LMIs in Control/Click here to continue/Applications of Linear systems/Mixed H2-H∞ Optimal Voltage Control Design for Smart Transformer Low-Voltage Inverter
LMIs in Control/Click here to continue/Applications of Linear systems/Mixed H2-H∞ Optimal Voltage Control Design for Smart Transformer Low-Voltage Inverter
Smart transformers are often used in situations with variable loads such as the integration of renewable energy sources. This section examines a system of Linear Matrix Inequalities as analyzed by Wei Hu, Yu Shen, Zhichun Yang, and Huaidong Min in their paper for Mixed / Optimal Voltage Control Design for Smart Transformer Low-Voltage Inverter.
The System[edit | edit source]
State space modelling is used in order to develop a system that describes the inverter behavior.
The system formulation for a simple inverter system draws directly from electric circuit theory. where the above variables are defined as follows:
- is the resistance
- is the inductance
- is the capacitance
This system is further augmented by adding multiple resonant controllers to ensure the system can reach zero steady-state error when tracking sinusoidal target outputs. The augmented system is then derived as follows:
where
The Data[edit | edit source]
The data required to solve this problem includes the values of resistance, inductance, capacitance, switch frequency, output peak voltage, and the DC link voltage.
The Optimization Problem[edit | edit source]
The optimization problem aims to minimize a combined / norm of the system as defined above. In order to accomplish this task, constraints and the objective must first be defined.
- Objective: Combined / norm
- Constraints: Closed-loop poles are restricted to a desired section of the complex plane,
The LMI: Mixed H2-H∞ Optimal Voltage Control[edit | edit source]
In the above LMIs, the coefficients a and b represent the weighting factor applied to the and norms respectively. R is some given positive-definite matrix.
Conclusion[edit | edit source]
Mixed / optimal control can be effectively used to design efficient and useful smart transformers.
Implementation[edit | edit source]
This LMI can be implemented using MATLAB when combined with YALMIP and an LMI solver such as SeDuMi.
Related LMIs[edit | edit source]
External Links[edit | edit source]
- [1] – Mixed H2/H∞ Optimal Voltage Control Design for Smart Transformer Low-Voltage Inverter – Wei Hu, Yu Shen, Zhichun Yang, and Huaidong Min
- [2] - LMIs in Control Systems: Analysis, Design, and Applications – Guang-Ren Duan and Hai-Hua Yu
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.