Marco Liserre [e-mail]

1
Modulation and current/voltage control of the
grid converter
Marco Liserre liserre_at_ieee.org
2
Introduction

• Modulation and ac current control are the core of
  grid-connected converters
• They are responsible of the safe operation of the
  converter and of the compliance with standards
  and grid codes
• Ac voltage control is a standard solution in
  WT-system however can be adopted also in
  PV-system for reinforcing stability or offering
  ancillary services
• Introduction
• Model of the grid converter
• Overview of modulation techniques
• Current control
• Voltage control

A glance at the lecture content
3
Introduction modulation and current/voltage
control

• PI-based current control implemented in a
  synchronous frame is commonly used in three-phase
  converters
• In single-phase converters the PI controller
  capability to track a sinusoidal reference is
  limited and Proportional Resonant (PR) can offer
  better performances
• Modulation has an influence on design of the
  converter (dc voltage value), losses and EMC
  problems including leakage current

4
Introduction harmonic limits for PV inverters

• In Europe there is the standard IEC 61727
• In US there is the recommendation IEEE 929
• the recommendation IEEE 1547 is valid for all
  distributed resources technologies with aggregate
  capacity of 10 MVA or less at the point of common
  coupling interconnected with electrical power
  systems at typical primary and/or secondary
  distribution voltages
• All of them impose the following conditions
  regarding grid current harmonic content

The total THD of the grid current should not be
higher than 5
5
Introduction harmonic limits for WT inverters
In Europe the standard 61400-21 recommends to
apply the standard 61000-3-6 valid for polluting
loads requiring the current THD smaller than 6-8
depending on the type of network.
in case of several WT systems
in WT systems asynchronous and synchronous
generators directly connected to the grid have no
limitations respect to current harmonics
6
Model of the grid converter
converter switching function
ac voltage equation
7
Use of a synchronous frame
ab-frame dq-frame
8
Overview of modulation techniques
9
Modulation techniques

• Characteristic parameters of these strategies
  are
• the ratio between amplitudes of modulating and
  carrier waves (called modulation index M)
• the ratio between frequencies of the same
  signals (called carrier index m)
• These techniques differ for the modulating wave
  chosen with the goal to obtain
• a lower harmonic distortion,
• to shape the harmonic spectrum
• to guarantee a linear relation between
  fundamental output voltage and modulation index
  in a wider range
• The space vector modulations are developed on the
  basis of the space vector representation of the
  converter ac side voltage

10
Modulation techniques

• analogic or digital,
• natural sampled or regular sampled
• symmetric or asymmetric

Optimization both for the linearity and harmonic
content
11
Sinusoidal PWM (SPWM)
Output voltage averaged over one switching period
12
Sinusoidal PWM (SPWM)
Assuming a sinusoidal control signal
the fundamental frequency componentof the output
voltage is given by
The inverter stays in its linear rangewhile
.
The harmonics in the output voltage appear as
sidebands of fS and its multiples
The hth harmonic corresponds to the kth
sidebandof j times the frequency modulation
ratio m.For even values of j only exist
harmonics forodd values of k, and viceversa.
13
Bipolar and unipolar modulations

• bipolar
• unipolar

14
Bipolar and unipolar modulations
Due to the unipolar PWM the odd carrier and
associated sideband harmonics are completely
cancelled leaving only odd sideband harmonics
(2n-1) terms and even (2m) carrier groups
15
Three-phase modulation techniques
The basic three-phase modulation is obtained
applying a bipolar modulation to each of the
three legs of the converter. The modulating
signals have to be 120 deg displaced. The
phase-to-phase voltages are three levels PWM
signals that do not contain triple harmonics. If
the carrier frequency is chosen as multiple of
three, the harmonics at the carrier frequency and
at its multiples are absent.
16
Extending the linear range (m1,1)
SPWM
SVM
64
17
Three-phase continuous modulation techniques

• Continuous modulations
• sinusoidal PWM with Third Harmonic Injected
  THIPWM. If the third harmonic has amplitude 25
  of the fundamental the minimum current harmonic
  content is achieved if the third harmonic is 17
  of the fundamental the maximal linear range is
  obtained
• suboptimum modulation (subopt). A triangular
  signal is added to the modulating signal. In case
  the amplitude of the triangular signal is 25 of
  the fundamental the modulation corresponds to the
  Space Vector Modulation (SVPWM) with symmetrical
  placement of zero vectors in sampling time.

18
Three-phase discontinuous modulation techniques

• The discontinuous modulations formed by
  unmodulated 60 deg segments in order to decrease
  the switching losses
• symmetrical flat top modulation, also called
  DPWM1
• asymmetrical shifted right flat top modulation,
  also called DPWM2
• asymmetrical shifted left flat top modulation,
  also called DPWM0.

19
Multilevel converters and modulation techniques

• Wind turbine systems high power -gt 5 MW Alstom
  converter
• Photovoltaic systems many dc-links for a
  transformerless solution

Different possibilities

• alternative phase opposition (APOD) where
  carriers in adjacent bands are phase shifted by
  180 deg
• phase opposition disposition (POD), where the
  carriers above the reference zero point are out
  of phase with those below zero by 180 deg
• phase disposition (PD), where all the carriers
  are in phase across all bands.

20
Multilevel converters and modulation techniques

• carrier shifting

21
Carrier shifting
22
PD Modulation for NPC
Best WTHD !
23
Current Control
PWM current control methods
ON/OFF controllers
Separated PWM
linear
non-linear
fuzzy
passivity
PI
predictive
resonant
hysteresis
Delta
optimized
dead-beat
feedforward
24
PI current control

• Typically PI controllers are used for the
  current loop in grid inverters
• Technical optimum design (damping 0.707
  overshoot 5)

25
Shortcomings of PI controller
steady-state magnitude and phase error limited
disturbance rejection capability

• When the current controlled inverter is connected
  to the grid, the phase error results in a power
  factor decrement and the limited disturbance
  rejection capability leads to the need of grid
  feed-forward compensation.
• However the imperfect compensation action of the
  feed-forward control due to the background
  distortion results in high harmonic distortion of
  the current and consequently non-compliance with
  international power quality standards.

26
Use of a PI controller in a rotating frame
b
q
w
d
i
d
a
The voltage used for the dq-frame orientation
could be measured after a dominant reactance
The current control can be performed on the grid
current or on the converter current
27
Use of a PI controller in a rotating frame

• active and reactive power control can be
  achieved
• vdc control can be achieved too

28
Use of a PI controllers in a rotating frame in
single-phase systems

• an independent Q control is achieved
• A phase delay block create the virtual
  quadrature component that allows to emulate a
  two-phase system
• the vb component of the command voltage is
  ignored for the calculation of the duty-cycle

29
Use of a PI controllers in two rotating frames

• Under unbalanced conditions in order to
  compensate the harmonics generated by the inverse
  sequence present in the grid voltage both the
  positive- and negative-sequence reference frames
  are required
• Obviously using this approach, double
  computational effort must be devoted

30
Dead-beat controller

• The dead-beat controller belongs to the family of
  the predictive controllers
• They are based on a common principle to foresee
  the evolution of the controlled quantity (the
  current) and on the basis of this prediction
• to choose the state of the converter (ON-OFF
  predictive) or
• the average voltage produced by the converter
  (predictive with pulse width modulator)
• The starting point is to calculate its derivative
  to predict the effect of the control action
• The controller is developed on the basis of the
  model of the filter and of the grid, which is
  used to predict the system dynamic behavior the
  controller is inherently sensitive to model and
  parameter mismatches

31
Dead-beat controller

• The information on the model is used to decide
  the switching state of the converter with the aim
  to minimize the possible commutations (ON-OFF
  predictive) or the average voltage that the
  converter has to produce in order to null it.

• In case it is imposed that the error at the end
  of the next sampling period is zero the
  controller is defined as dead-beat. It can be
  demonstrated that it is the fastest current
  controller allowing nulling the error after two
  sampling periods.

32
Dead-beat controller
neglecting R !
33
Dead-beat controller limits
due to PWM !



due to parameter error !
34
Resonant control

• Resonant control is based on the use of
  Generalized Integrator (GI)
• A double integrator achieves infinite gain at a
  certain frequency, called resonance frequency,
  and almost no attenuation outside this frequency
• The GI will lead to zero stationary error and
  improved and selective disturbance rejection as
  compared with PI controller

GI
35
Resonant control

• The resonant controller can be obtained via a
  frequency shift

Bode plots of ideal and non-ideal PR with KP 1,
Ki 20, ? 314 rad/s ?c 10 rad/s
36
Resonant control

• The stability of the system should be taken into
  consideration
• The phase margin (PM) decreases as the resonant
  frequency approach to the crossover frequency

PM
37
Tuning of resonant control

• The gain Kp is founded by ensuring the desired
  bandwidth
• The integral constant Ki acts to eliminate the
  steady-state phase error

Ki 100 Ki
500

• A higher Ki will "catch" the reference faster but
  with higher overshoot
• Another aspect is that Ki determines the
  bandwidth centered at the resonance frequency, in
  this case the grid frequency, where the
  attenuation is positive. Usually, the grid
  frequency is stiff and is only allowed to vary in
  a narrow range, typically 1.

38
Discretization of generalized integrators
GI integrator decomposed in two simple
integrators
Forward integrator for direct path and backward
for feedback path
The inverter voltage reference
Control diagram of PR implementation
Difference equations
39
Use of Presonant controller in stationary frame
The voltage used for reference generation could
be measured after a dominant reactance
The current control can be performed on the grid
current or on the converter current
40
PI vs PR for single-phase grid inverter current
control
The current loop of PV inverter with PI controller
The current loop of PV inverter with PR
controller
PI
PR
Inverter
Plant
.

• No grid voltage feed-forward is required
• GIs tuned to the low harmonics can be used for
  selective harmonic compensation by cascading the
  fundamental component GI

41
From PI in a rotating-frame to Pres for each
phase

• In the hypothesis
• H11(s)H22(s)
• H12(s)H21(s)0

42
Linear controllers from PI in a rotating-frame
to Pres for each phase
each current is determined only by its voltage !
43
Linear controllers results (ideal grid
conditions)
PI controller in a rotating frame
current error
harmonic spectrum
Presonant controller for each phase
current error
harmonic spectrum
44
Linear controllers results (equivalence of PI in
dq and Pres in ab)
PI controller in a rotating frame
triggering LCL-filter resonance
Presonant in stationary frame
triggering LCL-filter resonance
45
Ac voltage control

• When it is needed to control the ac voltage
  because the system should operate in stand-alone
  mode, in a microgrid, or there are requirements
  on the voltage quality a multiloop control can be
  adopted

The ac capacitor voltage is controlled though
the ac converter current. The current
controlled converter operates as a current source
to charge/discharge the capacitor.
46
Ac voltage control

• The repetitive controller ensures precise
  tracking of the selected harmonics and it
  provides the reference of the PI current
  controller. Controlling the voltage Vc the PV
  shunt converter is improved with the function of
  voltage dips mitigation. In presence of a voltage
  dip the grid current Ig is forced by the
  controller to have a sinusoidal waveform which is
  phase shifted by almost 90 with respect to the
  corresponding grid voltage.

47
Conclusions

• The PR uses Generalized Integrators (GI) that are
  double integrators achieving very high gain in a
  narrow frequency band centered on the resonant
  frequency and almost null outside.
• This makes the PR controller to act as a notch
  filter at the resonance frequency and thus it can
  track a sinusoidal reference without having to
  increase the switching frequency or adopting a
  high gain, as it is the case for the classical PI
  controller.
• PI adopted in a rotating frame achieves similar
  results, it is equivalent to the use of three
  PRs one for each phase
• Also single phase use of PI in a dq frame is
  feasible
• Dead-beat controller can compensate current error
  in two samples but it is affected by PWM limits
  and parameters mismatches

48
Bibliography

• D. G. Holmes and T. Lipo, Pulse Width Modulation
  for Power Converters, Principles and Practice.
  New York IEEE Press, 2003.
• M. Kazmierkowski, R. Krishnan, and F. Blaabjerg,
  Control in Power Electronics Selected Problems.
  Academic Press, 2002.
• X. Yuan, W. Merk, H. Stemmler, and J. Allmeling,
  Stationary-frame generalized integrators for
  current control of active power filters with zero
  steady-state error for current harmonics of
  concern under unbalanced and distorted operating
  conditions, IEEE Trans. on Industry
  Applications, vol. 38, no. 2, pp. 523532, 2002.
• D. Zmood and D. G. Holmes, Stationary frame
  current regulation of PWM inverters with zero
  steady-state error, IEEE Trans. on Power
  Electronics, vol. 18, no. 3, pp. 814822, 2003.
• M. Bojrup, P. Karlsson, M. Alaküla, L. Gertmar,
  A Multiple Rotating Integrator Controller for
  Active Filters, Proc. of EPE 1999, CD-ROM.
• R. Teodorescu, F. Blaabjerg, M. Liserre and A.
  Poh Chiang Loh, Proportional-Resonant
  Controllers and Filters for Grid-Connected
  Voltage-Source Converters IEE Proceedings on
  Electric Power Applications.
• A. Timbus, M. Liserre, R. Teodorescu, P.
  Rodriguez, F. Blaabjerg, Evaluation of Current
  Controllers for Distributed Power Generation
  Systems, IEEE Transactions on Power Electronics,
  March 2009, vol. 24, no. 3, pp. 654-664.
• R. A. Mastromauro, M. Liserre, A. Dell'Aquila,
  Study of the Effects of Inductor Nonlinear
  Behavior on the Performance of Current
  Controllers for Single-Phase PV Grid Converters,
  IEEE Transactions on Industrial Electronics, May
  2008, vol. 55, no 5, pp. 2043 2052.
• IEEE Std 1547-2003 "IEEE Standard for
  Interconnecting Distributed Resources with
  Electric Power Systems", 2003.
• IEEE Std 1547.1-2005 "IEEE Standard Conformance
  Test Procedures for Equipment Interconnecting
  Distribut ed Resources with Electric Power
  Systems", 2005.
• IEC Standard 61727, Characteristic of the
  utility interface for photovoltaic (PV)
  systems,, 2002.
• IEC Standard 61400-21 Wind turbine generator
  systems Part 21 measurements and assessment of
  power quality characteristics of grid connected
  wind turbines, 2002.
• IEC Standard 61000-4-7, Electromagnetic
  Compatibility, General Guide on Harmonics and
  Interharmonics Measurements and Instrumentation,
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• IEC Standard 61000-3-6, Electromagnetic
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  1996.

49
Acknowledgment

• Part of the material is or was included in the
  present and/or past editions of the
• Industrial/Ph.D. Course in Power Electronics for
  Renewable Energy Systems in theory and
  practice
• Speakers R. Teodorescu, P. Rodriguez, M.
  Liserre, J. M. Guerrero,
• Place Aalborg University, Denmark
• The course is held twice (May and November) every
  year