# Bringing Renewable Energy to the Electrical Engineering Undergraduate Education and Research at UPRM

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2 Session WD SIMULATION OF RENEWABLE ENERGY SOURCES I. Thermoelectric generator The used electrical TEG mathematical model considers the boundary conditions and shape of the TEG P-V curve. The power, P, and the voltage, V, can be obtained by (1) and () respectively. The variables V x, I x, and P max are the opencircuit voltage, short-circuit current, and maximum power for the TEG at a given cooling water temperature, T. P=I V=V x -I-V x I /I x V [0, V x ],P [0, P max ] (1) V=V x - V x I/I x () The model given by () describes a linear equation whose slope and the constant term are equal to -V x /I x and V x respectively. This equation is suitable both for circuit analysis and for integration of renewable sources to undergraduate courses. In Simulink, the model given by () was developed as is shown in Fig.. The data to verify the proposed TEG model was obtained from the paper written by Chu et. al. [9]; the open voltage and the maximum current are V x = 17.5V and I x = 1A respectively. Fig. shows the V-I and P- I characteristics using the proposed TEG Model. These results are very similar to the results provided in [9]. FIGURE 1 SIMULINK TEG BLOCK. II. Photovoltaic generator The photovoltaic module model used in this paper was proposed in [7]. The relationship between the current (I) and the voltage (V), for any PVM is given by (3). This model takes into consideration the short-circuit current (I x ) and the open-circuit voltage (V x ) at any given irradiance level (E i ) and temperature (T), and the PVM characteristic constant (b). I(V)=[I x /(1-exp(-1/b))] [1-exp(V/(b V x )-1/b)] (3) For the exponential model in (3), the constant b is the only one that needs to be calculated. This is computed using an algorithm based on the Fixed Point Theorem shown in (4), where ξ is the maximum permitted error; V oc and I sc are the open-circuit voltage and the short-circuit current at Standard Test Condition (STC); V op and I op are the optimal voltage and the optimal current at STC. The PVM model given by (3) was developed in Saber, Spice and Simulink[10]. These implementations are suitable for analyzing the PVM characteristics, as well as, being appropriate to analyze a photovoltaic system in simulation. Fig. 3 shows the scheme implemented in Saber to obtain the PVM characteristic curves; the resistor connected to the PVM increases from 1.0mΩ to 5.0kΩ; then, the simulation is repeated for different irradiance values. The PVM output current vs. PVM output voltage, and also the PVM power vs. PVM voltage are shown in Fig. 4. In addition, using a pyranometer and a DC electronic load real data were obtained. Fig. 5 shows the measured data and the calculated data using the model described previously. (4) FIGURE PROPOSED TEG MODEL AT 318K. FIGURE 3 SABER SCHEMATIC DIAGRAM. WD-

3 III. Fuel cells A fuel cell behavioral model was proposed in [8]. This electrical model considers the boundary conditions and shape of the fuel cell V-I curve as given in [8]. The variables V, and I are the voltage, and current for a fuel cell with units in volts and amperes. I H, V H and V L are the high current, the high voltage and low voltage for a fuel cell. V H can be obtained when the current is zero. V L can be obtained when the current is I H. The range of existence of I will be from 0 to I H and the range of existence of V(I) will be from V L to V H. The fuel cell can be described in terms of the values obtained by the fuel cell V-I and P-I curves using either (5) or (6). V = V L + (V H -V L ) [arcos(i/i H -1)/π] k (5) P = V L I + I(V H -V L ) [arcos(i/i H -1)/π] k (6) The variable k is the characteristic constant for the fuel cell based on the V-I and P-I curves given in [8]. P max and I op are the maximum power, and the optimal current to obtain the maximum power for a fuel cell. k = ln[(p max -I op V L )/(I op V H -I op V L )] ln[arcos(i op /I H - (7) 1)/π] -1 Using Matlab and the behavioral mathematical model given in (5), the V-I and the P-I relationship are calculated for a H-100 by Horizon fuel cell technologies. These relationships are shown in Fig. 6, and they are very similar to presented in the product datasheet. Session WD FIGURE 4 PVM CHARACTERISTICS CURVES AT DIFFERENT IRRADIANCE AND T=50 C. EXAMPLES OF APPLICATION I. Thermoelectric generator feeding a DC motor State space modeling can be used to model a permanent magnet direct current (PMDC) motor directly coupling to a TEG. This configuration is shown in Fig. 7. A differential equation can be derived by using Kirchoff s electrical voltage law around the electrical loop; this equation is given by (8), where R a, L a and K e are: the armature resistance; the armature inductance; and the back emf constant, respectively. FIGURE 5 I-V CHARACTERISTICS OF PVM SX-10M R a i a + L a di a /dt + K e ω m = V x -V x /I x i a (8) The sum of DC motor torques must be equal to zero; hence, the DC motor torque balance equation is given by (9), where J, B m, and T L are: the moment of inertia of the motor and connected load; the constant viscous friction coefficient; and the load torque, respectively. K e i a = J dω m /dt + B m ω m +T L (9) From (8) and (9) the state space model of the system, for armature current and angular speed, can be written as: d i a /dt =-R a/ L a i a -V x /I x L a i a -K e /L a ω m +V x /L a (10) dω m /dt = -B m /J ω m + K e /J i a - T L /J (11) FIGURE 6 CHARACTERISTICS CURVES OF FUEL CELLS H-100 BY HORIZON FUEL CELL TECHNOLOGIES WD-3

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