Direct and Indirect Measurements of Power System States in Off-nominal Condition Abstract—Wide area measurement is significant for modernized control of power system. Phasor measurement unit (PMU) being the prime element for wide area measurement system (WAMS), it provides proper feedback to the closed looped controller to take proper steps during power system transients. This paper aims to measure the state of six bus power system in off-nominal frequency condition. To achieve this firstly a three phase PMU is simulated using recursive algorithm and then the algorithm is made frequency adaptive by re-sampling. Pseudo measurement using ABCD parameter is also proposed and implemented. Keywords— ABCD parameter; non-dft frequency estimation; off-nominal phasor estimation; phasor measurement unit (PMU); recursive algorithm; re-sampling; wide area measurement system (WAMS). I. INTRODUCTION PMU is a device which measures voltage and current phasors of the corresponding bus all in real time. Modern PMU can also calculate frequency, rate of change of frequency (ROCOF), rate of change of phase angle difference (ROCOPAD) between voltage and current phasor. After evaluating these calculations PMUs send phasor information to a common base known as phasor data concentrator (PDC) or super phasor data concentrator (SPDC), which after rearranging and recalculating phasor information with respect to time stamp sends signal to manipulating element to control the grid. That is how wide area measurement is done. In [1]-[2] simulation model of PMU based on recursive and non-recursive algorithm through LABVIEW and MATLAB SIMULINK is proposed. But these algorithms are unable to calculate phasor in off-nominal frequency condition, moreover they are inappropriate for real time phasor estimation. To calculate phasor in off-nominal condition frequency is to be determined. Frequency in power system can be estimated using Kalman filter, DFT algorithm, or by non-DFT frequency estimator [3]-[5]. The algorithm for Kalman filtering is very complex. Although the DFT based frequency estimator can calculate all frequency component of a signal, the process is very slow. A non DFT frequency estimation process can calculate frequency by taking only three samples from a sinusoid, thus reducing the time complexity as in [5]. In [6]-[9] the commonly used phasor measurement units are performance and measurement class based. The common problem in [6]- [9] is that the input signal is unintentionally delayed after filtering operation thus delay compensator is required. For pseudo measurement Kirchhoff’s voltage and current laws are followed in [10] where as transmission line parameter are more prominent in this regard. In this paper a three phase PMU is simulated based on recursive algorithm. The recursive algorithm is made to take samples at sub-synchronous rate when the frequency is lower than nominal and super-synchronous rate when the frequency is higher than nominal by using re-sampling filter. Next this PMU is used to measure voltage and current phasor from the directly observable buses in off-nominal frequency condition. The buses which are out of reach of PMU is observed indirectly using ABCD parameter and sending end voltage of a transmission line. In section II there is a brief review of recursive algorithm, frequency estimation and re-sampling. Section III details the process of pseudo measurement of phasors. Simulations and results obtained for the prescribed method are analyzed in section IV. Section V concludes the performed work. II. REVIEW OF ADAPTIVE PMU A rotating vector from a pure sinusoid described in time domain named as phasor can be obtained having r.m.s. magnitude of the sinusoid and phase angle with respect to reference vertical axis. Two DFT based algorithms known as recursive and non-recursive algorithms are used to calculate and update these complex valued phasor as in [1], [2], [11], [14]. As recursive algorithm takes less time to update phasor compared to non-recursive algorithm it is used to obtain voltage and current phasors quickly from a large power system. Both of these algorithms fail to calculate phasor when the sinusoid is off-nominal. Thus re- sampling filter is helpful to get the input samples corrected when frequency becomes off-nominal. The recursive algorithm is made to take samples at sub-synchronous rate when the frequency is lower off-nominal and super- synchronous rate when the frequency is higher off-nominal by using re-sampling filter as in [11], [14]. III. PSEUDO MEASUREMENT USING ABCD PARAMETER As PMU is a costly device it is not economical to calculate all bus voltages and branch currents of whole network using PMU. When a part of a power system is out Dhruba Kumar 1 1 Department of Electrical Engineering National Institute of Technology Durgapur Durgapur, India Nada Ali 2 2 Department of Electrical and Electronics Engineering Birla Institute of Technology Mesra Ranchi, India 2016 2nd International Conference on Control, Instrumentation, Energy & Communication (CIEC) 978-1-5090-0035-7/16/$31.00©2016IEEE 240