A “TWO AHEAD” PREDICTIVE CONTROLLER FOR ACTIVE SHUNT POWER FILTERs

1. A “TWO AHEAD” PREDICTIVE CONTROLLER FOR ACTIVE SHUNT POWER FILTERs Milijana Odavic, Pericle Zanchetta, Mark Sumner Power Electronics, Machines and Control Group School of Electrical and Electronic Engineering

2. Presentation Overview • Introduction • Control problem overview • Mathematical model • Predictive current controller • Overall control structure • Experimental results • Current loop analysis • Conclusion • Future work

3. Introduction - the power supply needs to ensure only active power to the load Active shunt power filter ASF connected to the network The control structure: - dc-link voltage control - current control - method to determine the current references

4. Control problem overview Demands concerning a current controller design are: • minimisation of the phase and amplitude errors for a wide range of reference trajectories • fast dynamic response • robustness to model and parameter uncertainties • noise rejection

5. Control problem overview Simulation results - synchronous PI plus lead compensator • current control loop bandwidth ~ 1kHz • sensitive to measurement noise • sensitive to parameter variations • in reality bandwidth < 300 Hz d component q component Comparison of the real current (full line) and the 7th harmonic current references (broken line) Results: - amplitude discrepancy - 13% - phase delay - 24.

6. Mathematical model • predictive control is a model-based control method • appropriate model is essential for the controller design The discrete linear model of the ASF Equivalent single-phase representation of an ASF Ts-sampling period, k-sampling instant Assumptions: supply voltage and ASF voltage are constant over a control interval, e=E(k) and v=V(k) respectively.

7. Predictive current controller • the delay caused by the computational time is kept constant and equal to one sampling period • the aim of this controller is to predict the ASF voltage reference for the next sampling period to eliminate the current error at the instant k+2 Predictive controller principal Lm-inductance value used by controller, L – actual inductance L=Lm / L - relative input inductance error parameter

8. Predictive current controller Reference prediction Two-step-ahead extrapolation of current reference using GA optimisation is proposed - based on the minimization of the following fitness function - prediction error is negligible (a factor of 10-4). Table I GA optimisation parameters of reference prediction

9. Predictive current controller Predictive current controller Reference prediction • the extrapolation uses values from a few previous sampling instants • at the instant of step change in reference, a big error is introduced • when a reference change is detected, the prediction over the next few sampling instants is frozen Comparison of the measured reference current and two-ahead predicted reference current (at t=0.027s step change from 15A to 5A)

10. Predictive current controller ASF current prediction Linear prediction of ASF current at instant k+1: • desired value of the current at the instant k+1 is i*(k+1). • the proposed prediction adds the predicted value of the current reference change over the current sampling period to the measured current at the instant k • accuracy of the proposed ASF current prediction mainly depends on the accuracy of the reference prediction • non model based prediction • no supply voltage and ASF voltage values needed

11. Overall control structure Block diagram of the proposed control strategy (single phase representation)

12. Simulation results • results of simulation model developed in MATLAB/SIMULINK • good current reference tracking in steady state and dynamic condition Simulation results of the comparison of the phase current i(k) and the current reference i*(k) (at t = 0.027 s step change in amplitude and frequency)

13. Experimental rig • floating point PowerPC 603e microprocessor • slave fixed point DSP TMS320F240 • three phase PWM unit • four independent fast 12-bit A/D converters • four 16-bit multiplexed channels Experimental rig of the fully digital ASF

14. Experimental rig Commercial three phase converter is adjusted to achieve control via DSpace1104 control board PCB for inverter protection and watch dog circuit

15. i [A] t [s] Experimental results Comparison of the phase current (red) and the current reference (blue) (fundamental, 5th and 7th harmonic components) Comparison of the phase current (red) and the current reference (blue) (fundamental and 5th harmonic components) Switching/sampling frequency fs=5 kHz L=3.75 µH, R=0.3 Ω minimal phase and amplitude mismatch

16. i [A] i [A] t [s] t [s] Experimental results fundamental component 5th harmonic component Comparison of the phase current (red) and the current reference (blue) (step change in amplitude from 8A to 10A) Switching/sampling frequency fs=5 kHz L=3.75 µH, R=0.3 Ω minimal phase and amplitude mismatch

17. Current loop analysis Stability verification Characteristic equation of the closed current control loop: To get root locus of the system as the parameters ΔL vary, the characteristic equation is then rewritten into the desired form: Root locus of the system as the relative input inductance error parameter L=Lm / L (gain)varies Lm-inductance value used by controller, L – actual inductance

18. Current loop analysis Noise rejection Predictive controller output signals in the presence of 3% voltage and 5% current measurement noise

19. Conclusion • Proposed two ahead predictive current controller verified at fundamental frequency and at the 5th and the 7th harmonics • minimal phase and amplitude mismatch in steady state and dynamic conditions • performance of the proposed controller depends on the system model accuracy • stability analysis confirm good operation of the controller, even when Lm=2L (significant parameter mismatch)

20. Future work • build cascaded H-bridges five level ASF • adjust the proposed controller for the multilevel applications