Predictive Control of a Three-Phase Neutral Point Clamped Inverter

V aN[V]V aN[V](a) PWM150100500−50−100−1500 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04(b) Predictive150100500−50−100−1500 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04Fig. 6.Time [s]Load voltage on phase a: (a) PWM (b) Predictive.i β[A]i [A] αPWM20100−10−200.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.04520100−10−200.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045Time [s]Fig. 8. Load current response applying step on i ∗ α : PWM Method.Magnitude [%]Magnitude [%]40302010(a)PWM02.0 4.0 6.0 8.0 10.040302010(b)Predictive02.0 4.0 6.0 8.0 10.0Frequency [kHz]Fig. 7.Load voltage spectrum: (a) PWM (b) Predictive.i [A]i [A]β αPredictive20100−10−200.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.04520100−10−200.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045Time [s]Fig. 9. Load current response applying step on i ∗ α : Predictive Method.using the following quality function:g = |i ∗ α(k +1)− i α (k +1)| + |i ∗ β (k +1)− i β(k +1)|+λ|Vc 1 (k +1)− Vc 2 (k +1)| (14)The λ weighting factor was selected to be sufficiently small toallow the algorithm to select switching states within a givenvoltage vector. The value selected was λ =0.001. As shownin Fig. 10, the presented method succeeded maintainingvoltage balance without affecting the current control.C. Reduction of the switching frequency.Choosing alternative 2 of equation (12), it is possibleto reduce considerably the average switching frequency persemiconductor, f s . This was proven using the followingquality function:g = |i ∗ α(k +1)− i α (k +1)| + |i ∗ β (k +1)− i β(k +1)|+λ · n c (15)The λ weighting factor was set at 0.001. The switchingfrequency f s was reduced from 835[Hz] to 645[Hz] withoutharming reference tracking. Increasing λ to 0.332 (emphasisin reducing the switching frequency), a frequency of 299[Hz]was achieved. That represents only a 35.8% of the originalaverage switching frequency per semiconductor or the f spresented by the PWM method. Results for the load currenton phase a, for λ =0.001 and λ =0.332, are presented inFig. 11.As expected, applying a greater λ implies in most casesreducing the switching frequency. In general, the trade-offis a slight increase of the reference tracking error. In thecase presented (Fig.11) the mean absolute reference trackingerror increased from 0.3137[A] to 0.3534[A]. To expose thepossibilities of the proposed method, a graph showing therelation between the design parameter λ and the switchingfrequency and mean absolute reference tracking error ispresented in Fig.12.The designer should select a λ parameter that fits hisrequirements in terms of switching frequency and reference1367