Controlofathree-phasegrid-connectedinverterforphotovoltaicapplicationswithafuzzyMPPTund

Control of a Three-Phase Grid-Connected Inverter for Photovoltaic Applications with a Fuzzy MPPT Under Unbalanced Conditions Jaime Alonso-Mart í nez, Joaqu í n Eloy-Garc í a, Santiago Arnaltes DEPT. OF ELECTRICAL ENGINEERING - CARLOS III UNIVERSITY OF MADRID Avda. Universidad, 30 Legané s (Madrid), Spain Tel.: +34 / 91.624.88.52. Fax: +34 / 91.624.94.30. E-Mail: jalonsom@ing.uc3m.es Keywords ?Fuzzy control?, ?Photovoltaic?, ?Power Quality?, ?Fault handling strategy?, ?System integration?. Abstract Grid codes are being revised to include additional requirements for renewable energy, as the installed power increases. Therefore it is needed to develop control systems that are able to fulfil those new requirements, which usually include the ability to operate under unbalanced grid voltages without polluting the grid, among others. This paper presents a three-phase inverter for connection of photovoltaic generators to the grid, with a fuzzy maximum power point tracking and the ability to control reactive power. The main feature of the inverter is that the control system has been designed to deal with unbalanced voltage conditions. Introduction Grid connection has become the main application of photovoltaic systems. Although the first grid-connected photovoltaic system was designed as a single phase system, the increasing power of such systems demanded the utilization of three-phase inverter to connect the generator to a three phase grid. In Spain, cumulated photovoltaic capacity at the end of 2008 exceeded 3 GWp, and the last modification of the photovoltaic regulation scheme aims at limiting its growth to 400 MWp per year [1]. In such a scenario, the contribution to power quality and grid stability of PV systems is likely to become relevant. Proper integration of PV systems in the grid may therefore require additional functionality from the inverter. Grid codes have been developed in Spain specifically for the integration of other renewable energy production technologies, such as wind power generation [2], and it is likely that in a near future, PV generation will have to comply with similar requirements. These grid codes deal, among other topics, with voltage sags and unbalanced conditions. Furthermore, in Spain, PV systems of up to 100 kVA can be connected to the low-voltage distribution network, where voltage unbalance is more likely to happen, mainly caused by single-phase loads, or even by single-phase distributed generation. The control system of the inverter should be able to deal with such a situation. Otherwise, the AC currents injected to the grid will be greatly distorted, with a high presence of even harmonics, as shown in Fig. 1, Fig. 2 and Fig. 3 where a voltage unbalance occurs at t=0.2s and the inverter is not ready to deal with it. Fig. 1: Grid Line Voltages. At t=0.2s a voltage unbalance starts. Fig. 2: Phase currents. At t=0.2s a two-phase, 20% depth voltage unbalance starts. Fig. 3: Phase currents. Harmonic content during voltage sag with standard inverter control. Proposed System Description An unbalanced three-phase voltage system can be decomposed in a positive, negative and homopolar sequence three phase systems. At the inverter terminals the homopolar sequence is zero because the transformer required for the connection has usually one of the sides connected in delta. But the negative sequence voltage will produce a negative sequence current if no action is taken by the inverter [3]. Also, in unbalanced conditions the AC instantaneous power is oscillatory leading to DC power oscillations and therefore to DC voltage oscillations, that will produce AC current distortion. The control system proposed in this paper is capable of dealing with such a situation. IpvIaIbIcEaEbEcUdcFig. 4: Proposed electrical scheme IaIbIcIc*Ib*Ia*UdcUdc* I x*I y*I d*I q*? *Ix*Iy*Iq*EaEbEc?Udc IpvMPPTUdc I pvPLLFig. 5: Proposed control scheme The system that has been simulated consists of a photovoltaic array with a peak power of 100kW connected through a DC bus to a three-phase inverter that is connected to an ideal 400V grid through a simple filter, as shown in Fig. 4. The control strategy features a PLL block shown in Fig. 5. This PLL will obtain the phase angle of the positive and negative sequence of the unbalanced grid voltage. The positive sequence angle reference will be used for controlling the power output of the inverter while the negative sequence angle reference is used for avoiding a negative sequence current to flow into the inverter [3][4]. When the angle reference is extracted by the PLL described above, the phase currents distortion is greatly reduced in the case of a voltage unbalance, as the simulation results show. Other features of this inverter include decoupled control of active and reactive power, a fuzzy maximum power point tracking system, and the absence of an intermediate stage of DC/DC control. The control system was simulated in Matlab-Simulink, and the power circuit was simulated in Psim. Fuzzy MPPT For a given irradiance and cell temperature, the relationship between voltage, current and power are functions similar to the ones shown in Fig. 6. The voltage that corresponds to the module maximum power changes with temperature and irradiance variations, so a MPP tracking system is needed to ensure that the PV module is operating as close as possible to the optimum voltage. Usual MPPT methods include Perturb and Observe (P&O), incremental conductance, fuzzy logic and other methods [6, 7]. 0 5 10 15 20 25 30050100150Voltage (V)Power(W)Current(Ix10) P maxFig. 6: Module power and current vs. voltage for G=1000W/m2 and T=298K System Topology and MPPT integration Usually the MPPT controls a DC-DC converter to maintain an optimal DC voltage at the output of the generator, while the voltage at the input of the inverter is kept constant. With an appropriate sizing of the PV array the DC-DC converter can be avoided due to the relatively small changes in the optimum voltage in operating conditions [5]. This will save one stage in the system and therefore will increase efficiency. In the usual configuration with a DC-DC converter the MPPT system outputs a signal to change the duty cycle of the converter. In the proposed system, the MPPT will output a DC voltage reference Udc* to the inverter control, as shown in the proposed control scheme.Fuzzy MPPT algorithmHere is presented a method based on a fuzzy controller that has been designed to be integrated in the inverter instead of a DC-DC converter, and uses a reduced set of membership functions (and therefore is simpler to fine-tune) without compromising performance. Fuzzy logic controllers are suitable for nonlinear problems where the desired system behaviour in terms of input and output variables can be expressed as a set of semantic rules. They present a robust performance and good response in noisy environments. dV/dtV * dcGain∫V pvI pvGainGainFuzzyEngineFig. 7: Fuzzy MPPT diagram The control diagram of the MPPT is shown in Fig. 7. The variation over a sample time of PV module voltage and power Δ Udc and Δ Ppv are computed. Then a gain and saturation are applied to those signals, before feeding them to the fuzzy engine. The output of the fuzzy engine is the desired voltage variation for the DC bus Δ Udc* which is then integrated to obtain the desired voltage reference Udc*. These inputs and output were chosen so as to be able to define a set of semantic rules for the fuzzy engine that lead to maximum power point tracking. The shape of the P-V curve (Fig. 6), with an absolute maximum makes suitable a hill-climbing approach. The chosen rules are shown in Table I. Table I: Fuzzy rules If Δ Udc is NEG and Δ Ppv is NEG then Δ Udc* is POS If Δ Udc is NEG and Δ Ppv is ZERO then Δ Udc* is ZERO If Δ Udc is NEG and Δ Ppv is POS then Δ Udc* is NEG If Δ Udc is ZERO and Δ Ppv is ANY then Δ Udc* is ZERO If Δ Udc is POS and Δ Ppv is NEG then Δ Udc* is NEG If Δ Udc is POS and Δ Ppv is ZERO then Δ Udc* is ZERO If Δ Udc is POS and Δ Ppv is POS then Δ Udc* is POS Usually, a large number of membership functions are defined, such as negative-big, negative-medium, negative-small, etc. This is not strictly necessary, and introduces additional complexity to the controller tuning, as the boundaries between seven or more membership functions have to be defined, for each variable. In this case, a minimalistic set of membership functions have been chosen: negative (NEG) positive (POS) and zero (ZERO). Their shapes for all input and output variables are as shown in Fig. 8. They are all normalized to [-1 1] and [0 1] so the characteristics are controlled by the input and output gains. This greatly reduces tuning complexity. Fig. 8: Membership function plots for Δ Udc Δ Ppv and Δ Udc* Simulation results Figures Fig. 9, Fig. 10 and Fig. 11 show the system response to a two-phase, 20% depth voltage unbalance starting at t=0.2s Fig. 9 shows the phase currents before and after the voltage unbalance. Currents still show a small amount of distortion during the voltage unbalance, as can be seen in Fig. 10. This oscillation is caused by the DC voltage oscillation, which in turn causes an oscillation in the active current reference. This oscillation could be eliminated if needed by filtering the active current by means of a narrow stopband filter centered at 100Hz, which is the frequency of the power and DC oscillations caused by the unbalance [3]. When dealing with unbalanced conditions, the fuzzy MPPT shows excellent performance. Fig. 11sows that the MPPT algorithm keeps effectively tracking the optimal operating point after the voltage unbalance has started. Performance is slightly worse than in normal operation, due to the DC voltage oscillation caused by the unbalance. In Fig. 12, a deep step in irradiance (from 1000 to 300 W/m2) is introduced during the voltage unbalance. The MPPT control quickly drives the system to the optimal operation point. Fig. 9: Phase currents. At t=0.2s a voltage unbalance starts, but injected currents show little distortion Fig. 10: Phase currents. Harmonic content during voltage unbalance, with proposed control strategy 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.30.950.960.970.980.991Fig. 11: MPPT Efficiency (PV power / Max Power). At t=0.2s a voltage unbalance starts. 0.6 0.65 0.7 0.750.80.850.90.951Fig. 12: MPPT Efficiency (PV power / Max Power) during voltage unbalance. At t=0.6s a step in irradiance occurs. Conclusion An inverter for photovoltaic applications has been presented. The inverter features an excellent behavior in case of a voltage unbalance, therefore contributing to system stability. This is likely to become an important feature as the photovoltaic installed power increases in many countries as Spain or Germany. The changes made to achieve this excellent behavior in case of a voltage unbalance do not substantially affect the rest of the characteristics of this inverter, such as its fast dynamic response, its accurate and fast maximum power point tracking and almost instantaneous tracking of power factor reference. References [1] Royal Decree 1578/2008 (September, 26) on the feed-in tariff scheme for photovoltaic power generation plants connected to the grid after the expiration date of the feed-in tariff scheme described in the Royal Decree 661/2007 (may, 25). BOE (Spanish official state bulletin), 2008, no. 234, pp 39117-39125. [2] Spanish grid operator Operating Procedure P.O. 12.3: “ Wind farm response requirements during voltage sags ” . BOE (Spanish official state bulletin), 2006, no. 254, pp. 37017 – 37019. [3] J. Eloy-Garcia, S. Arnaltes, y J. Rodriguez-Amenedo, “ Direct power control of voltage source inverters with unbalanced grid voltages, ” Power Electronics, IET, vol. 1, 2008, pp. 395-407. [4] L. Limongi et al., “ Analysis and Comparison of Phase Locked Loop Techniques for Grid Utility Applications, ” Power Conversion Conference - Nagoya, 2007. PCC 07, 2007, pp. 674-681. [5] R. Hudson et al., “ Design considerations for three-phase grid connected photovoltaic inverters, ” Photovoltaic Specialists Conference, 2002. Conference Record of the Twenty-Ninth IEEE, 2002, pp. 1396-1401. [6] H. Desai y H. Patel, “ Maximum Power Point Algorithm in PV Generation: An Overview, ” Power Electronics and Drive Systems, 2007. PEDS 07. 7th International Conference on, 2007, pp. 624-630. [7] T. Esram y P. Chapman, “ Comparison of Photovoltaic Array Maximum Power Point Tracking Techniques, ” Energy conversion, IEEE transactions on, vol. 22, 2007, p á gs. 439-449.