High-Speed High-Performance Model Predictive Control of Power Electronics Systems

High-Speed High-Performance Model Predictive Control of Power Electronics Systems S. MARIÉTHOZ, S. ALMÉR, A. DOMAHIDI, C. FISCHER, M. HERCEG, S. RICHTER, O. SCHULTES, M. MORARI Automatic Control Laboratory, ETH Zurich HTTP://WWW.CONTROL.EE.ETHZ.CH mariethoz@control.ee.ethz.ch

Outline 2/19 High-Speed High-Performance MPC of Power Electronics Systems Introduction Power Electronics Systems Application Areas Control challenges Modelling power electronics system dynamics Linear Explicit MPC based on model averaging Hybrid approach: objective/ status/ future challenges Conclusions

Application Areas 3/19 High-Speed High-Performance MPC of Power Electronics Systems 1. Renewable energy generation Wind Turbine AC grid PM Gen. Filter/ transformer DC Filter current source inverter AC Filter AC grid Back-to-back voltage source inverters PV array Components: electric drives, frequency/level power converters 2. High-voltage DC electrical energy transmission AC/DC converter A HVDC distributed line model AC/DC converter B Components: frequency/level power converters

Application Area summary 4/19 High-Speed High-Performance MPC of Power Electronics Systems 1. Renewable energy generation,transmission, Electrical energy storage 2. Transportation, Industry/robotics, Consumer electronics Components: electric drives, frequency/level power converters Power electronics systems Broad range of applications System made of different types of Electric drives Frequency/level power converters Improving performance of these two types of components large impact

Control challenges 5/19 High-Speed High-Performance MPC of Power Electronics Systems 1. Dynamic performance and constraint satisfaction 2. Systematic control approach MPC 3. Very fast dynamic modes Fast switching/sampling frequencies (100Hz-1MHz) Fast MPC 4. Semiconductor switches power losses and operating limitations Constrained power losses and operating frequency 5. Energy conversion desired high energy efficiency 6. Grid applications desired high power quality 7. Low-power applications desired low size and consumption of control system System design and control optimization

Outline 6/19 High-Speed High-Performance MPC of Power Electronics Systems Introduction Power Electronics Systems Application Areas Control challenges Modelling power electronics system dynamics Linear Explicit MPC based on model averaging Hybrid approach: objective/ status/ future challenges Conclusions

Electric drives Frequency/level conversion 7/19 High-Speed High-Performance MPC of Power Electronics Systems Wind Turbine AC grid PM Gen. Filter/ transformer Back-to-back voltage source inverters Power electronics systems Controllable semiconductor switches

Subsystem decomposition 8/19 High-Speed High-Performance MPC of Power Electronics Systems Wind Turbine AC grid PM Gen. Filter/ transformer DC link PM AC sync. generator subsystem: electric drive Grid inverter subsystem: frequency/level conversion Structured system: modes and objectives

Subsystem decomposition 8/19 High-Speed High-Performance MPC of Power Electronics Systems Wind Turbine PM Gen. AC grid Filter/ transformer DC link PM AC sync. generator subsystem: electric drive Grid inverter subsystem: frequency/level conversion Structured system: modes and objectives Linear subsystems with binary inputs Much simpler hybrid dynamics ẋ = Fx + G u u + G w w u = i s i v i s i {0, 1} i s i = 0

Modelling approaches 9/19 High-Speed High-Performance MPC of Power Electronics Systems 1. Hybrid system approach Linear subsystems with binary input ẋ = Fx + F u u + F w w u = i s i v i i s i = 1 s i {0, 1} 2. Model averaging approach relaxed binary constraints Linear subsystems with linearly constrained continuous input ẋ = Fx + G u u + G w w u = i d iv i i d i = 1 d i [0, 1]

Modelling approaches 9/19 High-Speed High-Performance MPC of Power Electronics Systems 1. Hybrid system approach Linear subsystems with binary input ẋ = Fx + F u u + F w w u = i s i v i i s i = 1 s i {0, 1} Accurate model loss or distortion minimization 2. Model averaging approach relaxed binary constraints Linear subsystems with linearly constrained continuous input ẋ = Fx + G u u + G w w u = i d iv i i d i = 1 d i [0, 1] Model sufficient for control MPC of averaged dynamics

Outline 10/19 High-Speed High-Performance MPC of Power Electronics Systems Introduction Power Electronics Systems Application Areas Control challenges Modelling power electronics system dynamics Linear Explicit MPC based on model averaging Hybrid approach: objective/ status/ future challenges Conclusions

Linear Explicit MPC based on model averaging 11/19 High-Speed High-Performance MPC of Power Electronics Systems Discretization of averaged dynamics with sampling period T s x k+1 = Ax k + B u u k + B w w k u k = i d kiv ki i d ki = 1 d ki [0, 1] Formulation of tracking linear MPC problem x l x e l Q + u l u e l R k+n min u k l=k track equilibrium point s.t. x l+1 = Ax l + B u u l + B w w l u l = d li v li d li = 1 d li [0, 1] i i linear input and state constraints Can be solved parametrically: 1. Exactly if shape and orientation of input set does not change 2. Limitation: length of horizon and dimension of parameter 3. Yields relaxed variables d ki need feasible binary solution

Obtain feasible binary solution 12/19 High-Speed High-Performance MPC of Power Electronics Systems Duty cycle interpretation of d ki Apply input vectors v ki with duty cycles d ki over T s using pulse-width-modulation (PWM) apply v ki during time interval d ki T s switching period Approach: Very good dynamic performance Losses and distortion depend on PWM scheme

13/19 High-Speed High-Performance MPC of Power Electronics Systems Linear explicit MPC of 2-level induction motor drive 1. Objective: track torque (currents) and flux

13/19 High-Speed High-Performance MPC of Power Electronics Systems Linear explicit MPC of 2-level induction motor drive 1. Objective: track torque (currents) and flux 2. State-of-the-art scheme requires 5 khz for good tracking performance 3. EMPC gives better performance at 1.5 khz 4. EMPC run-time on low-cost DSP 10µs (total 30µs) 5. EMPC better energy efficiency and dynamic performance i s,d,q [A] 5 0 5 0.5 1 1.5 2 2.5 3 u s,d,q, u DC [V] 200 100 0 100 0.5 1 1.5 2 2.5 3 0.6 ˆψr [Wb] 0.4 0.2 0 200 0.5 1 1.5 2 2.5 3 P [W] conduction losses minimum losses 1500 Hz ˆωr [rad/s] 100 0 100 200 switching losses ripple losses 0.5 1 1.5 2 2.5 3

Linear explicit MPC of 9-level induction motor drive 14/19 High-Speed High-Performance MPC of Power Electronics Systems 9-level induction motor drive low-distortion high efficiency drive

Linear explicit MPC of 9-level induction motor drive 14/19 High-Speed High-Performance MPC of Power Electronics Systems 9-level induction motor drive low-distortion high efficiency drive hierarchical approach with linear explicit MPC

Outline 15/19 High-Speed High-Performance MPC of Power Electronics Systems Introduction Power Electronics Systems Application Areas Control challenges Modelling power electronics system dynamics Linear Explicit MPC based on model averaging Hybrid approach: objective/ status/ future challenges Conclusions

Hybrid system approach 16/19 High-Speed High-Performance MPC of Power Electronics Systems Averaging approach gives satisfactory dynamic performance Why bothering about hybrid approach?

Hybrid system approach 16/19 High-Speed High-Performance MPC of Power Electronics Systems Averaging approach gives satisfactory dynamic performance Why bothering about hybrid approach? Losses and distortion Switching losses in semiconductor devices occur during transitions They depend on the switched currents and voltages: switching period Conduction losses depend on high frequency currents f switching Distortion depends on high frequency currents/voltages f switching Averaged model valid only below f switching High-frequency model of voltages and currents required to evaluate losses and distortion

Hybrid system approach 16/19 High-Speed High-Performance MPC of Power Electronics Systems Averaging approach gives satisfactory dynamic performance Why bothering about hybrid approach? Energy efficiency maximization Primary control output defined as an integral over cycle infinitely many solutions Exploit this property to minimize losses such that primary output (e.g. average power) = reference other constraints (e.g. distortion limit) switching loss criterion state-of-the-art optimized grid inverter operating range max gain ~40% Hybrid approach can provide significant loss reduction Computational complexity MIP voltage magnitude

Hybrid system approach 17/19 High-Speed High-Performance MPC of Power Electronics Systems Fairly systematic modelling approach Tractable problems too complex for parametric programming too slow for targeted applications Can implement particular cases using look-up tables and interpolation 1 hybrid approach 0.95 efficiency 0.9 0.85 standard rectangular modulation 0.8 0.75 200 400 600 800 P 1000 1200 1400 Broader range of applications Efficient Solvers/Schemes/Control Systems

Outline 18/19 High-Speed High-Performance MPC of Power Electronics Systems Introduction Power Electronics Systems Application Areas Control challenges Modelling power electronics system dynamics Linear Explicit MPC based on model averaging Hybrid approach: objective/ status/ future challenges Conclusions

Conclusions 19/19 High-Speed High-Performance MPC of Power Electronics Systems Power electronics systems Broad range of applications Many different types of Level/frequency power converters, electric drives Structure and modelling approaches determine complexity and performance Linear explicit MPC based on model averaging improved dynamic performance low complexity compatible with high frequency MHz Hybrid approach improved energy efficiency and power quality already some real-time applications remaining computional challenges for broadening applications