1. Modulation and current/voltage control of the grid converter
Marco Liserre
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2. A glance at the lecture content
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
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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
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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%
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5. Introduction: harmonic limits for WT inverters
In Europe the standard recommends to apply the standard 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
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6. Model of the grid converter
converter switching function
ac voltage equation
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7. Use of a synchronous frame
ab-frame dq-frame
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8. Overview of modulation techniques
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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
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10. Modulation techniques
analogic or digital,
natural sampled or regular sampled
symmetric or asymmetric
Optimization both for the linearity and harmonic content
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11. Sinusoidal PWM (SPWM)
Output voltage averaged over one switching period:
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12. Sinusoidal PWM (SPWM) Assuming a sinusoidal control signal:
the fundamental frequency component of the output voltage is given by:
The inverter stays in its “linear range” while
The harmonics in the output voltage appear as sidebands of fS and its multiples 1 15 13 17 31 29 33 27 35 25 45 47 43 49 41 39 51
The hth harmonic corresponds to the kth sideband of j times the frequency modulation ratio m. For even values of j only exist harmonics for odd values of k, and viceversa.
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13. Bipolar and unipolar modulations
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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
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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.
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16. Extending the linear range (m=1,1)
SPWM
SVM
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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.
THIPWM1/6
THIPWM1/4
SVPWM
Maximum linear range
Minimum current harmonics
Maximum linear range and almost optimal current harmonics
Triple harmonic injection 1/6
Triple harmonic injection 1/4
Space vector - Triangular 1/4
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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.
DPWM0 =-/6
DPWM1 =0
DPWM2 =/6
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19. Multilevel converters and modulation techniques
Wind turbine systems: high power -> 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.
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20. Multilevel converters and modulation techniques
carrier shifting
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21. Carrier shifting
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22. PD Modulation for NPC
Best WTHD !
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23. PWM current control methods
ON/OFF controllers
Separated PWM
linear
non-linear
passivity
fuzzy PI
predictive
resonant
hysteresis
Delta
optimized
feedforward
dead-beat
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24. PI current control
Typically PI controllers are used for the current loop in grid inverters
Technical optimum design (damping overshoot 5%)
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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.
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26. Use of a PI controller in a rotating frameb q w ) ( t i d ) ( t e i q 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 d q b a ) ‘( t e (
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27. Use of a PI controller in a rotating frame
active and reactive power control can be achieved
vdc control can be achieved too
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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
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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
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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
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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.
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32. Dead-beat controller
neglecting R !
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33. Dead-beat controller: limits
due to PWM !
due to parameter error !
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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
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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
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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
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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 = 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%.
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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
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39. Use of P+resonant controller in stationary frame
The voltage used for reference generation could be measured after a dominant reactance a b ) ( t e i
The current control can be performed on the grid current or on the converter current
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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
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41. From PI in a rotating-frame to P+res for each phase
In the hypothesis
H11(s)=H22(s)=
H12(s)=H21(s)=0
H11(s)
H12(s)
H21(s)
H22(s) +
Vd(s)
Vq(s)
Ed(s)
Eq(s)
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42. each current is determined only by its voltage !
Linear controllers : from PI in a rotating-frame to P+res for each phase z va vb vc
each current is determined only by its voltage !
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43. Linear controllers : results (ideal grid conditions)
PI controller in a rotating frame
harmonic spectrum
current error
P+resonant controller for each phase
harmonic spectrum
current error
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44. Linear controllers: results (equivalence of PI in dq and P+res in ab)
PI controller in a rotating frame
triggering LCL-filter resonance
P+resonant in stationary frame
triggering LCL-filter resonance
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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.
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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.
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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 PR’s 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
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48. Bibliography Marco Liserre liserre@ieee.org
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. 523–532, 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. 814–822, 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
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 – 2052.
IEEE Std "IEEE Standard for Interconnecting Distributed Resources with Electric Power Systems", 2003.
IEEE Std "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 “Wind turbine generator systems Part 21: measurements and assessment of power quality characteristics of grid connected wind turbines”, 2002.
IEC Standard , “Electromagnetic Compatibility, General Guide on Harmonics and Interharmonics Measurements and Instrumentation”, 1997.
IEC Standard , “Electromagnetic Compatibility, Assessment of Emission Limits for Distorting Loads in MV and HV Power Systems”, 1996.
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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
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