Instantaneous Active and ReactivePower Measuring Method in Three Phase Power System

Instantaneous Active and Reactive Power Measuring Method in Three Phase Power System A. TAHRI, A. DRAOU Applied Power Electronics Laboratory, Department of Electrotechnics, University of Sciences and Technology of Oran BP 1505 El Mnaouar (31000 Oran), ALGERIA, Fax:+213–41–421581 Contact author: Dr. Azeddine Draou, Senior member IEEE, Email: adraou@yahoo.com Abstract This paper describes an electronic means of measuring the instantaneous active and reactive power absorbed by any electrical equipment. The measurements are based on the Clark (α-β) and Park (d-q) transformations. The system is useful to teach electrical machines in Park’s coordinates and it allows also the study and control of some power electronics converters that are connected to three phase power network, such as static VAR compensator. The principle of the measuring method of the active and reactive power is described, and analyzed for different tests. The effectiveness of the proposed measuring method is confirmed by experimental investigation employing a test system. Keywords Active power, Reactive power, SVC, Clark and Park, EPROM Introduction Up to now, the reactive power doesn’t really have a physical significance, but it remains recognized as an essential factor in the conception and the efficient operating of AC electric network [1]. The application of Clark (α-β) and Park (d-q) transforms to three phase system in order to calculate the instantaneous active and reactive power is a useful tool for study and analysis of many electrical systems [2]. There are many industrial applications that require the knowledge of the instantaneous value of the active and reactive power. In fact, they are used to manage the economical aspect of their system [1, 3, 4]. The instantaneous active and reactive powers are also used in the control of converters connected to electric network [5]. These converters can control the flow of active and reactive power in the power system to improve voltage regulation, and increasing transient stability margin [4, 5]. In this paper, an inexpensive electronic circuit that calculate Clark (α-β), Park (d-q) components and the instantaneous active and reactive power for three phase AC system is presented and discussed thoroughly. The effectiveness of the proposed electronic method that calculates the instantaneous active and reactive currents and power is confirmed by experimental results through a laboratory prototype. Theoretical Analysis α-β transformation Voltages and currents can be transformed from abc system to α-β coordinates as follows, where X denotes voltage or current: (1) d-q transformation From α-β transformation the d-q coordinates are given by: (2) Active and reactive power The active and reactive power for three phase balanced system can be written in d-q coordinates as follows, where , , and are the voltages and currents in d-q coordinates: (3) Proposed Measuring System General description The block diagram of the proposed measuring system is presented in fig. 1. The whole system is divided in three subsystems connected in cascade.  The function of subsystem 1 is to synchronize all of the system to the AC mains using PLL and to generate the adequate addresses to generate sine and cosine functions which are stored in two EPROMS. In the subsystem 2, the measured voltages and currents are transformed from abc to Clark and Park coordinates.  And in the third subsystem the instantaneous active and reactive power are calculated. Detailed description Subsystem 1: Subsystem 1 is frequency synthesizer. The clock frequency is 16.16.16.8.50Hz = 1.638 MHz synchronized to the AC main. This clock frequency is used to drive the address generator. The address generator is composed of four 74HC161 synchronous pre-settable binary counters and two 74HC245 buffers. The addresses obtained are suitable to read in parallel two EPROMs of , where sine and cosine functions are stored. Hence the obtained address generator is shown in fig. 2. Subsystem 2: The measured voltages and currents in abc frame are transformed in Clark and Park coordinates. The Clark transform given by equation (1) is obtained using simple operational amplifiers as shown in fig. 3. Figure 1. Proposed measurement system Figure 2. Address generator Figure 3. Clark transform Circuit Park coordinates are obtained from Clark coordinates by using equation (2). The sine and cosine functions generated by the address generator and synchronized to the AC mains are used to obtain the Park coordinates by using the analog multiplier AD534JD as shown in fig. 4. Figure 4. Park transform Circuit Subsystem 3: The instantaneous active and reactive power calculator is also obtained using the analog multiplier AD534JD as shown in fig. 5. Figure 5. Instantaneous active and reactive power calculator