High-Speed High-Performance Model Predictive Control of ...€¦ · Control challenges 1.Dynamic...

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

[email protected]

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


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


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


Outline





Conclusions


Electric drives — Frequency/level conversion

PM

Gen.

Wind

Turbine

AC

grid

Filter/

transformer


Power electronics systemsI Controllable semiconductor switches

I interconnect different points of circuits



PM

Gen.

Wind

Turbine

AC

grid

Filter/

transformer


Power electronics systemsI Controllable semiconductor switchesI interconnect different points of circuits



PM

Gen.

Wind

Turbine

AC

grid

Filter/

transformer


Power electronics systemsI Controllable semiconductor switchesI interconnect different points of circuits⇒ switched waveforms



PM

Gen.

Wind

Turbine

AC

grid

Filter/

transformer


Power electronics systemsI Dynamics⇒ Complex hybrid systems

x =∑

i si (Fix + Gviv) si ∈ {0, 1}∑

i si = 1


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


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


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


i divi∑

i di = 1 di ∈ [0, 1]

I Model sufficient for control⇒MPC of averaged dynamics


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


i divi∑

i di = 1 di ∈ [0, 1]I Model sufficient for control⇒MPC of averaged dynamics


Outline





Conclusions



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


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


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


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


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


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


Outline





Conclusions


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



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



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


Outline





Conclusions


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


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