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Modeling of a single-phase photovoltaic inverter
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Solar Energy Materials & Solar Cells 91 (2007) 1713–1725 www.elsevier.com/locate/solmat
Modeling of a single-phase photovoltaic inverter T.I. Marisa, St. Kourtesib, L. Ekonomouc, G.P. Fotisd, a
Department of Electrical Engineering, Technological Educational Institute of Chalkida, 334 40 Psachna Evias, Greece b Hellenic Public Power Corporation S.A., 22 Chalcocondyli Str., 104 32 Athens, Greece c Hellenic American University, 12 Kaplanon Str., 106 80 Athens, Greece d National Technical University of Athens, School of Electrical and Computer Engineering, High Voltage Laboratory, 9 Iroon Politechniou St., Zografou, 157 80 Athens, Greece Received 3 March 2007; received in revised form 25 May 2007; accepted 25 May 2007 Available online 27 June 2007
Abstract The paper presents the design of a single-phase photovoltaic inverter model and the simulation of its performance. Furthermore, the concept of moving real and reactive power after coupling this inverter model with an a.c. source representing the main power distribution grid was studied. Brief technical information is given on the inverter design, with emphasis on the operation of the circuit used. In the technical information section, a description of real and reactive power components is given with special reference to the control of these power components by controlling the power angle or the difference in voltage magnitudes between two voltage sources. This a.c. converted voltage has practical interest, since it is useful for feeding small house appliances. r 2007 Elsevier B.V. All rights reserved. Keywords: Photovoltaic inverter; Modeling; Simulation; Single phase; PSCAD/EMTDC software
1. Introduction In recent years, the need for renewable energy has become more pressing. Among them, the photovoltaic (PV) system such as solar cell is the most promising energy. The PV energy is free, abundant and distributed through the earth. PV energy applications can be divided into two categories: one is stand-alone system and the other is gridconnected system. Stand-alone system requires the battery bank to store the PV energy and it is suitable for low-power system. Grid-connected system does not require the battery bank and has become the primary PV application for highpower applications. The main purpose of the gridconnected system is to transfer maximum solar array energy into grid with a unity power factor. Because of the high cost of PV modules, PV generation systems are attractive only for remote isolated areas and for smallscale applications [1] such as PV refrigerators and waterpumping systems.
Corresponding author. Tel.: +30 6972702218; fax: +30 2107723504.
E-mail address: [email protected] (G.P. Fotis). 0927-0248/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.solmat.2007.05.027
The output power of PV cell is changed by environmental factors, such as illumination and temperature. Since the characteristic curve of a solar cell exhibits a non-linear voltage–current characteristic, a controller named maximum power point tracker (MPPT) is required to match the solar cell power to the environmental changes. Many algorithms have been developed for tracking maximum power point of a solar cell [2–5]. In literature, several models have been developed for the modeling and simulation of the different components of stand-alone PV power systems based on simulation approaches, which performed in various programming environments such as Pspice, Matlab Simulink and Labview [6,7]. Generally, it is very difficult to develop an analytical equation or numerical model capable of predicting the performance of the PV system under the variable climatic conditions (influencing the system) for the next day. These systems can be considered non-linear, which means that are very complex and very difficult to find a suitable model by classical approaches. There have been studies where artificial neural networks (ANN) have been considered as a suitable approach for such a complex system modeling [8–10].
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The aim of the work presented here is to build an EMTDC model of a single-phase photovoltaic inverter and to investigate switching strategies for harmonic minimization. This inverter device is intended for domestic use and will allow users to exploit voltage from PV cells. The produced AC converted voltage will be useful for feeding small house appliances or by employing appropriate techniques, real and reactive power exported from the inverter can reinforce the main power stream in the ‘‘distribution grids’’. For the simulation of this model, the PSCAD/EMTDC software [11,12] package was used and the waveforms of interest were taken. A low rating, mains connected device was designed and used to demonstrate that real and reactive power can flow in the desired direction just by changing the phase shift or the voltage magnitude. First of all an inverter model that would convert the d.c. voltage supplied from a battery into an a.c. voltage was designed, offering the capability of feeding this into the grid through an inductance. Having obtained the coupling of the inverter’s output with the grid voltage and by changing the relative phases, or voltage magnitudes of one with respect to the other, effort has been paid in order to demonstrate that phase shift between the two voltages leads to a real power flow and difference in magnitude of the two voltages leads to reactive power flow. 2. Technical background information An inverter is a d.c. to a.c. converter, i.e. it can convert d.c. voltage into a.c. for feeding into an a.c. utility network. It is possible to obtain a single-phase or a three-phase output from such a device, but in this work only the behavior of a single-phase inverter was studied. An inverter system consists of the d.c. input, the power circuit and the control circuit. The inverter finds very useful applications in standby power supplies or uninterruptible power supplies (UPS) and also in a.c. motor control. Inverters can be broadly classified either as voltage-source or current-source inverters. The d.c. input voltage into an inverter can be obtained in various ways. In UPS systems, it is almost invariably obtained from a storage battery. This is because some form of energy storage is required to provide for mains power failure. In a.c. motor control, the d.c. link voltage is obtained from rectified mains. For the case described in this work, the voltage-fed or voltage-source inverter (VSI) was powered from a stiff, low-impedance d.c. voltage source provided in the form of a battery supplying voltage at 38 V d.c. The inverter power circuit consists of the main switching devices, which carry the load current and are subjected to the d.c. link voltage. The power circuit also includes protection circuits, such as reverse conduction diodes, when inductive loading is expected. Such a reactive feedback diode is characteristic of a voltage-source
inverter, providing a reverse current path for load current that permits an energy flow from a reactive load, through the inverter, to the d.c. supply. These components are subjected to the same order of voltage magnitudes and currents as the main switching devices. The choice of the main devices depends on factors such as the d.c. link voltage, the load current, the maximum operating frequency, etc. The devices need to be forcecommutated devices with high switching frequencies, for example, insulated gate bipolar junction transistors (IGBTs), power MOSFETS or gate-turn-off thyristors (GTOs) that can provide natural turn-off facilities. To produce the required output waveform, the devices are switched in a particular sequence determined by the control circuit. The control circuit determines the waveform of the output voltage and its frequency. In inverters having high power ratings the control circuit may incorporate protection circuits such as current limiting. 3. PSCAD/EMTDC simulation package description EMTDC and PSCAD [11,12] are a group of related software packages, which provide the user with a very flexible power systems electromagnetic transients tool. PSCAD enables the user to design the circuit that is going to be studied. EMTDC is the software, which actually performs the electromagnetic transients analysis on the user-defined power system. EMTDC enables the user to simulate the circuit performance under any conditions or disturbances of a complicated or non-linear model or process. The operation of such a model can be tested by subjecting it to disturbances and parameter variations and the stability of its response can be observed. The EMTDC provides the facility that already available models can be interfaced with an electric circuit or control system. This gives the opportunity to the user to set up and study DC transmission systems without too much difficulty, as well as making digital computer models as good as any real-time hardware based DC simulator. EMTDC can be used to model, circuit elements (resistors, inductors and capacitors), mutually coupled windings, cables and distributed, multiphased, untransposed transmission lines. Also it can model both Thevenin and Norton sources, switches, thyristors, diodes and gate-turn-off devices. The EMTDC alone cannot provide the user with a complete analysis of the power system under study, so the analysis is assisted by some auxiliary programs. Graphics plotting of output of any desired quantity can be provided in the package. Fourier analysis of any desired output is possible, using an auxiliary program known as EMTFS. Another capability of the EMTFS program is the synthesizing of an EMTDC output representing the response to some complicated model, up to a fourth order linear function using an optimization technique. It is possible to obtain a frequency response of a model built on EMTDC from a single time-domain run. A perturbating input signal consisting of either a train or pseudo-random pulses, or
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summation of sine waves can be applied. If both input signal and output responses are Fourier analyzed, the frequency response can be derived. 4. Presentation of the simulation results 4.1. Inverter design procedure The whole design of the inverter circuit was implemented using gate-turn-off thyristor (GTO) models. These GTO models are normally used as controlling switches in highvoltage devices with large power ratings, whereas in this design, they are just used to provide the switching pulses and finally produce the output. The inverter device was intended for use alongside a photovoltaic (PV) controller that would act as the supply to the circuit. The PV controller was a battery of 38 V. The rating of this inverter mains connected device is about 500 V A or 1 kV A maximum. A ‘‘triggering’’ block was used to provide the appropriate gate triggering pulses, which when applied to the gate terminals of the thyristors would result in a square wave output. A triggering block was created simply by creating the new component and programming it to perform the operation required. This triggering block has one input and five outputs out of which only four are used. The input to this triggering block was a square-pulse of magnitude varying between 0 and 1 and the outputs are the four triggering pulses for the four thyristors. Triggering pulses were obtained from the block, which were applied on the respective gate terminals of each of the four thyristors. This enabled the thyristors to switch ON and OFF in the pre-defined intervals and finally to produce the anticipated square waveform. The output of the thyristor was a square wave having a peak of 36 V, measured using the measuring facilities of the simulation program. Ideally, this waveform should have a peak value of 38 V, equal to the supply voltage. This is the case because in order to get 38 V as the peak value of the voltage, the ON state voltage drops from diodes and thyristors conducting were not considered. In the simulation, these voltage drops were set to 1 V for both thyristors and diodes, and the final result was an output waveform with a peak at 36 V. 4.2. Representation—generation of the grid voltage Once the correct output from the inverter was obtained, a sinusoidal wave for representing the grid voltage had to be generated. It was simple and easy to represent this grid voltage using the output of a low-impedance a.c. source. This a.c. source was to be used as a supply for obtaining a 50 Hz, 230 V rms sinusoid that would represent the grid voltage. The initial parameters of this source, i.e. magnitude and frequency were respectively set to 230 V rms and 50 Hz. Once this output was generated it was coupled in the circuit as the grid voltage.
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4.3. Coupling of the two circuits After designing and implementing the inverter device and the a.c. source equivalent circuit, the two circuits were coupled together through an inductance. The value of this inductance had to be calculated taking into account the rating of the device and the voltage rating of the circuit. An inductance of value 67.35 mH was used to couple the two circuits together. Another adjustment that needed to be considered before the two circuits could successfully be coupled together was to ‘‘lock’’ the phase of the inverter output voltage onto that of the grid voltage. This means that the phase of the inverter voltage had to be made equal to the phase of the grid voltage. It is possible to achieve this task in various ways such as using a phase-locked-loop (PLL), but in this work a much simpler implementation technique was employed. This technique used a duplicate of the grid voltage source, where its output used after being passed through a zero-crossing detector (ZCD) to trigger the thyristors in the inverter device. The output of the source is a sinusoidal voltage, but after being passed through the ZCD this output is converted into a square pulse of frequency 50 Hz and magnitude 230 V rms. The ZCD, as its name implies detects zero crossings on the input waveform and triggers at each zero crossing. As soon as the detector detects a zero crossing, it triggers to a pre-set value and as soon as it detects a second zero crossing it triggers back to zero. In this way a sinusoidal input is easily converted into a square wave. The ZCD output was used as the input to the triggering block. Applying a square-pulse generated from the grid voltage sinusoid at the input of the triggering block, the triggering pulses obtained will eventually produce a squarewave output that will be in phase with the grid voltage. This phase compatibility is shown in Fig. 1, but in order to have the two voltages in phase the triggering pulses had to be swapped around. The completed network is given in Fig. 2. The work described above was to bring the two voltages in phase so as to prevent the large current flows in the inverter circuit. If the two voltages were out of phase when connected together, this would cause large power flows leading to large current flows. The rating of the inverter limits the current that could flow in the circuit up to a maximum value calculated equal to 2.174 A rms. All the power flow measurements, given later in this paper, were taken with current between 1 and 2 A. 4.4. Power measurements With appropriate phase manipulation between the two voltages and voltage magnitude manipulation the respective transfer of real and reactive powers is feasible. In order to measure real and reactive power, the complex power had to be measured first. The complex power at any point in the system can be found by simply multiplying the corresponding voltage and current at that point.
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Fig. 1. Inverter output and grid voltage waveforms.
The current at point C in the circuit was measured by using an ammeter connected in series in the circuit. The voltage at that point was also measured. Multiplying graphically the waveforms of these two quantities, the waveform corresponding to the complex power was derived and from that an rms value for the complex power can be deduced. Fig. 3 displays the waveforms of current (Ia) and voltage (V2). Setting the d.c. supply to 250 V rms, the current was limited between the acceptable limits and it actually had an rms value of 1.3 A. The current waveform was seen to be very distorted, containing all orders of harmonics. The
inverter output waveform was also changed, since the load became inductive and a ‘‘step’’ was observed in the waveform. The voltage at point C, the grid voltage V2 is a sinusoid of peak value equal to 325.27 V, but as it will be discussed later an increase in the a.c. source’s series inductance will inject harmonics into this voltage waveform. The complex power was measured using the current and voltage values at point C. A two input–one output multiplier was used in order to obtain the complex power waveform. The complex power waveform was seen to be distorted due to the contribution from the current wave-
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Fig. 2. The complete network.
form. Also the rms value of the complex power was measured by plotting the graph of rms complex power versus time. The real power was measured by passing the complex power waveform through a first-order control transfer function of the form G/(1+St), where G is the gain introduced between the input and the output and t is the time constant of the system. This transfer function has no zeroes and has only one pole that being at S ¼ 1/t. The gain was set to 1 and the time constant t was also set to 1 s. The value of the time constant needed to be as large as possible. A large time constant enables a more accurate measurement of the real power. The instantaneous values would not be taken into account and the output waveform indicates that real power had reached a steady-state value. For these measurements, the magnitude of the fundamental of the inverter output voltage was set to 250 V rms resulting in a current flow of 1.3 A through the circuit. Real power is known to be a function of the power angle d (the phase shift between the fundamental of the inverter output and the grid voltage). To have a real power flow between the two sides of the circuit, a phase shift of a few degrees was introduced and that effect was monitored. The current remained fixed at 1.3 A rms and a phase shift of +21 was introduced resulting in the inverter output voltage leading the grid voltage by 21. The phase shift on the inverter voltage was introduced by shifting the input to the triggering block; so shifted output triggering pulses were obtained. These shifted pulses when applied to the thyristor models’ gate terminals produced a square wave of the same
shape as before but this time shifted by the initial angle introduced on the input pulse to the triggering block. This method established the desired phase shift between the two voltages and hence, in the leading mode of operation, real power was observed to flow from the inverter side to the grid side. The real power flow was monitored and relative graphs showing the voltage waveform V2, the current Ia, the complex power waveform and the real power waveform were plotted. Measurements were taken with supply voltage equal to 250 V rms and phase shifts of +21 and 21 and the above waveforms were recorded each time. Figs. 4 and 5 give the waveforms obtained for the leading and lagging mode of operation, respectively. In the leading mode of operation, the inverter voltage leads the grid voltage by 21 and real power flows from the d.c. side, the inverter side, towards the a.c. side, the a.c. source side. Similarly, in the lagging mode of operation, the inverter voltage lags the grid voltage by 21 hence real power flows from the a.c. side towards the d.c. side. The waveforms given in Fig. 4, for the leading mode of operation, are the current Ia, voltage V2 at point C, the complex power in MVA, and on the same set of axes the rms complex power and the real power. Graph 1 shows the current waveform seen to be heavily distorted and also its rms waveform indicating that the rms value of the current was 1.3 A. In graph 2, the voltage waveform for V2 is a sinusoidal voltage as expected having a peak value of 325.9 V. Graph 3 shows the resulting waveform for the complex power. This was obtained after multiplication of
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Fig. 3. Current and grid voltage waveforms.
Ia and V2, and it is distorted owing to the contribution of the current waveform. Finally, graph 4 shows, plotted on the same pair of axes, the rms complex power and real power variation with time. The rms waveform for the complex power was obtained after passing the complex power wave through an rms conversion block with a smoothing time constant of t equal to 0.001 s. The rms value of the complex power was measured to be 265 V A and the real power value was 43 W. The same procedure was followed in order to obtain the graphs for the lagging mode of operation of the model. The input to the triggering block was given a negative phase shift of 21, which resulted in producing a square wave lagging the grid voltage by 21. Once again the same
quantities were measured and their respective graphs were plotted to demonstrate the lagging mode of operation of the model. Graph 1 in Fig. 5 shows the current waveform Ia for the lagging mode of operation. The rms value of this current remains unchanged since the voltage magnitudes of the two waveforms were not altered. Graph 2 gives the sinusoidal voltage wave, which is exactly the same as for the leading mode of operation. The shape of the waveform for the complex power is unchanged but the rms value of the complex power is increased from 265 to 295 MV A. The real power is reversed in sign but it is increased in magnitude from 43 W for the leading mode to 126 W for the lagging mode. The reversed sign of real power indicates that in the lagging mode of operation, real power flows
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Fig. 4. Leading mode waveforms for supply voltage equal to 250 V.
from the a.c. side towards the d.c. side. When the inverter was operating in the leading mode, real power was noticed to flow exactly in the opposite direction. 4.5. Voltage magnitude manipulation—reactive power flow The magnitude of the fundamental of the inverter output voltage was set to 250 V rms and the magnitude of the grid voltage to 230 V rms. This had as a result a current of rms value 1.3 A to flow through the circuit. The current flow was due to the voltage difference between the a.c. side and the d.c. side and it was expected that a reactive power flow occurred in the same direction. There was no easy way to measure the reactive power, so the flow of reactive power
was demonstrated by inspection of the current waveshapes for different supply voltages that would increase or decrease the magnitude of the fundamental of the inverter output. One set of measurements and graphs was obtained using a supply voltage of 250 V rms and a phase shift of +21 leading. These graphs were given not only in Fig. 4 but also in Fig. 6 to support the reactive power flow demonstration. Another set of graphs was taken this time using a supply voltage of 230 V rms and a phase shift of 21 leading. These results are shown in Fig. 7. Comparing the two current waveforms obtained for supply voltages equal to 250 and 230 V rms, it is obvious that in the second case, where the supply voltage was
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Fig. 5. Lagging mode waveforms for supply voltage equal to 250 V.
reduced the current spikes seem to have reduced in terms of magnitude. The rms value of the current was increased from 1.3 to 1.6 A. A shift towards the left was observed in this waveform compared with the respective one obtained for supply voltage equal to 250 V rms. This slight shift to the left indicates that in the latter case reactive power was flowing from the grid towards the inverter. This direction of reactive power flow justifies the statement that a decrease in voltage magnitude of the fundamental of the inverter output results in importing power from the a.c. side towards the d.c. side. For a supply voltage equal to 250 V, reactive power was exported from the inverter model towards the grid. The shape of V2 is the same as before. The complex power waveform did not change but there was an increase in the
complex power rms value to 362 V A and real power decreased to a value 43 W. 4.6. Harmonic injection into the grid voltage The waveforms in Fig. 8 were obtained to demonstrate the effect, which had on the grid voltage V2, an increase of the series inductance of the a.c. voltage source. This inductance was increased from a value of 0.001 H to a value of 0.01 H, i.e. by a factor of 10 and harmonic injection was evident on the grid voltage waveform V2. Fig. 8 shows waveform V2 containing harmonics, alongside the current waveforms, complex and real power waveforms for supply voltage equal to 250 V rms. Similarly, Fig. 9 shows results obtained with supply voltage set to 230 V rms.
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Fig. 6. Leading mode waveforms for supply voltage equal to 250 V.
The reason for this harmonic injection is that the a.c. source is active for a frequency of 50 Hz (the pre-defined frequency of the pure sinusoid generated by this source). In the case of higher frequency, i.e. 100 Hz twice the fundamental frequency, and trying to simulate the circuit at the second harmonic the only ‘‘source’’ present would be the inverter, which has an output containing this second harmonic. At this frequency, the a.c. source becomes short circuited and the remaining circuit acts as a voltage divider, dividing the square inverter output between the series inductance and the coupling inductance. The larger the series inductance the more voltage containing harmonics will appear across it as the voltage drop. A series of simplified networks can be drawn in order to demonstrate
the voltage divider action at frequencies multiple of the fundamental 50 Hz. 5. Conclusions In this paper, a model of a single PV voltage inverter was designed and simulated. The simulation was performed using the PSCAD/EMTDC simulation package. This inverter model was used in conjunction with an a.c. voltage source to show real and reactive power flow. The first concern was to establish the satisfactory operation of the inverter circuit and this was ensured obtaining a square wave as the output. The network used to demonstrate power flow comprised of the inverter model and the a.c.
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Fig. 7. Leading mode waveforms for supply voltage equal to 230 V.
source (representing the main distribution grid). With the introduction of a relative phase shift between the two output voltages, it was noticed that real power started flowing from the most advanced (in phase terms) side of the network towards the least advanced. This agrees with general power transmission theory stating that real power is a function of the power angle d (phase shift between two voltages). The leading and lagging modes of operation of the model were examined. It has been proved that the inverter’s performance can be improved using faster switching devices. Furthermore,
reliability can be also increased eliminating unwanted harmonics from the output using harmonic-elimination techniques. Harmonics can be injected into the network by increasing the series inductance to the source. The presence of these harmonics leads to harmonic distortion that may have a number of undesirable consequences. For this reason, the harmonic content of voltages in power distribution networks needs to be kept within acceptable proportions. Finally, the operation of the inverter device in this work showed the model’s ability to both absorb and generate
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Fig. 8. Leading mode waveforms, harmonics injection in grid voltage with supply voltage equal to 250 V.
reactive power. It was shown that increasing the supply voltage at the input of the inverter, resulted in exporting reactive power from the inverter, and decreasing it, resulted in importing reactive power to the model. When the d.c. supply was increased, the magnitude of the fundamental of the inverter output was increased with respect to the grid voltage magnitude. The difference in voltage magnitudes leads to VAR flows. Decreasing supply voltage leads
to exactly the opposite effects, i.e. absorption of reactive power by the inverter. This ability may prove to be useful if such models were installed in houses, being fed from the main distribution grid. With the appropriate phase or voltage magnitude adjustments between the two ‘‘sources’’, the inverter can compensate for some of the power needed to supply such loads. If inverter devices were installed in many houses, for example, then the power
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Fig. 9. Leading mode waveforms, harmonics injection in grid voltage with supply voltage equal to 230 V.
demand for these loads would be reduced by a total amount equal to the power that these devices can generate. In a case like this, the demand would drop significantly. In practical applications, the inverter will be powered from PV cells, so the supply will cost less. The cells will provide d.c. voltage that will be converted into a.c. by the inverter. This allows less operational costs and it is another way of exploiting the free nature resources for power generation.
References [1] Y. Sukamongkol, S. Chungpaibulpatana, W. Ongsakul, Renew. Energy 27 (2002) 237. [2] E. Koutroulis, K. Kalaitzakis, et al., IEEE Trans. Power Electron. 16 (2001) 46. [3] F. Valenciaga, P.F. Puleston, P.E. Battiaiotto, IEE Proc. Control Theor. Appl. 148 (2001) 448. [4] T. Noguchi, S. Togashi, R. Nakamoto, IEEE Trans. Ind. Electron. 49 (2002) 217.
ARTICLE IN PRESS T.I. Maris et al. / Solar Energy Materials & Solar Cells 91 (2007) 1713–1725 [5] D.P. Hohm, M.E. Ropp, Comparative study of maximum power point tracking algorithm using an experimental, programmable, maximum power point tracking test bed, in: Proceedings of Photovoltaic Specialists Conference, 2000, pp. 1699–1702. [6] D.F. Hasti, Photovoltaic power system application, IEEE Power Engineering Review, Sandia National Laboratories, 1994, pp. 8–19. [7] E. Koutroulis, K. Kalaitzakis, Renew. Energy 28 (2003) 139. [8] A. Mellit, M. Benghanem, H. Salhi, An adaptive artificial neural network for modelling and simulation of a stand-alone photovoltaic power system, in: Proceedings of the Third Conference on Systems, Signals, and Devices, IEEE, 2005.
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[9] A. Mellit, M. Benghanem, Modeling and simulation of stand-alone power system using artificial neural network, in: Solar World Congress, ISES/ASES, 2005. [10] A. Mellit, M. Benghanem, S.A. Kalogirou, Renew. Energy 32 (2007) 285. [11] PSCAD/MTDC power system simulation software, User’s Manual, Manitoba HVDC Research Centre, EMTDC version 2, Winnipeg, Canada, 1994 release. [12] Manitoba HVDC Research Center, PSCAD/EMTDC Power System, Simulation Software User’s Manual, Version 3, 1998 release.
Solar Energy Materials & Solar Cells 91 (2007) 1713–1725 www.elsevier.com/locate/solmat
Modeling of a single-phase photovoltaic inverter T.I. Marisa, St. Kourtesib, L. Ekonomouc, G.P. Fotisd, a
Department of Electrical Engineering, Technological Educational Institute of Chalkida, 334 40 Psachna Evias, Greece b Hellenic Public Power Corporation S.A., 22 Chalcocondyli Str., 104 32 Athens, Greece c Hellenic American University, 12 Kaplanon Str., 106 80 Athens, Greece d National Technical University of Athens, School of Electrical and Computer Engineering, High Voltage Laboratory, 9 Iroon Politechniou St., Zografou, 157 80 Athens, Greece Received 3 March 2007; received in revised form 25 May 2007; accepted 25 May 2007 Available online 27 June 2007
Abstract The paper presents the design of a single-phase photovoltaic inverter model and the simulation of its performance. Furthermore, the concept of moving real and reactive power after coupling this inverter model with an a.c. source representing the main power distribution grid was studied. Brief technical information is given on the inverter design, with emphasis on the operation of the circuit used. In the technical information section, a description of real and reactive power components is given with special reference to the control of these power components by controlling the power angle or the difference in voltage magnitudes between two voltage sources. This a.c. converted voltage has practical interest, since it is useful for feeding small house appliances. r 2007 Elsevier B.V. All rights reserved. Keywords: Photovoltaic inverter; Modeling; Simulation; Single phase; PSCAD/EMTDC software
1. Introduction In recent years, the need for renewable energy has become more pressing. Among them, the photovoltaic (PV) system such as solar cell is the most promising energy. The PV energy is free, abundant and distributed through the earth. PV energy applications can be divided into two categories: one is stand-alone system and the other is gridconnected system. Stand-alone system requires the battery bank to store the PV energy and it is suitable for low-power system. Grid-connected system does not require the battery bank and has become the primary PV application for highpower applications. The main purpose of the gridconnected system is to transfer maximum solar array energy into grid with a unity power factor. Because of the high cost of PV modules, PV generation systems are attractive only for remote isolated areas and for smallscale applications [1] such as PV refrigerators and waterpumping systems.
Corresponding author. Tel.: +30 6972702218; fax: +30 2107723504.
E-mail address: [email protected] (G.P. Fotis). 0927-0248/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.solmat.2007.05.027
The output power of PV cell is changed by environmental factors, such as illumination and temperature. Since the characteristic curve of a solar cell exhibits a non-linear voltage–current characteristic, a controller named maximum power point tracker (MPPT) is required to match the solar cell power to the environmental changes. Many algorithms have been developed for tracking maximum power point of a solar cell [2–5]. In literature, several models have been developed for the modeling and simulation of the different components of stand-alone PV power systems based on simulation approaches, which performed in various programming environments such as Pspice, Matlab Simulink and Labview [6,7]. Generally, it is very difficult to develop an analytical equation or numerical model capable of predicting the performance of the PV system under the variable climatic conditions (influencing the system) for the next day. These systems can be considered non-linear, which means that are very complex and very difficult to find a suitable model by classical approaches. There have been studies where artificial neural networks (ANN) have been considered as a suitable approach for such a complex system modeling [8–10].
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The aim of the work presented here is to build an EMTDC model of a single-phase photovoltaic inverter and to investigate switching strategies for harmonic minimization. This inverter device is intended for domestic use and will allow users to exploit voltage from PV cells. The produced AC converted voltage will be useful for feeding small house appliances or by employing appropriate techniques, real and reactive power exported from the inverter can reinforce the main power stream in the ‘‘distribution grids’’. For the simulation of this model, the PSCAD/EMTDC software [11,12] package was used and the waveforms of interest were taken. A low rating, mains connected device was designed and used to demonstrate that real and reactive power can flow in the desired direction just by changing the phase shift or the voltage magnitude. First of all an inverter model that would convert the d.c. voltage supplied from a battery into an a.c. voltage was designed, offering the capability of feeding this into the grid through an inductance. Having obtained the coupling of the inverter’s output with the grid voltage and by changing the relative phases, or voltage magnitudes of one with respect to the other, effort has been paid in order to demonstrate that phase shift between the two voltages leads to a real power flow and difference in magnitude of the two voltages leads to reactive power flow. 2. Technical background information An inverter is a d.c. to a.c. converter, i.e. it can convert d.c. voltage into a.c. for feeding into an a.c. utility network. It is possible to obtain a single-phase or a three-phase output from such a device, but in this work only the behavior of a single-phase inverter was studied. An inverter system consists of the d.c. input, the power circuit and the control circuit. The inverter finds very useful applications in standby power supplies or uninterruptible power supplies (UPS) and also in a.c. motor control. Inverters can be broadly classified either as voltage-source or current-source inverters. The d.c. input voltage into an inverter can be obtained in various ways. In UPS systems, it is almost invariably obtained from a storage battery. This is because some form of energy storage is required to provide for mains power failure. In a.c. motor control, the d.c. link voltage is obtained from rectified mains. For the case described in this work, the voltage-fed or voltage-source inverter (VSI) was powered from a stiff, low-impedance d.c. voltage source provided in the form of a battery supplying voltage at 38 V d.c. The inverter power circuit consists of the main switching devices, which carry the load current and are subjected to the d.c. link voltage. The power circuit also includes protection circuits, such as reverse conduction diodes, when inductive loading is expected. Such a reactive feedback diode is characteristic of a voltage-source
inverter, providing a reverse current path for load current that permits an energy flow from a reactive load, through the inverter, to the d.c. supply. These components are subjected to the same order of voltage magnitudes and currents as the main switching devices. The choice of the main devices depends on factors such as the d.c. link voltage, the load current, the maximum operating frequency, etc. The devices need to be forcecommutated devices with high switching frequencies, for example, insulated gate bipolar junction transistors (IGBTs), power MOSFETS or gate-turn-off thyristors (GTOs) that can provide natural turn-off facilities. To produce the required output waveform, the devices are switched in a particular sequence determined by the control circuit. The control circuit determines the waveform of the output voltage and its frequency. In inverters having high power ratings the control circuit may incorporate protection circuits such as current limiting. 3. PSCAD/EMTDC simulation package description EMTDC and PSCAD [11,12] are a group of related software packages, which provide the user with a very flexible power systems electromagnetic transients tool. PSCAD enables the user to design the circuit that is going to be studied. EMTDC is the software, which actually performs the electromagnetic transients analysis on the user-defined power system. EMTDC enables the user to simulate the circuit performance under any conditions or disturbances of a complicated or non-linear model or process. The operation of such a model can be tested by subjecting it to disturbances and parameter variations and the stability of its response can be observed. The EMTDC provides the facility that already available models can be interfaced with an electric circuit or control system. This gives the opportunity to the user to set up and study DC transmission systems without too much difficulty, as well as making digital computer models as good as any real-time hardware based DC simulator. EMTDC can be used to model, circuit elements (resistors, inductors and capacitors), mutually coupled windings, cables and distributed, multiphased, untransposed transmission lines. Also it can model both Thevenin and Norton sources, switches, thyristors, diodes and gate-turn-off devices. The EMTDC alone cannot provide the user with a complete analysis of the power system under study, so the analysis is assisted by some auxiliary programs. Graphics plotting of output of any desired quantity can be provided in the package. Fourier analysis of any desired output is possible, using an auxiliary program known as EMTFS. Another capability of the EMTFS program is the synthesizing of an EMTDC output representing the response to some complicated model, up to a fourth order linear function using an optimization technique. It is possible to obtain a frequency response of a model built on EMTDC from a single time-domain run. A perturbating input signal consisting of either a train or pseudo-random pulses, or
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summation of sine waves can be applied. If both input signal and output responses are Fourier analyzed, the frequency response can be derived. 4. Presentation of the simulation results 4.1. Inverter design procedure The whole design of the inverter circuit was implemented using gate-turn-off thyristor (GTO) models. These GTO models are normally used as controlling switches in highvoltage devices with large power ratings, whereas in this design, they are just used to provide the switching pulses and finally produce the output. The inverter device was intended for use alongside a photovoltaic (PV) controller that would act as the supply to the circuit. The PV controller was a battery of 38 V. The rating of this inverter mains connected device is about 500 V A or 1 kV A maximum. A ‘‘triggering’’ block was used to provide the appropriate gate triggering pulses, which when applied to the gate terminals of the thyristors would result in a square wave output. A triggering block was created simply by creating the new component and programming it to perform the operation required. This triggering block has one input and five outputs out of which only four are used. The input to this triggering block was a square-pulse of magnitude varying between 0 and 1 and the outputs are the four triggering pulses for the four thyristors. Triggering pulses were obtained from the block, which were applied on the respective gate terminals of each of the four thyristors. This enabled the thyristors to switch ON and OFF in the pre-defined intervals and finally to produce the anticipated square waveform. The output of the thyristor was a square wave having a peak of 36 V, measured using the measuring facilities of the simulation program. Ideally, this waveform should have a peak value of 38 V, equal to the supply voltage. This is the case because in order to get 38 V as the peak value of the voltage, the ON state voltage drops from diodes and thyristors conducting were not considered. In the simulation, these voltage drops were set to 1 V for both thyristors and diodes, and the final result was an output waveform with a peak at 36 V. 4.2. Representation—generation of the grid voltage Once the correct output from the inverter was obtained, a sinusoidal wave for representing the grid voltage had to be generated. It was simple and easy to represent this grid voltage using the output of a low-impedance a.c. source. This a.c. source was to be used as a supply for obtaining a 50 Hz, 230 V rms sinusoid that would represent the grid voltage. The initial parameters of this source, i.e. magnitude and frequency were respectively set to 230 V rms and 50 Hz. Once this output was generated it was coupled in the circuit as the grid voltage.
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4.3. Coupling of the two circuits After designing and implementing the inverter device and the a.c. source equivalent circuit, the two circuits were coupled together through an inductance. The value of this inductance had to be calculated taking into account the rating of the device and the voltage rating of the circuit. An inductance of value 67.35 mH was used to couple the two circuits together. Another adjustment that needed to be considered before the two circuits could successfully be coupled together was to ‘‘lock’’ the phase of the inverter output voltage onto that of the grid voltage. This means that the phase of the inverter voltage had to be made equal to the phase of the grid voltage. It is possible to achieve this task in various ways such as using a phase-locked-loop (PLL), but in this work a much simpler implementation technique was employed. This technique used a duplicate of the grid voltage source, where its output used after being passed through a zero-crossing detector (ZCD) to trigger the thyristors in the inverter device. The output of the source is a sinusoidal voltage, but after being passed through the ZCD this output is converted into a square pulse of frequency 50 Hz and magnitude 230 V rms. The ZCD, as its name implies detects zero crossings on the input waveform and triggers at each zero crossing. As soon as the detector detects a zero crossing, it triggers to a pre-set value and as soon as it detects a second zero crossing it triggers back to zero. In this way a sinusoidal input is easily converted into a square wave. The ZCD output was used as the input to the triggering block. Applying a square-pulse generated from the grid voltage sinusoid at the input of the triggering block, the triggering pulses obtained will eventually produce a squarewave output that will be in phase with the grid voltage. This phase compatibility is shown in Fig. 1, but in order to have the two voltages in phase the triggering pulses had to be swapped around. The completed network is given in Fig. 2. The work described above was to bring the two voltages in phase so as to prevent the large current flows in the inverter circuit. If the two voltages were out of phase when connected together, this would cause large power flows leading to large current flows. The rating of the inverter limits the current that could flow in the circuit up to a maximum value calculated equal to 2.174 A rms. All the power flow measurements, given later in this paper, were taken with current between 1 and 2 A. 4.4. Power measurements With appropriate phase manipulation between the two voltages and voltage magnitude manipulation the respective transfer of real and reactive powers is feasible. In order to measure real and reactive power, the complex power had to be measured first. The complex power at any point in the system can be found by simply multiplying the corresponding voltage and current at that point.
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Fig. 1. Inverter output and grid voltage waveforms.
The current at point C in the circuit was measured by using an ammeter connected in series in the circuit. The voltage at that point was also measured. Multiplying graphically the waveforms of these two quantities, the waveform corresponding to the complex power was derived and from that an rms value for the complex power can be deduced. Fig. 3 displays the waveforms of current (Ia) and voltage (V2). Setting the d.c. supply to 250 V rms, the current was limited between the acceptable limits and it actually had an rms value of 1.3 A. The current waveform was seen to be very distorted, containing all orders of harmonics. The
inverter output waveform was also changed, since the load became inductive and a ‘‘step’’ was observed in the waveform. The voltage at point C, the grid voltage V2 is a sinusoid of peak value equal to 325.27 V, but as it will be discussed later an increase in the a.c. source’s series inductance will inject harmonics into this voltage waveform. The complex power was measured using the current and voltage values at point C. A two input–one output multiplier was used in order to obtain the complex power waveform. The complex power waveform was seen to be distorted due to the contribution from the current wave-
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Fig. 2. The complete network.
form. Also the rms value of the complex power was measured by plotting the graph of rms complex power versus time. The real power was measured by passing the complex power waveform through a first-order control transfer function of the form G/(1+St), where G is the gain introduced between the input and the output and t is the time constant of the system. This transfer function has no zeroes and has only one pole that being at S ¼ 1/t. The gain was set to 1 and the time constant t was also set to 1 s. The value of the time constant needed to be as large as possible. A large time constant enables a more accurate measurement of the real power. The instantaneous values would not be taken into account and the output waveform indicates that real power had reached a steady-state value. For these measurements, the magnitude of the fundamental of the inverter output voltage was set to 250 V rms resulting in a current flow of 1.3 A through the circuit. Real power is known to be a function of the power angle d (the phase shift between the fundamental of the inverter output and the grid voltage). To have a real power flow between the two sides of the circuit, a phase shift of a few degrees was introduced and that effect was monitored. The current remained fixed at 1.3 A rms and a phase shift of +21 was introduced resulting in the inverter output voltage leading the grid voltage by 21. The phase shift on the inverter voltage was introduced by shifting the input to the triggering block; so shifted output triggering pulses were obtained. These shifted pulses when applied to the thyristor models’ gate terminals produced a square wave of the same
shape as before but this time shifted by the initial angle introduced on the input pulse to the triggering block. This method established the desired phase shift between the two voltages and hence, in the leading mode of operation, real power was observed to flow from the inverter side to the grid side. The real power flow was monitored and relative graphs showing the voltage waveform V2, the current Ia, the complex power waveform and the real power waveform were plotted. Measurements were taken with supply voltage equal to 250 V rms and phase shifts of +21 and 21 and the above waveforms were recorded each time. Figs. 4 and 5 give the waveforms obtained for the leading and lagging mode of operation, respectively. In the leading mode of operation, the inverter voltage leads the grid voltage by 21 and real power flows from the d.c. side, the inverter side, towards the a.c. side, the a.c. source side. Similarly, in the lagging mode of operation, the inverter voltage lags the grid voltage by 21 hence real power flows from the a.c. side towards the d.c. side. The waveforms given in Fig. 4, for the leading mode of operation, are the current Ia, voltage V2 at point C, the complex power in MVA, and on the same set of axes the rms complex power and the real power. Graph 1 shows the current waveform seen to be heavily distorted and also its rms waveform indicating that the rms value of the current was 1.3 A. In graph 2, the voltage waveform for V2 is a sinusoidal voltage as expected having a peak value of 325.9 V. Graph 3 shows the resulting waveform for the complex power. This was obtained after multiplication of
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Fig. 3. Current and grid voltage waveforms.
Ia and V2, and it is distorted owing to the contribution of the current waveform. Finally, graph 4 shows, plotted on the same pair of axes, the rms complex power and real power variation with time. The rms waveform for the complex power was obtained after passing the complex power wave through an rms conversion block with a smoothing time constant of t equal to 0.001 s. The rms value of the complex power was measured to be 265 V A and the real power value was 43 W. The same procedure was followed in order to obtain the graphs for the lagging mode of operation of the model. The input to the triggering block was given a negative phase shift of 21, which resulted in producing a square wave lagging the grid voltage by 21. Once again the same
quantities were measured and their respective graphs were plotted to demonstrate the lagging mode of operation of the model. Graph 1 in Fig. 5 shows the current waveform Ia for the lagging mode of operation. The rms value of this current remains unchanged since the voltage magnitudes of the two waveforms were not altered. Graph 2 gives the sinusoidal voltage wave, which is exactly the same as for the leading mode of operation. The shape of the waveform for the complex power is unchanged but the rms value of the complex power is increased from 265 to 295 MV A. The real power is reversed in sign but it is increased in magnitude from 43 W for the leading mode to 126 W for the lagging mode. The reversed sign of real power indicates that in the lagging mode of operation, real power flows
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Fig. 4. Leading mode waveforms for supply voltage equal to 250 V.
from the a.c. side towards the d.c. side. When the inverter was operating in the leading mode, real power was noticed to flow exactly in the opposite direction. 4.5. Voltage magnitude manipulation—reactive power flow The magnitude of the fundamental of the inverter output voltage was set to 250 V rms and the magnitude of the grid voltage to 230 V rms. This had as a result a current of rms value 1.3 A to flow through the circuit. The current flow was due to the voltage difference between the a.c. side and the d.c. side and it was expected that a reactive power flow occurred in the same direction. There was no easy way to measure the reactive power, so the flow of reactive power
was demonstrated by inspection of the current waveshapes for different supply voltages that would increase or decrease the magnitude of the fundamental of the inverter output. One set of measurements and graphs was obtained using a supply voltage of 250 V rms and a phase shift of +21 leading. These graphs were given not only in Fig. 4 but also in Fig. 6 to support the reactive power flow demonstration. Another set of graphs was taken this time using a supply voltage of 230 V rms and a phase shift of 21 leading. These results are shown in Fig. 7. Comparing the two current waveforms obtained for supply voltages equal to 250 and 230 V rms, it is obvious that in the second case, where the supply voltage was
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Fig. 5. Lagging mode waveforms for supply voltage equal to 250 V.
reduced the current spikes seem to have reduced in terms of magnitude. The rms value of the current was increased from 1.3 to 1.6 A. A shift towards the left was observed in this waveform compared with the respective one obtained for supply voltage equal to 250 V rms. This slight shift to the left indicates that in the latter case reactive power was flowing from the grid towards the inverter. This direction of reactive power flow justifies the statement that a decrease in voltage magnitude of the fundamental of the inverter output results in importing power from the a.c. side towards the d.c. side. For a supply voltage equal to 250 V, reactive power was exported from the inverter model towards the grid. The shape of V2 is the same as before. The complex power waveform did not change but there was an increase in the
complex power rms value to 362 V A and real power decreased to a value 43 W. 4.6. Harmonic injection into the grid voltage The waveforms in Fig. 8 were obtained to demonstrate the effect, which had on the grid voltage V2, an increase of the series inductance of the a.c. voltage source. This inductance was increased from a value of 0.001 H to a value of 0.01 H, i.e. by a factor of 10 and harmonic injection was evident on the grid voltage waveform V2. Fig. 8 shows waveform V2 containing harmonics, alongside the current waveforms, complex and real power waveforms for supply voltage equal to 250 V rms. Similarly, Fig. 9 shows results obtained with supply voltage set to 230 V rms.
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Fig. 6. Leading mode waveforms for supply voltage equal to 250 V.
The reason for this harmonic injection is that the a.c. source is active for a frequency of 50 Hz (the pre-defined frequency of the pure sinusoid generated by this source). In the case of higher frequency, i.e. 100 Hz twice the fundamental frequency, and trying to simulate the circuit at the second harmonic the only ‘‘source’’ present would be the inverter, which has an output containing this second harmonic. At this frequency, the a.c. source becomes short circuited and the remaining circuit acts as a voltage divider, dividing the square inverter output between the series inductance and the coupling inductance. The larger the series inductance the more voltage containing harmonics will appear across it as the voltage drop. A series of simplified networks can be drawn in order to demonstrate
the voltage divider action at frequencies multiple of the fundamental 50 Hz. 5. Conclusions In this paper, a model of a single PV voltage inverter was designed and simulated. The simulation was performed using the PSCAD/EMTDC simulation package. This inverter model was used in conjunction with an a.c. voltage source to show real and reactive power flow. The first concern was to establish the satisfactory operation of the inverter circuit and this was ensured obtaining a square wave as the output. The network used to demonstrate power flow comprised of the inverter model and the a.c.
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Fig. 7. Leading mode waveforms for supply voltage equal to 230 V.
source (representing the main distribution grid). With the introduction of a relative phase shift between the two output voltages, it was noticed that real power started flowing from the most advanced (in phase terms) side of the network towards the least advanced. This agrees with general power transmission theory stating that real power is a function of the power angle d (phase shift between two voltages). The leading and lagging modes of operation of the model were examined. It has been proved that the inverter’s performance can be improved using faster switching devices. Furthermore,
reliability can be also increased eliminating unwanted harmonics from the output using harmonic-elimination techniques. Harmonics can be injected into the network by increasing the series inductance to the source. The presence of these harmonics leads to harmonic distortion that may have a number of undesirable consequences. For this reason, the harmonic content of voltages in power distribution networks needs to be kept within acceptable proportions. Finally, the operation of the inverter device in this work showed the model’s ability to both absorb and generate
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Fig. 8. Leading mode waveforms, harmonics injection in grid voltage with supply voltage equal to 250 V.
reactive power. It was shown that increasing the supply voltage at the input of the inverter, resulted in exporting reactive power from the inverter, and decreasing it, resulted in importing reactive power to the model. When the d.c. supply was increased, the magnitude of the fundamental of the inverter output was increased with respect to the grid voltage magnitude. The difference in voltage magnitudes leads to VAR flows. Decreasing supply voltage leads
to exactly the opposite effects, i.e. absorption of reactive power by the inverter. This ability may prove to be useful if such models were installed in houses, being fed from the main distribution grid. With the appropriate phase or voltage magnitude adjustments between the two ‘‘sources’’, the inverter can compensate for some of the power needed to supply such loads. If inverter devices were installed in many houses, for example, then the power
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Fig. 9. Leading mode waveforms, harmonics injection in grid voltage with supply voltage equal to 230 V.
demand for these loads would be reduced by a total amount equal to the power that these devices can generate. In a case like this, the demand would drop significantly. In practical applications, the inverter will be powered from PV cells, so the supply will cost less. The cells will provide d.c. voltage that will be converted into a.c. by the inverter. This allows less operational costs and it is another way of exploiting the free nature resources for power generation.
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ARTICLE IN PRESS T.I. Maris et al. / Solar Energy Materials & Solar Cells 91 (2007) 1713–1725 [5] D.P. Hohm, M.E. Ropp, Comparative study of maximum power point tracking algorithm using an experimental, programmable, maximum power point tracking test bed, in: Proceedings of Photovoltaic Specialists Conference, 2000, pp. 1699–1702. [6] D.F. Hasti, Photovoltaic power system application, IEEE Power Engineering Review, Sandia National Laboratories, 1994, pp. 8–19. [7] E. Koutroulis, K. Kalaitzakis, Renew. Energy 28 (2003) 139. [8] A. Mellit, M. Benghanem, H. Salhi, An adaptive artificial neural network for modelling and simulation of a stand-alone photovoltaic power system, in: Proceedings of the Third Conference on Systems, Signals, and Devices, IEEE, 2005.
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[9] A. Mellit, M. Benghanem, Modeling and simulation of stand-alone power system using artificial neural network, in: Solar World Congress, ISES/ASES, 2005. [10] A. Mellit, M. Benghanem, S.A. Kalogirou, Renew. Energy 32 (2007) 285. [11] PSCAD/MTDC power system simulation software, User’s Manual, Manitoba HVDC Research Centre, EMTDC version 2, Winnipeg, Canada, 1994 release. [12] Manitoba HVDC Research Center, PSCAD/EMTDC Power System, Simulation Software User’s Manual, Version 3, 1998 release.