Ahmed, Hafiz

Benbouzid, Mohamed

English

This Letter proposes demodulation type PLL for phase and frequency estimation of single-phase system that can reject DC offset. Using results from the adaptive estimation literature, this Letter proposes a linear parametric model-based initial phase angle estimation approach. Then by using differentiation and integration operation on the estimated initial phase angle, the frequency is estimated. This avoids the use of any low-pass filter unlike conventional demodulation- based technique. Moreover, unlike existing demodulation-based technique, the proposed technique can completely reject DC offset. Comparative experimental results, provided with state-of-the-art DC offset rejection-based enhanced phase locked-loop, clearly demonstrate the suitability of the proposed technique.</p

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Demodulation Type Single-Phase PLL with DC Offset Rejection  Hafiz Ahmed and Mohamed Benbouzid   Accepted manuscript PDF deposited in Coventry University’s Repository    Original citation:   Ahmed, Hafiz, and Mohamed Benbouzid. "Demodulation Type Single-Phase PLL with DC Offset Rejection." Electronics Letters (2020). http://dx.doi.org/10.1049/el.2019.3718    ISSN: 0013-5194       Publisher: IET     This paper is a postprint of a paper submitted to and accepted for publication in Electronics Letters and is subject to Institution of Engineering and Technology Copyright. The copy of record is available at the IET Digital Library.  Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.  Demodulation Type Single-Phase PLL with DCOffset RejectionH. Ahmed and M. BenbouzidThis letter proposes demodulation type PLL for phase and frequencyestimation of single-phase system that can reject DC offset. Usingresults from the adaptive estimation literature, this letter proposes alinear parametric model-based initial phase angle estimation approach.Then by using differentiation and integration operation on the estimatedinitial phase angle, the frequency is estimated. This avoids the use ofany low-pass filter unlike conventional demodulation-based technique.Moreover, unlike existing demodulation-based technique, the proposedtechnique can completely reject DC offset. Comparative experimentalresults, provided with state of the art DC offset rejection-based enhancedphase locked-loop (EPLL), clearly demonstrate the suitability of theproposed technique.1. Introduction: Phase and frequency play a very important role in variouscontrol, monitoring, protection, and quality assessment of power systemand grid-connected converters (GCC). Some potential applications are:grid synchronization of GCC [1, 2, 3], control of PWM rectifier [4], gridmonitoring [5, 6] etc. to name a few. All these applications require fast andaccurate estimation of phase and frequency.In this letter our focus is on phase and frequency estimation for single-phase system. Some of the existing techniques for single-phase systemsare: Kalman filter [7], adaptive observer [8], phase-locked loop (PLL)[9, 10, 11, 12], enhanced PLL (EPLL) [13, 14], adaptive filter-basedfrequency-locked loop (FLL) [15], and demodulation-based technique[16, 17].Kalman filter works very well in noisy environment. It can provide fastand accurate estimation. However, the performance and stability dependon tuning the process and measurement noise parameters. In addition,initial conditions also play a great role. Kalman filter requires PLL/FLLto estimate the frequency. As such the tuning of the whole system canbe complicated. Adaptive observer [8] uses the same dynamical model asKalman filter, however, from a deterministic framework. Adaptive observeris sensitive to unmodeled dynamics. Moreover, performance degrades innoisy environment.PLL [9, 10, 11, 12] is undoubtedly the most popular technique availablein the literature. Many existing PLL results for single-phase system use theidea of synchronous reference frame - PLL (SRF-PLL) originally proposedfor three-phase system. To apply SRF-PLL in single-phase system, avirtual orthogonal signal needs to be generated to implement Clarke toPark transformation. Tuning the parameters of PLL requires a trade-offbetween fast dynamic response and estimation accuracy. Enhanced PLL[13, 14] can be considered as a nonlinear version of the PLL. FLLs [15]also require orthogonal signal to be generated. Then using the oppositephase relationship between the input variables, the frequency can be easilyestimated.Traditional demodulation-based frequency estimation technique [16] isvery simple. By multiplying fixed frequency signals with the grid voltagesignal, the demodulated voltages can be obtained. Then by using high orderlow-pass filter (LPF) tuned at two times the fundamental frequency, thefrequency can be estimated. LPF’s are non-ideal in nature. In nominaloperating condition, this may not be an issue. However, during off-normal operating conditions, LPFs may introduce large attenuation of thefiltered signal’s amplitude due to high cut-off frequency. To overcomethis issue, frequency adaptive quadrature oscillator-based demodulationtechnique is reported in [17]. An advantage of [17] is that the cut-off frequencies are significantly lower than standard demodulation-based technique. Moreover, the presence of two LPFs also provideadditional robustness. However, these benefits come at the cost of highercomputational complexity. One important limitation of the conventionaland modified demodulation-based techniques are that they can’t handle DCoffset explicitly. DC offset may arise from signal conversion by analog-to-digital converter, transformer saturation etc.In this letter, we focus on demodulation-based technique. The objectiveis to propose an improved estimator that can reject DC offset and similarlyworks to demodulation based-technique. The proposed estimator usesresults from the adaptive estimation literature [18] to estimate the initialphase angle of the grid voltage signal. Then by using differentiation andFig. 1. Block diagram of the proposed DT-PLL.integration operation on the estimated phase angle, the frequency andinstantaneous phase are estimated. Comparative experimental results areprovided with DC offset rejection-based EPLL [13].The rest of this letter is organized as follows: Sec. 2 describes theconventional demodulation-based technique and the proposed techniquewhile Sec. 3 deals with the comparative experimental results. Finally, Sec.4 concludes this letter.2. Unknown Parameter Estimation:(a)Conventional Demodulation-based TechniqueA single-phase grid voltage signal is given by:ν(t) =A sin(ωt+ φ︸ ︷︷ ︸θ) +A0 (1)where A is the amplitude, ω= ωn + ∆ω is the angular frequency (withωn = 100pi being the nominal angular frequency and ∆ω is the frequencydeviation), φ is the phase, θ ∈ [0, 2pi) is the instantaneous phase, andA0 is the DC offset. To estimate the unknown parameters ω and θ,conventional demodulation-based techniques [16] work by estimatingthe phase, ϕ= ∆ωt+ φ. Assuming A0 = 0, conventional demodulationtechnique is summarized below:From the grid signal v(t), the demodulated voltages can be obtained asfollow:vc(t) = v(t) cos(ωnt) =A2sin(ϕ) +A2sin(2ωnt+ ϕ) (2)vs(t) = v(t) sin(ωnt) =A2cos(ϕ)− A2cos(2ωnt+ ϕ) (3)As can be seen from Eq. (2) and (3), demodulated voltages contain doublefundamental frequency component which can be easily removed using asuitably designed LPF. From the filtered demodulated voltages, the phasecan be estimated as:ϕˆ= arctan(vcf/vsf )unwrapped (4)where the subscript f indicates filtered signal and unwrapped indicatesthat the estimated phase is wrapped. Then the angular frequency can beestimated as :ωˆ= ωn + ˙ˆϕ (5)Conventional demodulation-based technique requires two high order LPFswith the cut-off frequency being two times the fundamental frequency.LPFs have non-ideal characteristics. As such, large attenuation of theamplitude during large frequency deviation may not be avoided. Toovercome this limitation, Reza et al. [17] proposed quadrature oscillator-based frequency adaptive demodulation technique. This technique stillrequires two low-pass filter, however, the cut-off frequency is lower thanthe fundamental frequency. This overcomes the amplitude attenuationproblem, however, comes at the cost of computational complexity.Moreover, neither the conventional nor the modified technique can handleDC offset.ELECTRONICS LETTERS Vol. 00 No. 00Fig. 2 Simulation results for parameter tuning. Grid signal(—–); amplitude (––); α= 100, β = 12.5 (—–); α= 400, β = 50 (—–); α= 500, β = 100 (—–); α= 1000, β = 200 (—–).(b)Proposed TechniqueUsing trigonometric manipulation, the grid voltage signal (1) can bewritten as:v(t) = sin(ωt)A cos(φ) + cos(ωt)A sin(φ) +A0v(t) =[sin(ωt) cos(ωt) 1]︸ ︷︷ ︸CT A cos(φ)A sin(φ)A0︸ ︷︷ ︸x(6)where x= [x1 x2 x3]T is the parameter vector. Eq. (6) is a linearparametric model provided that ω is constant. In practice, ω is not constant,as such, ω needs to be estimated. This will be discussed later on. Assumingthat ωˆ is available, then the estimator adapted from [18, Ch. 4] can beapplied to estimate the parameters:˙ˆx1 = α sin(ωˆt)(v − vˆ) (7a)˙ˆx2 = α cos(ωˆt)(v − vˆ) (7b)˙ˆx3 = β(v − vˆ) (7c)vˆ= CˆT xˆ (7d)where α, β > 0 are tuning gains. In Eq. (7), time argument is avoidedfor notational simplicity. As shown in [18], an advantage of estimator(7) is that it provides exponential convergence of the estimation errors.Similar to demodulation-based technique, the estimator (7) also usemultiplication of trigonometric function to extract the phase. However,unlike demodulation-based techniques, no low-pass filtering is required.Moreover, the estimator (7) can be used to generate quadrature signal fromv as well. Quadrature signal of v i.e. vQ =A cos(ωt+ φ) can be estimatedasνˆQ = cos(ωˆt)xˆ1 + sin(ωˆt)xˆ2 (8)Estimator (7) has the following transfer function:vˆ(s) = v(s)/(τs+ 1) (9)where τ = 1/(α+ β). Transfer function (9) shows that low-pass filteringis an inherent property of the estimator. This can be very useful in practicalapplication.From the estimated parameter vector xˆ, the phase of the grid voltagesignal can be extracted as:φˆ= arctan(xˆ2/xˆ1)unwrapped (10)In the nominal condition, φˆ represents only the phase angle. However,during frequency variation, in addition to the phase angle, φˆ also containsthe deviation from the nominal frequency. As a result, the time derivative ofφˆ can be approximated as the frequency deviation dynamics i.e. ˙ˆ∆ω= ˙ˆφ.Then passing this signal through an integrator with gain γ, the estimatedfrequency deviation ∆ˆω can be easily obtained. Block diagram of theproposed demodulation type PLL (DT-PLL) is given in Fig. 1.Due to the presence of trigonometric quantities in the estimatordynamics (7), small-signal modeling-based parameter tuning can beFig. 3. Experimental results for Test-I.Fig. 4. Experimental results for Test-II.complicated for DT-PLL. Simulation studies can be very useful in thisregard. To tune the estimator parameters, first we set the frequencyestimation gain as γ = 50. Then two simulation tests have been considered.In the first case, amplitude jump of +0.5p.u. is considered while in thesecond test DC offset jump of +0.15p.u. is considered. Results of thesimulation are given in Fig. 2. This figure shows the estimated amplitudesfor four different values of α and β. For smaller values of α and β, theconvergence speed can be observed to be very slow while high value of αand β leads to oscillation in the estimated amplitude. α= 400 and β = 50found to be a comprise between convergence speed and peak overshoot.As such this values are selected. Frequency estimation speed is controlledby γ. Through extensive numerical simulation, γ = 50 was found to be agood value.3. Results and Discussions: To demonstrate the effectiveness of theproposed DT-PLL, dSPACE 1104 board-based experimental study isconsidered. As a comparison tool, we have selected DC offset rejection-based enhanced PLL (EPLL) [13]. Both techniques are implemented inMatlab/Simulink for code generation purpose with sampling frequency10KHz. EPLL parameters are selected as: µ0 = 85, µ1 = µ3 = ωn, andµ2 = 30000. Parameters values are taken from [13]. DT-PLL parametersare selected as: α= 400, β = 50, and k= 50. In all the figures presented inthis Section, X−axis indicates 20msec./Div.Test I +2Hz Frequency jump: Fig. 3 shows the actual grid voltage,estimated frequency and the phase estimation error. From Fig. 3, it can beobserved that the the estimated frequency by DT-PLL converged very fastin ≈ 2.5 cycles without any overshoot while EPLL took ≈ 3 cycles witharound 0.3Hz overshoot. Similarly the phase estimation error converged in≈ 2 cycles for DT-PLL while EPLL took ≈ 2.5 cycles. These results showthat DT-PLL is very effective in frequency tracking. It is to be mentionedhere that many PLL can provide ≈ 2 cycle convergence. However, thoseresults are in general obtained without any DC bias estimation loop.DC bias estimation loop slows down the dynamic response. As such theconvergence time of DT-PLL is competitive w.r.t. existing literature.Test II −0.5p.u. Amplitude jump: In this test, large amplitudejump is considered. In the context of low voltage ride through (LVRT)capability, this test is very significant. As shown in Fig. 4, both techniquesreacted very fast to the amplitude jump. However, DT-PLL convergedsignificantly faster than EPLL. Both techniques don’t employ any explicit2Fig. 5. Experimental results for Test-III.Fig. 6. Experimental results for Test-IV.gain normalization technique. However, experimental results show thatDT-PLL is significantly less sensitive to voltage sag.Test III +45◦ Phase jump: Fig. 5 shows comparative results for phasejump test. This figure demonstrates that DT-PLL has significantly lesspeak overshoot compared to EPLL. Moreover, fast convergence can alsobe observed for DT-PLL.Test IV +0.1p.u. DC jump: Fig. 6 shows the results for DC offsetjump test. Experimental results show that both techniques have similarpeak overshoot. However, DT-PLL converged ≈ 0.5∼ 1 cycle faster thanEPLL.Test V Harmonics robustness: In this test, suddenly the grid voltageis corrupted with harmonics. Considered harmonics components are:3rd − 1.3%, 5th − 2.9%, 7th − 1.7%, 9th − 2.6%, 11th − 1.8%, 13th − 1%,sub-harmonics 30Hz− 3.1%, and inter-harmonics 170Hz− 2.7%. Fig.7 shows the results for harmonics robustness test. Experimental resultsconfirm that the proposed PLL has higher harmonic filtering capabilitythan that of EPLL. Proposed technique has a ripple magnitude of ≈±0.4Hz and ≈±3.2◦ while EPLL has a ripple magnitude of ≈±1Hz and≈±5◦. As such the proposed technique can be claimed to be very suitableeven in distorted grid condition.4. Conclusion: A demodulation type single-phase PLL has been proposedin this letter to estimate the phase and frequency of single-phase system.First, a linear parametric model has been developed. Then a simpleestimator is proposed to estimate the initial phase angle similar toconventional demodulation-based technique. Using the initial phase angle,a simple frequency tracker is proposed. Comparative experimental resultswith enhanced phase locked-loop demonstrated the effectiveness of theproposed demodulation type PLL.H. Ahmed (Coventry University, United Kingdom)M. Benbouzid (University of Brest, UMR CNRS 6027 IRDL, France)E-mail: hafiz.h.ahmed@ieee.orgReferences1 M. Merai, M. W. Naouar, I. Slama-Belkhodja, and E. Monmasson, “Anadaptive PI controller design for DC-link voltage control of single-phasegrid-connected converters,” IEEE Transactions on Industrial Electronics,vol. 66, no. 8, pp. 6241–6249, 2018.Fig. 7. Experimental results for the harmonics robustness test.2 F. Baradarani, M. R. D. Zadeh, and M. A. Zamani, “A phase-angle estimation method for synchronization of grid-connected power-electronic converters,” IEEE Transactions on Power Delivery, vol. 30,no. 2, pp. 827–835, 2014.3 B. Lekouaghet, A. Boukabou, N. Lourci, and K. Bedrine, “Control ofpv grid connected systems using mpc technique and different inverterconfiguration models,” Electric Power Systems Research, vol. 154, pp.287–298, 2018.4 A. Rahoui, A. Bechouche, H. Seddiki, and D. O. Abdeslam, “Gridvoltages estimation for three-phase PWM rectifiers control without ACvoltage sensors,” IEEE Transactions on Power Electronics, vol. 33, no. 1,pp. 859–875, 2017.5 V. Choqueuse, P. Granjon, A. Belouchrani, F. Auger, and M. 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Demodulation Type Single-Phase PLL with DC Offset Rejection

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Demodulation Type Single-Phase PLL with DC Offset Rejection

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