EE603 2006 Design Problem

You are to design a closed loop continuous conduction mode inverter to change a DC voltage from a 24V solar cell to a single phase 60Hz 110Vrms power grid. The power electronics is to be isolated from the grid by a 60Hz transformer and the current into the grid is to be in phase with the grid voltage. The solar cells may be modeled by a battery. The primary system requirements are

Input voltage	24V - 28V DC
Output voltage	Single phase 60Hz 110Vrms AC
Switching frequency	100kHz
Rated (maximum) output power	1000W
Peak-to-peak output ripple current	< 5% of Ioutpeak
Heatsink surface temperature	85C

A completed design must include

MOSFET manufacturer and part number

Inductor value

Capacitor value

60Hz transformer specification

Average MOSFET losses

MOSFET junction temperature

Control design and control gains

Average model and simulation results

Detailed model and simulation results

Figure 1 Schematic and block diagram of the solar cell to utility interface.

Let the duty cycle of V_A be equal to D and the duty cycle of V_B be equal to 1-D.

Figure 2 Simpler approximate circuit.

You are to complete your design by answering the following questions.

Due April 17, 2006

1. How many switching cycles are there per one half cycle of the 60Hz?

2. Draw the open loop average model for the circuit in Fig. 1 and the simpler approximate circuit in Fig. 2.

3. What is the general form of the duty cycle D(t) of V_A as a function of time?

4. What is the maximum possible peak primary voltage?

5. Neglecting leakage inductance and magnetizing inductance, what should the 60Hz transformer’s turns ratio be?

6. What is the peak of the average primary current and the peak of the average secondary current assuming the currents are phase with the output voltage?

7. Sketch the average current from the solar array.

8. What is the minimum value of L treating the power system as an ideal voltage source?

9. Ideally the C is not required in the circuit in Fig.1. Why not? Estimate the required value of C in the circuit in Fig. 2 to make the ripple voltage across the load less than 5% of the peak voltage. Use this same value of C in the circuit in Fig. 1.

10. What is the transfer function V_out(s) / d(s) for the linearized open loop system in Fig. 2 in terms of L, C and Do

11. What is the open loop transfer function I_out(s) / d(s) for the linearized open loop system in terms of L and Do assuming an ideal transformer?

12. What value must the resistor R_L in Fig. 2 have so the average inductor currents in Figs. 1 and 2 have equal peak values at maximum power and rated output voltage?

13. Using your average open loop model of the circuit in Fig. 2, simulate the open loop circuit in Fig. 2 with the required duty cycle choosing the time varying duty cycle to obtain a sinusoidal current equal to half rated power. Plot the inductor current and solar array output current. Repeat the simulation for rated power.

14. What is the rms current and an expression for the conduction losses in the power MOSFETs at the maximum power condition?

Due April 24, 2006

15. Estimate the switching losses in the MOSFETs at the maximum power condition. Assume the MOSFETs switch in 100ns. Read the lecture notes “Computing the inverter losses in a 3-phase PWM motor drive” on the EE603 web page.

16. Choose your MOSFET. State its requirements and show your chosen device meets these requirements. Estimate the junction temperature of the MOSFETs using your estimated average power dissipated in the MOSFET.

17. Make a detailed Spice model of the circuit in Fig. 2 using the time varying duty cycle used in step 13. If your chosen MOSFET is in the B2 Spice library use the library model. If it is not you will have to estimate its Kp and threshold voltage from the MOSFET’s specification. Use voltage controlled voltage sources for your gate drive circuits. Simulate the detailed open loop system with the required duty cycle choosing the time varying duty cycle to obtain a sinusoidal current equal to half rated power. Make sure you do not have a shoot-through current. Plot the inductor current and solar array output current.

18. Choose the magnetizing inductance of the transformer so that the magnetizing current seen from the primary is less than 10% of the output current reflected to the primary. Choose the transformer’s leakage inductance to be 1% of its magnetizing inductance.

19. The inductor current has two frequency components, 60Hz and 100kHz. Estimate the peak-to-peak ripple current flowing in the power system voltage source with and without the transformer’s leakage inductance.

20. Draw a block diagram of the closed loop system in Fig. 1. Use proportional-integral control.

21. What is the linearized closed loop transfer function I_out(s) / I_command(s) in terms of L, Do, Kp, and Ki?

22. Choose your gains to make the system stable and obtain a settling time less than 1ms. Simulate the closed loop system using the average model of the inverter to verify your system is stable. Simulate your average model for two 60Hz cycles. Plot V_out and I_out to show they are 60Hz sine waves and that they are in phase.