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TRANSFORMER-BASED PHOTOVOLTAIC SYSTEM WITH CASCADED CONVERTERS WITH DISCONTINUOUS SYNCHRONIZED MODULATION
V. Oleschuk, A. Sizov Institute of Power Engineering of the Academy of Sciences of Moldova
Resume. The paper presents results of analysis of operation of photovoltaic system on the base of dual inverters with discontinuous synchronized pulsewidth modulation (PWM). Two basic schemes of discontinuous synchronized PWM, applied for control of dual-inverter system under different operation conditions, have been analyzed and compared.
Key words: voltage source inverter, photovoltaic system, modulation strategy, voltage synchronization.
SISTEMUL FOTOVOLTAIC CU TRANSFORMATORUL PE BAZA DE INVERTOARE CASCADE
CU MODULAREA SINCRONA DISCONTINUA V. Olesciuk, A. Sizov Institutul de Energetica al Academiei de §tiin^e a Moldovei Rezumat. Lucrarea prezinta rezultatele analizei de functionare a sistemului fotovoltaic pe baza invertoarelor duble cu modulare sincrona discontinua. Doua scheme de baza ale modularii discontinui sincrone, destinate pentru controlul sistemelor cu dublu-invertor in conditii diferite de exploatare, au fost analizate §i comparate. Cuvinte-cheie: invertor de tensiune, sistem fotovoltaic, strategie de modulare, sincronizare de tensiune.
ТРАНСФОРМАТОРНАЯ ФОТОПРЕОБРАЗОВАТЕЛЬНАЯ СИСТЕМА НА БАЗЕ КАСКАДНЫХ ПРЕОБРАЗОВАТЕЛЕЙ С ПРЕРЫВИСТОЙ СИНХРОННОЙ МОДУЛЯЦИЕЙ
В. Олещук, А. Сизов Институт энергетики Академии наук Молдовы Аннотация. Представлены результаты исследования работы фотопреобразовательной системы на базе сдвоенных (каскадных) инверторов напряжения с алгоритмами синхронной прерывистой модуляции. Проанализированы и сопоставлены характеристики систем с двумя базовыми разновидностями синхронной прерывистой модуляции и при различных условиях функционирования.
Ключевые слова: автономный инвертор напряжения, фотопреобразовательная система, стратегия модуляции, синхронизация напряжения.
I. INTRODUCTION
Multilevel converters and drives are a subject of increasing interest in the last years due to some advantages compared with conventional three-phase systems.
Some of the perspective topologies of power converters are now cascaded (dual) two-level converters which utilize two standard three-phase voltage source inverters [1]-[3]. In particular, dual-inverter-based open-end winding motor drives have some advantages such as redundancy of the space-vector combinations and the absence of neutral point fluctuations
[4]-[7]. These new drive topologies provide also one of the best possible use of semiconductor switches.
Almost all versions of classical space-vector PWM are based on an asynchronous principle, which results in sub-harmonics (of the fundamental frequency) in the spectrum of the output voltage and current of converters, which are very undesirable for high power applications [8],[9].
In order to provide voltage synchronization in dual- inverter fed drives, a novel method of synchronized PWM has been applied for control of these systems with single DC voltage
source [10], and for the systems with two DC sources: without power balancing between sources [11], and with power balancing algorithms [12], including application of hybrid schemes of PWM [13].
Besides adjustable speed AC drives, photovoltaic systems are among perspective areas of application of the dual-inverter topology [14]-[16]. In particular, fig. 1 presents dual inverter system supplied by two insulated strings of photovoltaic panels with the resulting DC voltages
Vl and Vh [14].
Fig. 1. Topology of dual-inverter-based photovoltaic system [14]
The presented in fig. 1 system topology is based on direct connection of two photovoltaic modules (strings) to dual (cascaded) inverters. And dual inverters are connected to a grid by a three-phase transformer with the open winding configuration on primary side, and this configuration is one of the most suitable for photovoltaic systems with a higher power range.
So, this paper presents analysis of operation of dual-inverter-based photovoltaic system with algorithms of discontinuous synchronized PWM. In particular, it is known, that schemes of discontinuous modulation are the most suitable PWM schemes for control of inverters in the zone of higher modulation indices [8], and these control modes are typical for control of majority of photovoltaic installations based on cascaded inverters.
II. BASIC PROPERTIES OF THE METHOD OF SYNCHRONIZED
MODULATION
In order to avoid asynchronism of conventional space-vector modulation, novel space-vector-based method of synchronized PWM [17] can be used for control of each inverter in a dual-inverter system for photovoltaic generation.
figs. 2 - 3 present switching state sequences of standard three-phase inverter inside the interval 00-900. They illustrate schematically two basic discontinuous versions of space-vector PWM (fig. 2 - discontinuous PWM with the 300-non-switching intervals (DPWM30); fig. 3 -discontinuous PWM with the 600-non-switching intervals (DPWM60)) [17].
Fig. 2. Switching state sequence, pole voltages Va, Vb, Vc, and line-to-line voltage Vab of three-phase inverter with discontinuous PWM with the 300-non-switching intervals
(DPWM30)
yl y2 V3
A _> A._ A_
|U n n n
P3 p2 pl p2 p3
X2 X
phase aj |___
p4
X4
X3
phase b
phase c_
Fig. 3. Switching state sequence, pole voltages Va, Vb, Vc, and line-to-line voltage Vab of three-phase inverter with discontinuous PWM with the 600-non-switching intervals
(DPWM60)
The upper traces in figs. 2 - 3 are switching state sequences (in accordance with conventional designation [17]), then - the corresponding pole voltages of standard three-phase inverter. The lower traces in figs. 2 - 3 show the corresponding quarter-wave of the line-to-line output voltage of the inverter. Signals pj represent total switch- on durations during switching cycles r, signals yk are generated in the centers of the corresponding p. Widths of notches Xk represent duration of zero states [17].
So, one of the basic ideas of the proposed PWM method is in continuous synchronization of the positions of all central pl -signals in the centers of the 600-clock-intervals (to fix positions of the p -signals in the centers), and then - to generate symmetrically all other active p - and y -signals, together with the corresponding notches.
For the presented photovoltaic power conversion system (fig. 1) rational determination of the switching frequency Fs of inverters and duration of sub-cycles r, providing continuous voltage synchronization during fluctuation of the grid fundamental frequency F, can be based on (1),(2) for discontinuous versions of modulation (DPWM) [16]:
Fs(DPWM) = F(8n - 5) (1)
rDPWM =
l/[6F(2n-1.5)], (2)
where n=2,3,4....
Equations (3)-(8) present set of control functions for determination of durations of all control signals of three-phase inverters with synchronized PWM in absolute values (seconds) for both undermodulation and overmodulation control regimes of dual inverters [17]:
For j=2,...i-1:
Pj =pcos[(/-1 - (3)
Yj = P,+1{05 - 087 tan[(i' - j - 025)r]}Kov2 (4)
p =P" =pcos[(i-1.2511 (5)
y =P”{0.5 - 0.87 tan[(i - 2.25)r +
(p-1 + p + A_l)/2]}KtK„ 2
A, =r-(p, +p,+1)/2 (7)
X, =X=(r-p■) KovK, (8)
where: p = 1.1m if m<0.907, and p =r if m>0.907; is coefficient of
synchronization [17].
III. SYNCHRONOUS OPERATION OF CASCADED INVERTERS SUPPLIED BY
PHOTOVOLTAIC STRINGS
Synchronous control of the output voltage of each inverter of dual-inverter-based system with algorithms of synchronized PWM provides synchronous symmetrical regulation of the phase voltages V1, V2 and V3 of the system. Rational phase shift between waveforms of the output voltages of the two inverters is equal in this case to one half of the switching interval (sub-cycle) t [1].
In the case, when the two DC-link voltage sources have equal voltages (VL=VH), the resulting voltage space-vectors are equal to the space-vector patterns of conventional three-level inverter [1],[3],[6].
The phase voltages V1, V2, V3 of the dual-inverter system with two isolated DC-sources (fig. 1) are calculated in accordance with (9)-(12) [4]:
V0 = 1/3(Vil + V2L + V3L + V1H + V2H + V3H) (9)
V1 = V1L + V1H - V0 (10)
V2 = V2L + V2H - V0 (11)
V3 = V3L + V3H - Vo, (12)
where Y1L, Y2L, Y3L, Vih, Y2H, Y3H are the corresponding pole voltages of each three-phase inverter (fig. 1), Vo is zero sequence (triplen harmonic component) voltage.
Control of photovoltaic power conversion systems on the base of dual inverters has some peculiarities. In particular, in the case of direct connection between the two photovoltaic strings and the two inverters, in order to provide maximum power point tracking of photovoltaic panels, operation of control board should be based on continuous analysis of DC-currents of photovoltaic strings [14]. And, in particular, in the case of non-equal currents of two DC-sources, control of the system should be based on the corresponding specific regulation of modulation indices of dual inverters [15]. And this control is somewhat similar to power sharing process between two dual inverters for traction systems, analyzed in [7],[12].
A. Operation of the System with Equal DC-Currents
Operation of photovoltaic system with equal DC-currents of two strings of photovoltaic panels is the basic operation mode for majority of photovoltaic applications. Modulation indices of two cascaded inverters should have in this case relatively high level
[15],[16]. To illustrate operation of the dual-inverter system for transformer-based photovoltaic installation with equal DC-currents, for the case when modulation indices of two inverters are equal to mH = mL = 0.9, fig. 4 - fig. 7 show basic voltage waveforms on the primary side of the system, controlled by algorithms of synchronized discontinuous PWM with the 300-non-switching intervals (DPWM30, figs. 4 - 5), and by algorithms of discontinuous modulation with the 600-non-switching intervals (DPWM60, figs. 6 - 7).
In particular, the presented figures show pole voltages Vih, Vil,, line-to-line voltages
Y1H2H, Y1L2L of the two inverters, and of the phase voltage Yi (with its spectrum in figs. 5 and 7) on the primary side of transformer. Fundamental frequency of the system is F=50Hz, and average switching frequency is Fs = 1.35 kHz for each modulated inverter, DC-voltages are equal to Vdc = YH = Vl = 300 Y.
0 0.005 0.01 0.015 0.02
time (s)
Fig. 4. Pole voltages Vih and V1L, line voltages Vmm and V1L2L, and phase voltage Vi of the system with discontinuous synchronized PWM with the 300-non-switching intervals
(DPWM30, mH=mL=0.9)
Fig. 5. Spectrum of the phase voltage Y1 of the system with discontinuous PWM (DPWM30,
mH=mL=0.9)
Fig. 6. Pole voltages V1H and V1L, line voltages V1H2H and V1L2L, and phase voltage V1 of the system with discontinuous synchronized PWM (DPWM60, mH=mL=0.9)
Fig. 7. Spectrum of the phase voltage Y1 of the system with discontinuous PWM (DPWM60,
mH=mL=0.9)
B. Operation of the System with Non-Equal DC-Currents
In the case of non-equal currents from two strings of photovoltaic panels control of the system should be based on the corresponding specific regulation of modulation indices of dual inverters. In particular, in order to provide rational power sharing between inverters,
modulation index of the inverter, supplied by the bigger current, should be decreased correspondingly in comparison with modulation index of the inverter, supplied by smaller DC-current [15].
As an example of operation of the dual-inverter system with synchronized PWM with non-equal DC-currents and, correspondingly, non-equal modulation indices of cascaded inverters (mH=0.9, mL=0.7), fig. 8 - fig. 11 present basic voltage waveforms of the system, with spectra of the phase voltage on the primary side of three-phase transformer, for the system controlled by algorithms of discontinuous modulation with the 300-non-switching intervals (DPWM30, figs. 8 - 9), and for the system controlled by algorithms of discontinuous synchronized PWM with the 600-non-switching intervals (DPWM60, figs. 10 - 11). Fundamental frequency of the system is F = 50Hz, and average switching frequency is equal to Fs = 1.35 kHz for each modulated inverter.
The presented results show, that spectra of the phase voltage of dual-inverter systems with synchronized PWM do not contain even harmonics and sub-harmonics.
Fig. 8. Pole voltages Y1H and Y1L, line voltages Vih2h and Y1L2L, and phase voltage Y1 of the system with discontinuous PWM with the 300-non-switching intervals (DPWM30,
mH=0.9, mL=0.7)
Fig. 9. Spectrum of the phase voltage V1 of the system with discontinuous PWM (DPWM30, mH=0.9, mL=0.7)
C. Operation of the System with Big Difference of Modulation Indices of Dual Inverters
It is interesting to analyze behavior of dual-inverter-based photovoltaic system for the case of big difference of value of modulation indices of two inverters. In particularly, in practice this case can be connected with big difference in solar irradiance level for the corresponding photovoltaic panels [15].
To illustrate operation of the dual-inverter system with big difference between modulation indices of two inverters (mH = 0.9, mL = 0.5mH = 0.45), fig. 12 - fig. 15 show basic voltage waveforms on the primary side of the system, controlled by algorithms of synchronized discontinuous PWM with the 300-non-switching intervals (DPWM30, figs. 12 -13), and of the system controlled by algorithms of discontinuous PWM with the 600-nonswitching intervals (DPWM60, figs. 14 - 15).
And in these cases spectra of the phase voltage of the system with discontinuous synchronized PWM contain only odd (non-triplen) harmonics.
Fig. 10. Pole voltages Y1H and Y1L, line voltages Vih2h and Y1L2L, and phase voltage Y1 of the system with discontinuous PWM with the 600-non-switching intervals (DPWM60,
mH=0.9, mL=0.7)
Fig. 11. Spectrum of the phase voltage Vj of the system with discontinuous PWM (DPWM60, mH=0.9, mL=0.7)
Fig. 12. Pole voltages Y1H and Y1L, line voltages Y1H2H and Y1L2L, and phase voltage Y1 of the system with discontinuous PWM with the 300-non-switching intervals (DPWM30, mH=0.9,
mL=0.45)
Fig. 13. Spectrum of the phase voltage Y1 of the system with discontinuous PWM (DPWM30,
mH=0.9, mL=0.45)
Fig. 14. Pole voltages Y1H and Y1L, line voltages Y1H2H and Y1L2L, and phase voltage Y1 of the system with discontinuous PWM with the 600-non-switching intervals (DPWM60, mH=0.9,
mL=0.45)
Fig. 15. Spectrum of the phase voltage Y1 of the system with discontinuous PWM (DPWM60, mH=0.9, mL=0.45)
D. Spectral Assessment of Phase Voltage Quality of Dual-Inverter System
Total Harmonic Distortion (THD) factor of voltage is one of the most suitable criteria for analysis of power quality in grid-connected photovoltaic systems. In particular, in accordance with the majority of standards for 50-Hz power systems, total voltage harmonic distortion has to be calculated up to the 40th voltage harmonic [18].
Fig. 16 presents the calculation results of Total Harmonic Distortion factor (THD) for the phase voltage Y1 on the primary side of three-phase transformer as a function of modulation index mL, (mH=const=0.9 in this case) of dual-inverter-based system, controlled by algorithms of two discontinuous (DPWM30 and DPWM60) schemes of synchronized
40
modulation. The THD factor ( THD = (1/ V^) £ ) has been calculated until the 40-th low-
k=2
order (k-th) voltage harmonic. The fundamental frequency of the system is 50Hz, and the average switching frequency of each modulated inverter is equal to J. 35 kHz.
Fig. 16. THD factor of the phase voltage Y1 versus modulation index mL for the systems with two discontinuous (DPWM30 and DPWM60) versions of synchronized PWM (k=40)
The presented calculation results show, that in the case of different values of modulation indices of dual inverters the use of discontinuous synchronized modulation with the 600-non-switching intervals (DPWM60) allows slightly better spectral composition of phase voltage in comparison with application of discontinuous PWM with the 300-non-
switching intervals (DPWM30). Also, due to relatively low switching frequency of dual inverters, low-order harmonics (with order less than 40) appeared in voltage spectra in these control modes (see figs. 9, 11, 13, 15), contributing to an increase of the THD factor in this case. So, in order to provide improved spectral characteristics of the phase voltage, it is necessary to increase switching frequency of dual inverters for these control conditions.
IV. CONCLUSION
Novel method of synchronized space-vector modulation, disseminated for control of dual-converter system on the base of two three-phase inverters, supplied by two insulated photovoltaic strings, allows both continuous phase voltage synchronization and required power distribution between two inverters by the corresponding control of the corresponding modulation indices.
The presented results of simulation of dual-inverter-based system controlled by novel algorithms of discontinuous synchronized PWM, illustrate the fact, that spectra of the phase voltages do not contain even harmonics and sub-harmonics for any operation conditions of the system. In particular, the analyzed control algorithms can also provide continuous voltage synchronization during fluctuation of the grid fundamental frequency. So, high power/high current systems on the base of dual inverters with relatively low switching frequencies are the most perspective field for application of the proposed algorithms of synchronized modulation.
Analysis of spectral composition of the phase voltage in dual-inverter system shows that for the case of non-equal modulation indices of dual inverters the use of discontinuous synchronized modulation with the 600-non-switching intervals allows slightly better spectral composition of the phase voltage in comparison with application of discontinuous PWM with the 300-non-switching intervals.
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Valentin Oleschuk (oleschukv@hotmail.com), Dr.Sc., is Chief Scientist of the Power Engineering Institute of the Academy of Sciences of Moldova. He is author and co-author of two books and more than 230 publications in the area of power electronics and electric drives, including 70 IEEE publications. He is also the author of 89 patents and authors certificates in this field. His research interests include control and modulation strategies for power converters, electric drives and renewable energy systems.
Alexandr Sizov (alexandrsizov@yahoo.com) is Scientific Collaborator of the Power Engineering Institute of the Academy of Sciences of Moldova. He is author and co-author of more than 60 publications and 10 patents and authors certificates. His research interests include elaboration, modelling and simulation of control algorithms and control systems for power electronic converters, electric drives and renewable energy systems.
