SINGLE-PHASE TO THREE-PHASE CONVERTER OPERATION UNDER FREQUENCY VARIATION AND NON-LINEAR LOAD RICARDO Q. MACHADO*, JOSÉ A. POMILIO* AND SIMONE BUSO** *
State University of Campinas School of Electrical and computer Engineering 13081-970 Campinas – Brazil **
Department of Information Engineering Via Gradenigo 6/B 35131 Padova – Italy Emails:
[email protected],
[email protected],
[email protected] Abstract This paper describes a line-interactive single-phase to three-phase converter. A typical application is in rural areas supplied by the single-wire with earth return. The traditional objective of feeding a three-phase induction motor is not anymore the main concern for such conversion. Due to the evolution of the agro business, some of the local load (as electronic power converters, computers, communication equipments, etc.) requires high quality power, intended as sinusoidal, symmetrical and balanced three-phase voltage. Additionally, to maximize the power got from the feeder, the system provides a unitary power factor to the feeder. A three-phase VSI-PWM converter is used for this purpose. The power converter does not process all the load power, as in the conventional solutions, but only the fraction necessary to regulate the three-phase bus voltage. As it does not manage active power, it is not necessary to have a source at the DC side. The control strategy, design highlights and experimental results are presented. Keywords Single-phase to three-phase conversion, digital control, rural electrification, PWM inverter. Resumo Este trabalho descreve a conexão direta entre um sistema monofásico e outro trifásico onde as principais aplicações são sistemas rurais de pequeno porte. Devido à nova necessidade dos consumidores que solicitam energia de boa qualidade para alimentar cargas sensíveis como: computadores, equipamentos de comunicação e eletrodomésticos cuja fonte utiliza conversores chaveados têm sido o enfoque de vários estudos nesta área. Para obter-se a mínima quantidade energia proveniente do alimentador isto é, fator de potência unitário será utilizado um conversor trifásico do tipo VSI-PWM. O conversor não necessita processar toda energia como em aplicações convencionais mas somente uma parte da mesma. Outro ponto interessante deste trabalho é a não necessidade de fonte de energia conectada no link CC pois ele não processará energia ativa. Uma estratégia de controle será apresentada e resultados experimentais irão comprovar tais afirmações. Palavras-chave Conexão mono trifásica, controle digital, eletrificação rural, inversor PWM.
1
Introduction
In spite of the distribution of electric power be typically three-phase, in some situations the costumers can have access only to a single-phase. This happens in residential, light commercial and rural areas. Sometimes a specific appliance needs three-phase power, what requires some kind of power conversion (Moncrief, 1996). In rural areas it is common the use of a single wire feeder with earth return. The power quality is normally very poor in terms of voltage regulation and distortion. Three-phase induction motor is a typical load in rural applications. For such a load, it is not important to filter the switching high-frequency components produced by the converter because the load naturally acts as a low-pass filter. The 1φ3φ conversion can be done using some kind of PWM converter (Enjeti, 1993; Lee, 2002; Covic, 1995; da Silva, 1995; Ohnishi, 1998; Tshivhilinge, 1998; Douglas, 1998). In the conventional conversion system, the load power is processed twice: by the single-phase rectifier and by the three-phase inverter. The topologies presented in the above references also have a rectifier followed by an inverter, but they incorporate some upgrading to
improve certain performance aspect such as: minimize the number of power switches; reduce the cost; improve the power factor to the single-phase feeder; guarantee good voltage quality to the load; etc. Besides the motors, even in rural applications, it increases the use of electric and electronic loads that are sensitive to the power quality as, for example, power electronics converters, computers, etc. Some of these loads are low power factor nonlinear loads. The single-phase feeder could directly feed these loads. However, considering the power limitation of the feeder, it would be interesting to maximize the active power availability, what can be get with unitary power factor. This improvement could be done using some kind of power factor corrector or active power filter. This article presents a single-phase to threephase conversion system that improves the local power quality for linear and non-linear loads, and guarantees unity power factor to the single-phase feeder. The system is shown in Figure 1. The single-phase feeder is connected to the local three-phase bus through a small series reactance (XLS). A three-phase Static Power Converter (SPC- PWM) also is connected to the bus through
a low-pass filter (Lconv.Cconv). The inverter controls the local power quality, producing three-phase balanced, symmetrical and sinusoidal voltages. It also controls the single-phase power flow, by adjusting the local voltage amplitude and phase angle. Harmonics currents of the load flow locally, resulting the feeder current is sinusoidal, except for the harmonic components already present in the single-phase voltage. In this sense, the converter also works as an active filter for the current harmonics and as a reactive compensator (Marra, 2000). Additionally, part of the load power is not processed by the converter, and flows directly from the grid, what improves the overall efficiency. As this PWM inverter does not deliver active power to the load, it is not necessary to have a DC power source, but the system could operate as a line interactive UPS if a DC source is available, since the islanding situation is adequately managed (Bekiarov, 2003).
phase bus voltage, as shown in Figure 2. The limits for the amplitude variation, which are within an acceptable range, are shown in Table 1 (CELPE, 1978). The reactor that connects the grid with the three-phase bus is calculated considering the feeder capacity (Machado, 2004). The operation point is calculated considering the active load power (PL) and the actual source voltage (Vsource), as indicated by eqs. (1) and (2). This voltage is the reference for the inverter.
PL X LS 2 V source
(1)
Vsource cos β
(2)
β = arctan
VAB =
The inverter output voltage control system is shown in Figure 3. There is an inner fast current loop and an outer voltage loop with some feedforward inputs. These additional inputs minimize the voltage error and preserve the high-quality waveform, even for non-linear loads. The design procedures were adapted from Machado (2003 and 2004).
2 Basic System Operation As explained before, one of the control strategy goals is to produce a grid current that results unity power factor for the single-phase feeder. As the voltage at this feeder can vary, it is necessary to adjust both amplitude and phase of the AC three-
L oad p iLA
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L
and q
L
iLC
p
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AB
sou rce
vB
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vC
iO B
iO C
p conv
L conv
C
DC
sou rce
S
v sou rce
vBC vA
and q
C
SPC
Figure1. Single-phase to three-phase conversion system.
conv
S in g le - p h a s e fe e d e r
I source
to get these results. The basic idea is to use the event time unit (ETU) of the DSP. The synchronization error between two waveforms must modify the controller frequency according to a dead-beat algorithm. To explain the controller operation let us refer to Figure 4. Suppose there is a small difference between the sampling period (T*sw) and the actual switching period Tsw. We call e(k) the phase error at the instant k.Tsource. Tsource is the source voltage period. According to (eq. 4), at k.Tsource, the sampling period is increased, so as to result e(k+1)=0. In order to do that, the increment is equal to the error divided by N, summed to the “memory” of all previous errors, that is stored in variable TI (integral of the error). e( k ) ∆Tsw ( k ) = + TI ( k ), N (4) e( k ) T I ( k ) = TI ( k − 1 ) + N This guarantee that after instant (k+1).Tsource the synchronization error will be equal to zero and, in the absence of other perturbation, will remain equal to zero. In any case, the controller guarantees a dynamic response equal to a voltage source period, which is the faster possible. Particular care must be taken in the implementation to limit the controller action, in presence of large perturbation. The design procedures were adapted from Rossetto (2003).
Vsource
β
VAB
VLS
Figure 2. Phasorial diagram. Table 1. Three-phase voltage range
High limit
Low limit
Worst case
1.05Vn source
0.90Vn source
Typical case
1.05Vn source
0.95Vn source
3 Control Strategies To guarantee the terminal inverter voltage quality, closed loop control of the output current and voltage has been implemented. The proportionalintegral controller (PI) was chosen as control technique. The PI regulator has been associated with a feed-forward compensation of the output filter capacitive current component plus a turned resonant filter to provide good response to the voltage distortion. For the current control loop an additional feed-forward signal from of the voltage reference shown to be sufficient to have a good response. It is necessary to guarantee that the phase displacement between AC bus voltage and the reference voltage (vref) (internally generated by the control circuit) is kept as close to zero as possible. Since the reference voltage is generated and updated at the switching (and sampling) frequency, this frequency must be an integer multiple of the source frequency (in our implementation N=200). A digital PLL-based controller was implemented
Tsw ( k ) = T * sw + ∆Tsw ( k )
(5)
The PLL implementation uses a PI regulator associated with an anti wind-up algorithm. In eq. (6) Ymax represents the maximum allowed variation in the vsource period. The dynamic saturation limit, L, is calculated once for sampling cycle, so as to keep the control output within the limit Ymax. 1 L = Ymax − .e( k ) (6) 200
k cur Feed-forward
G2
iL convαβ
Capacitive current compesation
vCconvαβ
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Voltage control
PI v
+
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-
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Current control
PI i
+
+
SVM
+ -
Selecive filter
1 sLconv
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-
iCconvαβ
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k volt
inside DSP Figure 3. Inverter output voltage control system.
outside DSP
vCconvαβ
Ymax
L
e(k )
1 N
TI (k ) + +
+
T * sw (k ) +1µ s
∆Tsw (k ) + +
+ 1 Z
Tsw (k )
T * sw (k ) −1µ s
T * sw (k )
Figure 4. Block diagram of the PLL controller, with dynamic saturation.
4 Experimental Results The proposed control strategy has been implemented using a 16-bit fixed-point DSP-based controller ADMC 401 (Analog Devices). This DSP unit represents a powerful tool for digital control implementation for high-performance industrial applications due to its fast arithmetic unit (38.5 ns cycle and 26 MIPS). Space vector modulation was used to command the switches with 12 kHz as switching and sampling frequency and thus, we have 200 samples for one period of 60 Hz. The resolution for β angle adjusting is 0.03 degree due to event time unit resolution. A 3 kW experimental setup was built to verify the system operation.
4.1 PLL operation To analyze the PLL operation, a drastic situation was considered: a 0.5 Hz step variation was imposed to the single-phase source (programmable voltage source). There was a balanced three-phase 1500 W linear load at the AC bus. The synchronism between vref and vsource is quickly obtained due to the performance of the PLL controller. However, such variation produces a power flow fluctuation between the system (load + inverter) and single-phase feeder. For more realistic frequency changes, such oscillation is not so problematic. The single-phase source frequency variation instantaneously alters the angle β, and produces a power flow perturbation, and causes a variation in the DC link voltage. The specific PI regulator, which output is the desired angle β, is slowly adjusted, as presented in Figure 5. Figure 6 presents the same signals after stabilization. 4.2 Non-linear load Now, a 600 W non-linear load (three-phase rectifier with resistive load) is connected to the AC bus. Figure 7 presents the harmonic compensation capacity of the control for non-linear load. The internal reference voltage and single-phase voltage maintain the synchronism. The VAB THD is 2% for
an ILoad THD of 40%. The current harmonics flow through the inverter, maintaining sinusoidal source current.
vref=vsource ‘
‘
-psource -isource
‘
vsource
Figure 5. Top traces: intern reference and single-phase feeder voltage (360V/div.). Middle Traces: instantaneous source power (2500W/div.). Bottom Traces: source voltage (250V/div.) and source current (10A/div.). Horizontal: 50ms/div.
vref=vsource -psource
vsource=-isource
Figure 6. Top traces: intern reference and single-phase feeder voltage (360V/div.). Middle Traces: instantaneous source power (2500W/div.). Bottom Traces: source voltage (250V/div.) and source current (10A/div.). Horizontal: 10ms/div.
Figure 8 shows manly the inverter phase voltage and its reference. The phase displacement between Isource and Vsource results a PF of 0.99.
vref = vsource
Figs. 11 and 12 the displacement between vsource and isource is 2o, due to the angle adjust resolution. The source voltage THD is 1 %.
iload vsource
vAB iload
-isource
Figure 7. Top traces: intern reference and single-phase feeder voltage (180V/div.). Bottom Traces: output inverter voltage (250V/div.) and load current (5A/div.). Horizontal: 5ms/div.
Figure 9. Top traces: load current (10A/div.). Bottom Traces: source voltage (100V/div.) and source current (10A/div.). Horizontal: 10ms/div.
-isource *
vA = vA
vAB
vsource vDC
imotor
-isource Figure 8. Top traces: reference and filtered inverter voltage (360V/div.). Bottom Traces: source voltage (100V/div.) and source current (10A/div.). Horizontal: 5ms/div.
4.3 Dynamic analysis An additional 600 W resistive load was connected to the three-phase rectifier. When this additional load was connected, the control detects the inverter DC link voltage variation and quickly changes the angle β, as shown in Figure 9, absorbing from the grid the necessary additional power. After the load step the PF continues equal to 0.99. 4.4 Motor start- up Figure 10 shows a three-phase induction motor startup. The additional power necessary during the acceleration is partially provided by the inverter DC bus capacitor, while the control circuit changes the β angle in order to absorb power from the grid. The three-phase bus voltage remains almost constant due to decoupled control between the AC and the DC voltage controls. The DC voltage sag does not reflect in the AC voltage but produces an oscillation in single-phase current. In
Figure 10. From top to bottom: single-phase current (20A/div), AC bus voltage (500V/div.), DC link voltage (200V/div.) and motor current (5 A/div.). Horizontal: 50ms/div.
vsource
-isource
Figure 11. Single-phase feeder voltage (100V/div.) and current (10A/div.). Horizontal: 10ms/div.
3 Conclusions A line-interactive single-phase to three-phase conversion system was presented. It is suitable for sensitive loads because it guarantees the threephase power quality, what means: sinusoidal, bal-
anced and symmetrical voltages even with nonlinear loads. A three-phase inverter is controlled in order to stabilize the three-phase voltage while absorbing current from the single-phase, under unitary PF. Any frequency variation is quickly synchronized by the PLL control. A 3 kW experimental set-up was built to illustrate the potentialities of the proposed solutions.
vsourcevA -isource
-iA
Douglas, H. and Malengret, M. (1998). “Symmetrical PWM with a Split-Capacitor Single-Phase to Three-Phase Converter for Rural Electrification”, IEEE ISIE, South Africa, July 1998, pp. 289-293 Enjeti P. and Rahman A. (1993). “A New SinglePhase to Three-Phase Converter with Active Input Current Shaping for Low Cost AC Motor Drives”, IEEE Trans. On Industry Applications, vol. 29, no. 4, July/August 1993, pp.806-813 Lee, D-C; Kim T-Y; Lee G-M and Seok, J-K (2002) “Low-Cost Single-Phase to ThreePhase PWM AC/DC/AC Converters without Source Voltage Sensor”, IEEE ICIT´02, Bangkok, Thailand, 2002, pp. 792-797. Machado, R. Q., Buso, S., Pomilio, J. A. and Marafão, F. P. (2004). “Three-Phase to Single-Phase Direct Connection for rural cogeneration systems”, IEEE APEC, Anahein, USA, Feb. 2004.
Figure 12. Phase diagram of the single-phase feeder voltage (100V/div.) and single-phase current (10A/div.).
Acknowledgment The authors would like to acknowledge CAPES and FAPESP (proc. BEX0277/02-9 and 00/110389) for supporting this project. References Bekiarov, S. B. and Emadi, A. (2003). “A New On-Line Single-Phase to Three-Phase UPS Topology with Reduced Number of Switches”, IEEE PESC 2003, pp. 451-456. CELPE (1978) – Cia. de Eletricidade do Pernambuco Standard for Power delivery using the single wire earth return system (Norma para Fornecimento de Energia Elétrica pelo Sistema Monofásico com Retorno por terra – MRT). NE 08., 1978 (in Portuguese). Covic, G. A.; Peters, G. L. and Boys, J. T. (1995). “An Improved Single Phase to Three Phase Converter for Low Cost AC Motor Drives”, IEEE PEDS, Feb 1995, pp. 549-554. da Silva, E. R. C.; de Souza, S. B. and Coelho, F. A. (1995). “A Single Phase to Three Phase Soft-Switched Converter, Isolated and with Active Input Current Shape”, IEEE PESC, Atlanta, USA, June 1995, pp. 1252-1257.
Machado, R. Q., Buso, S., Pomilio, J. A. and Marafão, F. P. (2003). “Eletronic Control of a Three-Phase Induction Generator Directly Connected to a Single-Phase Feeder”, The 7th Brazilian Power Electronics Conference, COBEP, Fortaleza, Brazil USA, Sep. 2003, pp. 651-656. Marra, E. G. and Pomilio, J. A. (2000). “Induction Generator based System providing Regulated Voltage with Constant Frequency”. IEEE Transactions on Industrial Electronics, vol. 47, no. 4, pp. 908 – 914, Aug. 2000. Moncrief, W. A. (1996). “Practical Application and Selection of Single-Phase to Three-Phase Converters”, 39th IEEE Rural Electric Power Conference, pp. D3-1 to D3-9. Ohnishi T. (1998). “PWM Control Method for Single-Phase to Three-Phase Converter with a Three-Phase Switching Power Module”, IEEE PESC, May 1998, Japan, pp. 464-469. Rossetto, L. and Buso S. (2003). “PWM Line Voltage Regulator with Integrated PFC”, IEEE PESC, 2003. Tshivhilinge, E. N. and Malengret, M.(1998) “A Practical Control of a Cost Reduced SinglePhase to There-Phase Converter”, IEEE ISIE, South Africa, July 1998, pp. 445-449.
