This paper presents the assessment methodology for
voltage stability using Phasor Measurement Unit (PMU) with
complete system observability. For full power system
observability, the PMU placement is considered with and without
conventional power flow as well as injection measurement such
that minimum number of PMU’s is used. Data obtained by
PMU’s are used for voltage stability assessment with the help of
L-Index. As the PMU gives real time voltage and current phasors
and L-index is dependent on voltage and admittance values, thus
the L-index so obtained can be used as real time voltage stability
indicator. The case study has been carried out on IEEE-14 bus
system.
Phasor measurement unit and it's application pptKhurshid Parwez
The effective operation of power systems in the present and the future depends to a large extent on how well the emerging challenges are met today. Power systems continue to be stressed as they are operated in many instances at or near their full capacities. In order to keep power systems operating in secure and economic conditions, it is necessary to further improve power system protection and control system. Phasor measurement unit (PMUs), introduced into power system as a useful tool for monitoring the performance of power system, has been proved its value in the extensive applications of electric power system. In response, a research program that is specifically aimed at using PMU to improve the power system protection and control. To ensure that the proposed research program is responsive to particular industry needs in this area, and participants of the workshop identified two major research areas in which technological and institutional solutions are needed: 1) PMU implementation, 2) PMU applications. It’s recommends research, design, and development (RD&D) projects in this report. The objective of these projects is to improve the reliability of local and wide transmission grid by enabling and enhancing the system protection and control schemes by using PMU measurement data, reduce the economic burden of utilizes to implement PMUs.
This document discusses how wide area monitoring systems (WAMS) can improve power system protection. WAMS consist of phasor measurement units and phasor data concentrators that provide time-synchronized measurements across a wide area. This allows monitoring of dynamic system states. The document outlines several ways WAMS can enhance protection schemes, including adaptive relay settings, improved backup protection supervision, intelligent underfrequency load shedding adapted to conditions, and adaptive out-of-step relaying to prevent system separation. The goals are to avoid inappropriate relay operations, manage wide area disturbances, and ensure an appropriate balance of security and dependability in protection schemes.
Introduction of wide area mesurement syatemPanditNitesh
This document summarizes a seminar presentation on Wide Area Measurement Systems (WAMS). WAMS uses Phasor Measurement Units (PMUs) synchronized by GPS to monitor power grids. PMUs measure voltage and current phasors, while Phasor Data Concentrators (PDCs) collect and process data from multiple PMUs. The seminar discusses the components of WAMS including PMUs, PDCs, and communication protocols. It also reviews several implementations of WAMS and their applications in monitoring the electric grid.
This document describes the development of a phasor measurement unit (PMU) for remote power system monitoring. Key points include:
- A PMU was designed and developed to measure voltage, current, frequency and phase at the distribution level to monitor the power system remotely.
- Software was created to log measurements from the PMU and allow remote monitoring via web and mobile platforms.
- The PMU design uses an NI myRIO computing platform, current and voltage sensors, and a GPS receiver for time synchronization to provide synchrophasor data for applications like oscillation detection and frequency/voltage stability monitoring.
Wide Area Monitoring, Protection and Control (WAMPAC) Application in Transmis...IRJET Journal
This document provides a literature review on the application of Wide Area Monitoring, Protection and Control (WAMPAC) in transmission grids. It discusses technologies used in WAMPAC systems such as Phasor Measurement Units (PMUs), Flexible AC Transmission Systems (FACTS) devices, and Phase Shifting Transformers (PSTs). The literature review covers past research on optimal placement of PMUs and FACTS devices in transmission networks to maximize observability and control. It also examines the use of WAMPAC technologies to monitor system oscillations and stability. The review provides background information for a proposed project to model and simulate the application of WAMPAC technologies in a transmission grid.
A Survey On Real Time State Estimation For Optimal Placement Of Phasor Measur...IJSRD
The traditional methods of security assessment using offline data and SCADA data have become inconsistent for real time operations. The latest and propelled strategy in electric power system used for security assessment is “synchrophasor†measurement technique. The device called Phasor measurement unit (PMU) provides the time stamped data for proper monitoring, control and protection of the power system. PMU measures positive sequence voltage and current time synchronized to within a microsecond. The time synchronization of data is done with the help of timing signals from Global Positioning System (GPS). However, Phasor measurements units cannot be placed on every bus in a network mainly because of economical constraints. In this paper we provide a literature survey of determining the minimum number of Phasor measurement units to be placed in a given network so that the system becomes observable.
The modern-day power grid aims at providing reliable and quality power, which requires careful monitoring of the power grid against catastrophic faults.
Therefore one promising way is to provide the system a wide protection and control named as “Wide Area Measurement and Control System” /PMU is required.
The load dispatch center monitors and controls the power system to ensure reliable power supply. It collects data using a SCADA system and oversees elements like generators, transformers, and transmission lines. The load dispatch center performs economic and secure operation of the power system, and works to restore power lines after faults. It is responsible for functions like load forecasting, outage monitoring, voltage regulation, load scheduling, and coordination between grids.
The document discusses various maximum power point tracking (MPPT) algorithms for wind energy systems. It describes three main MPPT control methods: tip speed ratio control, power signal feedback control, and hill-climb search control. For each control method, it provides the basic principles, block diagrams, and examples of implementations for different types of wind turbine generators including permanent magnet synchronous generators, squirrel cage induction generators, and doubly fed induction generators.
An investigation on the application and challenges for wide area monitoring a...journalBEEI
This document discusses wide area monitoring and control (WAMC) in smart grids using phasor measurement units (PMUs). It outlines several applications of PMU-based WAMC including voltage stability monitoring, oscillation monitoring, and fault detection/location. It also discusses challenges of implementing WAMC including data handling of large PMU data streams and communication delays over different network infrastructures that can impact system control performance. Overall, the document provides an overview of the potential applications and technical challenges of deploying PMU-based WAMC in modern power systems.
This document discusses implementing a supervisory control and data acquisition (SCADA) system for power system automation using a microcontroller. SCADA systems allow utilities to remotely monitor and control substations to improve reliability and efficiency. Specifically, the document proposes using an 8085 microcontroller as a remote terminal unit (RTU) in a SCADA system to reduce costs compared to traditional implementations. It also suggests a distributed dual computer approach to avoid communication bottlenecks when monitoring a large number of RTUs from a control center. The goal is to provide a lower-cost but still user-friendly solution for power system automation and monitoring.
The document summarizes a project using a National Instruments Single Board RIO General Purpose Inverter Controller (GPIC) to implement a 3-phase inverter and variable frequency drive. It describes the hardware components, LabVIEW code, simulations, challenges faced, and solutions implemented. The project involved using the GPIC Inverter Research Board to generate 3-phase AC power from DC to drive a motor, with the goal of implementing variable frequency control. Various issues were addressed, such as insufficient voltage levels, sensor faults, and transformer limitations.
Phase Measurement Units based FACT’s Devices for the Improvement of Power Sys...IJECEIAES
This paper describes the importance of FACTS devices; it presents the outcome of the study of its reflectance on the performance of power system networks. It seeks to increase and guarantee the fact and accuracy of response systems under disturbance conditions when the phase measurement units are introduced as Real-Time Measurement (RTM) stations. This paper also describes the importance of FACTS devices. The combination of FACTS devices and PMUs is presented to increase the controllability performance of power systems. This paper demonstrates how PMUs measure voltage, current and their angles. It provides, through a communication link, a Phase Angle Data Concentrator (PDC) to make an appropriate decision to correct the power system state using the FACTS device (TCSC). We utilized the Graph-Theoretic Algorithm to optimize the number and location of PMUs. The technique proposed was tested on the Iraqi National Super Grid’s 24bus network, Diyala City’s regional 10bus network and the 14bus IEEE standard test system. The MATLAB/PSAT package was utilized for the simulation of results. It is evident that our proposed algorithm and technique achieved the purpose of this paper as confirmed by the level of accuracy of the results obtained from most of the cases tested.
Artificial intelligence techniques like artificial neural networks, fuzzy logic, and expert systems can help address complex problems in power systems that were previously difficult to solve. They have applications in areas like economic load dispatch, load forecasting, transmission capacity and optimal power flow, generator limits, and system protections. By using environmental sensors and AI techniques together, the performance of transmission lines can be improved by changing line parameters based on conditions and diagnosing and addressing any faults. AI provides benefits like increased reliability, efficiency, and cost savings within power systems.
Wide area protection systems aim to address vulnerabilities in modern power systems. Conventional protection systems provide local views but no overall system view, and actions are uncoordinated. Wide area protection systems fill this gap by analyzing real-time measurements across wide areas to recommend control strategies. They can help increase transmission capacity and reliability by taking action to prevent contingencies from causing instability. This paper surveys applications of synchrophasor-based wide area protection, including existing systems, case studies of disturbances, and technologies enabling wide area protection implementations.
Power system transmission issues and effectsAnand Azad
This document discusses power system transmission issues and effects. It covers 5 topics: 1) reliability requirements to maintain supply-demand balance and synchronous operation, 2) system planning criteria like the N-1 standard, 3) power transmission technologies like AC and DC, 4) system studies to evaluate steady-state operation and dynamic behavior, and 5) possible transmission system improvements like adding lines, fast fault clearing equipment, and advanced transmission technologies.
This document discusses monitoring in smart power grids using phasor measurement units (PMUs). It describes how PMUs provide real-time measurements that allow monitoring of key phenomena like islanding detection, line thermal monitoring, power system stability, and out-of-step stability. Monitoring is important for power assurance, visibility, efficiency and planning. PMU data supports applications like real-time monitoring, protection, and control and allows detection of oscillations and instability that could lead to blackouts. The conclusion emphasizes that modern monitoring delivers confidence in power system performance and ability to predict and prevent problems.
This document presents a preliminary study on developing a Wide Area Protection Monitoring System (WAPMS) that would automatically collect and analyze data from protection devices. The proposed system would gather information through various communication protocols, analyze the data to determine fault types and locations, and generate reports with diagnoses for operators. This would provide operators a comprehensive overview of the power system's behavior during faults to help make better decisions. The system is currently being tested in Colombia and future work involves predictive analytics to identify potential protection device failures.
Series of blackouts encountered in recent years in power system have been occurred because either of voltage or angle instability or both together was not detected within time and progressive voltage or angle instability further degraded the system condition, because of increase in loading. This paper presents the real-time assessment methodology of voltage stability using Phasor Measurement Unit (PMU) with observability of load buses only in power network. PMUs are placed at strategically obtained location such that minimum number of PMU’s can make all load buses observable. Data obtained by PMU’s are used for voltage stability assessment with the help of successive change in the angle of bus voltage with respect to incremental load, which is used as on-line voltage stability predictor (VSP). The real-time voltage phasors obtained by PMU’s are used as real time voltage stability indicator. The case study has been carried out on IEEE-14 bus system and IEEE-30 bus systems to demonstrate the results.
Reliability analysis of pmu using hidden markov modelamaresh1234
As modern electric power systems are transforming into smart grids, real time wide area monitoring system (WAMS) has become an essential tool for operation and control. With the increasing applications of WAMS for on-line stability analysis and control in smart grids, phasor measurement unit (PMU) is becoming a key element in wide area measurement system and the consequence of the failure of PMU is very severe and may cause a black out. Therefore reliable operation of PMU is very much essential for smooth functioning of the power system. This thesis is focused mainly on evaluating the reliability of PMU using hidden Markov model. Firstly, the probability of given observation sequence is obtained for the individual modules and PMU as a whole using forward and backward algorithm. Secondly, the optimal state sequence each module passes through is found. Thirdly, the parameters of the hidden Markov model are re-estimated using Baum-Welch algorithm.
Joint State and Parameter Estimation by Extended Kalman Filter (EKF) techniqueIJERD Editor
In order to increase power system stability and reliability during and after disturbances, power grid
global and local controllers must be developed. SCADA system provides steady and low sampling density. To
remove these limitation PMUs are being rapidly adopted worldwide. Dynamic states of power system can be
estimated using EKF. This requires field excitation as input which may not available. As a result, the EKF with
unknown inputs proposed for identifying and estimating the states and the unknown inputs of the synchronous
machine.
GPS technology provides an accurate timing signal that can be used to synchronize measurements across large power grids. Power companies have implemented GPS-based time synchronization devices in power plants and substations due to repeated power blackouts demonstrating the need for improved synchronization. Phasor measurement units (PMUs) use GPS signals to provide synchronized voltage and current phasor measurements from different substations. These synchronized phasor measurements allow various applications including improved monitoring, control, and prediction of issues like voltage instability.
Online monitoring of voltage stability margin using PMU measurements IJECEIAES
This document presents an approach for online monitoring of voltage stability margin in power systems using synchrophasor measurements from phasor measurement units (PMUs). The approach fits quadratic curves to the P-V and Q-V curves of each load bus using three sets of PMU measurements and pseudo-measurements. It determines the real and reactive power loading margins of each bus, and takes the minimum of these across all buses as the system's overall loading margins. It also identifies the most critical bus based on these margins. The approach updates the loading margins and critical bus identification regularly as system conditions change using new PMU measurements. Case studies on IEEE test systems and a large Indian power grid validate the effectiveness of the proposed online monitoring approach.
Application of Synchronized Phasor Measurements Units in Power Systemstheijes
The last decades, electric power industry is undergoing multiple changes due to the process of deregulation, providing efficient power generation, technological innovations, and eventually lower retail prices. In this environment, dynamic phenomena in power systems have made ever more urgent the development of reliable tools for their monitoring and control. An effective tool for the close monitoring of their operation conditions is the state estimator. The traditional estimators are based on real time measurements obtained through SCADA (Supervisory Control and Data Acquisition) system. These measurements are commonly provided by the remote terminal units (RTUs) installed at the high voltage substations. The phase angle of bus voltages can not be easily measured due to technical difficulties associated with the synchronization of measurements at RTUs. Global Positioning System (GPS) alleviated these difficulties and led to the development of Phasor Measurement Units (PMUs). This weakness was eliminated with the arrival of GPS, which led to the development of Phasor Measurement Units. A PMU unit, equipped with a GPS receiver, provides high accuracy voltage and current phasor measurements with respect to a common reference phase angle. In the first part of the paper, an overview of the PMU technology and a review about the optimal allocation of PMUs in power network are presented. The most important issues regarding design and operation of PMUs are discussed and an analysis of their commercial penetration in the electric energy markets is made. The second part of the paper presents a wide range of applications related with the choice of the strategic PMU placement as well as an algorithm for finding the optimal number of PMUs needed for full observability
These slides are all about Phasor Measurement Units (PMUs). An introduction to PMU is presented as a preliminary knowledge for the course 'Distribution Generation and Smart Grid'. Your valuable suggestions are welcome.
Fault location in sec interconnected network based on synchronized phasor mea...Abhishek Kulshreshtha
This document discusses using synchronized phasor measurements from Phasor Measurement Units (PMUs) to locate faults in interconnected power networks. It addresses the challenge that it is not economical to install PMUs at all network buses. The paper proposes using the Tree Search Method (TSM) to determine a near-optimal placement of PMUs that allows fault location. It presents simulation results applying TSM to standard test systems and a real network, showing the ability to accurately locate different fault types. Mathematical formulations for calculating fault distances are also discussed.
This document discusses the hardware implementation of a Phasor Measurement Unit (PMU) using a DSP microcontroller, GPS receiver, and supporting components. PMUs are used to measure voltage and current phasors in real time with synchronized time tags. The hardware PMU is tested in a LabVIEW environment. Measured voltage and current signals are converted to digital values and transmitted via an RS232 link. Output signals from the hardware are also sent via SMS using a GSM modem.
Cost effective test methodology using pmu for automated test equipment systemsVLSICS Design
In this paper, test methodology using parametric measurement unit is proposed for Automated Test
Equipment (ATE) systems using 600MHz Driver, Comparator, and Active load (DCL). ATE systems is a
very important means to reduce the device test cost, and the systems should be able to test several modes to
check the performance characteristics of the device. The proposed methodology provides four different
types of test operation for DC and AC analysis of the Device-Under-Test(DUT). Along with the proposed
methodology, the paper proposes ATE system integration methodology for cost effective ATE integration
for high speed test. The measured test results using the proposed method and system turned out to be well
within the target specifications with high accuracies
A Fault Detection and Classification Method for SC Transmission Line Using Ph...paperpublications3
Abstract: In this paper, fault detection and classification for Series Compensated Line (SCL) using phasor measurement unit is presented. The algorithm presented in this paper uses the PMU synchronized measurements and not depends on the data to be provided by the electricity utility. The compensated line parameters and Thevenin’s equivalent (TE) of the system at SCL terminals are calculated online, using three independent sets of pre-fault phasor measurements. The accuracy of fault location is performed with respect to fault location/position, types of fault, fault angle. The accuracy of the algorithm is simulated in MATLAB for 9-bus transmission system.
DETECTION OF UNSYMMETRICAL FAULTS IN TRANSMISSION LINES USING PHASOR MEASUREM...IRJET Journal
This document presents a new hybrid technique for detecting unsymmetrical faults in transmission lines using data from Phasor Measurement Units (PMUs). The technique analyzes positive sequence voltage and current measurements from PMUs. It was tested on the IEEE 9 Bus System in MATLAB/Simulink. The results showed the effectiveness of using positive sequence voltage magnitudes to identify faults - a drop or change indicated the faulty area. When this approach failed, positive sequence current magnitudes were analyzed instead, with a maximum value pinpointing the nearest bus to the fault. The technique provides an accurate way to detect faults compared to conventional non-PMU methods.
These slides focus on preliminary discussions about wide area monitoring, protection and control in future smart grid. Later in the class i will show its application through simulation and case study results.
Online Voltage Stability Analysis using Synchrophasor Technologyijsrd.com
Voltage instability has been a major problem in all the emerging power systems across the world. Several instances of blackouts in North America, including the 1996 Western Interconnection and the 2003 North East US /Canada blackout are primarily due to voltage collapse. So Monitoring and maintaining voltage stability in real-time is extremely important for operating a power system reliably. In this paper Synchrophasor technology is introduced. Synchrophasor technology has the capability to monitor voltage stability over a wide area in real time. In this paper different methods are introduced for finding the voltage collapse point in the system and also one new method given for identification of voltage collapse point.
Multiple Constraints Consideration in Power System State EstimationIOSR Journals
This document discusses a novel algorithm developed to consider multiple constraints in power system state estimation using weighted least squares. The algorithm detects missing measurement data, identifies and eliminates bad data, and evaluates network observability. It also considers measurement uncertainties from phasor measurement units. The algorithm is tested on the IEEE 14 bus system and is able to identify bad data, estimate missing data values, and determine observability while incorporating measurement uncertainties.
This document compares different state estimation methods for a smart distribution grid using synchrophasor technology. It analyzes how integrating phasor measurements from PMUs can improve state estimation accuracy compared to conventional measurements. The study examines different measurement configurations using conventional data, PMU data, or a hybrid approach. It models an 18-bus test grid using real load data from a 110kV distribution system. The results demonstrate that using PMUs can provide more accurate estimates of the system state by leveraging their precise, time-synchronized measurements.
This document summarizes research determining the optimal location for installing a unified power flow controller (UPFC) in an electric transmission system using particle swarm optimization (PSO) to minimize oscillations. The UPFC regulates voltages and controls power flows. PSO is an efficient method for solving nonlinear optimization problems with constraints. By varying parameters like power angle and incorporating time delays, the approach presents an innovative control scheme to apply UPFC beneficially for economical operation with reduced costs. Sensitivity analysis on the UPFC controller finds the optimal buses to place it and regulate flows.
The document proposes an artificial bee colony (ABC) algorithm based neuro fuzzy controller (NFC) to improve the performance of a unified power quality conditioner (UPQC) in compensating for power quality issues like voltage sags. The NFC uses the error and change in error voltage as inputs to a neural network. The ABC algorithm is used to optimize the neural network output. This optimized output is then used to generate optimal fuzzy rules and calculate the discharging capacitor voltage from a bias voltage generator, replacing the DC link capacitor. Simulation results show the proposed ABC-NFC method performs better than ANFIS, ANN, FLC and NFC in compensating for voltage sags.
Bulk power system availability assessment with multiple wind power plants IJECEIAES
The use of renewable non-conventional energy sources, as wind electric power energy and photovoltaic solar energy, has introduced uncertainties in the performance of bulk power systems. The power system availability has been employed as a useful tool for planning power systems; however, traditional methodologies model generation units as a component with two states: in service or out of service. Nevertheless, this model is not useful to model wind power plants for availability assessment of the power system. This paper used a statistical representation to model the uncertainty of power injection of wind power plants based on the central moments: mean value, variance, skewness and kurtosis. In addition, this paper proposed an availability assessment methodology based on application of this statistical model, and based on the 2m+1 point estimate method the availability assessment is performed. The methodology was tested on the IEEE-RTS assuming the connection of two wind power plants and different correlation among the behavior of these plants.
Comparison of Reference Signal Extraction MethodsRaja Larik
This document compares two reference signal extraction methods - synchronous reference frame (SRF) and instantaneous reactive power theory (p-q theory) - for an active power filter used to mitigate load harmonics from a grid-connected variable speed wind turbine system. The performance of each method is analyzed through MATLAB/SIMULINK simulations. The results show that the SRF method more effectively reduces the total harmonic distortion (THD) levels at the wind turbine generator and point of common coupling to within limits specified by IEEE standards, demonstrating it is the more feasible method for reference current generation and harmonic mitigation in this application.
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In this paper, Integer Programming based methodology is presented for
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In this algorithm, the searcher agents are collection of masses which
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Neste vídeo, trago os pontos chave do encontro, como:
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- Ingest Processor
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- Federated Analytics
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Deixo ainda, alguns links com relatórios e conteúdo interessantes que podem ajudar no esclarecimento dos produtos e funções.
https://www.splunk.com/en_us/campaigns/the-hidden-costs-of-downtime.html
https://www.splunk.com/en_us/pdfs/gated/ebooks/building-a-leading-observability-practice.pdf
https://www.splunk.com/en_us/pdfs/gated/ebooks/building-a-modern-security-program.pdf
Nosso grupo oficial da Splunk:
https://usergroups.splunk.com/sao-paulo-splunk-user-group/
Paharganj @ℂall @Girls ꧁❤ 9873777170 ❤꧂VIP Arti Singh Top Model Safe
Voltage Stability Assessment using Phasor Measurement Units in Power Network with Full System Observability
1. Abstract-- This paper presents the assessment methodology for
voltage stability using Phasor Measurement Unit (PMU) with
complete system observability. For full power system
observability, the PMU placement is considered with and without
conventional power flow as well as injection measurement such
that minimum number of PMU’s is used. Data obtained by
PMU’s are used for voltage stability assessment with the help of
L-Index. As the PMU gives real time voltage and current phasors
and L-index is dependent on voltage and admittance values, thus
the L-index so obtained can be used as real time voltage stability
indicator. The case study has been carried out on IEEE-14 bus
system.
Index Terms-- Voltage Stability, L-index, phasor measurement
unit
I. INTRODUCTION
he stability and security of electrical power system are of
much important issues for planning and operation
engineers as it supports the world economy to a great
extent. Power system is critical interdependent infrastructure
and, also, it is important to transmit electrical power from
generation to load end reliably, so its performance should be
effective [1]. To maintain these features, voltage stability is
one of the most important areas for engineers to maintain the
operation of power system within contractual, steady voltage
limits before and after any disturbances. These disturbances
are, may be, sudden loss of generation or lines, or changing
loads, which affects the operating point of system and
frequency. So, it is necessary to rapidly monitor and adjust to
system changes to attain a new operating point or an
equilibrium point keeping generation to load balance. This
ability of system is the goal of voltage stability assessment and
control [2].
In recent years, series of blackouts have been encountered in
power system. These blackouts have been occurred because
either of voltage or angle instability or both together was not
detected within time and progressive voltage or angle
instability further degraded the system condition, because of
increase in loading [3, 4]. Synchronized phasor measurements
are very important for wide area measurement systems used in
advanced power system monitoring, protection, and control
Authors are with the Department of Electrical Engineering, Indian
Institute of Technology, BHU, Varanasi. (e-mail: engi.saurabh@gmail.com,
satya.989@gmail.com, sps5957@indiatimes.com )
applications. Phasor measurement unit (PMU) becomes more
and more attractive to power engineers because it can provide
time synchronized measurements of voltage and currents
phasors [5]. Synchronization is achieved by same-time
sampling of voltage and current waveforms using timing
signals from the Global Positioning System Satellite (GPS).
The present and possible future applications of phasor
measurement units have been well documented [6]. Time
synchronization is not a new concept or a new application in
power systems. As technology advances, the time frame of
synchronized information has been steadily reduced from
minutes, to seconds, milliseconds, and now microseconds.
Several algorithms and approaches have been published in
the literature for the optimal placement of PMUs in power
system. Initiating work in PMU development and utilization is
done by Phadke et al. [5, 7]. An algorithm which finds the
minimal set of PMU placement needed for power system has
been developed in [8, 9] where the graph theory and simulated
annealing method have been used to achieve the goal. In [10]
a strategic PMU placement algorithm is developed to improve
the bad data processing capability of state estimation by taking
advantage of PMU technology. Providing selected buses with
PMUs can make the entire system observable. This will only
be possible by proper placement of PMUs among the system
buses. The authors in [11, 12, 13] developed an optimal
placement algorithm for PMUs by using integer programming.
However, the proposed integer programming becomes a
nonlinear integer programming under the existence of
conventional power flow or power injection measurements. In
[13, 15] had presented a generalized integer linear
programming formulation and solution approach for
placement.
Voltage and current phasors, obtained from PMU buses, can
be used to get full system data in control center computer
using simple KVL and KCL equations. These voltage and
current phasors are used to estimate the voltage stability via L-
index. L-index is, also, helps to determine the margin between
present operating point and the voltage instable operating
point.
In this paper a similar formulation of optimal PMU
placement problem is done by integer linear programming
with and without conventional power flow and power
injection measurement. L-index has been used to identify the
voltage stability. As the PMU gives real time voltage and
current phasors, L-index so obtained can be used for real time
voltage stability indication. Therefore, the voltage stability
Voltage Stability Assessment using Phasor
Measurement Units in Power Network with Full
System Observability
S. Kesherwani, Satyendra P. Singh, Student Member, IEEE, and S. P. Singh, Senior Member, IEEE
T
2. assessment problem using Phasor measurement unit is more
efficient and can be used in practice.
II. PMU TECHNOLOGY IN POWER SYSTEM
Phasor measurement technology (for application in the
power industry) was developed near the end of 1980s and the
first product appeared on the market in the early 1990s. Phasor
Measurement Units (PMUs) are used for Wide-Area
Measurement (WAMS) applications by power engineers and
system operators as a time-synchronized tool. The PMUs
measure time-synchronized voltage and current phasors that
are time-stamped with high precision. PMUs are equipped
with Global Positioning Systems (GPS) receivers that allow
for the synchronization of the several readings taken at distant
points. Recursive algorithm is used for calculating
symmetrical components of voltages and currents [16]. PMU-
based measurements support real-time measurements of
voltage and incident current phasors at observable system
buses. The voltage phasors contain enough information to
detect voltage-stability margin directly from their
measurements. A PMU at a substation measures voltage and
current with microsecond accuracy when the measurement
was taken. It also computes power from the measurements
(MW/MVAR) and frequency. Measurements are reported at a
rate of 20-60 times a second.
The architecture of PMU is shown in fig. 1, here, the
voltage or current in analog form is given to A/D converter
followed by anti-aliasing filter, these digital values are then
given to phasor microprocessor for computation of voltage or
current phasors. GPS receiver sends signal to phasor
microprocessor so that synchronized phasors are the output of
Modem. Phase-Locked Oscillator is used here to check the
frequency of voltage or current phasor and lock the frequency
for DFT calculation. The PMUs at different locations sends
the data, through communication channels, to Data
concentrators at RTUs and then to central utilities for advance
applications for power system control and protection, and/or
for other applications, as shown in fig. 2.
Fig.1. PMU Architecture
Fig.2. PMU utilization in a power system
The various features of PMUs are given below as follows:
• PMUs Measures 50/60 Hz AC waveforms (voltage and
current) typically at a rate of 48 samples per cycle.
• PMUs are then computed using DFT-like algorithms, and
time stamped with a GPS.
• The resultant time tagged PMUs can be transmitted to a local
or remote receiver at rates up to 60 samples per cycle.
The synchronized phasor measurement technology is
relatively new, and consequently several research groups
around the world are actively developing applications of this
technology. It seems clear that many of these applications can
be conveniently grouped as follows:
• Power System Real Time Monitoring
• Advanced network protection
• Advanced control schemes
III. PROBLEM FORMULATION
A. Topology Based Formulation Method
In this study, the OPP (optimal PMU placement) problem is
described to find a scheme with minimal PMUs and locations
to install such that the entire system becomes observable. The
rules which are followed to make the network observable-
• For PMU installed buses, voltage phasor and current
phasor of all its incident branches are known. These are
called as direct measurements.
• If voltage and current phasors at one end of a branch are
known then voltage phasor at the other end of the branch
can be obtained. These are called pseudo measurements.
• If voltage phasors of both ends of a branch are known
then the current phasor of this branch can be obtained
directly. These measurements are also called pseudo
measurements.
• For a zero-injection bus i in a N-bus system :
0 1
Where Yij is the ij-th element of admittance matrix of the
system and Vj is the voltage phasor of j-th bus.
Therefore, if there is a zero-injection bus without PMU, whose
incident branches current phasors are all known except one,
then the current phasor of the unknown one could be obtained
using KCL equations.
3. B. Integer Linear Method for PMU Placement
The OPP formulation based topological observability
method finds a minimal set of PMUs such that a bus must be
reached at least once by the PMUs. The optimal placement of
PMUs for an N bus system is formulated as follows [13]:
2
. .
… … … . 3
0,1
Where, N is total no. of system buses wk is weight factor
accounting to the cost of installed PMU at bus k, X is a binary
variable vector whose entries are defined as Eq. 4 and AX is a
vector function that its entries are non-zero if the
corresponding bus voltage is observable using the given
measurement set and according to observability rules
mentioned above, it ensure full network observability while
minimizing the total installation cost of the PMUs, otherwise
its entries are zero.
1
0
4
The entries in A are defined as follows:
,
1
1
0
5
And b is a vector whose entries are all ones as shown in
Eq. (6).
1
1..
1
6
The procedure for building the constraint equations will be
described for three possible cases where there are (1) no
conventional measurement, (2) flow measurements or (3) flow
measurements as well as injection measurements (they may be
zero injections or measured injections).
C. Voltage Stability Indicator
The voltage stability problem is mostly reactive power
related problem. So, it is necessary to identify the buses in
multi-bus power system that can provide reactive power to
support voltage magnitude of the bus. In multi-bus power
system, basically, all buses are divided into two categories
as Generator bus (PV bus and Slack bus) and Load bus (PQ
bus). Generator buses provide reactive power to maintain
voltage magnitude.
The power system can be represented as:
7
Subscript L means Load bus, and G means Generator bus.
The above equation can also be represented as,
8
When we consider the voltage at load node j, we know that,
9
or,
10
Multiplying at the both sides of the equation,
11
1
12
Here, ∑ , and
∑
The term V0j includes the contribution of all generators and
S shows the contribution of other loads at the node j.
13
The L index can be given as [14],
1 14
Thus, this value of index L indicates the proximity of
voltage collaps, including the contribution of all generators
and also the contributionof other loads.
The process for praposed methode, that is to search the
optimal location of PMUs for full observability of power
network using Linear integer programming technique and to
assess the voltage stability of system using L index, is given in
flow chart shown above in fig. 8.
4. Fig. 8. Flow chart for proposed case
IV. SOLUTION METHOD
A. PMU Placement
Case1: A system with no conventional measurements
In this case, the flow measurement and the zero injection
are ignored. In order to form the constraint set, the binary
connectivity matrix A, whose entries are defined below, will
be formed first:
,
1,
1,
0,
Matrix A can be directly obtained from the bus admittance
matrix by transforming its entries into binary form.
Fig. 3. 5-bus system
Consider the 5-bus system and its measurement
configuration shown above. Building the A matrix for the 5-
bus system of Fig (3) yields:
1 1 1 0 0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
15
The constraints for this case can be formed as:
1
1
1
1
1
16
The use of 1 in the right hand side of the inequality ensures
that at least one of the variables appearing in this will be non-
zero. The constraint f4 ≥ 1 implies that at least one PMU must
be placed at either one of buses 4 or 5 (or both) in order to
make bus 4 observable. Similarly, the second constraint f2 ≥ 1
indicates that at least one PMU should be installed at any one
of the buses 1, 2, or 4 in order to make bus 2 observable.
Case 2: A system with some flow measurements
This case considers the situation where some flow
measurements may be present. The modifications needed in
the formulation for this case will again be illustrated using the
5-bus example, where a flow measurement (P and Q) is added
for branch 1-2. In this case, the constraints for bus 1 and 2 will
have to be modified accordingly. The constraint equations
associated with the terminal buses of the measured branch can
be merged into a single constraint. So, for the example shown
above, the constraints for buses 1 and 2 are merged into a joint
constraint as follows,
1
1
_ 1
Which implies that if either one of the voltage phasors at
bus 1 or 2 is observable, the other one will be observable.
Applying this modification to the constraints for the shown
example of 5-bus system, the following set of final constraints
will be obtained:
_ 1
1
1
1
Here, the constraints corresponding to buses 1 and 2 are
merged into a single constraint.
Case 3: A system with both injection measurements and flow
measurements.
This case considers the most general situation where both
injection and flow measurements may be present, but not
enough to make the entire system observable. Injection
measurements whether they are zero injections or not, are
treated the same way.
Consider again the 5-bus system shown in Fig 3, where bus
4 is assumed to be a zero injection bus. In this case, it is easy
to see that if the phasor voltages at any three out of the four
buses 2, 3, 4 and 5 are known, then the fourth one can be
calculated using the Kirchhoff’s Current Law applied at bus 4
where the net injected current is known. Hence, the constraints
associated with these buses will have to be modified
accordingly as shown below:
5. _ · · 1
_ · · 1
_ · · 1
If two sets are A and B, where set A is a subset of set B,
Then A+B=B and A·B=A, where ‘.’ serves as the logical
“AND” and ‘+’ as logical “OR”. So, substituting the
expression for f3 in the expression for f1_new , we can write f1_new
as:
· ·
· ·
· · · · · ·
Proceeding with the simplifications, the product x1· f4· f5 is
eliminated because it is the subset of x1, which already exists
in the expression. Using similar reasoning, x3· f4 ·f5 and x4 ·f4
·f5 are also eliminated. Finally, the expression for f1_new
simplifies to the following:
_ 1
Applying similar simplification logic to all other
expressions will give modified constraints.
Note that the constraints corresponding to all other buses
will remain the same as given in equation (7). One exception
is the constraint for bus 4 where the injection is measured (or
known). This constraint will be eliminated from the constraint
set. The reason for removing the constraints associated with
injection buses is that their effects are indirectly taken into
account by the product terms augmented to the constraints
associated with the neighboring buses.
B. L-index
For the 5-bus system shown in fig. 3 there are two load
buses (bus 4 and bus 5) and three generator buses (bus 1, slack
bus, and bus 2 and bus 3). So for load bus 4, the value of L-
index can be examined using equation (14) as shown below,
Form equation (11),
Here, ∑
In which ∑ and,
. Thus, by using above equation L-indicator can be calculated
as,
1
V. TEST RESULTS
The proposed formulation has been tested on IEEE-14 bus
system. Binary integer programming under MATLAB has
been used to solve this problem expressed by equations (2)
and (3). The proposed integer linear programming algorithm
has been tested on different cases.
IEEE 14-bus system is shown in Figure (4) The Information
of the system and zero injections are given in the Table I. The
results without and with zero injection measurement are
displayed in Tables II.
Fig. 4. IEEE 14-bus system without PMUs
Fig. 5. IEEE 14-bus system with PMUs
TABLE I
SYSTEM INFORMATION OF IEEE BUS SYSTEMS
System Total
number of
branches
Total number
of zero
injection
Zero
injection
buses
IEEE 14-bus 20 1 7
TABLE II
SIMULATION RESULTS FOR THE 14-BUS SYSTEM WITH AND
WITHOUT CONSIDERING ZERO INJECTIONS
System Ignore zero injection Consider zero injection
Number
of PMUs
Location
of PMUs
Number
of PMUs
Location of
PMUs
IEEE
14-bus
4 2, 6, 7, 9 3 2, 6, 9
Effect of considering zero injections—
In this case, Integer Programming method expressed by
equations (2) and (3) has been used to solve the optimal PMU
placement Problem with and without considering zero
injections. Results are given in Table II.
The voltage stability assement methdology is tested on
IEEE-14 bus sytem. In this paper, L-index method discussed
in section III.C is used to check the voltage stability of
different load buses. The effect of loading at any load bus is
assessed at increasing the load on that bus it self , to its
6. neighbouring bus connect to the bus under c
to the other weak load buses using L-index
shown in fig. 6 and fig. 7.
Fig. 6. Voltage/L-index V/s loading at Bus
bus system
Fig. 7. Voltage/L-index V/s loading at Bus 4
system
As shown in fig. 6, value of L-Index t
voltage of Bus 14 is approaching to colla
increase in load at bus 14. The effect of incr
Bus 14 on L-index of a neighboring Bus 9 a
also shown in same fig. 6. The L-index of b
0.0677 to 0.2597 and that of bus 5, varies
0.0356. Variation in L-index at buses 4, 5
increase in load at bus 4 is demonstrated in
observed from this figure that the L index of
unity as the voltage of bus 4 approaches co
effect of increase in loading at Bus 4
neighboring Bus 5 and a far from Bus 13,
same fig. 7. The variation in L-Index of Bus
to 0.404 and of Bus 13 is from 0.032 to 0.063
Thus from above figures it can be conclud
of loading at any bus is more on its neigh
respect to a bus which is far from the bus und
As the effect of increase in load at bus 1
neighboring bus 9 with respect to a far bus 5
and the effect of increase in load at bus
neighbor bus 5 with respect to a far bus 13, sh
VI. CONCLUSION
This paper proposes a simple algori
placement of PMUs in power system for ful
network for voltage stability assessment. The
formulated using topology based algorithm
integer linear programming. Besides the pl
consideration and
x. The results are
s 14 for IEEE 14-
4 for IEEE 14-bus
tends to unity as
apse point due to
rease in loading at
and a far Bus 5, is
bus 9 varies from
s from 0.0197 to
5, and 13 due to
n fig.7. It can be
f bus 4 approaches
ollapse point. The
on L-index of
is also shown in
s 5 is from 0.0197
38.
ded that the effect
hboring bus with
der consideration.
4 is more on its
5, shown in fig 6,
4 is more on its
hown in fig. 7.
ithm of optimal
ll observability of
e OPP problem is
and solved using
lacement of mere
PMUs, this study also considers the
conventional measurements are pr
voltage stability assessment proble
index method and solved using MA
present case also accomplished the tw
to develop practical methods for dete
for PMUs with voltage stability ass
develop methods for implementation
Simulation results on IEEE-14 bus
the proposed placement method
assessment is satisfactorily prov
measurements with minimum numb
index to determine the stability of po
VII. REFEREN
[1] IEEE/CIGRE, Joint Task Force on S
“Definition and classification of power
Power Syst., vol. 19, no. 3, pp. 1387–14
[2] G. K. Morison, B. Gao, and P. Kundur,
static and dynamic approaches,” IEEE
pp. 1159–1171, Aug. 1993.
[3] Kundur P, “Power System Stability an
Engineering Series, McGraw-Hill, 1994
[4] Taylor C.W, “Power System Voltage
Engineering Series, McGraw-Hill, 1993
[5] A. G. Phadke, J. S. Thorp, and K. J.
Phasor Measurements”, IEEE Transact
No. 1, pp. 233- 241, February 1986.
[6] EPRI Final Rep., 1997 “Assessment o
Phasor Measurement Technology in Po
Eng.,
[7] A. G. Phadke, “Synchronized phasor m
IEEE Computer Applications in Power,
1993.
[8] L. Mili, T. Baldwin and R. Adapa, “Ph
Voltage Stability Analysis of Power Sy
Conference on Decision and Control, H
[9] T. L. Baldwin, L. Mili, M. B. Boisen,
Observability With Minimal Phasor M
Transactions on Power Systems, Vol. 8,
[10] Xu, B.; Abur, A.; “Observability analy
for systems with PMUs.” Proceedings
and Exposition, vol.2, pp: 943-946, 10-1
[11] J. Chen and A. Abur, “Placement o
Detection in State Estimation.” IEEE Tr
No. 4, Nov. 2006.
[12] B. Milosevic and M. Begovic, “N
Algorithm for Optimal Phasor Measur
On Power Systems, Bol. 18, No. 1, Feb.
[13] B. Gou, “Optimal placement of PMUs
IEEE Trans. Power Syst., vol. 23, no. 3,
[14] D. Thukaram and C.Vyjayanthi, “Relati
evaluation of network reactive powe
deregulated system”. IET Gener. Tran
1000-1019, Jun. 2009.
[15] Gou, B. “Generalized integer linear
optimal PMU placement” IEEE Tran
Aug. 2008.
[16] B. Singh, N.K. Sharma, A.N. Tiwari
“Applications of phasor measurement
system networks incorporated with FA
Journal of Engineering, Science and Te
82, 2011.
placement of PMUs when
esent in the system. The
em is formulated using L
ATLAB programming. The
wo objectives. First one is,
ermining optimal locations
sessment and second is to
n and to obtain test results.
test systems indicate that
d with voltage stability
vides observable system
ber of PMUs and, also, the
ower network.
NCES
Stability Terms and Definitions,
r system stability,” IEEE Trans.
401, Aug. 2004.
, “Voltage stability analysis using
Trans. Power Syst., vol. 8, no. 3,
d Control”, EPRI Power System
4. ISBN 0-07-035958-X.
Stability”, EPRI Power System
3. ISBN 0-07-063164-0.G. K
Karimi, “State Estimation with
tions on Power Systems, Vol. 1,
of Applications and Benefits of
ower Systems,” GE Power Syst.
measurements in power systems”,
, Vol. 6, Issue 2, pp. 10-15, April
asor Measurement Placement for
ystems.” Proceedings of the 29th
onolulu, Hawaii, Dec. 1990.
, and R. Adapa, “Power System
Measurement Placement”, IEEE
, No. 2, pp. 707-715, May 1993.
ysis and measurement placement
of 2004 IEEE PES Conference
13 Oct. 2004..
of PMUs to Enable Bad Data
rans. on Power Systems, Vol. 21,
Nondominated Sorting Genetic
rement Placement.” IEEE Trans.
. 2003.
by integer linear programming,”
, pp. 1525–1526, Aug. 2008.
ive electrical distance concept for
er and loss contributions in a
nsm. Distrib., vol. 3, Iss. 11, pp.
programming formulation for
s. Power Syst., 23: 1099-1104,
, K.S. Verma, and S.N. Singh,
units (PMUs) in electric power
ACTS controllers.” International
echnology Vol. 3, No. 3, pp. 64-