Monitoring and Control of Electrical Power Systems using Machine Learning Techniques

Monitoring and Control of Electrical Power Systems using Machine Learning Techniques bridges the gap between advanced machine learning techniques and their application in the control and monitoring of electrical power systems, particularly relevant for heavily distributed energy systems and real-time application. The book reviews key applications of deep learning, spatio-temporal, and advanced signal processing methods for monitoring power quality. This reference introduces guiding principles for the monitoring and control of power quality disturbances arising from integration of power electronic devices and discusses monitoring and control of electrical power systems using benchmark test systems for the creation of bespoke advanced data analytic algorithms.

• Covers advanced applications and solutions for monitoring and control of electrical power systems using machine learning techniques for transmission and distribution systems
• Provides deep insight into power quality disturbance detection and classification through machine learning, deep learning, and spatio-temporal algorithms
• Includes substantial online supplementary components focusing on dataset generation for machine learning training processes and open-source microgrid model simulators on GitHub

• Language: English
• Publisher: Elsevier Science
• Release date: Jan 11, 2023
• ISBN: 9780323984041

Book preview

Preface

Emilio Barocio     Guadalajara, Mexico

Rafael Segundo     Winterthur, Switzerland

Petr Korba     Zürich, Switzerland

Machine learning techniques have found their way into applications in the field of electrical power systems in the twenty-first century. The main reason is the strong pressure from politics in all developed countries around the globe to reach carbon neutrality in the near future. In many countries, there is a strong push to be independent of fossil fuels and, at the same time, there is a nuclear phase-out. This leads to a massive integration of volatile renewable energy sources into the existing grids. This has a strong impact on the stable operation of the electric power system, which is becoming a challenging problem. It has already become evident that we may not always be able to handle this challenge yet. To be more specific, we remind the reader of the recent incidents, such as the separation of the Continental European power system in January 2021 (which was successfully mitigated in the end), the great Texas blackout of 2021, and other similar incidents.

Ensuring security and quality of power supply is essential for our modern society. Thanks to fast power electronics, information, and communication technologies developed and available recently. New insights into all grid levels across the entire power system can be obtained by means of properly analyzed fast sampled and often time-synchronized measurements. More specifically, we experience a massive roll out of smart meters in low-voltage grids and installations of phasor measurement units in every substation of the high-voltage grid worldwide. These technologies yield a big amount of data, which can be used to monitor, analyze, and to detect the presence and the source of faults. Automatic control loops can be designed to speed up the appropriate action required to secure the power supply; this can hardly be done fast enough manually by a human operator.

This book gives an overview of applications for monitoring and control of electric power systems using machine learning techniques. It has been our intension to bridge the gap between theory and practice. We trust that we have done so in this text by presenting guiding principles developed to solve practical problems encountered in distribution and transmission grids in our research projects and to demonstrate the achieved functionality on concrete examples.

This book is intended for students and researchers interested in advanced methods for monitoring, control, and optimization of power quality using machine learning techniques and engaging engineers from the utilities and the power system industry.

Experts from all over the globe have been recruited to contribute to this book. It would not have been possible to come up with this book without the diligent work and support of several international research teams from Switzerland, Mexico, Italy, Greece, Germany, Brazil, and the UK; many thanks to all of them for their valuable contributions to the monitoring and control of power systems and to this volume. The book covers advanced applications and solutions for monitoring and control of electrical power systems in transmission and distribution, provides deep insight into power system dynamics, power quality disturbance detection and classification through machine learning, deep learning, and spatio-temporal algorithms. Supplementary online components and datasets for machine learning training processes and open-source grid models are included on GitHub.

December 2022

1: Derivation of generic equivalent models for distribution network analysis using artificial intelligence techniques

Eleftherios O. Kontisa; Theofilos A. Papadopoulosb; Mazheruddin H. Syedc; Grigoris K. Papagiannisa    aAristotle University of Thessaloniki, Thessaloniki, Greece

bDemocritus University of Thrace, Xanthi, Greece

cUniversity of Strathclyde, Glasgow, United Kingdom

Abstract

The growing penetration of distributed energy resources and the use of new types of loads have emerged the need to develop robust and up-to-date equivalent models for distribution network (DN) analysis. In this aspect, several approaches have been proposed in the literature to derive generic sets of model parameters that can represent the DN for a wide range of operating conditions. In this chapter, conventional generalization techniques based on statistical analysis as well as modern ones, using artificial neural networks (ANNs) and clustering techniques, are developed. Both static models, which facilitate DN steady-state analysis and dynamic models suitable for transient analysis, are considered. The performance of the developed generalization approaches (GAs) is evaluated using measurements acquired from laboratory-scale active and passive DN configurations. This is dictated by the need to evaluate all examined GAs under practical conditions. A comparative assessment of all examined GAs is conducted, highlighting their distinct advantages and drawbacks.

Keywords

active distribution networks; artificial neural networks; equivalent models; k-means clustering; parameter estimation

Acknowledgement

This research is co-financed by Greece and the European Union (European Social Fund – ESF) through the Operational Programme Human Resources Development, Education and Lifelong Learning in the context of the project Reinforcement of Postdoctoral Researchers – 2nd Cycle (MIS-5033021), implemented by the State Scholarships Foundation (IKY). This work was also part funded by the European Union's Horizon 2020 research and innovation programme under grant agreement No 870620 – ERIGrid 2.0 project.

1.1 Introduction

Traditionally, power systems analysis is performed by using detailed models [1], [2]. However, the penetration of distributed energy resources (DERs), the use of new types of loads, e.g., non-linear power electronic loads, electric vehicles, etc., the need for more operational flexibility and the application of advanced voltage and frequency control strategies prevent system operators to develop and maintain accurate and up-to-date system models [3]. Moreover, detailed information of the network structure, network assets, and control parameters of DERs is rarely available to system operators [4]. Thus specific power system buses, e.g., at key substations and feeders, are represented by equivalent models, simulating the aggregated behavior of the downstream network components (lines, transformers, etc.), the actual load, and the possibly existing DERs [5].

Equivalent modeling approaches are generally categorized into component- and measurement-based [5]. The component-based or knowledge-based approach is a bottom-up methodology; thus implies the detailed knowledge of the various network components, hindering its practical application [6], [7]. On the other hand, the measurement-based or behavior-based modeling approach, as a top-down methodology, is used to derive equivalent models with/without prior knowledge of the actual system, i.e., gray- /black-box equivalent models, respectively [7]. This method does not require detailed network knowledge; instead relies on field measurements to derive the model parameters by applying identification techniques. During the last decades with the maturing of smart grid technologies and the improvement on data capture and storage capabilities, this approach has become more popular and has been adopted for the modeling of active distribution network (ADNs) and microgrids (MGs) par excellence.

Irrespective of the approach used for the model development, aggregated models can be grouped into static and dynamic [8], [9], [10]. Static equivalents express the real and reactive power at the connecting bus of interest at any time instant as a function of the voltage magnitude and/or frequency at that specific time instant [6]. The most known static models are the exponential, polynomial, linear, comprehensive, static induction motor, and power electronic-interfaced models [5]. Such models can be used for cases exhibiting near instantaneous time changes in power, following a voltage and/or frequency deviation, i.e., steady-state studies. They can be also used if the interest is on the new steady-state, rather than on the initial transient, e.g., long-term voltage stability studies. On the other hand, for dynamic studies involving small-signal and transient stability [4], frequency analysis [11], and short-term voltage stability [12], dynamic equivalents exhibiting time-dependent responses are preferred. They are formulated in terms of difference or differential equations to express the real and reactive power at any time instant with respect to voltage and/or frequency [6]. Although static models are not appropriate substitutes for dynamic studies, about 70% of power system operators worldwide still use static load models to conduct contingency analysis and power system stability studies [13]. This issue becomes more critical particularly in cases of high penetration of induction motors, e.g., residential air conditioners, or DERs [5].

A common drawback of the equivalent modeling methods [7], [8], [9], [10], [11] lies in the fact that their parameters are valid only for the operating condition from which they have been originally derived. This is because of their high dependency on the distribution network (DN) operating conditions (voltage level, network configuration, etc.), the load stochastic behavior, and the intermittent nature of DERs [4], [14]. To determine generic model parameters for measurement-based dynamic equivalent models, several approaches have been proposed in literature. In [14], [15], and [16], statistical analysis parameter identification is applied, by assigning the generic model parameters with the corresponding median or mean values obtained under different operating conditions. Other multisignal processing analysis techniques have been also introduced in [4], [17], [18], [19], [20], where the generic model parameters are derived in the least-square sense [17–20], or by adopting linear approximation functions [21], [22]. Although, these approaches extend the applicability of the equivalent models, their robustness is limited within the range of the available training data set, thus cannot predict new conditions beyond the original observation range [23]. Another significant issue is that human intervention is required to process and classify the available data into groups of similar characteristics, e.g., data groups obtained under similar network conditions [16], [17], or determine representative records.

The emergence of artificial intelligence (AI) has introduced new flexible, self-learning and automated techniques to develop generic black-box models. In these models, the DN is represented by a single artificial neural network (ANN) utilizing a large amount of data [24], [25]. However, such black-box models have no physical meaning and mathematical formulation background; thus they do not provide any insight into the system dynamics [23] and are practically infeasible, as they cannot be integrated into simulation environments (commercial software, etc.) and interact with other modules. In this context, other AI-based approaches have been proposed by deploying static or dynamic equivalent model formulations. In particular, in [15] generic models for conventional equivalent models, i.e., ZIP and exponential recovery (first- and second-order) are developed by using ANNs. Similarly, in [11] support vector clustering is adopted to derive generic parameters for a transfer function-based equivalent model. In [23], clustering and ANN are combined to derive robust sets of parameters for a variable-order equivalent model [26]. First, clustering is used to automatically divide the available set of recorded data into groups with similar characteristics. At the next stage, for each cluster the model parameters are estimated by applying the vector-fitting technique and are extended to a wide range of operating conditions via ANN modeling. Clustering is also used in [27] to classify data into clusters presenting similar dynamic behavior; at a second stage, representative model parameters of a discrete transfer function model are calculated in terms of nonlinear least squares (NLS) optimization. Similarly to [23] and [27], in [7] clustering is used to determine the optimal number of representative operating conditions and a long short-term memory (LSTM) recurrent neural network (RNN) is used to estimate the parameters of composite dynamic equivalent model. Finally, in [28], a combination of optimization-based estimation algorithms and AI techniques are adopted to obtain adaptable generic models of exponential recovery, composite, and first-order functions-based. In this work, two decision trees are used to relate a given disturbance with one of the examined models (classification) and with a set of parameters that best fit the selected model with the disturbance characteristics (prediction), respectively.

Based on the above analysis, it can be deduced that several conventional and AI-based approaches have been proposed in the literature for the derivation of generic sets of equivalent model parameters. However, their accuracy and robustness has not been systematically investigated and evaluated. Therefore this chapter formulates in the MATLAB® environment [29] six generalization approaches (based on the findings and recommendations of [15], [16], [23] and [27]) that can be used to derive robust/generic equivalent models for DN analysis. To provide didactic examples to the reader, the examined generalization approaches (GAs) are used to derive robust/generic sets of parameters for a static as well as a dynamic equivalent model. The former can be used for the steady-state analysis of DNs and the latter to represent DNs in stability studies. The performance of all the examined GAs is thoroughly tested using measurements obtained from a laboratory scale DN, consisting of static loads, induction motors, synchronous generators, and converter-interfaced DERs. This way, a comparative assessment of all examined GAs under practical conditions is conducted. The presented analysis provides a comprehensive assessment and insights concerning the distinct advantages and drawbacks of all methods. Finally, it is worth noting that all MATLAB codes used to implement the examined equivalent models and the examined GAs and all laboratory measurements used to evaluate the performance of the examined methods, are freely available at [30].

The rest of the chapter is organized as follows: In Section 1.2, the structure of the equivalent models, adopted to provide didactic examples to the reader, is presented alongside with the parameter estimation procedure. In Section 1.3, the examined GAs are described in detail. In Section 1.4, the performance of the examined GAs is evaluated using laboratory measurements. Section 1.5 briefly presents the MATLAB codes used for the implementation of the examined approaches. Finally, Section 1.6 discusses the main findings of the research and concludes the chapter.

1.2 Examined equivalent models

In this section, the structure of the adopted equivalent models is described and the parameter estimation procedure is briefly explained.

1.2.1 Structure of the examined equivalent models

Two representative equivalent models for DN analysis are examined. The first one is a static equivalent model, and the second one is a first-order dynamic counterpart. The steady-state model can be used to represent DNs in steady-state studies, and the dynamic model can be used to simulate DNs in stability studies. Concerning the static model, the well-established polynomial (ZIP) model is considered [5], [10]. The examined dynamic equivalent is a modified version of the conventional exponential recovery model (ERM) [31]. As discussed in [26], the conventional ERM fails to simulate and analyze reverse power flow phenomena that may occur in ADNs. Thus the modified ERM (MERM) of [26] is used to facilitate the analysis of these phenomena. The mathematical formulation as well as further details for both equivalent models are provided in the following subsections.

1.2.1.1 The ZIP model

The polynomial model is also referred as the ZIP model, since it consists of constant impedance (Z), constant current (I), and constant power (P) components. The ZIP model is described by the following equations:

(1.1)

(1.2)

with

(1.3)

(1.4)

Here, and denote the real and reactive power estimates, provided by the ZIP model, respectively. V is the network voltage and is the pre-disturbance voltage magnitude. and are the predisturbance total real and reactive power consumption, respectively. Parameters and represent the relative participation of constant impedance component; parameters , and , represent the relative participation of constant current and constant power components, respectively [5]. The relative participation of each component (Z,I,P) in the total mix lies in the range between 0 and 1 p.u., giving rise to their overall sum being equal to 1 p.u. This variant of the model is called the constrained ZIP model [5]. However, it may fail to provide accurate results, especially in networks hosting DERs. In these cases, the so-called accurate ZIP model can be used. In this variant, individual and parameters can be less than 0 p.u. and/or larger than 1 p.u. Once again, the sum of all parameters (and the sum of all parameters) should be equal to 1. Although the parameters of this variant do not have any physical meaning, the model can be more accurate compared to the constrained ZIP counterpart [5]. In this work, only the accurate ZIP model is considered.

1.2.1.2 The modified ERM

Real and reactive power is expressed by the MERM using the following equations [26]:

(1.5)

(1.6)

where

(1.7)

(1.8)

(1.9)

(1.10)

Here, and denote the real and reactive power estimates provided by the MERM. and are two first-order polynomial functions used to describe the steady-state behavior of real and reactive power, respectively. Parameters , are the polynomial coefficients of , whereas , and are the polynomial coefficients of . Additionally, and are two first-order polynomial functions used to describe the transient behavior of real and reactive power, respectively. is simulated using parameters and , whereas is approximated using coefficients and . Finally, and are the recovery time constants of real and reactive power responses, respectively [26].

1.2.2 Parameter estimation

The parameters of the examined equivalent models are estimated in terms of NLS optimization [32], [33], using the trust-region-reflective algorithm [29]. The aim of the optimization is to minimize via successive iterations the objective function of (1.11):

(1.11)

Here, N is the total number of the available samples. is the actual (measured) real or reactive power response of the examined DN at the n-th sample. is the estimated (by the adopted equivalent model) response at the n-th sample.

For the ZIP model, is approximated by using (1.1) and (1.2). In this case, constraints of (1.3) and (1.4) should be considered. Concerning the MERM, is approximated by using (1.5) and (1.6), taking into account (1.7)–(1.10). For both equivalents, no upper and lower bounds for the model parameters are considered.

1.3 Derivation of generic equivalent models

To develop generic equivalents, the methodology of Fig. 1.1 is adopted [23]. More specifically, a database is initially developed, containing M data sets. Each data set is comprised of three equally sized vectors , , and and of two auxiliary variables denoted as and . corresponds to the line-to-line RMS time domain response of voltage at the point of interconnection (POI) with the external power system. Moreover, and denote the total (three-phase) RMS time domain responses of real and reactive power at the POI. , , and practically reflect the dynamic behavior of the DN during the i-th disturbance; they are recorded during voltage disturbances/events. Variables and are used to reflect the load composition and the type of the DERs connected to the DN during the i-th disturbance. As discussed in [23], the values of and can be defined either using forecasts or ideally using smart meter recordings.

Figure 1.1 Concept for the derivation of generic equivalent models for DN analysis.

Once the database has been created, preprocessing is applied, aiming to determine predisturbance steady-state values of voltage ( ), real ( ), and reactive power ( ) for the M available data sets. These values are used to provide further insight concerning the DN operating conditions prior to the i-th disturbance. Subsequently, the M data sets are randomly divided into two groups. The first group contains data sets and is used to derive generic parameters for the examined equivalents, i.e., model parameters that can be used to analyze efficiently a wide range of network conditions. Generic parameters are derived by adopting the two-step procedure, described below:

•  Step-1: Parameter Estimation. The available dynamic responses of voltage, real, and reactive power are used to identify parameters for the examined equivalent models. In particular, for each one of the data sets and for each equivalent model, a dedicated set of parameters is identified. More specifically, for each data set, the NLS optimization of (1.11) is performed to estimate the equivalent model parameters. Concerning the ZIP model, sets and are identified for the j-th data set ( ). is used to simulate the real power behavior, and is utilized to analyze the reactive power behavior. Concerning the MERM, the modeling of real and reactive power responses is achieved using sets and , respectively.

•  Step-2: Application of a Generalization Approach. A generalization approach is applied, aiming to derive generic sets of parameters for the examined equivalent models. Six GAs are considered and compared. All approaches are described in detail in the next subsection.

1.3.1 Examined GAs

The examined GAs include the following: i) methods based on statistical analysis, ii) methods based on clustering and statistical analysis, iii) methods based on ANNs, and iv) methods based on clustering and ANNs. A more in depth analysis follows.

1.3.1.1 Generalization via statistical analysis

In this approach, generic model parameters are identified using statistical analysis. In particular, the generic parameters are determined as the mean values of the identified model parameters. It is worth noting that this approach is proposed by CIGRE for the derivation of robust/generic equivalents [5].

1.3.1.2 Generalization via clustering techniques and statistical analysis

In this approach, clustering is applied to automatically divide the available training data into a small number of groups, which present similar characteristics. Clustering can be performed either based on the predisturbance operating conditions [23], i.e., based on , , and , or based on the real and reactive power dynamic responses after a disturbance [27], i.e., based on , and .

To apply the clustering based on the predisturbance operating conditions, the following procedure is adopted [23]: , , and are combined for each one of the available training data sets into a single vector ; thus the set is created. Subsequently, X is forwarded as input to a clustering algorithm, i.e., the k-means++. k-means++ categorizes the available training data into L ( ) clusters , aiming to minimize the within cluster sum of squares [23], as shown in (1.12).

(1.12)

Here is the mean value of operating conditions contained in the l-th cluster.

Alternatively, to apply clustering in terms of the available dynamic responses, the following procedure is proposed: , and are combined for each one of the available training data sets into a single vector ; thus the set is created. Subsequently, S is forwarded as input to the k-means++ algorithm, which categorizes the dynamic responses into D ( ) clusters aiming to minimize the within cluster sum of squares [23], as shown in (1.13).

(1.13)

Here is the average dynamic behavior, i.e., average real and reactive power dynamic response of the data contained in the d-th cluster.

To derive the optimal number of clusters (i.e., L or D), the knee-point criterion for the curve of the within cluster sum of squares to between cluster sum variation ratio (WCBCR) is used. Following this criterion, the optimal number of clusters is defined by the knee of the WCBCR curve