Post on 08-Jul-2018
High-Speed High-Performance ModelPredictive Control of Power Electronics
Systems
S. MARIETHOZ, S. ALMER, 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
IntroductionPower Electronics Systems’ Application AreasControl challenges
Modelling power electronics system dynamics
Linear Explicit MPC based on model averaging
Hybrid approach: objective/ status/ future challenges
Conclusions
2/19 High-Speed High-Performance MPC of Power Electronics Systems
Application Areas
1. Renewable energy generation
AC gridAC Filter
DC
Fil
ter
current source inverter
PV
arra
y
PM
Gen.
Wind
Turbine
AC
grid
Filter/
transformer
Back-to-back voltage source inverters
I Components: electric drives, frequency/level power converters2. High-voltage DC electrical energy transmission
AC/DC
converter A HVDC distributed line model
AC/DC
converter B
I Components: frequency/level power converters
3/19 High-Speed High-Performance MPC of Power Electronics Systems
Application Area summary
1. Renewable energy generation,Transmission, Electrical energy storage2. Transportation, Industry/robotics, Consumer electronics
I Components: electric drives, frequency/level power converters
Power electronics systemsI Broad range of applicationsI System made of different types of
I Electric drivesI Frequency/level power converters
I Improving performance of these two types of components
⇒ large impact
4/19 High-Speed High-Performance MPC of Power Electronics Systems
Control challenges
1. Dynamic performance and constraint satisfaction2. Systematic control approach
I MPC3. Very fast dynamic modes
⇒ Fast switching/sampling frequencies (100Hz-1MHz)I Fast MPC
4. Semiconductor switches⇒ power losses and operating limitationsI Constrained power losses and operating frequency
5. Energy conversion⇒ desired high energy efficiency6. Grid applications⇒ desired high power quality7. Low-power applications⇒ desired low size and consumption of control
system
I System design and control optimization
5/19 High-Speed High-Performance MPC of Power Electronics Systems
Control challenges
1. Dynamic performance and constraint satisfaction2. Systematic control approach
I MPC3. Very fast dynamic modes
⇒ Fast switching/sampling frequencies (100Hz-1MHz)I Fast MPC
4. Semiconductor switches⇒ power losses and operating limitationsI Constrained power losses and operating frequency
5. Energy conversion⇒ desired high energy efficiency6. Grid applications⇒ desired high power quality7. Low-power applications⇒ desired low size and consumption of control
system
I System design and control optimization
5/19 High-Speed High-Performance MPC of Power Electronics Systems
Outline
IntroductionPower Electronics Systems’ Application AreasControl challenges
Modelling power electronics system dynamics
Linear Explicit MPC based on model averaging
Hybrid approach: objective/ status/ future challenges
Conclusions
6/19 High-Speed High-Performance MPC of Power Electronics Systems
Electric drives — Frequency/level conversion
PM
Gen.
Wind
Turbine
AC
grid
Filter/
transformer
Back-to-back voltage source inverters
Power electronics systemsI Controllable semiconductor switches
I interconnect different points of circuits
7/19 High-Speed High-Performance MPC of Power Electronics Systems
Electric drives — Frequency/level conversion
PM
Gen.
Wind
Turbine
AC
grid
Filter/
transformer
Back-to-back voltage source inverters
Power electronics systemsI Controllable semiconductor switches
I interconnect different points of circuits
7/19 High-Speed High-Performance MPC of Power Electronics Systems
Electric drives — Frequency/level conversion
PM
Gen.
Wind
Turbine
AC
grid
Filter/
transformer
Back-to-back voltage source inverters
Power electronics systemsI Controllable semiconductor switchesI interconnect different points of circuits
7/19 High-Speed High-Performance MPC of Power Electronics Systems
Electric drives — Frequency/level conversion
PM
Gen.
Wind
Turbine
AC
grid
Filter/
transformer
Back-to-back voltage source inverters
Power electronics systemsI Controllable semiconductor switchesI interconnect different points of circuits⇒ switched waveforms
7/19 High-Speed High-Performance MPC of Power Electronics Systems
Electric drives — Frequency/level conversion
PM
Gen.
Wind
Turbine
AC
grid
Filter/
transformer
Back-to-back voltage source inverters
Power electronics systemsI Dynamics⇒ Complex hybrid systems
x =∑
i si (Fix + Gviv) si ∈ {0, 1}∑
i si = 1
7/19 High-Speed High-Performance MPC of Power Electronics Systems
Subsystem decomposition
PM
Gen.
Wind
Turbine
AC
grid
Filter/
transformer
DC
link
Grid inverter subsystem:
frequency/level conversionPM sync. generator subsystem:
electric drive
AC
Structured system: modes and objectives
I Linear subsystems with binary inputs⇒Much simpler hybrid dynamicsx = Fx + Guu + Gww u =
∑i si vi si ∈ {0, 1}
∑i si = 0
⇒ 2 modelling and control approaches
8/19 High-Speed High-Performance MPC of Power Electronics Systems
Subsystem decomposition
PM
Gen.
Wind
Turbine
AC
grid
Filter/
transformer
DC
link
Grid inverter subsystem:
frequency/level conversionPM sync. generator subsystem:
electric drive
AC
Structured system: modes and objectivesI Linear subsystems with binary inputs⇒Much simpler hybrid dynamics
x = Fx + Guu + Gww u =∑
i si vi si ∈ {0, 1}∑
i si = 0
⇒ 2 modelling and control approaches
8/19 High-Speed High-Performance MPC of Power Electronics Systems
Subsystem decomposition
PM
Gen.
Wind
Turbine
AC
grid
Filter/
transformer
DC
link
Grid inverter subsystem:
frequency/level conversionPM sync. generator subsystem:
electric drive
AC
Structured system: modes and objectivesI Linear subsystems with binary inputs⇒Much simpler hybrid dynamics
x = Fx + Guu + Gww u =∑
i si vi si ∈ {0, 1}∑
i si = 0
⇒ 2 modelling and control approaches
8/19 High-Speed High-Performance MPC of Power Electronics Systems
Modelling approaches
1. Hybrid system approachI Linear subsystems with binary input
x = Fx + Fuu + Fww u =∑
i si vi∑
i si = 1 si ∈ {0, 1}
I Accurate model⇒ loss or distortion minimization
2. Model averaging approach⇒ relaxed binary constraintsI Linear subsystems with linearly constrained continuous input
x = Fx + Guu + Gww u =∑
i divi∑
i di = 1 di ∈ [0, 1]
I Model sufficient for control⇒MPC of averaged dynamics
9/19 High-Speed High-Performance MPC of Power Electronics Systems
Modelling approaches
1. Hybrid system approachI Linear subsystems with binary input
x = Fx + Fuu + Fww u =∑
i si vi∑
i si = 1 si ∈ {0, 1}I Accurate model⇒ loss or distortion minimization
2. Model averaging approach⇒ relaxed binary constraintsI Linear subsystems with linearly constrained continuous input
x = Fx + Guu + Gww u =∑
i divi∑
i di = 1 di ∈ [0, 1]I Model sufficient for control⇒MPC of averaged dynamics
9/19 High-Speed High-Performance MPC of Power Electronics Systems
Outline
IntroductionPower Electronics Systems’ Application AreasControl challenges
Modelling power electronics system dynamics
Linear Explicit MPC based on model averaging
Hybrid approach: objective/ status/ future challenges
Conclusions
10/19 High-Speed High-Performance MPC of Power Electronics Systems
Linear Explicit MPC based on model averaging
I Discretization of averaged dynamics with sampling period Tsxk+1 = Axk + Buuk + Bwwk uk =
∑i dkivki
∑i dki = 1 dki ∈ [0, 1]
I Formulation of tracking linear MPC problem
minuk
k+N∑l=k
‖xl − xel ‖Q + ‖ul − ue
l ‖R track equilibrium point
s.t. xl+1 = Axl + Buul + Bwwl
ul =∑
i
dlivli
∑i
dli = 1 dli ∈ [0, 1]
linear input and state constraintsI Can be solved parametrically:
1. Exactly if shape and orientation of input set does not change2. Limitation: length of horizon and dimension of parameter3. Yields relaxed variables dki ⇒ need feasible binary solution
11/19 High-Speed High-Performance MPC of Power Electronics Systems
Obtain feasible binary solution
I Duty cycle interpretation of dki
I Apply input vectors vki with duty cycles dki over Tsusing pulse-width-modulation (PWM)⇒ apply vki during time interval dki Ts
switching period
I Approach:I Very good dynamic performanceI Losses and distortion depend on PWM scheme
12/19 High-Speed High-Performance MPC of Power Electronics Systems
Linear explicit MPC of 2-level induction motor drive1. Objective: track torque (currents) and flux
2. State-of-the-art scheme requires 5 kHz for good tracking performance3. EMPC gives better performance at 1.5 kHz4. EMPC run-time on low-cost DSP 10µs (total 30µs)5. EMPC⇒ better energy efficiency and dynamic performance
i s,d,q
[A]
0.5 1 1.5 2 2.5 3−5
0
5
ψr[W
b]
0.5 1 1.5 2 2.5 30
0.2
0.4
0.6
ωr[r
ad/
s]
0.5 1 1.5 2 2.5 3
−200
−100
0
100
200
u s,d,q,
u DC[V
]
0.5 1 1.5 2 2.5 3
−100
0
100
200
P[W
]
minimum
losses 1500 Hz
switching losses
ripple losses
conduction losses
13/19 High-Speed High-Performance MPC of Power Electronics Systems
Linear explicit MPC of 2-level induction motor drive1. Objective: track torque (currents) and flux2. State-of-the-art scheme requires 5 kHz for good tracking performance3. EMPC gives better performance at 1.5 kHz4. EMPC run-time on low-cost DSP 10µs (total 30µs)
5. EMPC⇒ better energy efficiency and dynamic performance
i s,d,q
[A]
0.5 1 1.5 2 2.5 3−5
0
5
ψr[W
b]
0.5 1 1.5 2 2.5 30
0.2
0.4
0.6
ωr[r
ad/
s]
0.5 1 1.5 2 2.5 3
−200
−100
0
100
200
u s,d,q,
u DC[V
]
0.5 1 1.5 2 2.5 3
−100
0
100
200
P[W
]
minimum
losses 1500 Hz
switching losses
ripple losses
conduction losses
13/19 High-Speed High-Performance MPC of Power Electronics Systems
Linear explicit MPC of 2-level induction motor drive1. Objective: track torque (currents) and flux2. State-of-the-art scheme requires 5 kHz for good tracking performance3. EMPC gives better performance at 1.5 kHz4. EMPC run-time on low-cost DSP 10µs (total 30µs)5. EMPC⇒ better energy efficiency and dynamic performance
i s,d,q
[A]
0.5 1 1.5 2 2.5 3−5
0
5
ψr[W
b]
0.5 1 1.5 2 2.5 30
0.2
0.4
0.6
ωr[r
ad/
s]
0.5 1 1.5 2 2.5 3
−200
−100
0
100
200
u s,d,q,
u DC[V
]
0.5 1 1.5 2 2.5 3
−100
0
100
200
P[W
]
minimum
losses 1500 Hz
switching losses
ripple losses
conduction losses
13/19 High-Speed High-Performance MPC of Power Electronics Systems
Linear explicit MPC of 9-level induction motor drive9-level induction
motor drive
I low-distortion high efficiency drive
I hierarchical approach with linear explicit MPC
I high-dynamic performance
I unified approach
14/19 High-Speed High-Performance MPC of Power Electronics Systems
Linear explicit MPC of 9-level induction motor drive9-level induction
motor drive
I low-distortion high efficiency drive
I hierarchical approach with linear explicit MPC
I high-dynamic performance
I unified approach
14/19 High-Speed High-Performance MPC of Power Electronics Systems
Linear explicit MPC of 9-level induction motor drive9-level induction
motor drive
I low-distortion high efficiency drive
I hierarchical approach with linear explicit MPC
I high-dynamic performance
I unified approach
14/19 High-Speed High-Performance MPC of Power Electronics Systems
Linear explicit MPC of 9-level induction motor drive9-level induction
motor drive
I low-distortion high efficiency drive
I hierarchical approach with linear explicit MPC
I high-dynamic performance
I unified approach
14/19 High-Speed High-Performance MPC of Power Electronics Systems
Linear explicit MPC of 9-level induction motor drive9-level induction
motor drive
I low-distortion high efficiency drive
I hierarchical approach with linear explicit MPC
I high-dynamic performance
I unified approach
14/19 High-Speed High-Performance MPC of Power Electronics Systems
Outline
IntroductionPower Electronics Systems’ Application AreasControl challenges
Modelling power electronics system dynamics
Linear Explicit MPC based on model averaging
Hybrid approach: objective/ status/ future challenges
Conclusions
15/19 High-Speed High-Performance MPC of Power Electronics Systems
Hybrid system approach
I Averaging approach gives satisfactory dynamic performance⇒ Why bothering about hybrid approach?
Losses and distortionI Switching losses in semiconductor devices occur during transitionsI They depend on the switched currents and voltages:
switching period
I Conduction losses depend on high frequency currents ≥ fswitching
I Distortion depends on high frequency currents/voltages ≥ fswitching
I Averaged model valid only below fswitching
⇒ High-frequency model of voltages and currents required to evaluatelosses and distortion
16/19 High-Speed High-Performance MPC of Power Electronics Systems
Hybrid system approach
I Averaging approach gives satisfactory dynamic performance⇒ Why bothering about hybrid approach?
Losses and distortionI Switching losses in semiconductor devices occur during transitionsI They depend on the switched currents and voltages:
switching period
I Conduction losses depend on high frequency currents ≥ fswitching
I Distortion depends on high frequency currents/voltages ≥ fswitching
I Averaged model valid only below fswitching
⇒ High-frequency model of voltages and currents required to evaluatelosses and distortion
16/19 High-Speed High-Performance MPC of Power Electronics Systems
Hybrid system approach
I Averaging approach gives satisfactory dynamic performance⇒ Why bothering about hybrid approach?
Energy efficiency maximizationI Primary control output defined as an integral over cycle⇒ infinitely many solutions
I Exploit this property to minimize losses such thatprimary output (e.g. average power) = referenceother constraints (e.g. distortion ≤ limit)
grid inverter
operating range
voltage magnitude
swit
chin
g
loss
crit
erio
n max gain
~40%
state-of-the-art
optimized
⇒ Hybrid approach can provide significant loss reductionI Computational complexity⇒MIP
16/19 High-Speed High-Performance MPC of Power Electronics Systems
Hybrid system approach
I Fairly systematic modelling approachI Tractable problems
I too complex for parametric programmingI too slow for targeted applications
I Can implement particular cases using look-up tables and interpolation
1400120010008006004002000.75
0.8
0.85
0.9
0.95
1
Pef
fici
ency
standard rectangular modulation
hybrid approach
I Broader range of applications
⇒ Efficient Solvers/Schemes/Control Systems
17/19 High-Speed High-Performance MPC of Power Electronics Systems
Outline
IntroductionPower Electronics Systems’ Application AreasControl challenges
Modelling power electronics system dynamics
Linear Explicit MPC based on model averaging
Hybrid approach: objective/ status/ future challenges
Conclusions
18/19 High-Speed High-Performance MPC of Power Electronics Systems
Conclusions
I Power electronics systemsI Broad range of applicationsI Many different types of Level/frequency power converters, electric drives
I Structure and modelling approaches⇒ determine complexity and performance
I Linear explicit MPC based on model averagingI improved dynamic performanceI low complexity compatible with high frequency ≥MHz
I Hybrid approachI improved energy efficiency and power qualityI already some real-time applicationsI remaining computional challenges for broadening applications
19/19 High-Speed High-Performance MPC of Power Electronics Systems