1. Modeling and Advanced Control Design for DC/DC Converters in Microgrids
Chris Leonard and Baylor Howard
Advisor: Dr. Jing Wang
Department of Electrical and Computer Engineering
Bradley University
May 4, 2019

2. Outline Introduction Project Background Problem Statement Objectives
Modeling
Basic Circuit
Switch ON/OFF
Averaged State Space Model
Control Design
Simulation
Linear Model
Nonlinear Model
Conclusion
References

3. Introduction

4. Figure 1 PV Microgrid Block Diagram
Problem Background
Renewable energy accounts for 11%
Solar: 6% of renewables (0.66% overall)
Source: US Energy Information Administration
Microgrids are used in off-grid locations
Many DC/DC converters
and DC/AC inverters are in Microgrids
For load and needs of feeding to main grid
Ensuring MPPT
It is of importance to develop advanced
control algorithms to ensure the steady output of converters in the presence of model uncertainties and input perturbations.
Figure 1 PV Microgrid Block Diagram

5. Figure 3 Boost Converter
DC/DC Converters
Converters are used for MPPT in microgrids
Converters are used to meet the needs of DC loads.
There are step down BUCK converters.
There are step down BOOST converters.
Figure 2 Buck Converter
Figure 3 Boost Converter

6. Project Objectives Modeling Analysis
Study the averaged state space model
Develop advanced control algorithms for DC/DC converter
Linear Design
Nonlinear Design
Functional Requirements
The proposed design will be non-model based (not relying on system parameters).
The proposed PWM control signal is ensured to be in the range of duty cycle.
The proposed control can handle input perturbation (robustness)
The proposed control can handle load uncertainty.
The proposed control is robust to existing ESRs for inductors and capacitors.

7. Modeling

8. Figure 4 Basic Buck Converter
Circuit Model
Buck converter model with PWM switching control
Ts switching period; D duty cycle of PWM signal
[kTs, (k+D)Ts] switch on; [k+D)Ts, (k+1)Ts) switch off
Figure 4 Basic Buck Converter

9. Circuit Mode: Switch On
PWM switch is ON for time interval [kTs, (k+D)Ts)
Figure 5 Buck Converter Switch On

10. Circuit State Space Model
Define: inductor current; load voltage
Based circuit laws (KVL, KCL)

11. Circuit Mode: Switch Off
PWM switch is OFF for time interval [(k+D)Ts, (k+1)Ts)
Figure 6 Buck Converter Switch Off

12. Circuit State Space Model
Time Interval
State Equation
A and B matrix

13. Averaged State Space Model
The input to RLC circuit behaves like a square wave signal with frequency
If Ts is small enough, a Fourier analysis can show that the circuit output is dominated by the DC component of a square wave signal.
Thus, the following averaged state space model is used for control design.

14. Control Design

15. Linear Design
The design is based on linearization around the equilibrium point of the system.
Let the desired output voltage be
The equilibrium point is
Define error signals
Linearized model is

16. Linear Design The control is
Gain matrix K can be obtained using pole placement method.

17. Linear Design The possible issues with linear design
Model based; need know system parameters L, C, R
If there are uncertainties, control gain K obtained from nominal values may not render stable poles any more.
The obtained control ΔD may be out of range for duty cycle, and the proper scaling has to be used.

18. Nonlinear Design The proposed new control is
Stability analysis can be done using Lyapunov direct method.

19. Nonlinear Design Lyapunov function
We can show that its derivative along the system trajectory
Which ensure e1 goes to zero and e2 goes to zero.

20. Nonlinear Design The benefits using this new design Simulation study
Nonlinear model based; robustness to systems uncertainties
Control input is guaranteed in the range of [0,1]; no scaling factor needed.
Simulation study
Input perturbation
Load change

21. Simulation

22. Figure 7 MATLAB Square Wave
Simulation
Parameters
L1 = 1.33mH
C1 = 94uF
R1 = 4 Ω
Vin = 42, 44V
Vout = 12V
D = 12/42
Ts = 0.01 ms
Figure 7 MATLAB Square Wave

23. Figure 8 Linear Pspice Model
Linear Design
Figure 8 Linear Pspice Model

24. Figure 9 Linear Pspice Output - Transient Sweep
Linear Design Output
Figure 9 Linear Pspice Output - Transient Sweep

25. Figure 10 Linear Pspice Output - Monte Carlo
Linear Design Output
Linear model with load change at R=4[𝛀] at 5% tolerance with n=50 samples
Figure 10 Linear Pspice Output - Monte Carlo

26. Figure 11 Linear Pspice Output - Monte Carlo Histogram
Linear Design Output
Figure 11 Linear Pspice Output - Monte Carlo Histogram

27. Figure 12 Nonlinear Pspice Model
Nonlinear Model
Figure 12 Nonlinear Pspice Model

28. Nonlinear Model Output
Figure 13 Nonlinear Pspice Output - Transient Sweep

29. Nonlinear Model Output
Nonlinear model with load change in R=4[𝛀] at 5% tolerance with n=50 samples
Figure 14 Nonlinear Pspice Output - Monte Carlo

30. Nonlinear Model Output
Figure 15 Nonlinear Pspice Output - Monte Carlo Histogram

31. Nonlinear Model Output
L,C,R at tolerance of 5% with n=50 samples
Figure 16 Nonlinear Pspice Output - Monte Carlo v2

32. Nonlinear Model Output
The nonlinear model output grouping with L,C,R variances is close to target output of 12 [v]
Figure 17 Nonlinear Pspice Output - Monte Carlo Histogram v2

33. Cost Used MATLAB & Pspice TMS320C2000 Digital Power Kit
Available resources in lab
TMS320C2000 Digital Power Kit
$200
Two channel DC/DC buck converter
Figure 18 TMS320C2000

34. Division of Labor Chris PSpice modeling Controls theory application
State space model design
Physical buck converter attempt
Baylor
DC/DC converter modeling
MATLAB & Pspice
Linear model of system
Simulation testing
H-Bridge inverter work

35. Conclusion
Due to the environmental impact of finite fossil fuels on our atmosphere, it is imperative that we take the necessary steps towards sustainable energy sources such as solar power.
This project thoroughly studied the control techniques and strategies for DC/DC converters, namely strategies for linear and nonlinear control of buck and boost converters.
The simulation results which were obtained verify the effectiveness of the proposed converter design.
Once implemented, our system will be able to improve power efficiency within microgrids due to it’s precise variable input tracking.

36. Future Work Implement system with H-Bridge Inverter Use C2000 MCU
3-phase power
Battery storage
PV panel efficiency
Figure 19 C2000 MCU

37. References
Y. Lu, “Advanced grid-tied photovoltaic micro-inverter”, University of Canterbury, Christchurch, New Zealand, 2015.
Texas Instruments, “Digitally controlled solar micro inverter design using C2000 Piccolo microcontroller,” TIDU405B datasheet, Oct.2014 [Revised June 2017].
D. Hart, “Power Electronics.” New York: McGraw-Hill, 2011.