Power Distribution System State Estimation
2: Electrical and Computer Engineering Department, EESCUniversity of São Paulo, Brazil
State estimation is a key function for realtime operation and control of electrical power systems since its role is to provide a complete, coherent, and reliable network realtime model used to set up other realtime operation and control functions. In recent years it has extended its applications to monitoring active distribution networks with distributed energy resources. The inputs of a conventional state estimator are a redundant collection of realtime measurement, load and production forecasts and a mathematical model that relates these measurements to the complex nodal voltages, which are taken as the state variables of the system. The goal of state estimation is to adjust models so that they are closer to observed values and deliver better forecasts. In power systems, this is key to maintaining power quality and operating generation and storage units well.
This book, written by international authors from industry and universities, systematically addresses state estimation in power distribution systems. Chapters convey techniques for distribution system state estimation, such as classical methods, threephase network modelling, power flow calculation, fast decoupled approaches and their new application via complex per unit normalization, the Bayesian method, and multiarea state estimation. Also, synchronized and nonsynchronized measurements with different sample rates, realtime monitoring, and practical experiences of distribution state estimation are covered.
Researchers involved with electrical power and electrical distribution systems, professionals working in utilities, advanced students and PhD students will find this work essential reading.
 Book DOI: 10.1049/PBPO183E
 Chapter DOI: 10.1049/PBPO183E
 ISBN: 9781839532016
 eISBN: 9781839532023
 Page count: 387
 Format: PDF

Front Matter
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1 Introduction
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Recent developments in new electrical equipment and devices, associated with socalled smart grids, are changing the paradigms of operation and control of electrical power systems. If, on the one hand, smart grids concepts and technologies have brought innumerous advantages and opportunities, creating new data sources at unprecedented volume (e.g., phasor measurement units, intelligent electronic devices, and smart meters), on the other hand, it has increased the complexity of the power system in all voltage levels (due to intermittent dispersed energy resources, sensitive loads, new storage technologies, and growing electric vehicles fleet). The distribution system is clearly the segment of the electrical system most affected by the evolution of smart grids, driving the search for new tools and methodologies capable of meeting the needs of the sector.

2 Realtime monitoring of distribution systems: Brazilian experience
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The objective of this chapter is to share the valuable experiences of COPEL, a Brazilian electricity utility, by providing new insights and the challenges faced during the development of the Project of Research and Development (R&D) of Brazilian Electricity Regulatory Agency number 28660271/2013.
This R&D project resulted in the development and implementation of a (i) service restoration software (SRS) and (ii) realtime monitoring tool (RTMT) to provide better quality load values to characterize the prefault steadystate condition for the execution of that SRS.
The focus of this chapter is the RTMT which will be presented in detail together with infield verification in a single distribution feeder of Londrina City, in Brazil, to evaluate the accuracy of the estimated load. This feeder is responsible for the energy supply of 7,305 consumers, with 560 buses (192 with distribution transformers) and 559 branches. Its nominal voltage is 13.8 kV. Also, the application of the developed RTMT in providing the load values for the solution of the service restoration problem in a real large distribution system (DS) is presented. For this application, the processing time required by each step of the RTMT will be presented to show that it satisfies the performance requirements on practically sized DSs. Finally, initial results of two further applications of the RTMT are presented, the first into the DS state estimation problem and the second along with a load nowcasting method.

3 Practical experiences of distribution state estimation in real life
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Distribution and transmission networks are fundamentally different (their purpose, concept, amount of realtime data, security, dimensions, and degree of automation). Accordingly, it is natural that an efficient distribution state estimation (DSE) model and procedure for its solution follow the characteristics of the distribution network (DN). Only such specialized model and procedure for its solution, integrated into the industrialgrade product, can be robust, fast, and their results are accurate enough for application in various distribution power utilities (DPUs) worldwide.
This chapter presents the experiences of reallife applications of the specialized DSE firmly integrated into the advanced distribution management system (ADMS). These experiences have been gathered over the years by realizing a large number of Schneider Electric projects worldwide.

4 Threephase network model for steadystate analysis of distribution systems
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The electrical network model is the core of any computational analysis of power systems. It captures the physical phenomena through mathematical relations among different electrical quantities of the power system. The level of details of such models is a fundamental step to ensure adequate accuracy in the analysis of different matters by power systems engineers.
This chapter introduces the basic concepts regarding threephase network models for distribution system steadystate analysis, emphasizing a state estimation perspective. A general twoport branch model is conceived for each component of the distribution system. Also, general equations to calculate currents and power flows in the network as well as their derivatives are presented. Different types of equipment are exemplified along with the respective particularities of their admittance matrix models, from the classical distribution system components to the novels of modern power grids, such as distributed generation (DG), energy storage devices, electric vehicles, and flexible power electronic converters.

5 Currentbased power flow calculation methods for distribution systems
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This chapter presents three currentbased power flow calculation methods devoted to distribution systems, namely, the branch currentbased load flow (BCBLF), the admittance matrixbased load flow (AMBLF) and the classical BFSLF. Due to similarities, the BCBLF and the AMBLF are presented simultaneously. The formulations presented are devoted to threephase radial distribution systems; however, the AMBLF can be successfully applied to meshed distribution systems exactly as it is presented. After describing the basic theoretical aspects of the methods, detailed results based on small size distribution networks are presented and discussed.

6 Classical methods applied to distribution system state estimation
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This chapter presents twostate estimation approaches devoted to distribution systems, namely, the Branch CurrentBased State Estimator (BCBSE) and the Admittance MatrixBased State Estimator (AMBSE). The formulation presented is devoted to distribution networks and, therefore, threephase network modelling is adopted. After a detailed description of the methods, the results of simulations performed in both approaches are presented and discussed.

7 Fastdecoupled power flow method for active distribution systems
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Distributed generation (DG) brought significant changes to the planning and operation of distribution systems (DS). The presence of DG, allied with advanced technologies of measurement and control related to Smart Grid concepts, converts the DS into active networks, subject to bidirectional power flows. As a consequence, aiming to improve the efficiency and reliability of the power supply, active networks begin to operate more often as closedloop circuits or even as fully meshed topologies.
This context points to the need to update traditional computational methods related to DS analysis to incorporate the consequences of technological advances. At the same time, such updated methods must still consider intrinsic invariable characteristics of the distribution networks, like the lowvoltage levels and the low X/R ratio of DS lines.
This chapter presents a fastdecoupled power flow (FDPF) formulation combined with the complex per unit (cpu) normalization technique that extends the wellknown efficiency of FDPF algorithm to active distribution system analysis. The formulation bases of power flow calculation and cpu technique are fully described. Simulation results with DS under distinct operational conditions are presented to demonstrate the effectiveness and versatility of the cpubased FDPF approach.

8 Fastdecoupled distribution system state estimation
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This chapter describes a cpubased DSSE methodology. The alternative approach uses the cpu system to efficiently extend the fastdecoupled approaches, originally developed to TS, so as to accommodate the distribution network characteristics.
It also includes the bussection model for the network, where strategically located switches/breakers (switchable branches) or suspect regions/substations can be explicitly represented. This allows commonly used maneuvers in DS system be easily handled at the same time that contributes to the topology error processing algorithms.
Enabling the use of decoupling techniques for SD offers a series of advantages involving modern DS, whose advances and needs move toward the characteristics previously exclusive to TS, such as active nature, advanced measurement infrastructure, meshed topology, and so on.
Finally, the decoupled formulation is especially important to reduce the numerical burden associated with the dimension of the DSSE, where a high number of nodes and measurements (a single feeder may contain thousands of buses) needs to be handled in realtime operation.

9 Bayesian approach for distribution system state estimation
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When dealing with the new Smart Grid scenario, it is clear that the distribution grid will play a fundamental role. Indeed, the most important changes in the electric system will probably concern the distribution network [1], which was traditionally considered mainly a passive infrastructure but, in the last decade, underwent strong transformations, pushed by market liberalisation and technological evolution. Distributed generation (DG) has already become one of the key factors of the new paradigm, and thus distribution grids can no longer be conceived only as a mean to transfer energy from transmission network to the users. Possible bidirectional flows must be considered by every new approach to network management and control, which will rely on the contribution from all the different and fast changing players interfaced with the network.

10 Multiarea state estimation for distribution systems
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The large scale of real distribution systems makes difficult the development of computational tools for realtime monitoring of these systems. Thus, the decomposition of distribution networks into smaller subnetworks emerges as an alternative for this development, embracing the use of smaller models, instead of a single largescale model, parallel computing and decentralized processing architectures.
This chapter introduces decomposition methods to perform state estimation in largescale distribution networks, employing the concepts of multiarea state estimation (MASE). A brief contextualization of scalability and decentralization is presented to emphasize the need of such architectures. Then, the main ideas of MASE are discussed. Two multiarea state estimation algorithms are presented, both make use of specialized methods for distribution system state estimation. However, one based on the traditional approach of the nodal voltage state estimation and the other on currentbased model. Finally, numerical examples with both estimators illustrate the accuracy and computational aspects.

11 Including synchronized and nonsynchronized measurements with different sample rates in distribution system state estimation
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The distribution system (DS) was considered a predictable, collectively managed system that needed little realtime interventions unless under emergency situations. As more distributed energy resources (DER), such as photovoltaics (PV), electric vehicles (EV), and distributed generators, are integrated, and actively participate in demand side management programs, the intermittent bus netloads would cause power flows and feeder voltage profiles in the distribution network to become more diversified and unpredictable. To maintain the service quality, there is an urgent need for active monitoring of the grid in realtime and intervention by the operator when necessary.
Complex interactions among different functions in modern distribution networks have significantly changed the feeder load profiles, network configuration, and operation practice. To mitigate possible impacts of DER on the network security and power quality, smart grid initiatives have been deployed, which created new sources of data. Data gathered promptly at various information systems from intelligent electronic devices (IEDs), automated feeder switches and voltage regulators, smart inverters of DER and phasor measurement units (PMUs) provide an opportunity to enhance system situation awareness [16]. Through active monitoring systems, operators are not just seeking to improve network reliability and efficiency but also maximize utilization of existing assets to accommodate DER integrations without compromising established operational restrictions [710].
A distribution system state estimation (DSSE)based realtime network model is an essential instrument in the control and protection of distribution networks to meet the changes in technology, environment, and commerce. However, due to economic and technical limitations, measurements cannot be independently utilized to estimate the complete DS states. Synergy among all types of sensor data can refine and achieve network models for analyses more promptly when needed. This chapter introduces techniques suitable for DSSE in presence of nonsynchronized measurements with different sampling rates.

12 State estimation for low voltage distribution grids
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This chapter discusses the subject of distribution system state estimation (DSSE) in low voltage distribution grids (LVDG). In theory, DSSE schemes developed for medium voltage distribution grids (MVDG) are also applicable to LVDGs because of their similar characteristics. However, several limiting factors exist in LVDGs that can severely impact the DSSE performance. First, the measurement infrastructure in LVDGs is lacking with a limited sensor deployment and an absence of communication between the end consumers and the operator. In addition, scarce measurement devices and a slow reporting rate from smart meters with asynchronous measurements render most LVDGs unobservable. Second, there is a lack of reliable and accurate systemrelated information. This includes information about the topology, parameters and equipment used in any given LVDG which results to a system model with considerable uncertainty. Third, most DSSE methodologies developed for MVDGs are for threewire networks or fourwire networks with the neutral wire multigrounded. This allows simplifying the problem formulation as the neutral voltage can be approximated to 0 V. In LVDGs, this assumption typically does not hold, and the nonzero neutral voltage has a detrimental impact on the operation of the classical DSSE. These limiting factors along with their impact and mitigation strategies in order to develop adequate DSSE solutions for LVDG are discussed in this chapter.

13 Conclusions
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This book has covered various practical and theoretical aspects of the Distribution System State Estimation (DSSE) process, which is currently one of the engineering topics of greatest interest to researchers, public agents, and industry. In recent years, DSSE has become an essential application in advanced distribution management systems, an inevitable process for the implementation of several features envisioned by the smart grid concept.
In this chapter, a historical context is initially provided to show how the interest in developing DSSE algorithms unfolded, highlighting the challenges encountered by the pioneers and the techniques developed. A summary of the alternative modeling and different approaches for DSSE covered in the book is presented in the sequel, and their main features to meet the needs of the emerging active Distribution Systems (DSs) nominated. The chapter ends with the presentation of future research directions expected for DSSE in the coming years.

Back Matter
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