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Transformer-based photovoltaic system with cascaded converters with discontinuous synchronized modulation

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 V_L and V_H [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.

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 V_a, V_b, V_c, and line-to-line voltage V_ab of three-phase inverter with discontinuous PWM with the 30⁰-non-switching intervals (DPWM30)

Fig. 3. Switching state sequence, pole voltages V_a, V_b, V_c, and line-to-line voltage V_ab 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 represent total switch - on durations during switching cycles , signals are generated in the centers of the corresponding . Widths of notches 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 -signals in the centers of the 60⁰-clock-intervals (to fix positions of the -signals in the centers), and then - to generate symmetrically all other active- and -signals, together with the corresponding notches.

For the presented photovoltaic power conversion system (fig. 1) rational determination of the switching frequency F_s of inverters and duration of sub-cycles , 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]:

(1)

, (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:

(3)

(4)

(5)

(6)

(7)

, (8)

where: if m<0.907, and if m>0.907; K_s is coefficient of synchronization [17].

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) [1].

In the case, when the two DC-link voltage sources have equal voltages (V_L=V_H), 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 (V_1L + V_2L + V_3L + V_1H + V_2H + V_3H) (9)

V₁ = V_1L + V_1H - V₀ (10)

V₂ = V_2L + V_2H - V₀ (11)

V₃ = V_3L + V_3H - V₀, (12)

where V_1L, V_2L, V_3L, V_1H, V_2H, V_3H are the corresponding pole voltages of each three-phase inverter (fig. 1), V₀ 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].

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 m_H = m_L = 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 V_1H, V_1L, line-to-line voltages V_1H2H, V_1L2L of the two inverters, and of the phase voltage V₁ (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 F_s = 1.35 kHz for each modulated inverter, DC-voltages are equal to V_dc = V_H = V_L = 300 V.

Fig. 4. Pole voltages V_1H and V_1L, line voltages V_1H2H and V_1L2L, and phase voltage V₁ of the system with discontinuous synchronized PWM with the 30⁰-non-switching intervals (DPWM30, m_H=m_L=0.9)

Fig. 5. Spectrum of the phase voltage V₁ of the system with discontinuous PWM (DPWM30, m_H=m_L=0.9)

Fig. 6. Pole voltages V_1H and V_1L, line voltages V_1H2H and V_1L2L, and phase voltage V₁ of the system with discontinuous synchronized PWM (DPWM60, m_H=m_L=0.9)

Fig. 7. Spectrum of the phase voltage V₁ of the system with discontinuous PWM (DPWM60, m_H=m_L=0.9)

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 (m_H=0.9, m_L=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 F_s = 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 V_1H and V_1L, line voltages V_1H2H and V_1L2L, and phase voltage V₁ of the system with discontinuous PWM with the 30⁰-non-switching intervals (DPWM30, m_H=0.9, m_L=0.7)

Fig. 9. Spectrum of the phase voltage V₁ of the system with discontinuous PWM (DPWM30, m_H=0.9, m_L=0.7)

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 (m_H = 0.9, m_L = 0.5m_H = 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-non-switching 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 V_1H and V_1L, line voltages V_1H2H and V_1L2L, and phase voltage V₁ of the system with discontinuous PWM with the 60⁰-non-switching intervals (DPWM60, m_H=0.9, m_L=0.7)

Fig. 11. Spectrum of the phase voltage V₁ of the system with discontinuous PWM (DPWM60, m_H=0.9, m_L=0.7)

Fig. 12. Pole voltages V_1H and V_1L, line voltages V_1H2H and V_1L2L, and phase voltage V₁ of the system with discontinuous PWM with the 30⁰-non-switching intervals (DPWM30, m_H=0.9, m_L=0.45)

Fig. 13. Spectrum of the phase voltage V₁ of the system with discontinuous PWM (DPWM30, m_H=0.9, m_L=0.45)

Fig. 14. Pole voltages V_1H and V_1L, line voltages V_1H2H and V_1L2L, and phase voltage V₁ of the system with discontinuous PWM with the 60⁰-non-switching intervals (DPWM60, m_H=0.9, m_L=0.45)

Fig. 15. Spectrum of the phase voltage V₁ of the system with discontinuous PWM (DPWM60, m_H=0.9, m_L=0.45)

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 V₁ on the primary side of three-phase transformer as a function of modulation index m_L, (m_H=const=0.9 in this case) of dual-inverter-based system, controlled by algorithms of two discontinuous (DPWM30 and DPWM60) schemes of synchronized modulation. The THD factor () has been calculated until the 40-th low-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 1.35 kHz.

Fig. 16. THD factor of the phase voltage V₁ versus modulation index m_L 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.

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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synchronous modulation inverter photoconversion

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