The power flow computer program is fundamentally important for power system analysis and design. Many textbooks teach the Newton-Raphson method of power flow solution. The typical formulation of the Jacobian matrix in the NR method is cumbersome, inelegant, and laborious to program. Recent papers have introduced a method for calculating the Jacobian matrix that is concise, elegant, and simple to program.The concise formulation of the Jacobian matrix makes writing a power flow program more accessible to students. However, its derivation in the research literature involves advanced manipulations using higher dimensional derivatives, which are challenging for dual level students. This paper presents alternative derivations of the concise formulation that are suitable for undergraduate students, where some cases can be presented in lecture while other cases are assigned as exercises. These derivations have been successfully taught in a dual level course on computational methods for power systems for about ten years.
With the advent of real-time PMU data acquisition technology, the possibility of solutions to several instability problems in power system has increased. However, PMUs may undergo different data quality issues like recording bad data or missing data. Some paper mentions about 5-10% of missing samples in some historical PMU's dataset. This paper assumes 0-10% of missing phasor samples by randomly deleting measurements and explores imputation methods of handling missing data in real time. The simulation is carried out in a DT-based stability prediction and one-shot control scheme of WECC's 176-bus model. Several control performances are evaluated to decide a useful method of missing data recovery for the response based one shot control scheme. A PMU data quality issue is not limited to missing samples only but also interference with noises. Later part of this paper performs simulation considering noisy phasor measurements. A 45 dB of Gaussian distributed noise is deliberately added to phasor samples and simulation is performed with different DT indices and thresholds for real time stability prediction and control actuation.Index Terms-Decision trees, one shot control, phasor measurement units, power system transient stability, response based system, wide area control I. INTRODUCTIONA wide area monitoring system (WAMS) technology involves several synchronized phasor measurement units (PMUs) across the network that measure and collect phasor samples to a central location. These samples serve important role in monitoring and analyzing different characteristics of a power system such as state estimation, fault detection, etc. The concept of synchronized phasor measurements and their application to improve monitoring, protection and control of a power system is well explained in [1]. The advent of realtime PMU data acquisition has provided solutions to various instability problems, however, one cannot ignore several data quality issues associated with this technology. Data quality issues, for example, recording non-numeric data, bad data or simply missing data might occur due to problems related to synchronization signals, equipment errors and malfunction, communication noises, etc [2]. Reference [3] mentions that on an average, 5-10% of missing samples in some historical PMUs data sets have been recorded.Monitoring and analysis of phasor samples with missing values has significant effect on the overall quality of the result
The paper describes algorithms to screen realtime frequency data for detecting nearby loss of generation events. Results from Fourier calculation are combined with other features to effectively distinguish a nearby loss of generation from similar remote disturbances. Nearby in this context usually refers to an event occurring around 50-100 miles from the measurement location. The proposed algorithm can be trained using pattern recognition tools like decision trees to enable smart devices including appliances like residential air conditioners and dryers to autonomously detect and estimate the source of large frequency disturbances. An area of application of this strategy is to actuate controls such as location targeted under frequency load shedding (UFLS) so that loads closest to a tripped generator are the most likely to shut down.
The work done in this paper addresses various methods of handling missing phasor samples obtained from power flow simulations using DSA tools like TSAT and PSAT. Pseudorandom numbers in MATLAB are used to simulate 0-10% of missing samples and are recovered using different extrapolation techniques. After recovery, samples are subjected to decision trees to assess the performance of one shot stabilizing controls like in [1], [2].The power system model used is the 176 bus model of Western Electrical Coordinating Council (WECC).
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