Line Flow Measurements Research Articles

Load Oscillating Attacks of Smart Grids: Vulnerability Analysis

We investigate the vulnerability of a power transmission grid to load oscillation attacks. We demonstrate that an adversary with a capability to oscillate a small fraction of load and monitor some tie line flows can launch a successful load oscillation attack to destabilize the grid. The adversary is assumed to be able to compromise smart meters at a subset of load buses and control their switches. In the reconnaissance stage of the proposed attack, the adversary estimates the line flow sensitivity factors (LFSFs) associated with the monitored tie lines by perturbing a small amount of load at compromised buses and observing how the monitored line flow changes. The learned LFSF values are used to select a target line and optimize the oscillation attack magnitudes at the compromised load buses to cause the target line to trip. In the execution stage, the oscillation attack frequency is adjusted in real time, based on the monitored target line flow measurements, in order to maximize the attack impact under the system condition at the attack time. We experimentally demonstrate that the proposed attack strategy can result in a much more severe consequence than benchmark oscillation attacks, using the COSMIC time-domain simulator with two test cases, the IEEE RTS-96 and Polish 2383-Bus Systems. The proposed attack strategy succeeded in causing a full blackout by oscillating only 8% of the load in the IEEE RTS-96 test system, and 1.7% of the load in the Polish test system.

On the minimal set of controllers and sensors for linear power flow

We consider a linear power flow model with interval-bounded nodal power injections and limited line power flows. We determine the minimal number of power injections to control based on a minimal set of measurements, such that the overall system is feasible for all assignments of the non-controlled power injections. For the important case where the possible measurements are the nodal power injections, we show that the problem can be solved efficiently as a mixed-integer linear program (MILP). When also line power flows are considered as potential measurements, we derive an iterative, greedy algorithm that provides a feasible, but potentially conservative solution. We apply the developed algorithms to both a simple microgrid and a modified version of the IEEE 118 bus test power system. We show that in both cases a sparse solution in terms of the number of required controllers and measurements can be obtained. Moreover, the number of required measurements can be reduced significantly if line flow measurements are considered additionally to nodal power injections.

Joint Estimation of Operational Topology and Outages for Unbalanced Power Distribution Systems

An electric power distribution system is operated in several distinct radial topologies by opening and closing of system's sectionalizing and tie switches. The estimation of the system's current operational topology is a precursor to implementing any optimal control actions (during normal operation) or restorative actions (during outage condition). This paper presents a mathematical programming approach to estimate the operational topology of a three-phase unbalanced power distribution system under both outage and normal operating conditions. Specifically, a minimum weighted least absolute value estimator is proposed that uses the line flow measurements, historical/forecasted load data, and ping measurements and solves a mixed-integer linear program (MILP) to estimate the operational topology and any outaged sections simultaneously. We thoroughly validate the accuracy of the proposed approach using IEEE 123-bus and a 1069-bus three-phase multi-feeder test system with the help of numerous simulations. It is observed that the approach performs well even at high percentages of measurement errors.

A Novel Distributed Control Strategy for Optimal Dispatch of Isolated Microgrids Considering Congestion

This paper presents a novel distributed control strategy for frequency control, congestion management, and optimal dispatch (OD) in isolated microgrids. The proposed strategy drives the distributed generators (DGs) within the microgrid to a dispatch that complies with the Karush–Kuhn–Tucker (KKT) conditions of a linear optimal power flow (OPF) formulation. The controller relies on local power and frequency measurements, information from neighboring DGs, and line-flow measurements transmitted through a communications network. Extensive simulations show a good performance of the controller against sudden changes in the load, congested lines and availability of DGs in the microgrid, and the ability to successfully drive the system to an optimal economic operation.

Outage Detection Using Load and Line Flow Measurements in Power Distribution Systems

An outage detection framework for power distribution networks is proposed. Given the tree structure of a distribution system, a detection method is developed combining the use of realtime power flow measurements on the edges of the tree with load forecasts at the nodes of the tree. The maximum likelihood detection decision for an arbitrary number of outages is shown to be efficiently computable due to decoupling across local areas determined by the sensor locations. To minimize the maximum missed detection probability, the optimal sensor placement is efficiently computed as well. Finally, a set of case studies is conducted using feeder data from the Pacific Northwest National Laboratories. It is shown that 10% mean detection error probability can be achieved by a sensor density of 30% for a typical feeder with the proposed optimal sensor placement and outage detection methods.

Overview of State Estimation Technique for Power System Control

The state estimator processes the information available and produces the best possible estimate of the true state of the system. .It is a digital processing scheme which provides a real-time data base for many of the central control and dispatch functions in a power system. The real-time data are processed by state estimator, a computer program which calculates voltage magnitudes and relative phase angles of the system buses. While the state estimator gives result similar to those available from conventional power-flow program, the input data and calculation procedure are quite different. Bus injections along with line flow measurements form the measurement vector in the state estimator in order to evaluate the final states of the power system. Test results without and with measurement noises have been presented. Estimator is also capable of identifying the bad data present in the measurement vector.

Observability enhancement by optimal PMU placement considering random power system outages

This paper enhances the observability of power networks by taking into consideration random component outages. The architecture of wide-area measurement system (WAMS) is analyzed in order to identify components that would affect the network observability. An iterative framework is devised to calculate a bus index in power networks equipped with phasor measurement units (PMUs) and conventional measurements. The average of bus indices represents a system index which provides an overall insight on the power network observability. The system index is utilized as a criterion to distinguish among multiple optimal PMU placements. Conventional bus injection and line flow measurements and the effect of zero-injection buses are considered in the proposed model. The numerical analyses are carried out for the proposed model and the results are discussed in detail.

A new decoupling strategy for power system state estimation

This paper presents a new decoupling strategy by strengthening P– δ and Q– V relationships based on line flow and voltage magnitude measurements in order to obtain a reliable convergence and higher computational speed. The real and reactive set of measurements are combined using simple multiplying factors such that the modified set is decoupled into two set of equations without making any assumption on r/ x ratios. The resulting Jacobian matrices that contain only line parameters are sparse and constant. The technique is applied on three test systems and is solved by WLS and WLAV methods to illustrate its superior performance.

A Reliable and Fast-decoupled Weighted Least Square State Estimation for Power Systems

This article presents a new, fast-decoupled WLS SE technique based on modified line flow and voltage magnitude measurements in rectangular coordinates. The measurement equations are rotated by appropriate line admittance angle for zeroing the off-diagonal blocks of the Jacobian matrix and decoupling the SE problem into two sub-problems without making any assumptions on voltage magnitudes, angles, and r/x ratios. The approach is simple and uses constant sub-Jacobian and gain matrices that need to be factorized only once and is solved similar to the FDSE technique. Test results of the PM on five test systems indicate that the PM is efficient, reliable, accurate, and suitable for on-line applications.

Load profile estimation in electric transmission networks using independent component analysis

It is important to estimate electric loads profiles in the deregulated environment where competing entities need to assess the load demands based on partial knowledge of the system. Independent component analysis (ICA) is a statistical technique used to separate linear mixtures of statistical independent source signals by maximization of negentropy. In this paper, we apply ICA to estimate load profiles using only a small set of active line flow measurements without prior knowledge of the electric network model parameters or topology. A filtering based preprocessing technique is used to ensure statistical independence of load components. The influence of measurement noise and nonlinearity of the power flow model are also investigated. The proposed approach is demonstrated for a five-bus system as well as the IEEE 30-bus system.

Rheological properties of suspension poly(vinyl chloride) formulations in extrusion dies

Effects of formulation and sample preparations on measured rheological properties relevant for constitutive modelling of die flow in poly(vinyl chloride) extrusion are reported. The effects are discussed in terms of morphological changes. For some formulations, in line flow measurements on an extruder give viscosity values different from capillary measurements. Numerical simulations have been performed in order to separate non-isothermal and viscoelastic effects in the extrusion experiments as well as self-consistency between constitutive models and measurements. Die swell values in agreement with observations were obtained.

A new approach to dynamic state estimation of power systems

This paper presents a new method of dynamic state estimation (DSE) based on Kalman filter, rather than extended Kalman filter. The complex line flow measurements are used to obtain the complex element voltages of the power system, which are then treated as the effective system measurements at the filtering stage. Since, the complex element voltages are linearly related to the complex bus voltages, use of the Kalman filter provides more accurate and faster estimation of the unknown complex bus voltages. At the prediction stage, Holt's two parameter exponential smoothing technique has been adopted for its reliable performance. The proposed new dynamic state estimation (NDSE) has been tested on 5-bus, 14-bus and 30-bus test systems and the numerical results are presented. The performance of the proposed NDSE has been compared with the existing DSE methods for various simulated test conditions. The error analysis of the methods studied reveals the superiority of the proposed NDSE method particularly under sudden change in operating conditions of the system.

Load modeling for distribution circuit state estimation

Due to the limited availability of telemetered data on distribution circuits, an integral part of any practical distribution circuit state estimator is a load modeling procedure that provides estimates of load demands at all circuit nodes. Traditional load modeling techniques used for distribution power flows are designed for power system peak studies, and are not suitable for providing real-time statistical load estimates. This paper presents a real-time load modeling technique which incorporates the use of customer class curves and provides a measure of the uncertainty (statistics) in the estimates. It also incorporates the possibility of multiple line flow measurements and makes use of customer billing information. The load modeling technique is combined with a probabilistic distribution circuit state estimation algorithm. Results of the combined load modeling and state estimation algorithm are provided on an actual 934-bus distribution circuit illustrating its feasibility.

New algorithm for diakoptical static state estimation

A new and efficient diakoptical static state estimation algorithm has been proposed. The main objective of developing this algorithm was to obtain an estimator with an improved performance in terms of robustness, accuracy, online CPU time, core memory occupation, intercomputer data transfer, scope for sparsity exploitation, and localisation of bad data effect. In the developed method, a system has been divided into a number of subsystems to take advantage of low dimensionality, sparsity, fast decoupled estimation and parallel processing. The co-ordination among the subsystem level estimators has been done, in each iteration, to improve accuracy of estimates at the cost of little CPU time and nominal data transfer, by the transformation of the tie line flow measurements into voltage drop between subsystems' slack busbar, and the involvement of a small-sized, sparse and constant coefficient matrix with real elements. Saving in CPU time and convergence have also been enhanced by making each iteration of the diakoptical estimator unified, within which no more iterations, either at the subsystem level or at the coordinating level, have been involved. The results of a comprehensive comparative study of the performance of the developed method against the integrated fast decoupled method have also been presented.

A line flow only power system state estimator

A power system state estimation algorithm using line flow measurements only is presented. The algorithm estimates the state of only one node at a time using measurements in the electrical vicinity of that node. Before any measurement is used, it is passed to a subroutine that tests for bad data. Thousands of tests were performed on the IEEE 14-bus and the IEEE 30-bus systems; results are compared with the line flow only (LFO) method. It is concluded that the proposed method is much faster than the LFO method and it can identify almost all bad data having an error greater than four times the maximum expected normal error.

Transformer Tap Position Estimation

The estimation of voltage transformer tap position is a desirable feature that can be appended to most state estimation algorithms. The primary requirement to estimate transformer tap position is the availability of a three-phase reactive-power measurement through either the fixed or tap side of the transformer. These ``measured'' flows can also be calculated, depending on the availability of reactive injection and reactive transmission line flow measurements around the fixed or tap side buses. The gain matrix of the state estimator is not modified so only the tables used to calculate real and reactive residual mismatch need to be updated during the state estimator solution. The computational cost of including transformer tap position estimation is extra iterations of the state estimator. A number of tests were conducted using the IEEE 118 bus system as a model. The results of one of these tests are presented along with the algorithm to modify the tap positions while the State Estimator solution proceeds. A practical stopping criterion for the algorithm is also presented. The extension of the algorithm to line parameter estimation is also discussed in the Appendix.

Transformer Tap Position Estimation

The estimation of voltage transformer tap position is a desirable feature that can be appended to most State Estimation algorithms. The primary requirement to estimate transformer tap position is the availability of a three phase reactive power measurement through either the fixed or tap side of the transformer. These "measured" flows can also be calculated, depending on the availability of reactive injection and reactive transmission line flow measurements around the fixed or tap side buses. The gain matrix of the State Estimator is not modified so only the tables used to calculate real and reactive residual mismatch need to be updated during the State Estimator solution. The computational cost of including transformer tap position estimationis extra iterations of the State Estimator.

The Solution of Ill-Conditioned Power System State Estimation Problems Via the Method of Peters and Wilkinson

Power system state estimation is usually formulated as a weighted least-squares problem and solved iteratively by the normal equations method. The normal equations solution method is well-known to exhibit a tendency to be numerically unstable on some networks. A manifestation of this numerical instability is an ill-conditioned set of linear equations that are to be solved at each iterative step. Recent papers have presented orthogonal factorization methods as remedies for this instability. Experience shows, however, that these methods tend to suffer from excessive fill-in when confronted with networks that have a high measurement redundancy. The folklore of power-system state estimation says that large numbers of bus injection measurements (as opposed to line flow measurements) tend to aggrevate the instability, no explanation for this observation, however, has appeared in the literature. This paper presents an analysis of the sources of ill-conditioning in the power system state estimation problem and offers an alternative solution method, due to Peters and Wilkinson, that overcomes this ill-conditioning without losing matrix sparsity.

The Solution of Ill-Conditioned Power System State Estimation Problems Via the Method of Peters and Wilkinson

Power system state estimation is usually formulated as a weighted least-squares problem and solved iterativeLy by the normal equations method. The normal equations solution method is well-known to exhibit a tendency to be numerically unstable on some networks. A manifestation of this numerical instability is an ill-conditioned set of linear equations that are to be solved at each iterative step. Recent papers have presented orthogonal factorization methods as remedies for this instability. Experience shows, however, that these methods tend to suffer from excessive fill-in when confronted with networks that have a high measurement redundancy. The folklore of power-system state estimation says that large numbers of bus injection measurements (as opposed to line fLow measurements) tend to aggrevate the instability; no explanation for this observation, however, has appeared in the literature. This paper presents an analysis of the sources of ill-conditioning in the power system state estimation problem and offers an alternative solution method, due to Peters and Wilkinson, that overcomes this ill-conditioning without losing matrix sparsity.

State Estimation of Interconnected HVDC/AC Systems

This paper describes efficient methods for converting redundant meter readings and other available information into the static state of the dc portion of an integrated multiterminal HVdc/ac system. Data processing algorithms which use line flow measurements, bus injection measurements and combinations of measurement types are presented. Some initial simulation results for a specific system are given, and interfacing between dc and ac state estimators is discussed.