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A Review of Predictive Control Techniques for Matrix Converters - Part II marcoriv@utalca.cl M. Rivera , P. Wheeler, A. Olloqui February 17, 2016

A Review of Predictive Control Techniques for Matrix Converters - Part II Outline Outline 1 Predictive Control Strategies and Applications 2 Limitations and/or Weaknesses 3 Open Questions and Future Trends 4 Conclusions

A Review of Predictive Control Techniques for Matrix Converters - Part II Predictive Control Strategies and Applications Predictive Control Strategies applied to MCs Model Predictive Control Predictive Predictive Predictive Predictive Torque Current Power Voltage Control Control Control Control Filter Imposed Reactive Reactive Common-mode Reduction of Reactive Basic Basic Basic power power resonance sinusoidal voltage switching power strategy strategy strategy minimization minimization mitigation waveform reduction losses minimization

A Review of Predictive Control Techniques for Matrix Converters - Part II Predictive Control Strategies and Applications Predictive Control Strategies � Predictive Current Control (PCC) AC ♣ Only one term in the cost function Source 3 v s a − i p b − i p c − i p g ( k +1) = | i ∗ a | + | i ∗ b | + | i ∗ c | (1) Filter 3 v i ♣ One drawback: variable switching S Aa ... S Cc Cost Matrix frequency i ∗ o Function Converter 3 Minimization ♣ Source currents are highly distorted 27 i p o ( k + 1) 3 i o Predictive 3 v o Model 3 3 R o Load L o

A Review of Predictive Control Techniques for Matrix Converters - Part II Predictive Control Strategies and Applications Predictive Control Strategies v sA i sA a) b) i ∗ a i a Experimental results using a three-phase variac as the AC-source; a) source voltage vsA [V] and current isA [A]; b) output current ia [A] and its reference i ∗ a [A].

A Review of Predictive Control Techniques for Matrix Converters - Part II Predictive Control Strategies and Applications Predictive Control Strategies � PCC with input reactive power minimization v i i o ♣ Two terms in the cost function 3 3 AC Source 3 i s g ( k + 1) = △ i o + γ q △ Q (2) Predictive 3 v s Model 3 △ io = | i ∗ a − ip a | + | i ∗ b − ip b | + | i ∗ c − ip c | Filter △ Q = | vs α is β − vs β is α | 27 Q p ( k + 1) 3 v i ♣ Input currents in phase with their Q ∗ S Aa ... S Cc Cost respective voltages Matrix Function Converter i ∗ o Minimization 3 ♣ Weighting factor selection 27 i p o ( k + 1) 3 ♣ The method is very sensitive to source i o Predictive 3 voltage distortion and input filter Model v o 3 resonances R o Load L o

A Review of Predictive Control Techniques for Matrix Converters - Part II Predictive Control Strategies and Applications Predictive Control Strategies v sA i sA a) b) i ∗ a i a Experimental results using a three-phase variac as the AC-source; a) source voltage vsA [V] and current isA [A]; b) output current ia [A] and its reference i ∗ a [A].

A Review of Predictive Control Techniques for Matrix Converters - Part II Predictive Control Strategies and Applications Predictive Control Strategies � PCC with active damping v i i o 3 3 AC Source ♣ The same cost function abc 3 PLL dq i s θ i Predictive 3 v dq i Model v s g ( k + 1) = △ i o + γ q △ Q (3) Digital 3 DC Blocker v dq Filter a − ip b − ip c − ip △ io = | i ∗ a | + | i ∗ b | + | i ∗ ih c | 27 Q p ( k + 1) 1 R 3 △ Q = | vs α is β − vs β is α | v i i dq I ∗ ih odq Q ∗ S Aa ... S Cc Cost Matrix ♣ The main idea: to emulate a Function Converter i ∗ dq o virtual resistor Minimization abc 3 i p 27 o ( k + 1) ♣ The harmonic content is 3 i o passed from the input to the Predictive 3 v o Model output side 3 R o Load L o

A Review of Predictive Control Techniques for Matrix Converters - Part II Predictive Control Strategies and Applications Predictive Control Strategies � PCC with active damping v i i o 3 3 AC Source ♣ The performance of the abc 3 PLL dq i s θ i system is improved Predictive 3 v dq i Model v s Digital 3 DC Blocker ♣ The power losses are reduced v dq Filter ih 27 Q p ( k + 1) 1 ♣ The price: PLL - Digital dc R 3 v i i dq I ∗ ih blocker implementation odq Q ∗ S Aa ... S Cc Cost Matrix Function Converter i ∗ dq o ♣ Sensitive to distortions in Minimization abc 3 source voltages i p 27 o ( k + 1) 3 i o Predictive 3 v o Model 3 R o Load L o

A Review of Predictive Control Techniques for Matrix Converters - Part II Predictive Control Strategies and Applications Predictive Control Strategies v sA i sA a) b) i ∗ i a a Experimental results using a three-phase variac as the AC-source; a) source voltage vsA [V] and current isA [A]; b) output current ia [A] and its reference i ∗ a [A].

A Review of Predictive Control Techniques for Matrix Converters - Part II Predictive Control Strategies and Applications Predictive Control Strategies � PCC with imposed sinusoidal source currents v s 3 i s 3 Predictive 3 Model v s V s I o δ 3 g ( k +1) = △ i o + γ i △ i s (4) PLL φ Filter 27 i p s ( k + 1) Eq. (6) Eq. (5) 3 v i I s Q ∗ S Aa ... S Cc Cost Matrix 3 Function Converter i ∗ o Minimization 3 ( λ V s ) 2 − 4 λ R f R L I ∗ 2 � I s = − λ V s ± o /η 27 i p o ( k + 1) 3 − 2 λ R f i o Predictive (5) 3 v o Model i ∗ sA = I s sin( w s t + θ ) 3 sB = I s sin( w s t − 2 π/ 3 + θ ) R o i ∗ Load L o i ∗ sC = I s sin( w s t + 2 π/ 3 + θ ) (6)

A Review of Predictive Control Techniques for Matrix Converters - Part II Predictive Control Strategies and Applications Predictive Control Strategies � PCC with imposed sinusoidal source currents v s 3 i s 3 Predictive 3 v s ♣ Sinusoidal input Model δ V s I o 3 PLL current regardless the φ Filter distortion on the input 27 i p s ( k + 1) Eq. (6) Eq. (5) side 3 v i I s Q ∗ S Aa ... S Cc ♣ Lower (THD) of both Cost Matrix 3 Function Converter i ∗ input and load currents o Minimization 3 27 i p o ( k + 1) ♣ Reducing the resonance 3 i o Predictive of the input filter 3 Model v o allowing longer lifetime 3 R o of the converter Load L o ♣ The price: higher switching frequency

A Review of Predictive Control Techniques for Matrix Converters - Part II Predictive Control Strategies and Applications Predictive Control Strategies v sA i sA a) i ∗ a i a b) Experimental results using a three-phase variac as the AC-source; a) source voltage vsA [V] and current isA [A]; b) output current ia and its reference i ∗ a [A].

A Review of Predictive Control Techniques for Matrix Converters - Part II Predictive Control Strategies and Applications Predictive Control Strategies � PCC with Common-Mode Voltage (CMV) v s 3 i s minimization and imposed 3 Predictive 3 v s Model sinusoidal input waveform δ V s I o 3 PLL φ Filter ♣ Control of CMV i p 27 s ( k + 1) Eq. (6) Eq. (5) 3 reduces overvoltage v i I s stress to the winding Q ∗ S Aa ... S Cc Cost Matrix i ∗ 3 Function insulation and bearing o Converter 3 Minimization deterioration 27 v p cm ( k + 1) 27 i p o ( k + 1) ♣ Increasing the lifetime v i Predictive 3 i o 3 Model Predictive of electric machines 3 Model v o 3 R o Load L o

A Review of Predictive Control Techniques for Matrix Converters - Part II Predictive Control Strategies and Applications Predictive Control Strategies � PCC with Common-Mode Voltage (CMV) v s 3 i s minimization and imposed 3 Predictive 3 v s Model sinusoidal input waveform δ V s I o 3 PLL φ Filter ♣ Is possible to include 27 i p s ( k + 1) Eq. (6) Eq. (5) 3 several control v i I s objectives in the cost Q ∗ S Aa ... S Cc Cost Matrix i ∗ 3 Function function o Converter 3 Minimization 27 v p cm ( k + 1) 27 i p o ( k + 1) v i Predictive 3 i o 3 Model Predictive 3 Model v o 3 R o g ( k +1) = △ i o + γ i △ i s + γ v | v cm ( k +1) | Load L o (7)

A Review of Predictive Control Techniques for Matrix Converters - Part II Predictive Control Strategies and Applications Predictive Control Strategies 10 10 v sA v sA i sA i sA 0 0 i ∗ i ∗ sA sA -10 -10 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 10 10 i a i a 0 0 i ∗ i ∗ a a -10 -10 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 300 300 v cm v cm 200 200 100 100 0 0 -100 -100 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 With CMV reduction Without CMV reduction

A Review of Predictive Control Techniques for Matrix Converters - Part II Predictive Control Strategies and Applications Predictive Control Strategies v i i o � PCC for Torque and Flux AC Control with input reactive Source 3 power minimization i s Predictive 3 v s Model 3 ♣ Hybrid combination Filter between PCC and FOC 27 Q p ( k + 1) 3 v i i ∗ S Aa ... S Cc ♣ No need for abc o Cost Matrix dq 3 Function Converter modulation techniques i ∗ dq Minimization Q ∗ o ω r 27 FOC i p o ( k + 1) 3 i o T ∗ Predictive 3 Ψ ∗ Model v o 3 IM ω ∗ ω r Load r ω r , θ r