negative values indicate the discharge mode. The percentage of rated capacity remaining in the battery is called the Battery State of Charge (SOC). The battery fractional SOC versus time is indicated in Fig. 10.

Layer 2

a{1}

ay

1

Process Output 1

y{1}

Fig. 4. Neural network controller

weights

w

IW{1,1}(1,:)'

p

z

dotprod 1 weights

w

IW{1,1}(2,:)'

p

pd {1,1}

10

a{2}

a{1}

1

0

Orbital Period (min)

a{1}

z

dotprod 2 weights

w

IW{1,1}(3,:)'

p

Mux

1

Mux

iz{1,1}

z

dotprod 3

Fig. 5. Weight block diagram of layer 1

587

Fig. 11 shows the PV output power, the battery power, and the load power profile. It is clear from figure that during sun periods, the generated power from PV feeds the load and the excess power charges the battery. In the contrary, during eclipse periods, the PV array unable to supply the load demand so the battery feeds the spacecraft subsystems.

500 400

Po w er (W )

300

18 16

200 100 PV Battery Load

0

-100

14

-200

P V C u rre n t (A )

12

-300

10

0

10

20

30

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50

60

70

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90

100

Orbital Period (min)

8

Fig. 11. The PV, battery, and load power profile

6 4

VII.

2

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100

Fig. 8. The typical PV current

10 8

B a tt e r y C h a r g e C u r r e n t ( A )

6 4 2 0

-2 -4 -6 -8

0

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100

Orbital Period (min)

Fig. 9. Battery charge current

30.45 30.4 30.35 30.3 30.25 30.2

30.15 30.1 30.05 30

0

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90

ANN TESTING AND VALIDATION RESULTS

The results of ANN are compared 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 provide correct prediction or classifications, the prediction results produced by ANN models can be validated against expert predictions for the same cases or it can be validated against the results of other computer programs. Having trained the network successfully, the next step is to test the network in order to judge its performance and to determine whether the predicted results confirm with the actual results. Fig. 12 depicts the mean square error which can be defined as the average squared difference between outputs 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 performance is equal to 9.9962 × 10–11 at epoch 637. The network response analysis is indicated in Fig. 13. It indicates the regression (R) which measures the correlation between outputs and targets. The value of (R) is equal to one which means that the output tracks the targets very well for training, testing, and validation. An ANN is trained using a back propagation with Levenberg–Marquardt algorithm. The weights of the hidden layer 1 are W {1, 1} = [3.7359 1.8456; –4.091 3.0433; 10.6508 –8.7314]. The weights of the hidden layer 2 are W {2, 1} = [0.00042502 0.052469 2.0515]. The bias to layer 1 is b {1} = [–5.8376; –3.1623; –0.95058]. The bias to layer 2 is b {2} = [–1.0515].

Orbital Period (min)

S O C (% )

0

100

Orbital Period (min)

Fig. 10. The battery state of charge

588

VIII. CONCLUSION

The obvious functions of a spacecraft power system are to generate and store electric power for use by the other spacecraft subsystems. This work presents the design, dimensioning, and simulation of the spacecraft power system. Also ANN is used to control the operation of the system as a result of its ability to handle large and complex systems with many interrelated parameters. Also it can map nonlinearity and it has generalization capability, therefore it can interpolate data. ANN is trained using a back propagation 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 proposed ANN introduces a good accurate prediction for the change in the battery charge current.

Mean squared Error (mse)

Best validation Performance is 9.9962e–11 at epoch 637

REFERENCES [1]

Peter Fortescue, John Stark, and Graham Swinerd, Spacecraft Systems Engineering, John Wiley & Sons Ltd. , England, 2003. [2] James A. Freeman, David M. Skapura, Neural Networks Algorithms, Applications, And Programming Techniques, Addison-Wesley Publishing Company, Inc., Paris,1991. [3] Andrea Milani and Giovanni F. Gronchi, Theory of Orbit Determination, Cambridge University Press, New York, 2010. [4] Mukund R. Patel, Spacecraft Power Systems, CRC Press, Boca Raton, Florida, 2005. [5] Wiley J. Larson, and James R. Wertz, Spacecraft Mission Analysis and Design, Micrcosm Press, Elo, Segrund, California, 2008. [6] Sung-Soo Jang, and Jaeho Choi," Energy balance analysis of small satellite in low earth orbit (LEO)," Proc. of 2nd IEEE International Conference on Power and Energy (PECon 08), Johor Baharu, Malaysia. PP. 967-971, 2008. [7] C. Hua, C. Shen, “Study of maximum power tracking techniques and control of DC/DC converters for photovoltaic power system”, Proc. of the 29th Annual IEEE Power Electronics Specialists Conference, 1998. [8] Patrick Bailey, Roger Hollandsworth, Jon Armantrout, “Advanced battery models from test data for specific satellite EPS applications,” Proc. of 4th International Energy Conversion Engineering Conference and Exhibit (IECEC), San Diego, California, 2006. [9] Ali Al-Alawi, Saleh M Al-Alawi, and Syed M Islam, “Predictive control of an integrated PV-diesel water and power supply system using an artificial neural network,” Renewable Energy , vol. 32, pp. 1426–1439, 2007. [10] B. Chuco Paucar, J.L. Roel Ortiz, K.S. Collazos L., L.C.Leite, and J.O.P Pinto, “Power operation optimization of photovoltaic stand alone system with variable loads using fuzzy voltage estimator and neural network controller,” IEEEPowerTech, 2007. [11] Adel Mellita*, Mohamed Benghanemb, “Sizing of stand-alone photovoltaic systems using neural network adaptive model,” Desalination,Vol. 209, PP. 64–72, 2007. [12] G. Colombo, U. Grasselli, A. De Luca, A. Spizzichino, And S. Falzinis, “Satellite power system simulation”, Acra Asmnautica, Vol. 40, No. I, PP. 4149, 1997.

637 Epoch

Fig. 12. Mean square error

Fig. 13. Regression between the network output and target

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