Data Driven approach to topology change location in distribution networks using microPMUs

Texto completo

(1)Instituto Tecnológico y de Estudios Superiores de Monterrey Campus Monterrey. School of Engineering and Sciences. Data-Driven Approach to Topology Change Location in Distribution Networks Using µPMUs A thesis presented by. Ernesto Adán Salas Esquivel Submitted to the School of Engineering and Sciences in partial fulfillment of the requirements for the degree of Master of Science in Energetic Engineering. Monterrey, Nuevo León, May, 2018.

(2)

(3)

(4)

(5)

(6)

(7) Dedication. A mis padres. Por ser mi motivación y mi soporte; a ellos, a quienes les debo todo lo que tengo y lo que soy, les dedico este trabajo, para retribuir un poco de todo lo que me han dado.. v.

(8)

(9) Acknowledgements. I would like to thank here to all the people who have supported me during my Master degree studies. First, to my advisor Dr. Jonathan Mayo Maldonado, not only for his support and guidance, but also for his engagement and constructive criticism that encouraged me to do my best. Working with you was an enriching experience and I always will be grateful with you for sharing your knowledge with me. I am also grateful to Dr. Jesús Elı́as Valdez Resendiz, for his instruction during the beginning of this thesis and also for his willing to advise me during the whole project. I would like to thank to Dr. Osvaldo Miguel Micheloud Vernackt, for giving me the opportunity of take this challenging project and also for encouraging to study a master degree. Also, thank you to Dr. Thabiso Maupong, for his instruction on behavioral theory, your advice was crucial to define the basis of this work. Thank you for sharing your codes with us, they were quite useful to develop the proposed algorithms. I also want to thank to Rodolfo Cuán, for creating an interface to manipulate µPMU data. Your tool was extremely helpful for the validation of the algorithms. I admire your motivation and I wish you the best in your future career. I believe you will be an excellent researcher in the future. I am extremely grateful to all my friends in the Master Degree program. Believe it or not, I truly enjoyed this two years with you. I hope you guys keep the gifts I gave you and the notes I left you; please take it as a reminder that I was a true friend, because to all of you, I only wish happiness and success. I specially want to thank to my parents, for being my support not only during this last years, but for my entire life. I hope I can give back all you have given to me and I wish I could become the person you always wanted me to be. Finally, I would like to thank my sponsors SENER and CONACYT for the scholarship you granted me.. vii.

(10)

(11) Data-Driven Approach to Topology Change Location in Distribution Networks Using µPMUs by Ernesto Adán Salas Esquivel Abstract Motivated by the aim to increase the renewable energy penetration into the grid, the Mexican government established the objective of producing the half of its energy from clean sources by 2050. This is also a tendency in the rest of the world, but utilities are not yet prepared to deal with the challenges that the proliferation of this change will bring. A way to solve such issues is by evolving from the antiquated power system model to a smart grid, by building a control and communications infrastructure, and by introducing sensing and metering technologies. In this sense, micro-phasor measurement units (µPMU) are devices tailored for such purpose; but this technology requires specializing research in order to develop tools for its applications on field. Driven by this urgency, we established the objective of building an application based on the µPMU technology. Therefore, in this thesis we propose an algorithm to topology change location in distribution networks using µPMU data; based on a behavioral system theory in which we use any set of variables that are available for measurement within a network. Such approach differentiates from classic methods, since it does not require any information about the network model, and it does not assume any particular character of disturbance to locate the occurrence within the network. MATLAB simulations and experimentation using µPMUs and a DSpace Data Acquisition Card were implemented with satisfactory results, since the algorithm demonstrated to be capable to locate single topology changes in distribution networks.. ix.

(12)

(13) Nomenclature Ĥ. Noise-free Hankel matrix.. C. Set of complex numbers.. C•×•. Space of complex matrices with w columns and a finite unspecified number of rows.. C•×w. Space of complex matrices with w columns and a finite unspecified number of rows.. Cw. Space of complex vectors with w dimension.. Cm×n. Space of m × n dimensional complex matrices.. R. Set of real numbers.. WT. Set of all maps from T to W.. Z. Ring of integers.. B. The behavior.. HL (w). Hankel matrix of depth L, associated with the vector w.. Lw. Class of linear differential behaviors associated to an external variable of dimension w. NLB. Module of annihilators of B of order L.. || x ||2. L2 -norm of matrix x.. || x ||∞. Infinity-norm of matrix x.. σ, σ t. Time left shift operator.. L(B). The shortest lag of B.. w(B). The number of components of an element w in of B.. A∗. Conjugate transpose of the complex matrix A.. C[ξ]. Ring of polynomials with complex coefficients in the indeterminate ξ. xi.

(14) fi. Factor to tune γv .. fv. Factor to tune γv .. I•. Identity matrix of a finite dimension.. lef tkernel(A). Left kernel of matrix A.. N. Lag.. n(B). The McMillan degree of B.. R(ξ). Field of rational functions in the indeterminate ξ.. u. Input variable.. w(T ). Time series of length T.. y. Output variable.. col(A, B). If A, B are matrices with the same number of columns, it denotes the matrix obtained by stacking A over B.. Im A. Image of linear map A.. ker A. Kernel of a linear map A.. rank(R). Rank of the matrix R.. xii.

(15) List of Figures 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 4.1 4.2 4.3 4.4 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11. Main module. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . µGPS antenna. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . µPMU set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Input Terminals in PM1. µPMU connections. . . . µPMU display. . . . . . System display. . . . . .. . . Plotter Interface. . Y-axis display. . . X-axis display. . . Legend display. . . Export bottoms. . . Meter display.. . . . . . .. . . . . . .. . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. N-port admittance with port variable. . . . . . . . . . . . . . . . . . . . . . . . Proposed approach with an unconstrained selection of variables. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wrapping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Noisy measurement.. Circuit for Experiment 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Input voltage in Simulation 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . Circuit for Experiment 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Input voltage in Simulation 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . Circuit 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Voltages in Simulation 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Currents in Simulation 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Circuit RL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Voltage in Experiment 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Current in Experiment 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Voltage in Experiment 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xiii. 7 7 8 9 9 11 11 11 12 13 13 14 14 33 34 36 36 46 47 47 48 49 52 52 52 53 53 54.

(16) 5.12 5.13 5.14 5.15 5.16 5.17 5.18 5.19 5.20 5.21. Current in Experiment 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IEEE 13 Node Test Feeder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Node Test Feeder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Configuration for Experiment 2. . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Node Circuit in Simulink. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Voltages in Experiment 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Currents in Experiment 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . Currents in Experiment 4 and 5 when node 8 was disconnected. . . . . . . . . . . Connections for Experiment (3). . . . . . . . . . . . . . . . . . . . . . . . . . . Voltages in Experiment 4 and 5 when node 8 was disconnected.. xiv. 54 56 56 58 59 60 60 61 62 63.

(17) List of Tables 2.1 2.2. µPMU connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Research Opportunities . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 10 24. 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10. Circuit 3 Impedances . . . . . . . . . Dynamic Experiment Results . . . . . Line Segment Impedances . . . . . . Load Impedances . . . . . . . . . . . Experiment 3 Results . . . . . . . . . Results of Experiment 4. . . . . . . . Results of Experiment 5 for fv values Results of Experiment 5 for fi values . Accuracy for Single Changes . . . . . Accuracy for Single Changes . . . . .. 51 55 57 57 58 62 65 65 66 66. xv. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . ..

(18)

(19) Contents Abstract. xi. Nomenclature. xii. List of Figures. xiv. List of Tables. xv. 1. Introduction 1.1 Objective and contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2. Micro-Phasor Measurement Units (µPMU) 2.1 Synchrophasor technology . . . . . . . . . . . . . . 2.2 µPMU technical description . . . . . . . . . . . . . 2.2.1 µPMU components . . . . . . . . . . . . . . 2.2.2 µPMU connections . . . . . . . . . . . . . . 2.2.3 µPMU display . . . . . . . . . . . . . . . . 2.2.4 µPMU Plotter . . . . . . . . . . . . . . . . . 2.3 Potential Application Using Synchrophasors . . . . . 2.4 Potential Diagnostic Applications with µPMUs . . . 2.4.1 State estimation . . . . . . . . . . . . . . . . 2.4.2 Event detection . . . . . . . . . . . . . . . . 2.4.3 Fault location . . . . . . . . . . . . . . . . . 2.4.4 Topology verification . . . . . . . . . . . . . 2.4.5 Oscillation detection . . . . . . . . . . . . . 2.4.6 Characterization of distributed generation . . 2.4.7 Security . . . . . . . . . . . . . . . . . . . . 2.5 Potential Model Validation Applications with µPMUs 2.5.1 Loads . . . . . . . . . . . . . . . . . . . . . xvii. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. 1 2 3 5 5 6 6 7 10 11 14 15 15 16 17 18 18 18 19 20 20.

(20) 2.6. 2.7 2.8 3. 4. 5. 2.5.2 Phase identification . . . . . . . . . 2.5.3 Transformers and other devices . . 2.5.4 Network models . . . . . . . . . . 2.5.5 Line segment impedance . . . . . . Potential Control Applications with µPMUs 2.6.1 Protection coordination . . . . . . . 2.6.2 Phase-based control . . . . . . . . 2.6.3 Microgrid control . . . . . . . . . . Research opportunities . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . .. Behavioral System Theory 3.1 Dynamical Systems . . . . . . . . . . . . 3.1.1 General definition . . . . . . . . . 3.1.2 Linearity and Time-Invariance . . 3.2 Behavioral approach . . . . . . . . . . . 3.2.1 Equivalence of representations . . 3.2.2 Inputs and outputs . . . . . . . . 3.3 Persistency of excitation . . . . . . . . . 3.4 Module of annihilators . . . . . . . . . . 3.4.1 Obtaining module of annihilators 3.5 Minimal representation . . . . . . . . . . 3.6 Summary . . . . . . . . . . . . . . . . . Algorithms 4.1 System Identification Approach . 4.2 Data Processing . . . . . . . . . . 4.2.1 Transducer error . . . . . 4.2.2 High frequency noise . . . 4.2.3 Phase angle wrapping . . 4.2.4 Uncertainty . . . . . . . . 4.3 System identification algorithm . . 4.4 Topology change algorithm . . . . 4.4.1 Topology change detection 4.4.2 Topology change location 4.5 Summary . . . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. Experiments and Results. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. 20 20 21 21 21 21 22 22 22 24. . . . . . . . . . . .. 25 25 26 26 27 27 28 28 29 30 30 31. . . . . . . . . . . .. 33 33 35 35 35 36 37 39 40 40 41 43 45. xviii.

(21) 5.1. . . . . . .. 45 45 51 61 61 66. Conclusions and Future Work 6.1 General conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 67 67 70. 5.2 5.3 6. System Identification . . . 5.1.1 Simulations . . . . 5.1.2 Experiments . . . Topology Change Location 5.2.1 Experiments . . . Summary . . . . . . . . .. . . . . . .. . . . . . .. . . . . . .. A Appendix A.1 Digital low-pass filter code . . . A.2 Phase unwrapping code . . . . . A.3 System Identification code . . . A.4 Topology Change Location code. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. Bibliography. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . . . .. . . . .. . . . .. 73 73 73 73 76 83. xix.

(22)

(23) Chapter 1 Introduction Mexico established the challenging goal of producing 35% of its electricity from clean energy by 2024 [11]. A way to reach it is by transforming its old-fashioned electric network into a smart grid. In such scenario, most of that energy is expected to be generated with renewable resources, which will likely be interconnected to the network at the distribution level. Similarly, in California, it is projected to generate 33% of this electrical energy with renewable sources by 2020, while it is expected to interconnect additional 12,000 MW of renewable generation at the distribution level [52]. Therefore, distribution generation (DG) will play a key role in the development of such plans. Besides government regulations, there are several reasons to decentralize the generation, such as the constraints on the construction of new transmission lines, the increased customer demand for highly reliable electricity, the electricity market liberalization and concerns about climate changes [39]. However, in order to successfully integrate those resources, several technical challenges have to be tackled. For instance, the inclusion of DG will introduce bi-directional power flows into the network [24]; hence, changes to the protection and control of power flow strategies are required. Moreover, the incorporation of such technologies may have an impact on the power quality and voltage stability at customer level [46], [57]. In addition, new scenarios may arise, such as islanding operation of DG, which currently is mainly forbidden by utilities, but may become a common practice in the future. Therefore, control strategies may be developed to assure proper resynchronization [52]. In this sense knowing the status of the devices that interconnect those resources (topology verification) with the rest of the grid may be critical for the operator, in order to assure a proper operation condition. This feature, will also help to confirm the state of the grid, and in case of a fault, identify and locate it, allowing them to take prompt actions to restore the network. Such issues can not be addressed under the current hierarchical electric grid model, since utilities have no real-time information about the service parameters at the end of the line. In this sense, grid operators are rather blind and most of the actions to reestablish operation are made manually. This is because most of the distribution networks lack of real-time control and of communication capabilities. Utilities have limited control over their upstream functions; at least in the US, less than a quarter of the distribution network are equipped with information and. 1.

(24) CHAPTER 1. INTRODUCTION. 2. communications systems, and the distribution automation is estimated to be between 15% and 20% [16]. Therefore, taking in account that roots of power system issues are typically found in the distribution system, since nearly 90% of all power outages and disturbances have their origin at such level [16], the seek to reach a smart grid has to start at this level. At this point, it is clear that the intelligent monitoring and control at distribution level have become essential to face such challenges; nevertheless, the existing power infrastructure has significant room for improvement through automation, information management and condition monitoring [24]. Consequently, the inclusion of such capabilities will aid the utilities to transform their current network into a smart grid. i.e. an efficient and reliable infrastructure based on automated control, modern communications infrastructure, sensing and metering technologies [19]. Several technologies could be implemented to deal with lack of monitoring and communication issues, and in this sense, and also motivated by the new challenges due the increasing of DG penetration, the University of California at Berkeley, in conjunction with Power Standards Lab (PSL) and Lawrence Berkeley National Lab (LBNL), have worked to develop a high-precision measurement device, called micro-phasor measurement unit (µPMU) [52]. This device is able to capture angle differences down to ±0.01◦ and to sample A.C. voltage and current waveforms at 256 or 512 samples per cycle. It is also capable of measure, record and send the data via GPS [42]. Such features make it ideal to deal with communication issues, since a group of µPMUs could be synchronized using a GPS network; moreover, their high resolution allow the operators to see disturbances in distribution networks, where changes in phase between two measured points could be rather small; hence, this capability make them ideal for monitoring. However, µPMUs are a brand-new technology and there are not existing platforms to implement their data in real applications, which have been identified in [1] and [55]. Although some of such applications have been studied, they have not been applied on-field yet. Therefore, more research in the topic is imperative and it should be focused on the development of algorithms and platforms to implement µPMU data.. 1.1. Objective and contributions. As previously argued, the only way to reach clean energy goals is through the increasing of monitoring and control of the electric grid, in order to shift from a hierarchical network to a smart grid. In this sense, µPMUs arose as a feasible alternative to ensure the required necessities of this new grid, but the inclusion of such devices brings extra challenges associated to their data and their applications; therefore, more research is essential before utilities can adopt such equipment for on-field applications. In this sense, we contribute to such task, by proposing an algorithm capable of verifying the topology of distributions grid, monitored by µPMUs. Moreover, we propose particular solutions to some of the issues associated with measurements. In particular, the proposed approach would be capable to detect and locate events within.

(25) 1.2. OUTLINE OF THE THESIS. 3. a distribution network. Inherently, such tool contributes to verify the status of the system and helps to maintain the reliability of a distribution network with DG. Therefore, with the implementation of this algorithm, we contribute to: • Increase the penetration of distributed generation. • Maintain the reliability of the system. • Assure an uninterrupted service to customers with distributed generation installed. Those improvements are focused on dealing with the challenges faced by utilities under the new regulations that obligate them to increase clean energy generation; therefore, our final contribution will aid to reach such scenario.. 1.2. Outline of the thesis. The contents of the rest of this thesis is described below: • Chapter 2. A general description of the µPMU technology is provided in this chapter. First, we describe the capabilities and specifications of those devices. Then, we present a review of µPMU literature, which also includes a classification of potential research opportunities. • Chapter 3. We study the linear differential system theory in this chapter, which will allow us to develop the proposed algorithms. We also introduce the concepts of persistency of excitation and module of annihilators. • Chapter 4. In this chapter we identify issues associated with data quality and propose approaches to deal with them. We also describe our algorithm for system identification, that is used as a basis for our topology verification algorithm. Such final algorithm is capable of detect and locate topology changes in distribution networks using µPMU data. • Chapter 5. We specify simulations and experiments implemented to validate both algorithms. • Chapter 6. In the final chapter we provide general conclusions and establish future research directions..

(26)

(27) Chapter 2 Micro-Phasor Measurement Units (µPMU) In this chapter we give a brief description of the synchrophasor technology, including traditional PMUs and modern µPMU. We also present a technical description and a review of the state-of-art of such technologies. We finally present a summary of potential research opportunities for µPMUs.. 2.1. Synchrophasor technology. The first prototypes of the modern phasor measurement units (PMUs) using GPS were built at Virginia Tech at the earlies 1980s. The first commercial manufacture of PMUs with Virginia Tech collaboration was started by Macrodyne in 1991. A large number of manufacturers offer PMUs as a commercial product [40]. PMUs are a transmission system technology, mainly used for control and monitoring of transmission lines [14]. Some of the most notable benefits have come from observing subsynchronous oscillations across wide areas [53], but they are also used in a variety of applications, for improving monitoring, protection, and control. For details see [12]. Traditional PMUs can be deployed at distribution substations, but they are embedded in protective relays, and they are mainly used as a reference measurement against phase angles elsewhere on the transmission grid, not the distribution feeder. By contrast, the purpose of microsynchrophasors is specifically to compare voltage angles at different points on distribution circuits. In this case, such angle differences tend to be small; consequently, traditional PMUs with typical errors near 1%, may not provide enough precision for meaningful distribution measurements. In this sense, in [1], the following challenges to implement synchrophasors in distribution networks are identified: 1. Power flows are rather small; therefore, voltage angle differences may be two orders of magnitude smaller than those on transmission network. 2. Measurements are noisier in distribution than in transmission systems. There is not 5.

(28) CHAPTER 2. MICRO-PHASOR MEASUREMENT UNITS (µPMU). 6. knowledge about extracting the relevant signal from the noise in distribution system measurements. 3. Due to the short distance between components and the higher density of power electronics and controlled devices in distribution networks, the measurement noise includes harmonics and small transients. 4. The ratio of available empirical data points to the number of network nodes is much smaller in distribution than in transmission. Consequently, it is much more difficult to perform rigorous state estimation for the entire network. Therefore, given such constraints and the challenges that have arisen due the increase of distributed energy generation, the interest in development of the micro-phasor measurement units (µPMUs) was promoted. Such devices were developed as a commercial platform, by the private company Power Standards Lab (PSL), in conjunction with the University of California at Berkeley and the Lawrence Berkeley National Lab (LBNL), with the intention to study its applications for diagnostic and control purposes in distribution systems [55]. µPMUs are capable of dealing with the mentioned issues, since they can discern angle separations as small as 0.01◦ . Moreover, they sample A.C. voltage and current waveforms at 120 samples per cycle [42]. Such devices are also an improved option for distribution network applications, since can be directly connected to single or three-phase secondary distribution circuits up to 690 V (line-to-line) or 400 V (line-to-neutral). Measurements can be taken either from standard outlets or from overhead lines through potential transformers (PTs).. 2.2. µPMU technical description. A µPMU is a high-precision power disturbance recorder adapted for making voltage and current phase angle and magnitude measurements; which is also capable of storing, analyzing and communicating data online [2].. 2.2.1. µPMU components. This device is manufactured by Power Standard Lab (PSL) on an already existing hardware platform for power quality monitor, called PQube 3. However, a PQube 3 will require a specific calibration to be used as a µPMU, and must be equipped with extra devices [32]. A bare minimum µPMU is composed by the main module shown in the Figure (2.1), plus a synchronization module (MS1) and a GPS receiver (shown in Figure 2.2). The MS1 module interfaces with the GPS receiver to provide µPMU with GPS communication. The GPS receiver is designed to be weather-resistant and can be installed outdoors using a mounting hardware. Moreover, two extra modules can be included, one for direct power supply purposes and other one for backup during a power outage (UPS). The complete set, with the four modules is shown in the Figure (2.3), where the power supply module is identified as Power Manger.

(29) 2.2. µPMU TECHNICAL DESCRIPTION. 7. Figure 2.1: Main module.. Figure 2.2: µGPS antenna. (PM1) and the UPS is labeled as Power Storage (UPS1). UPS1 module provides the µPMU up to 30 minutes of backup power during a power outage.. 2.2.2. µPMU connections. For the purpose of this thesis, the whole set of four modules was implemented. The setup of the device could be summary in 5 steps: 1. Module assembling. The four modules must be put together, such as in the Figure (2.3). 2. Set up the GPS..

(30) CHAPTER 2. MICRO-PHASOR MEASUREMENT UNITS (µPMU). 8. Figure 2.3: µPMU set. Once the set is assembled, then the GPS antenna has to be connected to the MS1 by plugin a cable with an 8-pin terminal block on one end and an RJ-45 jack on the other. The 8-pin terminal block plugs into the MS1 module and the other end plugs into the GPS1 receiver. The antennas have to be set in an area with direct line of sight to the sky. The µPMU need to be connected to at least 4 satellites. 3. Connect µPMU to the network. The main module has to be plugged to a network switch/hub/router, or cellular modem with standard Ethernet cable. In the Figure (2.5) the port to connect such cable is shown, and is labeled with letter I. The µPMU is configured for a Dynamic Host Configuration Protocol (DHCP) for default; to configurate a Fixed IP, see [32]. 4. Connect instrument power wires. The µPMU has four options for being powered, using: (a). Power terminals in main module, for ±24, 48 VDC or 24 VAC , which are label with letter H in the Figure (2.5).. (b). Power over Ethernet (PoE) port (using an Ethernet cable), label with letter I in the Figure (2.5).. (c). High voltage terminal block on the rear side of the main module, such block corresponds to letters L, M, N and P in the Figure (2.5). Terminals labeled as L1 , L2 , L3 , N , and Ground.. (d). Input Terminals in PM1, for 100 to 240 VAC , shown in Figure (2.4).. 5. Connect wires to mains AC terminals..

(31) 2.2. µPMU TECHNICAL DESCRIPTION. 9. Figure 2.4: Input Terminals in PM1. Such as in the option (c) mentioned above, the wires have to be connected to terminal block with terminals labeled as L1 , L2 , L3 , N and Ground. These wires could be connected to a PT or directly to a voltage measurement point. On the other hand, for current measurement, wires have to be connected to terminal block label as K in the Figure (2.5). Also, such cables would be connected to a CT. It also extremely important to have a ground connection to the µPMU, since it is critical for accurate phase angle measurements. A complete overview of the connection terminals of the main module is shown in Figure (2.5) and detailed in Table (2.1).. Figure 2.5: µPMU connections..

(32) CHAPTER 2. MICRO-PHASOR MEASUREMENT UNITS (µPMU). 10. Number A B C D E F G H I J K L M N P. Description Coin-cell battery. SD memory card and adjacent High-Speed USB 2.0 port. Touchscreen display. Signal relay outputs. Analog inputs. Maximum ±60 V to earth. Can be used as differential inputs. Earth -functional. Used as the reference voltage. Digital input. 60 V tolerant. 1.5 V threshold. Wetted with 2.4 V at 3 mA. Power inputs. 24 VAC , or 24 VDC to 48 VDC (either polarity) nominal. 20 VA max. RJ-45 Ethernet port. 48 V PoE compatible. USB ports – For use with PSL accessories including temperature and humidity sensors. Current transformer inputs – 0.333 V nominal. L1 , L2 , L3 voltage inputs. 1000 Vrms . Neutral terminal, optional connection. Not connected. Earth - functional. Used as the reference voltage. Table 2.1: µPMU connections.. 2.2.3. µPMU display. As is shown in Figure (2.1), the main module has a touchscreen display to navigate through all the displays. Such feature allows the user to view live meters, recent events, system information, and perform actions like ejecting removable media and rebooting the unit. The home screen has four menus, shown in Figure (2.6), and described above: 1. System. This submenu allows the user to configure features such as Date /Time, Language and more. Also, shows details as network status, info about the device, such as: model or serial number. Moreover, it reports status of the UPS and the GPS in the advanced section. Some of those submenus are shown in the Figure (2.7). 2. Meters. Here, power, voltage and current magnitudes are displayed, as can be seen in Figure (2.8). 3. Actions. This screen is used to reboot the system and to eject USB drives..

(33) 2.2. µPMU TECHNICAL DESCRIPTION. 11. Figure 2.6: µPMU display.. Figure 2.7: System display.. Figure 2.8: Meter display.. 2.2.4. µPMU Plotter. The µPMU platform includes a data plotting web application called MicroPMU MultipleResolution Plotter. Which can be accessed using an internet browser and by typing the IP.

(34) CHAPTER 2. MICRO-PHASOR MEASUREMENT UNITS (µPMU). 12. address 172.16.1.100. The Plotting Application software is open source, and runs on the server; hence, in order to view the plotter, the IP configuration of either the WI-FI or Ethernet adapter must be changed so that the adapter is on the same network as the µPMUs, for such details, see [32]. The general view of the plotter interface is shown in the Figure (2.9), and each section is described below.. Figure 2.9: Plotter Interface.. 1. Plotter Header. This section allows the user to log in or select a language. Also, the Zoom Out Time button autoscales the X-axis (time) to fit all recorded data into the graph and the Autoscale All button autoscales the Y-axis (measurement values) to fit all recorded values within the time scale. 2. Selecting Streams. Here, recorded parameters of voltage or current magnitudes and angle can be selected and will be displayed in the plotter. 3. Setting Y-axis. Such display is shown in Figure (2.10.) Under this tab, it is to possible to autoscale the Y-axis in the plot, or select a minimum and maximum value manually. 4. Setting X-axis..

(35) 2.2. µPMU TECHNICAL DESCRIPTION. 13. Figure 2.10: Y-axis display. The range of X-axis can be controlled manually, using the scroll wheel on the mouse to zoom in and out. Also, the screen can be pan left or right by clicking and dragging the mouse. When zoomed in close enough, each individual measurement point can be seen; on the other hand, when zooming out, the plotter will automatically average the data points before displaying them. By zooming out farther, the data will appear as a line inside of a shaded area; such line represents the average value. Also, boundaries of the shaded area, as the plotted in Figure (2.9) represent the maximum and minimum values. Minimum and maximum X-axis values may also be manually set, by using the tab shown in Figure (2.11). The Start Date and End Date are available for setting such values in X-axis. Also, it is necessary to set the time zone.. Figure 2.11: X-axis display..

(36) CHAPTER 2. MICRO-PHASOR MEASUREMENT UNITS (µPMU). 14. 5. Setting color and labels. The color and label for each data stream in the graph could be changed in the legend tab shown in Figure (2.12). The complete color palette will be displayed by click the box under color column.. Figure 2.12: Legend display.. 6. Export Tool. Graphs could be shared with others using the Generate Permalink button, which is shown in Figure (2.13). Such feature creates a URL that displays the measurements with the associated time, axes, and parameters selected at the time it was generated. There is also the Export Graph to SVG Image bottom, it generates a picture of the graph to be downloaded and saved on the computer. Moreover, the Export Graph to CSV File create a comma separated values (CSV) file of the plotter data for the values set in the current screen. The available time intervals to choose from are 1 day, 1 hour, 30 minutes, 5 minutes, 1 minute, 1 second, 1 cycle and 0.5 cycle. It is also necessary to set the frequency (50 or 60 Hz). The CSV file will contain minimum, average, and maximum values for each parameter.. Figure 2.13: Export bottoms.. 2.3. Potential Application Using Synchrophasors. The real potential of synchrophasors obtained with µPMUs lies on the capability of manage such data and use it in different applications. Since the synchrophasors technology was developed three decades ago, there are several publications on the matter. However, most of them have a transmission level perspective; take for instance: [40], in which several PMU applications are explained, including: state estimation, network control and protection system coordination..

(37) 2.4. POTENTIAL DIAGNOSTIC APPLICATIONS WITH µPMUS. 15. While the description of the potential implementations is deeply explained, those are based on classic PMU technology in transmission networks, and do not take in account the distribution networks restrains. A similar perspective is presented in [12], where some PMU applications for transmission level are exposed, mainly focuses on: improved monitoring, protection coordination and control. On the other hand, there are a few publications in which synchrophasor applications at distribution level are the matter of study. • In [48], some of the enlisted and described applications are: phase verification, estate estimation, distributed generation control and protection coordination. • Based on emerging distribution-system issues, [28] exposes some study applications in which potential uses of PMUs are presented, such as: system reconfiguration, distributed generation planning, voltage fluctuations, control of islanded distribution networks and fault detection. • In [23], it is proposed to use PMUs in real-time time applications in the areas of protection and control, to be use for: voltage stability detection and correction, load/generator shedding, islanding control and intermittent generation source control and grid interconnection. • In [56], a list of potential applications for PMUs in distribution networks are presented. It classifies such applications based on the possible benefit and impact, and on the deployment challenge. Some of the main and more crucial are: angle and frequency monitoring, voltage stability monitoring, post-mortem-analysis and state estimation. At this point, it is easy to see that some of the applications are apt for both transmission and distribution networks. Tough, those only present approaches based on traditional PMUs, they could be easily substituted by µPMUs. In this sense, in: [2], [54], [53] and [55] some of those applications are adopted to be implemented in an electric grid at distribution level, using µPMUs. Those authors also include a few more uses for micro-synchrophasors. We identify that in most of the papers exposed before, there is a tendency to classify applications in diagnostic, control and model validation. Therefore, using such classification and mainly based on the work of Von Meier and Arghandeh, we present a summary of µPMU potential applications in the following section.. 2.4 2.4.1. Potential Diagnostic Applications with µPMUs State estimation. This is a process to identify, in near real-time, the operational state of the system, i.e. the steady-state voltage magnitudes and angles at each bus in a network; this implies that also the real and reactive power flowing throw the system and being injected into it, is known. In order to identify such parameters, available network models and empirical measurements are used..

(38) CHAPTER 2. MICRO-PHASOR MEASUREMENT UNITS (µPMU). 16. However, state estimation is more difficult for distribution than for transmission systems, because: • Distribution systems are harder to model than transmission systems, due phase imbalances, small X/R ratios, and large numbers of nodes and loads. • Distribution systems has less redundancy from Kirchhoff’s laws, since they have a great number of nodes, but just a few of them are measured; it leads to a high-dimensional mathematical problem. µPMUs could tackle such difficulties by feeding variables into a state estimator [2]. For instance, in [15], a Bayesian linear estimator is presented, it is based on a linear approximation of the power flow equations for distribution networks, using PMU data. It showed to be more efficient than standard nonlinear weighted least squares (WLS). Moreover, in [10] a linear three-phase state estimator for applications in distribution systems is presented, it is developed to use synchrophasor measurements obtained by µPMUs. Using such measurements, the algorithm creates a non-iterative, lineal model, which allow to know the status of the system in real time. It proved to work well even in three-phase unbalanced networks. However, this method requires a full observability of the network, therefore a large number of devices will be required.. 2.4.2. Event detection. In order to maintain the reliability of a power system, it is crucial to monitor its operating state in real time and detect anomalies. Such anomalies are classified in different events such as non-sinusoidal transients in voltage and current waveforms that may be caused by faults, topology changes, load behavior and source dynamics. These events include, among others: voltage sags, voltage swells, fault currents, voltage oscillations, and frequency oscillations. For a detailed classification, see [22]. For such purpose, µPMU data present a better alternative compared to SCADA measurements, since the first technology have a better resolution, on the order of several seconds, which could reveal events, in which SCADA would be blind. In [62] and [61] a mode model-less statistical and machine learning perspective is presented for event detection goals. It builds statistical models for nominal states and detects possible anomalies in order to build tight boundaries describing the support of the normal distribution. From an analytic perspective, [30] shows how µPMUs could help network operators to distinguish an event originated at transmission level from one which took place in the distribution network. However, for the last two works exposed, still being necessary to create analytic tools that helps to differentiate and classify the kind of event. In this sense, [4] presents an algorithm for detecting events using voltage time series data obtained from µPMU. It requires to create a cluster of data to reveal patterns of interest and link to specific kind of events; its main goal is to create an analytic framework that facilitates event detection, but it also opens the door.

(39) 2.4. POTENTIAL DIAGNOSTIC APPLICATIONS WITH µPMUS. 17. to use the proposed approach for component health monitoring, identification of devices with erroneous control schemes, and cyber security. On the other hand, from a model-base perspective, [1] created an algorithm to detect changes in the topology of a network, then it assigns such change to a specific category of event; moreover, it is capable of locate such fault in a small geographic area of the system. This algorithm was created to work with PMU data; but, it could be implemented using µPMU measurements. However, model-base approaches are prone to overwhelming system randomness and dynamics, due to the high time resolution of the measurements. Their main limitations are that the dynamics of a system may be hard to specify in many cases and that they have nonlinear structures [2].. 2.4.3. Fault location. This is also a critical feature to ensure the resilience of the grid operation, since could assure a fast service restoration after an outage. Therefore, the intention is to infer the geographical location of a fault on a distribution circuit by using µPMU measurements before and during the fault. Besides the approach exposed in [1], which was mentioned in the last subsection, in [29], an algorithm is proposed, that use pre-and post-fault voltage phasor values at the substation and remote µPMU, as well as current measurements at the substation, in order to pinpoint a fault in short time. The accuracy of fault location methods is dependent either on dense deployments of line sensors or unrealistically accurate models of distribution networks. However, the model exposed in [29] works with relatively few instrumentation devices and relatively low fidelity system models. We can also identify some other opportunity areas, whose were not tackled yet, such as: • Equipment health diagnostics. µPMU data can be used for early diagnosis of distribution equipment malfunction. For instance, in [17] it was demonstrated that an µPMU-based diagnosis of a tap changer malfunction is suitable, based on analyzing detailed voltage signatures during and after tap change events, enabling timely correction by the utility. Such application could be extended to more devices and would have significant potential for economic savings and improved safety. • High-impedance fault detection. The objective is to recognize the condition where an object makes an unintentional connection with the ground, but does not draw sufficient current to trip a protective device. High-impedance faults are typically invisible to operators, but can be identified with µPMU measurements. • FIDVR identification and risk detection..

(40) 18. CHAPTER 2. MICRO-PHASOR MEASUREMENT UNITS (µPMU) Fault-induced delayed voltage recovery (FIDVR) is an unstable operating condition that results from the interaction of installed air conditioners with capacitor bank controls. Anticipating it would hinge on identifying the contribution to total customer load from devices that pose an increased risk [54].. 2.4.4. Topology verification. For this case, the goal is to detect or confirm the actual status (open or closed) of field switches or breakers whose indicators may be unavailable remotely or considered unreliable. Knowledge of the network topology is essential to confirm safety operation and it is important for preventing customer outages and constraint violations (e.g. unintentional network loops, unsafe voltage across a switch while closing, high or low customer voltages, excessive load on a circuit section) through subsequent operations. In order to tackle this problem, model-based and model-less approaches have been proposed; for instance: [9] and [8] take a model-less perspective, and are based on the fact that time-series data taken from a dynamic system show specific patterns as signature from each topology change. On the other hand, in [3] as model-based approach is presented. It proposes a votingbased algorithm that looks for the minimal difference between measured and calculated voltage angle or voltage magnitude to indicate the actual topology. However, it is necessary to have prior-knowledge of all the possible configurations of the network topology; therefore, it is required to solve the system several times, which would be an extremely complex task for large networks.. 2.4.5. Oscillation detection. Due the power exchange between distributed energy resources, oscillations could occur on distribution systems; such phenomena are well known on transmission systems, but higherfrequency oscillations could be unobserved by conventional instrumentation in distribution networks. A study case, exposed in [56] suggests that future distribution systems with high penetrations of solar and wind generation could also experience oscillation issues. Since current models did not predict oscillations, the only way to find out if any oscillations exist is by visual inspection. It took synchrophasors to recognize their existence, and effective control methods are still in development.. 2.4.6. Characterization of distributed generation. This one of the main justifications to increase monitoring at distribution levels; since µPMU data would give a better understanding of how distributed generation affects the grid. It might help to guarantee power quality, estimate feeder hosting capacity, and evaluate costs and benefits associated with distributed resources..

(41) 2.4. POTENTIAL DIAGNOSTIC APPLICATIONS WITH µPMUS. 19. Distributed generation characterization may include the following: • Voltage regulation. Voltage variations may be caused by loads or variable generation on a circuit; hence, it is crucial to characterize feeder voltage changes with distributed generation behavior. µPMU measurements could be used to develop such applications, where use cases include assuring proper service voltage levels, preventing excessive operation of legacy voltage regulation equipment, and addressing voltage flicker. • Detect reverse power flow. The intention is identifying and anticipate when power flows in reverse direction on a distribution feeder. This may be a concern since the coordination of protective devices could be compromised under reverse flow conditions, also voltage regulation may be impacted. Phasor measurements of voltage and current unambiguously identify the direction of power flow, but there are no works on modeling or anticipating the circumstances under which it arises. • Disaggregate net metered distributed generation from load. When the distribution utility lacks access to separate load and generation, distributed generation masks an unknown amount of load. Therefore, it is imperative to infer the amount of load being offset by distributed generators behind a net meter, through measurements and correlated data. This would help to have better anticipation of changes in the net load and to assess the system’s risk exposure to sudden generation loss. In [47], an algorithm is proposed for estimating the photovoltaic generation at each household on a distribution feeder using only AMI data; such method could also be implemented with µPMU measurements. • Inverter characterization. The goal is to qualify and quantify the behavior of inverters in relation to stabilizing system A.C. frequency and damping disturbances in power angle or frequency. This might help to prevent unintended effects, such cascading trips.. 2.4.7. Security. Based on the fact that the topology or the state of the system could be known by using µPMU measurements, system operators would be able to identify an attack to the network by detecting unexpected operations or topology changes, or also via physical µPMU measurements inspection. Such attacks could be identified by checking the consistency of SCADA data against µPMU data independently. Based on that idea, [25] proposed a tool to discern physical and cyber-attacks in a distribution network..

(42) CHAPTER 2. MICRO-PHASOR MEASUREMENT UNITS (µPMU). 20. 2.5. Potential Model Validation Applications with µPMUs. 2.5.1. Loads. µPMU measurements of voltage and current at feeder level could validate and improve models of aggregate load, used to predict load response to voltage changes. Since those devices have the precision necessary to characterize the dynamic behavior of a load. Such behavior presents high volatility and intermittence; therefore, [43] presents a stochastic model to characterize it, by using the Ornstein-Uhlenbeck process. In this instance, µPMUs are utilized for the purpose of recording instantaneous power measurements for the development and validation of the proposed model.. 2.5.2. Phase identification. In order to facilitate proper balancing, it is important to identify the connection of singlephase loads and laterals to phases A, B or C. However, utilities have limited information about loads connected to three-phase distribution lines and also phases can be switched during the restoration, reconfiguration and maintenance activities. Correct phase labeling is also crucial in order to avoid excessive losses or reduced life cycle of network components. This is also an important parameter to take in account for the development of another applications, since phase mislabeling is a major source of error in diagnostic processes such as topology detection, state estimation and fault location [49]. Based on µPMU data, [58] developed a phase identification method for distribution networks, where phases can be severely unbalanced and unlabeled. Such as in other applications mentioned before, the key fact is that time-series voltage shows some specific patterns, which in this case are associated to connected phases at measurement points. This algorithm analyzes cross correlations over voltage magnitudes along with phase angle differences on two candidate phases to be matched, then a correlation would be observed if two measurement points are on the same phase. However, methods based only on voltage magnitude will fail to converge when the system is well balanced. On the other hand, methods based on voltage angle can not be trusted when more than one delta-wye transformer is presented, due the 30◦ phase shift.. 2.5.3. Transformers and other devices. Transformers characterization is a special case, since its impedance, voltage magnitude and phase shifts vary as a function of load. The importance of the last parameter was exposed in the last subsection, since phase shifts need to be taken in account for phase identification purposes..

(43) 2.6. POTENTIAL CONTROL APPLICATIONS WITH µPMUS. 2.5.4. 21. Network models. Distribution circuit models are inaccurate; therefore, the permanent physical characteristics of a such networks require empirical measurement for validation. µPMU data may help in such task by confirm, correct or improve the detail of distribution network models. In this sense, [44] created an impedance estimation model, based on µPMU measurements for impedance calculations; the intention is to recognize areas where the network model is inaccurate and may need resurveyed.. 2.5.5. Line segment impedance. Measurement of both current and voltage phasors at each end of any given line segment or device should, in principle, yield the impedance of that segment through simple application of Ohm’s law. However, it is difficult in practice, since small errors have large impact. A likely path to improve impedance calculations is the application of suitable regression techniques [55]. In [2], a study case is exposed, in which several µPMUs were installed and evaluated in several simple test configurations with the intention of recreate the impedance values of the components connecting them. Methods of overhead lines and the transformer impedance estimation worked well. The results compared reasonably well to the expected impedances from the utility models: transformer impedance estimations were within 15% of the modeled values and line impedance estimations were within 13 %. However, there are points beyond which that transformer error becomes significant enough that they have not been able to obtain even an approximate value of impedance. In the case of the underground cable, the attempt to characterize its impedance has failed, due to the lack of cross-phase excitation in the measurement data for the underground cable. The cable is lightly loaded, and the currents flowing through are not distinct enough from one to another to be analyzed through general measurement noise. Therefore, it is necessary to develop methods with higher accuracy by taking into account instrumentation transformer error.. 2.6. Potential Control Applications with µPMUs. 2.6.1. Protection coordination. A different approach to tackle the reverse power flow problem is to employ protection schemes that safely accommodate such flow. Under this perspective, the costly replacement of protective devices would be avoided, by creating relaying scheme that recommend settings to protection devices, based on µPMU data. This viability of this approach has been already demonstrated, but at transmission level, in [6]. Therefore, further research for distribution schemes still being crucial..

(44) CHAPTER 2. MICRO-PHASOR MEASUREMENT UNITS (µPMU). 22. 2.6.2. Phase-based control. Phasor-based control may be the base for managing net power flows, reducing voltage volatility, or matching phasors at tie switches or points of common coupling [38]. The key idea is that by tracking a target phasor rather than injecting a predetermined amount of power, a resource can inherently counteract changes occurring elsewhere in the network. Such approach will also reduce the computational needs for power flow and the dependence of algorithms on potentially inaccurate input data. On this matter, in [13], a linear approximation has been developed for the relationship between the measurable phasor profile and P , Q injections that will be suitable as a basis for control. Also, in [5], it was demonstrated the ability to track a reference phasor by simulating inverter control on a small test feeder with significant phase imbalance.. 2.6.3. Microgrid control. In order to maintain grid resilience, microgrid control holds particular interest. Therefore, some operational strategies, using µPMUs are proposed: • Islanding. The objective is to recognize a scenario in which the microgrid has separated from the grid but continue to operate as a power island. With greater penetration of distributed resources, it may become increasingly difficult to distinguish fault events from other abnormal conditions where it is desirable to keep distributed generation online. Therefore, analytics based on µPMU data may provide information of grid condition, to discern if the microgrid has to be disconnected or not. • Resynchronization. The intention is to create an algorithm capable of reconnecting an islanded microgrid to the main grid in a safety and uninterrupted way. In [7], such method was already implemented, by applying angle-based control of a single generator, using traditional PMU data. Therefore, future research could include several generations with µPMU measurements.. 2.7. Research opportunities. µPMUs are rather a new technology; therefore, there are several challenges to face and areas of opportunity to work in the recent future, in order to implement such devices in useful applications on- field. Most of those challenges and potential applications are already determined. In this sense, and based on the information exposed in the last section, we identify several research opportunities, which are shown in the Table (2.2)..

(45) 2.7. RESEARCH OPPORTUNITIES. Classification. Diagnostic. Models. 23. Application. Research Opportunity. References. State estimation. Optimize the number of µPMUs to get full observability. Propose a method that does not require full observability.. [10]. Event detection. Adapt current methods to be used with µPMU data. Improve analytic tools to classify events.. [62],[61], [30], [4], [1]. Fault location. Optimize the number of µPMU to implement this feature. Develop a method for diagnosis of distribution equipment malfunction. Improve current fault location methods for high-impedance fault detection and for FIDVR identification purposes.. [29]. Topology verification. Improve model-less algorithms and implement them on-field.. [9], [8], [3]. Oscillation detection. Create a model to predict oscillations in distribution networks, with µPMU data.. [56]. Characterization of DG. Make a tool to characterize feeder voltage changes with distributed generation behavior, using µPMU data. Create an algorithm, that using µPMU data could be able to identify and anticipate power flows. [47] Propose an approach to disaggregate net metered distributed generation from load, with µPMUs. Apply µPMUs to characterize the behavior of inverters to stabilize distribution system.. Security. Implement current algorithms on-field.. [25]. Loads. µPMUs for load validation goals.. [43]. Phase identification. Enhance current methods to take in account the presence of multiple delta-wye transformers.. [49], [58]. Transformers and other devices. Create a more accurate transformer model.. N/A.

(46) CHAPTER 2. MICRO-PHASOR MEASUREMENT UNITS (µPMU). 24. Table 2.2 continued from previous page Classification. Application. Research Opportunity. References. Network models. Increase the use of µPMU data in network model validations.. [44]. Line segment impedance. Improve actual method’s accuracy by taking into account instrumentation transformer error.. [55], [2]. Protection coordination. Develop an algorithm for coordination of protective devices in distribution networks, with µPMU data.. [6]. Phase-based control. Implement current algorithms on-field.. [38], [13], [5]. Microgrid control. Create an approach capable of discern if the microgrid has to be disconnected or not, with µPMU data. Improve current methods to include several generations and use µPMU measurements for it.. [7]. Control. Table 2.2: Research Opportunities. 2.8. Summary. In this chapter we have introduced a short description of the synchrophasor technology, mainly focused on µPMUs and their specifications. Moreover, we presented and classified potential applications for µPMU data, to deal with issues in distribution networks. We finally presented a list of research opportunities, shown in Table (2.2)..

(47) Chapter 3 Behavioral System Theory In this chapter we introduce the theory necessary to understand the concepts of the behavioral approach used to build proposed algorithms.. 3.1. Dynamical Systems. In a classical way, a dynamical system is defined in terms of its state. Such state evolves in an autonomous way, i.e. its path depends only on its initial value and on the laws of motion. But under this perspective, external influences are not included, but there is not such a thing as an insulated system; then, it is crucial to also model the environment, which will be rather absurd. That is why, a different approach was introduced by Kalman, in [26]. Here, a dynamical system is viewed as a black box, which receives inputs from the environment and reacts to it producing outputs. Such framework has been very successful, however, as a tool for modeling dynamical systems, the input/output point of view is unnecessarily restrictive, since, most physical systems do not have a preferred signal flow direction, and it is important to let the mathematical structures reflect this. Hence, in thesis, we take the approach proposed by Willems in [41], in which we view a dynamical system as a phenomenon embedded in its environment, and may interact with it. This framework is then based on the idea that a dynamical system consists of a family of laws which constrain the signals which the system can conceivably produce. The collection of all the signals compatible with these laws define what we call the behavior of the system. Thus, we take the description of a dynamical system in terms of its behavior, and in terms of the time trajectories that it permits. Such behavior is seen as a subset from a universum of possibilities, which consist of all the occurrences that the model allows to be possible. The set of time trajectories lies in the product of the input-space and the output-space which is the universum. Since the behavior is the set of trajectories which can be generated by the inputoutput system, such system describes a behavior; which shows that an input-output system is a special case of this theory [45]. 25.

(48) CHAPTER 3. BEHAVIORAL SYSTEM THEORY. 26. We are also focusing on linear time-invariant differential systems. Where linearity means that the systems obey the superposition principle. Also, time-invariance is a property of dynamical systems governed by laws that do not explicitly depend on time. Those concepts are formalized in the following subsection. Finally, being differential suggest that they can be described by differential equations, since dynamical systems are often described by behavioral differential or difference equations; therefore, the behavior will consist of the solution set of them [59].. 3.1.1. General definition. In order to discrete the attributes of the system whose evolve in time, we select the relevant set of time instances (T) and the set (W) in which the attributes take on their values. The dynamical laws specifying this time evolution tell us that certain trajectories can occur and that other can not. Under this perspective, a dynamical system (Σ) is defined by: Σ := (T, W, B). Where T is called the time axis, and takes its values from R for continuous-time system and Z for discrete-time systems. W is the signal space, it specifies the way in which the outcomes of the signals produced by the dynamical system are formalized as elements of a set. Such outcomes are the variables whose evolution in time we are describing. Finally, B is the already mention parameter called: behavior of the network. In such definition, B is a family of time trajectories taking values in W. Hence, the elements of B consist of all the trajectories compatible with the laws that govern the system (Σ).. 3.1.2. Linearity and Time-Invariance. A dynamical system Σ := (T, W, B) is said to be linear if: 1. W is a vector space over a field F, i.e. R of C. 2. B is a linear subspace of WT . As was mentioned before, a linear system obeys the superposition principle, which could be described in the following way: {w1 (·), w2 (·) ∈ B; α, β ∈ F} ⇒ {αw1(·) + βw2(·) ∈ B. This implies that trajectories in B satisfy standard multiplication by scalar and addition operations. Then, let σ be the backward shift operator, which is defined by: (σf )(t) := f (t + 1)..

(49) 3.2. BEHAVIORAL APPROACH. 27. The backward shift operator implies that if the trajectory of w belongs to a behavior then the shifted trajectory also belongs to that behavior as well. Thus, a dynamical system Σ := (T, W, B) will be time-invariant if σ t B = B for all t ∈ T, this condition is called the shift-invariance of B.. 3.2. Behavioral approach. Based on the theory described before we consider a dynamical system Σ := (T, W, B) which is linear and time-invariant, with a vector of variables w, the signal space Cw and the time axis Z. Then we assume that system associated to w can be linearly represented as: R0 w + R1 (σw) + · · · + RN (σ N w) = 0.. (3.1). Defined from the polynomial matrix as follows: R(ξ) = R0 + R1 ξ + · · · + RN ξ N ∈ C•×w [ξ] .. (3.2). N is a nonnegative integer called the lag and represents the order of the difference equation. Equation (3.1) can be also represented in a compact way as: R(σ)w = 0,. (3.3). Also, Equation (3.1) admits a kernel representation, thus we can write it as: B = ker(R(σ)). Then B can be defined as follows: B := {w : Z → Cw | R(σ)w = 0} .. 3.2.1. (3.4). Equivalence of representations. The system described in the Equation (3.1) is parameterized by the polynomial matrix R(ξ) ∈ C•×w [ξ]; however, there are many polynomial matrices that represents the same dynamical system. Thus, we are interested in knowing under which conditions two different kernel representations are the same, such as: B1 = B2 . Let assume that the equivalence between two behaviors with different kernel representations is presented (B1 and B2 ); and let call V ∈ C•×• [ξ] unimodular, if there exists V ⊤ ∈ C•×• [ξ] such that V ′ (ξ)V (ξ) = I• . Then, we formulate the following proposition: Proposition 1. Let B1 := ker(R1 (σ)) with R1 ∈ C•×w [ξ] and V ∈ C•×• [ξ]. Define B1 := ker(V R2 (σ)) with R2 ∈ C•×w [ξ], then B2 = B1 . Moreover, if V is unimodular, then B1 = B2 ..

(50) CHAPTER 3. BEHAVIORAL SYSTEM THEORY. 28 Proof. See Theorem 2.5.4. in [60].. Hence, we conclude that a kernel representation R(σ)w = 0 is equivalent to V R(σ)w = 0 when V is unimodular [36].. 3.2.2. Inputs and outputs. A set of data w ∈ B, of length T can be expressed as a time-series: w(1), w(2), w(3), ..., w(T ) u and can be partitioned into inputs and outputs as w := . y This is true if: u ∈ B. 1. u is free, i.e. for all u there exists y such that y 2. y does not contain any free components. If both conditions are satisfied, then u is called the input variable, and y is called the output variable. This also implies that u is maximally free, i.e. given u, none of the components of y are free.. 3.3. Persistency of excitation. Persistency of excitation of a signal is a key concept in the system identification approach proposed. First, let define a Hankel matrix of depth L, associated with the vector: w(1), w(2), w(3), ..., w(T ); with T > L ∈ Z associated to such time-series is hence defined by: .   HL (w) :=  . w (1) w (2) .. .. w (2) w (3) .. .. · · · w (T − L + 1) · · · w (T − L + 2) .. . ···. w (L) w (L + 1) · · ·. w (T). .   . . HL (w) has L rows and T − L + 1 columns. This lead us to the following definition: Definition 1. A vector u(1), u(2), u(3), ..., u(T ) is persistently exciting of order L if the Hankel matrix HL (u) has a full row rank. Also consider that a signal f is said to be exciting of order L if and only if rank HL (f ) = Lf . This definition implies that if HL (u) is full row rank, then we have sufficient condition to use the data for system identification purposes..

(51) 3.4. MODULE OF ANNIHILATORS. 3.4. 29. Module of annihilators. A module of annihilators is a subset of C•×w , and also is the submodule generated by the rows of R. Now, let n ∈ R1×w [ξ], then n is called an annihilator of w ∈ (Cw )Z if n(σ)w = 0. Also, let B ∈ Lw if n(σ)w = 0 for all w ∈ B then n is called an annihilator of B, which is written as n(σ)B = 0 [34], [60]. Therefore, the set of annihilators of B is defined by: NB := {n⊤ ∈ Cw [ξ] | n(σ)B = 0}.. (3.5). The module of annihilators of B of degree at most ∆ is denoted by N∆ B , where ∆ ∈ Z+ and is a nonnegative integer, then the annihilators of degree less than ∆ are defined by: NB := {n ∈ Cw [ξ] | each element of n is of degree ≤ ∆}.. (3.6). Then, under the assumptions of Lemma 2.38 in [34], any ∆ samples long trajectory w ∈ B[1 | ∆] can be written as a linear combination of the columns of N∆ B ; therefore, any element of the subspace spanned by the columns of N∆ is a trajectory of w ∈ B[1 | ∆] . B Let now recall that Equation (3.1) admits a kernel representation as in Equation (3.2), where N is the maximum of the degrees of the polynomial elements or R associated with this particular representation. Hence, let L(B) be the smallest possible lag over all the kernel representation of B. Also, let define n(B) as the McMillan degree, which is the smallest state-space dimension among all possible state representations of B. This leads to formulate the following proposition: u ∈ B. if u is persistently exciting of Theorem 1. Let w = w(1), w(2), w(3), ..., w(T ) =: y order N + n(B), then: lef tkernel(HN (w̃)) = NN B. Proof. See Theorem 1 in [60]. Theorem (1) yields to the following corollary: u ∈ B. If the Hankel matrix HL (u) Corollary 1. Let w = w(1), w(2), w(3), ..., w(T ) =: y is of full row rank, then there exists R ∈ C•×w such that Rw = 0 for all w ∈ B. Proof. The proof of this corollary follows readily from the arguments of Lemma 1 in [35], considering the module of annihilators of order zero. Since we are working with a steady-state system in frequency-domain, Equation (3.1) turns into: R0 w = 0. This implies that N = 0 and that n(B) = 0 and therefore, only the module of annihilators of order zero are required. Moreover, Theorem (1) implies that if HN (u) is full row rank, we can recover from w the laws of the system B that generated from w [34]. In order to do it, we have to compute its module of annihilators; a process to compute such parameter is presented above..

(52) CHAPTER 3. BEHAVIORAL SYSTEM THEORY. 30. 3.4.1. Obtaining module of annihilators. In order to obtain the module of annihilators, it is necessary to compute the leftkernel of the Hankel matrix. For such purpose we present an algorithm based on Singular Value Decomposition (SVD), which was proposed in [34]. SVD is a factorization which allow us to split any m by n matrix A into: U, Σ and V ∗ , such as: A := U ΣV ∗ . (3.7) Where: U is an orthogonal matrix with dimensions m by m. Σ is a diagonal matrix with dimensions m by n. V ∗ is also an orthogonal matrix with dimensions n by n. Σ has eigenvalues from A∗ A, those positive entries will be: σ1 , · · · , σr . They are the singular values of A. When such matrix has a rank r, the first r places on the main diagonal of Σ are fill with the singular values, and the rest is fill with zeros [51]. Remark 1. Last m − r columns of U give the bases for leftnullspace of A. Based on the Remark (1), we are able to obtain the leftkernel of any matrix A, by making a partition of the last m − r columns of the matrix U , obtained from SVD. Therefore, we propose the following algorithm: Algorithm 1. Algorithm for computing module of annihilators. u Input: Data w = = w(1), w(2), w(3), ..., w(T ). y Output: lef tkernel(HL (w̃)) = NB . 1. Build HL (w) 2. Compute SVD of HL (w) = U ΣV ∗ 3. Partition of U = U1 U2 s.t. U1 has r columns. 4. Compute U2∗ .. 5. end. Leftkerntel(A) denotes the subspace spanned by all vectors v such that vA = 0; this implies that NB HL (w) = 0. Therefore, we conclude the following: If the product of the calculated module of annihilators and the Hankel matrix is equal to zero (NB HL (w) = 0)), then the proper module of annihilators was calculated.. 3.5. Minimal representation. We already showed that we can recover from w the laws of the system B by computing its module of annihilators. However, we know that different sets of equations may define the same behavior, therefore now we are concentrated in get a representation that is as simple as possible, i.e. minimal. Moreover, we do not have the certainty that such solution would be unique. Motivated by such concerns, we state the following proposition:.