Abstract-An accurate small signal model of three phase photovoltaic inverters with a high order grid filter is derived in this paper. The proposed model takes into account the influence of both the inverter operating point and the PV panels characteristics on the inverter dynamic response. A sensitivity study of the control loops to variations of the dc voltage, the PV panels transconductance, the supplied power, and the grid inductance is performed using the proposed small-signal model. Analytical and experimental results carried out on a 100 kW photovoltaic inverter are presented.Index Terms-Renewable energies, modeling and control of power inverters, distributed generation I. INTRODUCTION HOTOVOLTAIC (PV) power generation is a concept of increasing interest. In the last years, a high number of photovoltaic farms with a power capacity up to some MW have appeared in the distributed power generation scenario. In order to disturb the distribution grid as little as possible, the switching harmonics generated by the power inverters must be properly filtered out, reaching a compromise between the cost and the weight of the filter, and fulfillment of international standards regarding the grid connection of power converters, like IEC/EN 61000-3-4 [1] and IEEE 15471 [2]. Such a compromise often requires the use of high order grid filters, typically in LCL configuration. However, the stability of the system may be compromised by the resonances of the LCL filter, so that a careful design of both the filter and the control strategy is mandatory. [15]- [18], showing that Phase Locked Loops (PLL) based on the transformation of the grid voltages to a synchronous reference frame are currently a very interesting alternative to achieve that objective. The power production capability of the generation system is another issue that merits special attention, because the exploitation benefits of a photovoltaic farm intimately depend on the capability of the inverter to extract the maximum available power that can be instantaneously extracted from the panels. To achieve this relevant objective, a high number of Maximum Power Point Tracking (MPPT) techniques have been proposed in the past. Some of the most recent ones may be found in [19]-[23], [29]-[32]. A preliminary version of this paper [24] presents a study of the dynamic response of a 100 kW PV inverter with an LCL grid filter. With regard to that preliminary version, the following novelties have been added in this paper: 1) a detailed derivation of the proposed small-signal model, which includes the dynamics of the PV panels around a maximum power point of their I-V characteristics; 2) a sensitivity study of the control loops to variations of the dc voltage, the generated power, the grid inductance and the PV panels transconductance; and 3) new experimental results focused on the validation of the proposed small-signal model. Fig. 1 shows the scheme of a three-phase Voltage Source Inverter (VSI) connected to the grid through an LCL filter. The series resistances of the inductor...

In photovoltaic (PV) double-stage grid-connected inverters a high frequency DC-DC isolation and voltage step-up stage is commonly used between the panel and the grid-connected inverter. This paper is focused on the modeling and control design of DC-DC converters with Peak Current mode Control (PCC) and an external control loop of the PV panel voltage, which works following a voltage reference provided by a maximum power point tracking (MPPT) algorithm. In the proposed overall control structure the output voltage of the DC-DC converter is regulated by the grid-connected inverter. Therefore, the inverter may be considered as a constant voltage load for the development of the small-signal model of the DC-DC converter, whereas the PV panel is considered as a negative resistance. The sensitivity of the control loops to variations of the power extracted from the PV panel and of its voltage is studied.The theoretical analysis is corroborated by frequency response measurements on a 230W experimental inverter working from a single PV panel. The inverter is based on a Flyback DC-DC converter operating in discontinuous conduction mode (DCM) followed by a PWM full-bridge single-phase inverter. The time response of the whole system (DC-DC + inverter) is also shown to validate the concept.

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