A New Power Calculation Method for Single-Phase Grid-Connected Systems Yongheng Yang, Frede Blaabjerg Department of Energy Technology Aalborg University Pontoppidanstraede 101, Aalborg East, DK-9220, Denmark yoy@et.aau.dk, fbl@et.aau.dk Abstract— A new method to calculate average active power and reactive power for single-phase systems is proposed in this paper. It can be used in different applications where the output active power and reactive power need to be calculated accurately and fast. For example, a grid-connected photovoltaic system in low voltage ride through operation mode requires a power feedback for the power control loop. Commonly, a Discrete Fourier Transform (DFT) based power calculation method can be adopted in such systems. However, the DFT method introduces at least a one-cycle time delay. The new power calculation method, which is based on the adaptive filtering technique, can achieve a faster response. The performance of the proposed method is verified by experiments and demonstrated in a 1 kW single-phase grid-connected system operating under different conditions. Experimental results show the effectiveness of the proposed power calculation method. Keywords— instantaneous power; active power; reactive power; single-phase system; photovoltaics; adaptive filtering I. INTRODUCTION Recent data shows that the development of single-phase photovoltaic systems connected to the grid is booming [1], [2]. The high penetration of single-phase renewable energy systems also introduces challenges to the control of the single-phase grid-connected systems. Thus, new grid codes are expected to be put up to regulate the interconnection of renewable energy systems and the grid [3]-[6]. In these grid codes, the grid- connected systems are required to be equipped with Low Voltage Ride-Through (LVRT) capability and to inject reactive power in the case of grid voltage faults. Therefore, the control systems should be redesigned and ready for such applications in the future. Traditional control schemes for single-phase systems include two cascaded loops – the inner current loop and the outer voltage loop, and normally the single-phase grid- connected systems are operating at unity power factor [5]-[9]. In that case, there is no need to calculate the average active power and the reactive power. In respect to control the single- phase systems under grid faults, possible solutions are based on single-phase PQ theory [5], [6], [10], [11], droop-control methods [12]-[14] and the instantaneous power control method as discussed in [15]. Therefore, it is necessary to calculate the average active power and reactive power fast and accurately in order to enhance the LVRT capability for single-phase systems. It should be pointed out that the power calculation is necessary not only in single-phase systems controlled by the single-phase PQ theory but also e.g. in the droop-controlled micro-grid [16]. A simple way to get the instantaneous power of single- phase systems is to multiply the measured grid voltage and grid current. However, the instantaneous power will present a variation at twice the grid fundamental frequency. By applying a well-designed filter after the multiplication, the average active power and the reactive power can be obtained [16], but the transient response is slow because of the filter delay. Another solution is based on the Discrete Fourier Transform (DFT). However, the main drawback of this method is that it introduces a period delay of the grid fundamental voltage. One possibility to calculate the average active and reactive power is based on the three-phase instantaneous power theory [10], [11]. In three-phase systems, the instantaneous active power and reactive power can be obtained easily with the help of the Clark Transform and the Park Transform. Thus, inspired by this concept, the “αβ” system can be built up by a phase shift of π/2 rad in respect to the fundamental period of the input voltage or current. Followed by the Park Transform (αβ→dq), the average active power and the reactive power can be calculated. Hence, the mission of the power calculation is shifted to create an Orthogonal Signal Generator (OSG) system, such as the Hilbert Transform based OSG, the inverse Park Transform based OSG and the second order generalized integrator based OSG [11], [17]. Those methods based on the OSG structure are more useful for single-phase applications since a grid synchronization unit is normally required. However, the transient responses of such methods are dependent on the performances of the OSG systems. Inspired by the Enhanced PLL proposed in [21], a novel average power calculation method is proposed in this paper. An overview of the possible power calculation methods for single- phase systems is firstly presented, followed by the description of the proposed method and a comparison of the power calculation methods by simulations and experiments. Finally, the proposed method is tested in a 1 kW single-phase system in low voltage ride-through operation mode. The experimental results show the effectiveness of the proposed method in the calculation of the average active and reactive power. It can also be used in other applications which require a fast and accurate average power calculation.