State estimation in active distribution networks using convex optimization

Active distribution networks present high penetration of distributed resources that require real-time monitoring. These networks are equipped with a supervision, control, and data acquisition (SCADA) system, which integrates information supplied by advanced measurement equipment. This thesis presents a state estimation model as an integral part of the SCADA system. Nevertheless, the state estimator is non-convex. Therefore, the application of conical approximations such as second-order cone and semidefinite programming proposes to guarantee a global optimum and uniqueness of the solution. The model includes direct angle measurement through meters and micro-phasor measurement units micro-pmu.The model evaluates different test systems in the international scientific literature. These quantified by stochastic metrics the difference between the estimated and actual value as root mean square error or the confidence level used to check for incorrect data and system reliability. In addition, the behavior of the micro-pmu investigates with total voltage error. These results show a high efficiency guaranteeing a global optimum and precision when using cvxPy in Python.Las redes de distribución activas presentan alta penetración de recursos distribuidos que requieren supervisión en tiempo real. Estas redes están equipadas con un sistema supervisión, control y adquisición de datos (SCADA), que integra información suministrada por los equipos de medición avanzada. Este trabajo presenta un modelo de estimación de estado como parte integral del sistema SCADA. No obstante, el estimador de estado es no convexo. Por ende, se propone la aplicación de aproximaciones cónicas como Second order cone y Semidefinite programming para garantizar un óptimo global y unicidad de la solución. El modelo incluye medición directa del ángulo gracias al uso de medidores inteligentes y micro unidades de medición fasorial micro-pmu. El modelo es evaluado en diferentes sistemas de prueba de la literatura científica internacional. Estos son cuantificados por métricas estocásticas que entregan la diferencia entre el valor estimado y el real como root mean square error o el nivel de confianza empleado para verificar datos incorrectos y la confiabilidad del sistema. Además, el comportamiento de las micro-pmu se indaga con el total voltaje error. Estos resultados muestran una alta eficiencia garantizando un óptimo global y precisión al emplear cvxPy en Python.MaestríaMagíster en Ingeniería EléctricaContents 1 Introduction 10 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2 Active distribution networks (ADNs) . . . . . . . . . . . . . . . . 12 1.3 The state estimation problem . . . . . . . . . . . . . . . . . . . . 14 1.4 Convex optimization-based Methods . . . . . . . . . . . . . . . . 15 1.5 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.6 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2 The state estimation problem in ADNs 19 2.1 Overview of the classic state estimation problem . . . . . . . . . 19 2.2 The state estimation as an optimization problem . . . . . . . . . 22 2.3 Available measurements in ADNs . . . . . . . . . . . . . . . . . . 24 2.4 SCADA systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.5 Phasor measurement units . . . . . . . . . . . . . . . . . . . . . . 27 2.6 Challenges in power distribution networks . . . . . . . . . . . . . 29 3 Convex model for the state estimation of ADNs 32 3.1 Convex optimization for state estimation . . . . . . . . . . . . . . 32 3.2 Convex cones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.3 Second-order cone programming . . . . . . . . . . . . . . . . . . 37 3.4 Application of SOC to the state estimation . . . . . . . . . . . . 38 3.5 Cone of Semidefinite matrices . . . . . . . . . . . . . . . . . . . . 40 6 Maria Valeria Fajardo Latorre Maria Valeria Fajardo Latorre 3.6 Application of SDP to the state estimation problem . . . . . . . 41 3.7 Stochastic metrics . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.7.1 Total vector error . . . . . . . . . . . . . . . . . . . . . . . 42 3.7.2 Root mean square error . . . . . . . . . . . . . . . . . . . 43 3.7.3 Confidence level criterion . . . . . . . . . . . . . . . . . . 43 4 Results 45 4.1 Test systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.2 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.3 Results for state estimation in different IEEE . . . . . . . . . . . 46 4.4 Confidence level criterion . . . . . . . . . . . . . . . . . . . . . . 54 4.5 Criterion of the voltage phasors . . . . . . . . . . . . . . . . . . . 55 4.6 Root-mean-square error . . . . . . . . . . . . . . . . . . . . . . . 56 4.7 Remarks in regard with the existing literature . . . . . . . . . . . 58 5 Conclusions 6

Three-Phase State Estimation for Distribution-Grid Analytics

Power-distribution grids consist of assets such as transformers, cables, and switches, of which the proper utilization is essential for the provision of a secure and reliable power supply to end customers. Distribution-system operators (DSOs) are responsible for the operation and maintenance of these assets. Due to the increased use of renewable sources such as wind and solar, grid assets are prone to operation conditions outside safe boundaries, such as overloading, large voltage unbalance, and a rise in voltage. At present, distribution grids are poorly monitored by DSOs, and the above-mentioned problems may thereby go unnoticed until the failure of a critical asset occurs. The deployment of smart meters in distribution grids has enabled measurements of grid variables such as power, current, and voltage. However, their measurements are used only for billing purposes, and not for monitoring and improving the operating condition of distribution grids. In this paper, a state-estimation algorithm is proposed that utilizes smart-meter data for offline analysis, and estimates the loading of grid assets and power losses. Single- and three-phase state-estimation algorithms are compared through simulation studies on a real-life low-voltage distribution grid using measured smart-meter data. The three-phase state-estimation algorithm based on the nonlinear weighted least-squares method was found to be more accurate in estimating cable loading and line power losses. The proposed method is useful for DSOs to analyze power flows in their distribution grids and take necessary actions such as grid upgrades or the rerouting of power flows

Identification of the phase connectivity in distribution systems through constrained least squares and confidence-based sequential assignment

This paper addresses the customer-phase identification problem in three-phase distribution grids including three-phase customers characterized by aggregated energy measurements. The proposed technique first solves a relaxed problem, in which the binary nature of the variables is ignored, which leads to a constrained, least-squares estimation, using as inputs the active and reactive energy readings provided by the smart meters, along with the energy delivered by each phase at the head of the feeder. With the estimated values of the decision variables, and their corresponding variances, a confidence-based selection technique is then applied for the sequential assignment of the customer with the highest joint probability of being connected to one of the three phases but not to the other two. The performance of the proposed procedure is assessed with five different scenarios in terms of accuracy for increasing number of loads and measurement errors. The robustness of the algorithm is additionally tested in the presence of model errors, and its performance is compared to that of existing methods.Project Solar to Vehicle (S2V) INV-3-2021-I-038Research project HySGrid+ CER-2019101

High impedance fault modeling and location for transmission line✰

A fault in a power system generates economic losses, security problems, social problems and can even take human lives. Therefore, it is necessary to have an efficient fault location strategy to reduce the exposure time and recurrence of the fault. This paper presents an impedance-based method to estimate the fault location in transmission lines. The mathematical formulation considers the distributed parameters transmission line model for the estimation of the fault distance, and it is obtained by the application of Gauss-Newton method. Said method considers available voltage and current measurements at both terminals of the transmission line as well as the line parameters. Moreover, the method can be used for locating high and low impedance faults. Additionally, it is proposed an adjustable HIF model to validate its performance, which allows to generate synthetic high impedance faults by setting specific features of a HIF from simple input parameters. The error in fault location accuracy is under 0.1% for more than 90% of the performance test cases. The easy implementation of this method and encouraging test results indicate its potential for real-life applications. © 202

Temporary Load Shedding - Optimization of power distribution system using load shedding Techniques

In today’s world, electrical energy is a necessity. The dependency on electricity is increasing day by day which caused the system to work under a stress state close to stability limits and disturbances. An efficient power system supplying electrical energy must be reliable, stable, secure, and reasonable to meet consumer needs. The power demand depends on several factors and weather is one of the main in them. The thesis is done with the cooperation of Arva As. for the Tromsøya region in northern Norway. In Northern Norway, during the winter season, the temperature falls to -20˚C which eventually causes the rise in demand for electricity to meet the heating needs. The heating of households plays a big role in increasing demand. To avoid contingency and keep the distribution grid stable during the winter season a temporary load shedding scheme has been proposed by using the load curves and grid model that was analyzed through power flow analysis. It includes procedures for detection of voltage stability on buses with voltage stability indexes and plans to temporarily shut the heating system and sources to avoid the stress on the grid in peak hours with available communication possibilities

Bridging Machine Learning for Smart Grid Applications

This dissertation proposes to develop, leverage, and apply machine learning algorithms on various smart grid applications including state estimation, false data injection attack detection, and reliability evaluation. The dissertation is divided into four parts as follows.. Part I: Power system state estimation (PSSE). The PSSE is commonly formulated as a weighted least-square (WLS) algorithm and solved using iterative methods such as Gauss-Newton methods. However, iterative methods have become more sensitive to system operating conditions than ever before due to the deployment of intermittent renewable energy sources, zero-emission technologies (e.g., electric vehicles), and demand response programs. Efficient approaches for PSSE are required to avoid pitfalls of the WLS-based PSSE computations for accurate prediction of operating conditions. The first part of this dissertation develops a data-driven real-time PSSE using a deep ensemble learning algorithm. In the proposed approach, the ensemble learning setup is formulated with dense residual neural networks as base-learners and a multivariate-linear regressor as a meta-learner. Historical measurements and states are utilized to train and test the model. The trained model can be used in real-time to estimate power system states (voltage magnitudes and phase angles) using real-time measurements. Most of current data-driven PSSE methods assume the availability of a complete set of measurements, which may not be the case in real power system data acquisition. This work adopts multivariate linear regression to forecast system states for instants of missing measurements to assist the proposed PSSE technique. Case studies are performed on various IEEE standard benchmark systems to validate the proposed approach. Part II: Cyber-attacks on Voltage Regulation. Several wired and wireless advanced communication technologies have been used for coordinated voltage regulation schemes in distribution systems. These technologies have been employed to both receive voltage measurements from field sensors and transmit control settings to voltage regulating devices (VRDs). Communication networks for voltage regulation can be susceptible to data falsification attacks, which can lead to voltage instability. In this context, an attacker can alter multiple field measurements in a coordinated manner to disturb voltage control algorithms. The second part of this dissertation develops a machine learning-based two-stage approach to detect, locate, and distinguish coordinated data falsification attacks on control systems of coordinated voltage regulation schemes in distribution systems with distributed generators. In the first stage (regression), historical voltage measurements along with current meteorological data (solar irradiance and ambient temperature) are provided to random forest regressor to forecast voltage magnitudes of a given current state. In the second stage, a logistic regression compares the forecasted voltage with the measured voltage (used to set VRDs) to detect, locate, and distinguish coordinated data falsification attacks in real-time. The proposed approach is validated through several case studies on a 240-node real distribution system (based in the USA) and the standard IEEE 123-node benchmark distribution system.Part III: Cyber-attacks on Distributed Generators. Part III of the dissertation proposes a deep learning-based multi-label classification approach to detect coordinated and simultaneously launched data falsification attacks on a large number of distributed generators (DGs). The proposed approach is developed to detect power output manipulation and falsification attacks on DGs including additive attacks, deductive attacks, and combination of additive and deductive attacks (attackers use the combination of additive and deductive attacks to camouflage their attacks). The proposed approach is demonstrated on several systems including the 240-node and IEEE 123-node distribution test system. Part IV: Composite System Reliability Evaluation. Traditional composite system reliability evaluation is computationally demanding and may become inapplicable to large integrated power grids due to the requirements of repetitively solving optimal power flow (OPF) for a large number of system states. Machine learning-based approaches have been used to avoid solving OPF in composite system reliability evaluation except in the training stage. However, current approaches have been utilized only to classify system states into success and failure states (i.e., up or down). In other words, they can be used to evaluate power system probability and frequency reliability indices, but they cannot be used to evaluate power and energy reliability indices unless OPF is solved for each failure state to determine minimum load curtailments. In the fourth part of this dissertation, a convolutional neural network (CNN)-based regression approach is proposed to determine the minimum amount of load curtailments of sampled states without solving OPF. Unavoidable load curtailments due to failures are then used to evaluate power and energy indices (e.g., expected demand not supplied) as well as to evaluate the probability and frequency indices. The proposed approach is applied on several systems including the IEEE Reliability Test System and Saskatchewan Power Corporation in Canada