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Modulation and current/voltage control of the grid converter

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Presentation on theme: "Modulation and current/voltage control of the grid converter"— Presentation transcript:

1 Modulation and current/voltage control of the grid converter
Marco Liserre Marco Liserre

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 Marco Liserre

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 Marco Liserre

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% Marco Liserre

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 Marco Liserre

6 Model of the grid converter
converter switching function ac voltage equation Marco Liserre

7 Use of a synchronous frame
ab-frame dq-frame Marco Liserre

8 Overview of modulation techniques
Marco Liserre

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 Marco Liserre

10 Modulation techniques
analogic or digital, natural sampled or regular sampled symmetric or asymmetric Optimization both for the linearity and harmonic content Marco Liserre

11 Sinusoidal PWM (SPWM) Output voltage averaged over one switching period: Marco Liserre

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. Marco Liserre

13 Bipolar and unipolar modulations
Marco Liserre

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 Marco Liserre

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. Marco Liserre

16 Extending the linear range (m=1,1)
SPWM SVM Marco Liserre 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. 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 Marco Liserre

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 Marco Liserre

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. Marco Liserre

20 Multilevel converters and modulation techniques
carrier shifting Marco Liserre

21 Carrier shifting Marco Liserre

22 PD Modulation for NPC Best WTHD ! Marco Liserre

23 PWM current control methods
ON/OFF controllers Separated PWM linear non-linear passivity fuzzy PI predictive resonant hysteresis Delta optimized feedforward dead-beat Marco Liserre

24 PI current control Typically PI controllers are used for the current loop in grid inverters Technical optimum design (damping overshoot 5%) Marco Liserre

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. Marco Liserre

26 Use of a PI controller in a rotating frame
b 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 ( Marco Liserre

27 Use of a PI controller in a rotating frame
active and reactive power control can be achieved vdc control can be achieved too Marco Liserre

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 Marco Liserre

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 Marco Liserre

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 Marco Liserre

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. Marco Liserre

32 Dead-beat controller neglecting R ! Marco Liserre

33 Dead-beat controller: limits
due to PWM ! due to parameter error ! Marco Liserre

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 Marco Liserre

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 Marco Liserre

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 Marco Liserre

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%. Marco Liserre

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 Marco Liserre

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 Marco Liserre

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 Marco Liserre

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) Marco Liserre

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 ! Marco Liserre

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 Marco Liserre

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 Marco Liserre

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. Marco Liserre

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. Marco Liserre

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 Marco Liserre

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. Marco Liserre

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 Marco Liserre 49


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