uninterruptible power supply multi-loop control …antenor/pdffiles/lesson2.pdfaugust 2001 lesson 2...

August 2001 Lesson 2 1

Lesson 2

Uninterruptible Power Supply Multi-LoopControl Employing Digital Predictive

Voltage and Current Regulators

Lesson 2Lesson 2

Uninterruptible Power Supply Multi-LoopControl Employing Digital Predictive

Voltage and Current Regulators

Goal of the workGoal of the work

Investigation of digital predictive voltage andcurrent regulators in multi-loop configuration forUPS’sMotivations:• high dynamic performance (i.e. low THD with

distorting loads, low overshoot under stepload changes, etc…);

• simple control design and implementation

Investigation of digital predictive voltage andcurrent regulators in multi-loop configuration forUPS’sMotivations:• high dynamic performance (i.e. low THD with

distorting loads, low overshoot under stepload changes, etc…);

• simple control design and implementation

Presentation outlinePresentation outlinePresentation outline

• Control technique derivation:• current loop• voltage loop

• Design criteria and implementationissues• Simulation results• Experimental results

•• Control technique derivation:Control technique derivation:•• current loopcurrent loop•• voltage loopvoltage loop

•• Design criteriaDesign criteria and implementation and implementationissuesissues•• SimulationSimulation results results•• ExperimentalExperimental results results

UPS system structure and modelUPS UPS system structure and modelsystem structure and model

Single-phase schemeSingle-phase schemevvoo++

LLCC iioo

VVdcdc

Averaged modelAveraged modeliioo

vvmm++

The control equation assumes that:The control equation assumes that:

)]k(v)k(v[LT)k(i)1k(i o

−−−−⋅⋅⋅⋅++++====++++ )]k(v)k(v[LT)k(i)1k(i o

−−−−⋅⋅⋅⋅++++====++++ + one sample delay+ one sample delay

The model works properlyin the UPS case if thesampling frequency ismuch higher (e.g. 15-20times) than the resonancefrequency of the output LCfilter.

Simple load modelSimple load model

+ one sample delay+ one sample delay

Current control loopCurrent controlCurrent control loop loop

++vOvvOO

iiLL(k)(k)

Current control loopReview of deadbeat controlCurrent controlCurrent control loop loop

Review of deadbeat controlReview of deadbeat control

current referencecurrent reference

inverter currentinverter current

instantaneousinstantaneousinverter voltageinverter voltage

iiLLii

Dead-Beat Current Control Equation (DBCCE)Dead-Beat Current Control Equation (DBCCE)

vvkTkTkT (k+1)T(k+1)T(k+1)T (k+2)T(k+2)T(k+2)T

iii***LLL iiiLLL

TsTTss

[[[[ ]]]] )1k(v)k(v)k(v)k(i)k(iTL)1k(v oomL

Sm ++++++++++++−−−−−−−−====++++ [[[[ ]]]] )1k(v)k(v)k(v)k(i)k(i

TL)1k(v oomL

Sm ++++++++++++−−−−−−−−====++++

iiiLLL(k+2)(k+2)(k+2)

0 0.2 0.4 0.6 0.8 10

Step response ofthe closed-loopcurrent control.Samplingfrequency: 15 kHz

Two sample delayTwo sample delayTwo sample delay

Current control loopCurrent controlCurrent control loop loop

Voltage control loopVoltage controlVoltage control loop loop

•• The The same same reasoning used for dead-beat currentreasoning used for dead-beat currentloop can be applied loop can be applied also to the voltage loop.also to the voltage loop.

•• A A key pointkey point is to make the is to make the sampling periodsampling period of ofthe the voltage controlvoltage control equal to equal to TWICETWICE the thesampling periodsampling period of the of the current loop.current loop.

•• Thus, Thus, the current closed loop the current closed loop control can becontrol can bemodeled as a modeled as a simple delaysimple delay (i.e. a two sampling (i.e. a two samplingperiod delay).period delay).

)1k(i)k(i)k(i)]k(v)k(v[T2

C)1k(i ooLo*o

*L ++++−−−−−−−−−−−−−−−−⋅⋅⋅⋅

⋅⋅⋅⋅====++++ )1k(i)k(i)k(i)]k(v)k(v[

T2C)1k(i ooLo

*L ++++−−−−−−−−−−−−−−−−⋅⋅⋅⋅

⋅⋅⋅⋅====++++

Dead-Beat Voltage Control Equation (DBVCE)Dead-Beat Voltage Control Equation (DBVCE)

)]k(i)k(i[CT2)k(v)1k(v oL

soo −−−−⋅⋅⋅⋅⋅⋅⋅⋅++++====++++

Simple load modelSimple load modelSimple load model iiooCCvvoo

Load current sensingLoad current sensingLoad current sensing

The control equation assumes that:The control equation assumes that:

+ one sample delay+ one sample delay

0 0.2 0.4 0.6 0.8 10

Step response ofthe closed-loopvoltage control.Samplingfrequency: 7.5 kHz

Two sample delayTwo sample delayTwo sample delay

Voltage control loopLoad current estimation

Voltage controlVoltage control loop loopLoad current estimationLoad current estimation

•• The load current The load current does not needdoes not need to be measured to be measured•• The following The following dead-beatdead-beat (system poles in the (system poles in the

origin) origin) estimationestimation is derived is derived (DBEE):(DBEE):

)1k(i)]1k(v)k(v[TC)1k(i~ Loo

So −−−−−−−−−−−−−−−−⋅⋅⋅⋅====−−−− )1k(i)]1k(v)k(v[

TC)1k(i~ Loo

So −−−−−−−−−−−−−−−−⋅⋅⋅⋅====−−−−

•• Estimation with Estimation with system poles away from thesystem poles away from theoriginorigin implies a implies a IIR low-pass filterIIR low-pass filter on the on theestimated current (*)estimated current (*)

•• Practically,Practically, a moving average a moving average (FIR) filter with 4(FIR) filter with 4taps was usedtaps was used

(*)(*)(*)

Voltage control loopControl refinements

Voltage controlVoltage control loop loopControl refinementsControl refinements

•• Feedforward of capacitor current referenceFeedforward of capacitor current reference(obtained from output voltage reference).(obtained from output voltage reference).

•• Feedforward of the estimated load current.Feedforward of the estimated load current.•• Interpolation between samplesInterpolation between samples

(reduction of oscillations on inverter voltage at half of the(reduction of oscillations on inverter voltage at half of thesampling frequency).sampling frequency).

•• Detuning of voltage controlDetuning of voltage control(voltage estimation at instant k+1 with system pole away(voltage estimation at instant k+1 with system pole awayfrom the origin from the origin (low-pass filtering action)(low-pass filtering action) - lower- lower sensitivitysensitivity totonoise).noise).

FeedforwardFeedforward of the estimated of the estimated load currentload current (DBEE) (DBEE)allows the allows the voltage dynamic equationvoltage dynamic equation to re-written: to re-written:

)]k(i)k(i[CT2)k(v)1k(v oL

soo −−−−⋅⋅⋅⋅⋅⋅⋅⋅++++====++++ )]k(i)k(i[

CT2)k(v)1k(v oL

soo −−−−⋅⋅⋅⋅⋅⋅⋅⋅++++====++++

)1h(iCT2)h(v)1h(v *

oo −−−−⋅⋅⋅⋅++++====++++ )1h(iCT2)h(v)1h(v *

oo −−−−⋅⋅⋅⋅++++====++++

h is the index for 2Tswsampling periodh is the index for 2Tswsampling period

FeedforwardFeedforward of also the capacitive current allows of also the capacitive current allowsDBVCEDBVCE to be re-written: to be re-written:

)1h(i)]h(v)h(v[T2

C)h(i *Co

*C −−−−∆∆∆∆−−−−−−−−⋅⋅⋅⋅

⋅⋅⋅⋅====∆∆∆∆ )1h(i)]h(v)h(v[

T2C)h(i *

*C −−−−∆∆∆∆−−−−−−−−⋅⋅⋅⋅

⋅⋅⋅⋅====∆∆∆∆

Where Where ∆∆∆∆∆∆∆∆iicc** stands for the stands for the deviation deviation of the of the iicc**

current from its current from its feed-forwarded value.feed-forwarded value.

��

�� −−−−−−−−−−−−⋅⋅⋅⋅++++====++++ )2h(i21)1h(i

CT)h(v)1h(v *

soo ��

��

�� −−−−−−−−−−−−⋅⋅⋅⋅++++====++++ )2h(i21)1h(i

CT)h(v)1h(v *

Linear interpolationLinear interpolation can be used to can be used to re-constructre-constructthe the ”missing” current sample.”missing” current sample. This modifies This modifiesagain the again the voltage dynamic equation:voltage dynamic equation:

and generates the followingand generates the following control equation: control equation:

)2h(i51)1h(i

54)]h(v)h(v[

52)h(i *

*C −−−−∆∆∆∆++++−−−−∆∆∆∆−−−−−−−−⋅⋅⋅⋅====∆∆∆∆ )2h(i

51)1h(i

54)]h(v)h(v[

52)h(i *

*C −−−−∆∆∆∆++++−−−−∆∆∆∆−−−−−−−−⋅⋅⋅⋅====∆∆∆∆

Voltage control loopControl timing

Voltage controlVoltage control loop loopControl timingControl timing

t = n ⋅⋅⋅⋅TSk-2 k-1 k k+1 k+2

t = m ⋅⋅⋅⋅TVh-1 h h+1TV

i*C(h+1)

i*C(h)

i*C(h-1)

iC(h+1)

iC(h-1)

InterpolatedInterpolatedsamplesample

v*o(h)

v*o(h-1) vo(h+1)

vo(h-1)

Voltage controlVoltage control

vm(k+1) vm(k+2)vm(k)vm (k-1)vm(k-2)

Inverter voltageInverter voltage

Current controlCurrent control

Voltage control loopEffects of Interpolation

Voltage controlVoltage control loop loopEffects of InterpolationEffects of Interpolation

0 0.005 0.01 0.015 0.02

Average voltage generated by VSIAverage voltageAverage voltage generated by VSI generated by VSI

withoutinterpolation

withoutwithoutinterpolationinterpolation

August 2001 Lesson 2 180 0.005 0.01 0.015 0.02

withinterpolation

withwithinterpolationinterpolation

Voltage control loopEffects of Interpolation

Voltage controlVoltage control loop loopEffects of InterpolationEffects of Interpolation

Average voltage generated by VSIAverage voltageAverage voltage generated by VSI generated by VSI

0.01 0.015 0.02 0.025 0.03

Actual and estimated load currentActual and estimated Actual and estimated load currentload current

Zohapproximation

ZohZohapproximationapproximation

0.01 0.015 0.02 0.025 0.03

Actual and estimated load currentActual and estimated Actual and estimated load currentload current

Fohapproximation

FohFohapproximationapproximation

Voltage control loopDe-tuning

Voltage controlVoltage control loop loopDe-De-tuningtuning

To improve theTo improve the controller’s robustness controller’s robustness it isit ispossible topossible to de-tune de-tune the voltage loop. This impliesthe voltage loop. This impliesthethe allocation allocation of the controllerof the controller pole away pole away from thefrom theorigin origin of the complex plane.of the complex plane.

)1h(iCT2)h(v)1h(v *

oo −−−−∆∆∆∆⋅⋅⋅⋅++++∆∆∆∆====++++∆∆∆∆ )1h(iCT2)h(v)1h(v *

oo −−−−∆∆∆∆⋅⋅⋅⋅++++∆∆∆∆====++++∆∆∆∆

Voltage dynamic equation for the Voltage dynamic equation for the deviationsdeviations from fromthe ideal the ideal trajectory.trajectory.

)1h(vT2C)h(i o

*C ++++∆∆∆∆−−−−====∆∆∆∆ )1h(v

T2C)h(i o

*C ++++∆∆∆∆−−−−====∆∆∆∆

The The control lawcontrol law which ensures a which ensures a dead-beat responsedead-beat responseis simply given by:is simply given by:

where where ∆∆∆∆∆∆∆∆vvoo represents the represents the estimatedestimated output voltage output voltagedeviation (due to deviation (due to calculation delaycalculation delay we can’t use the we can’t use theactual deviation).actual deviation).

(((( )))))h(v)h(vK)1h(iCT2)h(v)1h(v ooS

soo ∆∆∆∆−−−−∆∆∆∆++++−−−−∆∆∆∆⋅⋅⋅⋅++++∆∆∆∆====++++∆∆∆∆ (((( )))))h(v)h(vK)1h(i

CT2)h(v)1h(v ooS

soo ∆∆∆∆−−−−∆∆∆∆++++−−−−∆∆∆∆⋅⋅⋅⋅++++∆∆∆∆====++++∆∆∆∆

The The estimator estimator can have the classicalcan have the classical Luenberger Luenbergerstructure. Kstructure. Kss allows to select theallows to select the pole location. pole location.

If the If the polepole is located in the is located in the originorigin (dead-beat (dead-beatestimator) we have the usual estimator) we have the usual DBVCE for theDBVCE for thedeviation.deviation. Otherwise we have a Otherwise we have a de-tunedde-tuned controller controllerwith a with a first order response.first order response.

Control block diagramControl block diagramControl block diagram

Output filter capacitor and load modelOutput filter capacitor and load modelOutput filter capacitor and load model

+- ZC(z)

Deadbeat current controlDeadbeat current controlDeadbeat current control

Currentcontrol +

- ZC(z)iL

Feedforward of the estimated load currentFeedforwardFeedforward of the estimated load current of the estimated load current

Currentcontrol

Load currentestimator

+- ZC(z)

Feedforward of capacitor current referenceFeedforward of capacitor current referenceFeedforward of capacitor current reference

Currentcontrol

+- ZC(z)

io++vo

Feed-forward ofcapacitive current

Deadbeat voltage controlDeadbeat voltage controlDeadbeat voltage control

Currentcontrol

+- ZC(z)

io++vo

T = 2 T

Voltagecontrol

∆∆∆∆iC*

Currentcontrol

+- ZC(z)

io++vo

T = 2 T

Voltagecontrol

∆∆∆∆iC*Current reference

interpolation

Capacitor current reference interpolationCapacitor current reference interpolationCapacitor current reference interpolation

Currentcontrol

+- ZC(z)

io++vo

T = 2 T

Voltagecontrol

∆∆∆∆iC*Current reference

interpolation

Final schemeFinal schemeFinal scheme

Control implementationControl implementationControl implementation

•• The control program is implemented by means ofThe control program is implemented by means ofa a floating point DSP:floating point DSP:

−− ADSP21062: 33 Mips, 30 ns instruction cycleADSP21062: 33 Mips, 30 ns instruction cycle

•• The power converter is controlled by a motionThe power converter is controlled by a motioncontrol oriented control oriented fixed point DSP:fixed point DSP:

−− ADMC401: 26 Mips, 38.5 ns instruction cycleADMC401: 26 Mips, 38.5 ns instruction cycle

•• The two units are interfaced by means of a The two units are interfaced by means of a dualdualport RAMport RAM (1kword). A suitable (1kword). A suitable communicationcommunicationprotocolprotocol is implemented. is implemented.

ADSP21062ADSP21062

16 bit16 bit

ADMC401ADMC401

Dual Port Dual Port RAMRAM

PowerPowerConverterConverter

PWMSYNCPWMSYNC00

[µµµµs][µµµµs]

A/DA/DconversionconversionEOCEOCRAM write RAM write EOWEOW

ControlControlprogramprogramδδδδδδδδ readyready

RAM read RAM read

1818PWM write PWM write

WAITWAIT1919

A/DA/DPWMPWM

RAM writeRAM writeEOWEOWRAM read RAM read

Scheme andtiming of thecontrol system

•• The The control programcontrol program is written in is written in C language,C language, and andthe AD the AD C-compilerC-compiler for the ADSP 21062 is used. for the ADSP 21062 is used.

•• Given the very high performance of the DSP unit,Given the very high performance of the DSP unit,no no timing problemtiming problem is encountered, even for very is encountered, even for verycomplex algorithmscomplex algorithms and 20 kHz operating and 20 kHz operatingfrequency.frequency.

•• Data exchangeData exchange between the two units is dealt with between the two units is dealt withby means of simple by means of simple data memory writedata memory write (DM)(DM)instructions.instructions.

50% increase compared to PI control

50% increase 50% increase compared to PI controlcompared to PI control

12 [µµµµs]

A/Dconversion

t = kTS

k is evenyes

Eq. 11

Interpolation

Feed-forward of Ci

∆∆∆∆ i*C(h)

vm(k+1)Dead time compensation

DC link feed-forward

Dead-beat voltage controlinterpolation

Dead-beat voltage controlDead-beat voltage controlinterpolationinterpolation

Load current estimationLoad current estimationLoad current estimationCapacitor current estimationCapacitor current estimationCapacitor current estimation

Dead-beat current controlDead-beat current controlDead-beat current control

Timing of the controlalgorithm

Timing of the controlTiming of the controlalgorithmalgorithm

Experimental resultsExperimental resultsExperimental results

ooNominal output powerNominal output power PP 11 [kVA][kVA]

Nominal output voltageNominal output voltage VVoRMSoRMS 115115 [V][V]

Minimum load DFMinimum load DF coscos φφφφφφφφ 0.80.8DC link voltageDC link voltage VVDCDC 250250 [V][V]

Output frequencyOutput frequency ff oo 5050 [Hz][Hz]Output inductorOutput inductor LL 1.81.8 [mH][mH]Output capacitorOutput capacitor CC 120120 [[µµµµµµµµF]F]Switching frequencySwitching frequency ffss 1515 [kHz][kHz]

Experimental prototype’s parametersExperimental prototype’s parametersExperimental prototype’s parameters

Step loadvariations100% - 0%

Step loadStep loadvariationsvariations100% - 0%100% - 0%

Output voltage[100V/div]

Output voltageOutput voltage[100V/div][100V/div]

Current reference[10A/div]

Current referenceCurrent reference[10A/div][10A/div]

Actual current[10A/div]

Actual currentActual current[10A/div][10A/div]

Load current[10A/div]

Load currentLoad current[10A/div][10A/div]

Estimated current[10A/div]

Estimated currentEstimated current[10A/div][10A/div]

Reference voltage[200V/div]

Reference voltageReference voltage[200V/div][200V/div]

Step loadvariations100% - 0%

Step loadStep loadvariationsvariations100% - 0%100% - 0%

Load current[10A/div]

Load currentLoad current[10A/div][10A/div]

Estimated current[10A/div]

Estimated currentEstimated current[10A/div][10A/div]

Reference voltage[200V/div]

Reference voltageReference voltage[200V/div][200V/div]

Distorting loadDistorting loadDistorting load

THD=3.4%THD=3.4%

Distorting loadDistorting loadDistorting load

THD=3.4%THD=3.4%

Distorting loadPI control

Distorting loadDistorting loadPI controlPI control

THD=6.0%THD=6.0%

ReferenceReferenceReference

S. Buso, S.Fasolo, P. Mattavelli, “Uninterruptible PowerSupply Multi-Loop Control Employing Digital PredictiveVoltage and Current Regulators”, Applied PowerElectronics Conference (APEC) Proc., Anaheim,California, 4-8 March, 2001, pp. 907-913.

uninterruptible power supply multi-loop control …antenor/pdffiles/lesson2.pdfaugust 2001 lesson 2...

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