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Time-series Modelling of IEC 61850 GOOSE Communication Traffic between IEDs in smart grids - a parametric analysis
10th IFAC Symposium on Control of Power and Energy Systems 10th IFAC Symposium on Control of Power and Energy Systems Tokyo, Japan, September 2018of 10th Symposium on Control Power and Energy 10th IFAC IFAC Symposium on 4-6, Control andonline EnergyatSystems Systems Available www.sciencedirect.com Tokyo, Japan, September 4-6, 2018of Power 10th IFAC Symposium on 4-6, Control Tokyo, Japan, September 2018 Tokyo, Japan, September 4-6, 2018of Power and Energy Systems Tokyo, Japan, September 4-6, 2018
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IFAC PapersOnLine 51-28 (2018) 444–449
Time-series Modelling of IEC 61850 GOOSE Time-series Time-series Modelling Modelling of of IEC IEC 61850 61850 GOOSE GOOSE Communication Traffic between IEDs in smart Time-series Modelling of IEC 61850 GOOSE Communication Traffic between IEDs Communication Traffic between IEDs in in smart smart grids a parametric analysis Communication Traffic between IEDs in smart grids a parametric analysis grids - a parametric analysis grids - a parametric analysis R. Feizimirkhani ∗,∗∗ A. I. Bratcu ∗ Y. Bésanger ∗∗
∗ ∗∗ R. Feizimirkhani ∗,∗∗ Bésanger ∗,∗∗ A. I. Bratcu ∗ ∗∗ ∗ Y. ∗∗ R. A. I. Bratcu Y. Bésanger R. Feizimirkhani Feizimirkhani ∗,∗∗ A. I. Bratcu Y. Bésanger ∗,∗∗ ∗ ∗∗ A. I. Bratcu Y. Bésanger ∗R. Feizimirkhani Univ. Grenoble Alpes, CNRS, Grenoble INP*, GIPSA-lab, ∗ Grenoble Alpes, CNRS, Grenoble INP*, GIPSA-lab, ∗ ∗ Univ. Univ. Grenoble Alpes, CNRS, Grenoble Grenoble INP*, GIPSA-lab, GIPSA-lab, 38000 Grenoble, France CNRS, INP*, ∗ Univ. Grenoble Alpes, 38000 Grenoble, France Univ. Grenoble Alpes, CNRS, Grenoble INP*, GIPSA-lab, 38000 Grenoble, France (e-mail: [email protected]), 38000 Grenoble, France (e-mail: [email protected]), 38000 Grenoble, France (e-mail: [email protected]), ([email protected]) (e-mail: [email protected]), ([email protected]) ∗∗ (e-mail: [email protected]), ([email protected]) Univ. Grenoble Alpes, CNRS, Grenoble INP*, G2Elab, ([email protected]) ∗∗ Grenoble Alpes, CNRS, INP*, ∗∗ ([email protected]) ∗∗ Univ. Univ. Grenoble Alpes, CNRS, Grenoble Grenoble INP*, G2Elab, G2Elab, 38000 Grenoble, France, Univ. Grenoble Alpes, CNRS, Grenoble INP*, G2Elab, ∗∗ 38000 Grenoble, France, Univ. Grenoble Alpes, CNRS, Grenoble INP*, G2Elab, 38000 Grenoble, France, (e-mail: [email protected]) 38000 Grenoble, France, (e-mail: [email protected]) 38000 Grenoble, France, (e-mail: (e-mail: [email protected]) [email protected]) (e-mail: [email protected]) Abstract: Nowadays Nowadays power power grids grids are are intelligent intelligent since since their their protection, protection, supervision supervision and and control control are are Abstract: Abstract: Nowadays power grids are intelligent since their protection, supervision and control are held by a communication network through which different Intelligent Electronic Devices (IEDs) Abstract: Nowadays power grids are intelligent since their protection, supervision and control are held by a communication network through which Intelligent Electronic Devices (IEDs) Abstract: grids intelligent sincedifferent their protection, supervision and control are held by communication network through different Intelligent Electronic Devices (IEDs) are interoperating. interoperating. Topower design and are maintain anwhich efficient Substation Communication Network (SCN) held by aa Nowadays communication network through which different Intelligent Electronic Network Devices (IEDs) are To design and maintain an efficient Substation Communication (SCN) held by a communication network through which different Intelligent Electronic Devices (IEDs) are interoperating. To design and maintain an efficient Substation Communication Network (SCN) with high transmission quality, developing a unitary mathematical model of the SCN data traffic as are interoperating. To design and maintain an efficient Substation Communication Network (SCN) with high transmission quality, developing aaan unitary mathematical model of the SCN data traffic as are interoperating. Toofdesign and maintain efficient Substation Communication Network (SCN) with high transmission quality, developing unitary mathematical model of the SCN data traffic as underlying paradigm any control design approach is an important issue. In this paper, a stochastic with high transmission quality, developing a unitary mathematical model of the SCN data traffic as underlying paradigm of quality, any control design approach is an important issue. In this paper, aa stochastic with high transmission developing a aunitary model the data traffic as underlying paradigm any design is an important issue. In this paper, representation of data dataof traffic is derived, derived, andapproach parametric analysis over theof communication channel underlying paradigm oftraffic any control control design approach ismathematical an analysis importantover issue. Incommunication thisSCN paper, a stochastic stochastic representation of is and a parametric the channel underlying paradigm oftraffic any control design is anisanalysis important issue. Incommunication this paper, distribution a stochastic representation of data traffic is derived, derived, andapproach a parametric parametric analysis over thean communication channel characteristics is presented. The identification method illustrated on electrical representation of data is and a over the channel characteristics is presented. identification method is illustrated electrical distribution representation data traffic The is derived, and a parametric overon thean channel characteristics is presented. The identification method is illustrated on an grid containing containingof two renewable sources which are exchanging information byelectrical means of ofdistribution IEC 61850 characteristics istwo presented. The identification method isanalysis illustrated on ancommunication electrical distribution grid renewable sources which are exchanging information by means IEC 61850 characteristics is presented. The identification method is illustrated on an electrical distribution grid containing two renewable sources which are exchanging information by means of IEC 61850 GOOSE (Generic Object-Oriented Substation Event) communication protocol in the context of aa grid containing two renewable sources which are exchanging information by means of IEC 61850 GOOSE (Generic Object-Oriented Substation Event) communication protocol in the context of grid containing two renewable sources which are exchanging information byofmeans of IEC 61850 GOOSE (Generic Object-Oriented Substation Event) communication protocol in the context of simple distributed reactive power control. The co-simulation and code process both electrical andaa GOOSE (Generic Object-Oriented Substation Event) communication protocol in the context of simple distributed reactive power control. The co-simulation code process of both electrical and ® and ® protocol GOOSE (Genericconfigurations Object-Oriented Substation Event) communication in the context of a simple distributed reactive power control. The co-simulation and code process of both electrical and communication are performed in MATLAB /Simulink environment. simple distributed reactive power control. The co-simulation and code process of both electrical and ® ® /Simulink environment. communication configurations are performed in MATLAB ® ® simple distributed reactive power control. The co-simulation and code process of both electrical and ® ® /Simulink environment. environment. communication configurations configurations are are performed performed in in MATLAB MATLAB /Simulink communication © 2018, IFAC (International Federation of Automatic Control)® /Simulink Hosting by® Elsevier Ltd. All rights reserved. environment. communication configurations are performed in MATLAB Keywords: Smart Grid, Time Series, IEC 61850 GOOSE, Communication Traffic, ARMA Keywords: Smart Grid, Time Series, IEC 61850 GOOSE, Communication Traffic, ARMA Keywords: Keywords: Smart Smart Grid, Grid, Time Time Series, Series, IEC IEC 61850 61850 GOOSE, GOOSE, Communication Communication Traffic, Traffic, ARMA ARMA Keywords: Smart Grid, Time Series, IEC 61850 GOOSE, Communication Traffic, ARMA 1. INTRODUCTION nectivity between central management and individual bays 1. INTRODUCTION INTRODUCTION nectivity between central management and individual bays 1. nectivity between central management and individual bays and also connects different bays among themselves and 1. INTRODUCTION nectivity between central management and individual bays and also connects different bays among themselves and bays 1. INTRODUCTION nectivity between central management and individual and also connects different bays among themselves and bays with Supervisory, Control and Data Acquisition (SCADA) sysand also connects different bays among themselves and bays The energy sector as a whole is standing on the frontier of big Supervisory, Control and Data Acquisition (SCADA) sysThe energy energy sector sector as as aa whole whole is is standing standing on on the the frontier frontier of of big big with and also connects different bays among themselves anda bays with Supervisory, Control and Data Acquisition (SCADA) tem. On the other hand, process bus connects within bay, The with Supervisory, Control and Data Acquisition (SCADA) syschanges. An important challenge to enable all these changes The energy sector as a whole is standing on the frontier of big tem. On the other hand, process bus connects within a sysbay, changes. An important challenge to enable all these changes with Supervisory, Control and Data Acquisition (SCADA) sysThe energy sector as a whole is standing on the frontier of big tem. On the other hand, process bus connects within aaflowbay, primary equipment to IED, (Mackiewicz 2006). Messages changes. An important challenge to enable all these changes tem. On the other hand, process bus connects within bay, is the integration of multiple Distributed Energy Resources changes. An important challenge to enable all these changes primary equipment to IED, (Mackiewicz 2006). Messages flowis the integration of multiple Distributed Energy Resources tem. On equipment the the other hand, process bus connects within aflowbay, changes. Anthis important challenge to enable all theseResources changes primary to IED, (Mackiewicz 2006). Messages ing through IEC 61850 SCN (Substation Communication is the integration of multiple Distributed Energy primary equipment to IED, (Mackiewicz 2006). Messages flow(DERs). For union to be successful, Information and Comis the integration of multiple Distributed Energy Resources through the IEC 61850 SCN (Substation Communication (DERs). For this this union union to be be successful, successful, Information and ComCom- ing primary equipment to IED, (Mackiewicz 2006). Messages flowis the integration of multiple Distributed Energy Resources ing through the IEC 61850 SCN (Substation Communication Network) correspond to electrical information generated by (DERs). For to Information and through the IEC 61850 SCN (Substation Communication munication Technology (ICT) will have have Information to be be extensively extensively used ing (DERs). For this union to(ICT) be successful, and ComNetwork) correspond to electrical information generated by munication Technology will to used ing through the IEC 61850 SCN (Substation Communication (DERs). For this union to be successful, Information and ComNetwork) correspond to electrical information generated by various electrical devices. Messages can further be classified munication Technology (ICT) will have to be extensively used Network) correspond to electrical information generated by by the system operators. Only this combination of electrical munication Technology (ICT) will have to be extensively used various electrical devices. Messages can further be classified by the system operators. Only this combination of electrical Network) correspond to electrical information generated by munication Technology (ICT) will have to be extensively used various electrical devices. Messages can further be classified into three categories according to their distribution over time: by the system operators. Only this combination of electrical various electrical devices. Messages can further be classified grids and communication networks will allow challenges to by the system operators. Only this combination of electrical into three categories according to their distribution over time: grids and communication networks will allow challenges to various electrical devices. Messages can further be classified by the system operators. Only this combination of electrical into three categories according to their distribution over time: periodic, and burst. During operation of power grids and networks allow challenges to threerandom, categories according to theirthe distribution over time: be overcome and the the "smart "smart grid" to towill be truly truly smart (Andrén grids and communication communication networks will allowsmart challenges to into and burst. During the operation of power be overcome and grid" be (Andrén into threerandom, categories according to their distribution over time: grids and communication networks will allowsmart challenges to periodic, periodic, random, and burst. During the operation of power substation, the states of individual substation IEDs colbe overcome and the "smart grid" to be truly (Andrén periodic, random, and burst. During the operation ofare power et al. 2014). The inter-dependency of electrical dynamics and be overcome and the "smart grid" to be truly smart (Andrén substation, the states of individual substation IEDs are colet al. 2014). The The inter-dependency of electrical dynamics and periodic, random, and burst. During the operation of power be overcome and the "smart grid" to be truly smart (Andrén substation, the states of individual substation IEDs are collected periodically and sent to the control center. Such peet al. 2014). inter-dependency of electrical dynamics and substation, the states of individual substation IEDs are colcommunication systems is a challenge in its own right that et al. 2014). The inter-dependency of electrical dynamics and lected periodically and sent to the control center. Such pecommunication systems is aa challenge challenge in its its own own right that that substation, the states ofsent individual substation IEDsSuch are colet al. 2014). Thelightly. inter-dependency of electrical dynamics and lected periodically and to the control center. periodical data acquisition is required for decision-making, in communication systems is in right lected periodically and sent to the control center. Such pecannot be taken Since the communication network will communication systems is a challenge in its own right that riodical data acquisition is required for decision-making, in cannot be taken lightly. Since the communication network will lected periodically and sent to the control center. Such pecommunication systems is a challenge in its own right that riodical data acquisition is required for decision-making, in order to maintain the stability of the overall power system cannot be taken lightly. Since the communication network will riodical data acquisition is required for decision-making, in always be prone to unexpected errors, there will be a need to cannot be taken lightly. Since the communication network will order to maintain the stability of the overall power system always be prone to unexpected errors, there will be a need to riodical data acquisition is required for decision-making, in cannot be taken lightly. Since the communication network will order to maintain the stability of the overall power system operation. Burst data flow consists of protection action inforalways be prone to unexpected errors, there will be a need to order to maintain the stability of the overall power system simulate the effect of these malfunctions on the electrical grid. always be prone to unexpected errors, there will be a need to operation. Burst data flow consists of protection action inforsimulate the effecttoof ofunexpected these malfunctions malfunctions on the the electrical grid. order toswitch-changing maintain theflow stability of the overall power system always be prone errors, there will be a need to operation. Burst data flow consists of protection action information, information and record information simulate the effect these on electrical grid. operation. Burst data consists of protection action inforThis is why co-simulation of both networks is a very important simulate theco-simulation effect of theseofmalfunctions onisthe electrical grid. mation, switch-changing information and record information This is why why both networks networks very important operation. Burst dataofflow consists of bay protection action inforsimulate the effect of these electrical grid. mation, switch-changing information and record information about the sequence events in the is generThis of both is aaa very important mation, switch-changing information and level, recordand information factor in theco-simulation further implementation of on smart grids. If done done This is is in why co-simulation ofmalfunctions both networks isthe very important about the sequence of events in the bay level, and is generfactor the further implementation of smart grids. If mation, switch-changing information and record information This is why co-simulation of both networks is a very important about the sequence of events in the bay level, and is generated only when any fault occurs. During normal operation, factor implementation If the sequence offault events in the bay level, andoperation, is genercorrectly, this further will benefit benefit the stability stability of (Li,smart W., et etgrids. al. 2014). 2014). factor in in the the further implementation of smart grids. If done done about ated only when any occurs. During normal correctly, this will the (Li, W., al. about the sequence events inand the bay level, andoperation, is generfactor in the further implementation of smart grids. If done ated only when any occurs. During normal monitoring and control devices, protection devices, do not correctly, this will benefit the stability (Li, W., et al. 2014). ated only when anyoffault fault occurs. During normal operation, IEC 61850 is a communication standard playing the role of a correctly, this will benefit the stability (Li, W., et al. 2014). monitoring and control devices, and protection devices, do not IEC 61850 is a communication standard playing the role of a ated only when any fault occurs. During normal operation, correctly, this will benefit the stability (Li, W., et al. 2014). monitoring and control devices, and protection devices, do not change their states. IEDs connected to these electrical primary IEC 61850 is a communication standard playing the role of a monitoring and control devices, and protection devices, do not common language which makes it possible for IEDs of difIEC 61850language is a communication standard playing the role of a change their states. IEDs connected to these electrical primary common which makes it possible for IEDs of difmonitoring and control devices, andto protection devices, do not IEC 61850 is a communication standard playing the role of a change their states. IEDs connected these electrical primary devices at the bay level, periodically send their state inforcommon language which makes it possible for IEDs of difchange their states. IEDs connected to these electrical primary ferent manufacturers to communicate with each other. IEC common language which makes it possible for IEDs of difdevices at the bay level, periodically send their state inforferent manufacturers to communicate communicate with for eachIEDs other. IEC change their states. IEDs connected to these electrical primary common language which makes it possible of difdevices at the bay level, periodically send their state information through GOOSE messages. SCN data flow is mainly ferent manufacturers to with each other. IEC at the bay level, messages. periodically send their state infor61850 architecture includes three protocols: protocols: GOOSE (Generic ferent architecture manufacturers to communicate with GOOSE each other. IEC devices mation through GOOSE SCN data flow is mainly 61850 includes three (Generic at the the bay level, messages. periodically send their inforferent manufacturers to communicate with GOOSE each other. IEC devices mation through GOOSE SCN data flow is periodic while power and communication grid are stable. 61850 architecture includes three protocols: (Generic mation through GOOSE messages. SCN data flowstate is mainly mainly Object-Oriented Substation Event) messaging, MMS (Manu61850 architecture includes three protocols: GOOSE (Generic periodic while the power and communication grid are stable. Object-Oriented Substation Event) messaging, MMS (Manumation through GOOSE messages. SCN data flow is mainly 61850 architecture includes three protocols: GOOSE (Generic periodic while while the power and communication communication grid are are stable. Occurrence of aa fault distributes burst messages, while the Object-Oriented Substation Event) messaging, MMS (Manuthe power and grid stable. facturing Message Specification) and SV (Sampled (Sampled measured Object-Oriented Substation Event) messaging, MMS (Manu- periodic Occurrence of distributes burst messages, while the facturing Message Specification) and SV measured periodic while the power and communication grid are stable. Object-Oriented Substation Event) messaging, MMS (ManuOccurrence of aathefault fault distributes burst messages, while the random flow is minor part, (Zhang et al. 2017). facturing Message Specification) and SV (Sampled measured Occurrence of fault distributes burst messages, while the Values) with two interface buses: process bus and station bus. facturing Message Specification) and SV (Sampled measured random flow is the minor part, (Zhang et al. 2017). Values) with two interface buses: process bus and station bus. Occurrence of a fault distributes burst messages, while the facturing Message Specification) and SV (Sampled measured random flow is the minor part, (Zhang et al. 2017). In this paper, the power grid is assumed to be stable, so the Values) with two interface buses: process bus and station bus. random flow is the minor part, (Zhang et al. 2017). Station bus interconnects the whole substation, provides conValues) with two interface buses: process bus and station bus. In this paper, power is assumed to be stable, so the Station bus interconnects the whole substation, provides conrandom flowdata isthe the minorisgrid part, (Zhang et is al. 2017). Values) with two interface buses: process bus and station bus. In this paper, the power grid is assumed to be stable, so major SCN traffic periodic; this considered as the Station bus interconnects the whole substation, provides conIn this paper, the power grid is assumed to be stable, so Station bus interconnects the whole substation, provides con- major SCN data traffic is periodic; this is considered as the this SCN paper, the poweris is assumed toconsidered be stable, so the Station bushas interconnects wholebysubstation, provides con- In major SCN data traffic isgrid periodic; thistois isdescribe considered as the nominal case. Sometimes it is possible mathematThis work been financiallythe supported Grenoble Institute of Technolmajor data traffic periodic; this as nominal case. Sometimes it is possible to describe mathematThis work has been financially supported by Grenoble Institute of Technol major SCN data traffic is periodic; this is considered as the nominal case. Sometimes it is possible to describe mathematogy in the framework of AGIR project CY-PHY-GRID. This work has been financially supported by Grenoble Institute of Technolically aa deterministic physical phenomenon based on physinominal case. Sometimes it is possible to describe mathematThis work has been of financially supported by Grenoble Institute of Technology in the framework AGIR project CY-PHY-GRID. ically deterministic physical phenomenon based on physi nominal case. Sometimes it is possible to describe This work has been of financially supported by Grenoble Institute of Technol*Institute offramework Engineering Univ. project Grenoble Alpes ogy in AGIR CY-PHY-GRID. ically physical phenomenon based on ogy in the the of AGIR CY-PHY-GRID. ically aa deterministic deterministic physical phenomenon basedmathematon physiphysi*Institute offramework Engineering Univ. project Grenoble Alpes ogy in the framework of AGIR project CY-PHY-GRID. *Institute of Engineering Univ. Grenoble Alpes ically a deterministic physical phenomenon based on physi*Institute of Engineering Univ. Grenoble Alpes
*Institute Univ. Grenoble Alpes 2405-8963of©Engineering 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright © 2018 IFAC 444 Peer review©under of International Federation of Automatic Copyright 2018 responsibility IFAC 444Control. Copyright © 2018 IFAC 444 Copyright © 2018 IFAC 444 10.1016/j.ifacol.2018.11.743 Copyright © 2018 IFAC 444
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Fig. 2. Reactive power over time (kVAR) as the transmitted electrical load profile.
(a) Simulation block diagram of the communication architecture, (Sharma et al. 2015).
(b) Power grid configuration inside the block distribution grid, (Peirelinck et al. 2016).
Fig. 1. The co-simulation performed on an electrical distribution grid containing two renewable sources, and a load in interaction with its communication network. cal laws, which lead us to calculate the exact values of some time-dependent variable at any time instant. However, no phenomenon is totally deterministic, and random events can disturb the process. In power grids, load variations are typically unknown, and there is randomness through the data behavior, (Hong 2013). A model allowing to calculate the probability of the related values between two specified limits is called a probability model or a stochastic model, (Box et al. 1976). Data traffic has such a stochastic behavior and needs to be described by its probability model. There are different stochastic methods to fit a model to the SCN traffic. Most of the previous work on modelling and characterizing the network traffic has either focused on the TCP/IP based communication network, e.g. Internet, or evaluating the static amount of the SCN traffic, (Yang et al. 2017). In this paper, traffic is characterized and modelled by time-series methods, namely Auto Regressive Moving Average (ARMA) models, within a data-driven approach. This paper is organized as follows. Section 2 introduces a brief information of the overall case study in this work. Section 3 presents a detailed description of time-series analysis and ARMA modelling. In Section 4, the considered model is implemented over the IEC 61850 GOOSE data traffic in the considered case study. Section 5 evaluates the effects of some communication channel parameters on traffic model parameters. Finally, key facts are summarized and conclusions are derived in Section 6. 2. CASE STUDY DESCRIPTION One of the properties different nodes could independently control, without the need of a centralized supervisor, is the 445
reactive power absorbed or injected in the grid. Communication network in the smart grid enables implementation of some distributed and cooperative algorithms, such as voltage and/or reactive power control of a distribution grid based on the load prediction methods, in a way that local energy resources cooperate to guarantee a voltage within the defined boundaries, (Manbachi et al. 2014). This change is expected to continue; therefore the communication network, and the devices connected to it, should be able to adapt to this changing nature. The case study considered here includes two renewable generating units, Photovoltaic (PV) and Wind Turbine (WT), committed to compensate the reactive power of a load unit supposed known. Each unit is equipped with an IED and communicates through a Virtual Local Area Network (VLAN). A co-simulation model of electrical and communication grid implemented in MATLAB® /Simulink® (Electrical grid: PowerSim toolbox, Communication grid: SimEvents toolbox) has been used to obtain the data traffic flow, namely the reactive power variation transmitted over IEC 61850 GOOSE (Peirelinck et al. 2016). The focus is here on modelling the variation of number of data packets flowing through the communication channel over time, exchanging information about how much reactive power is able to provide each of them at a given time. Fig. 1 illustrates (a) the IEC 61850 communication network by which (b) a Low Voltage distribution network including the PV, WT and load unit are interconnected. 3. TIME-SERIES MODELLING Time series is a sequence of equispaced data over time. Data will be measured over equal time spaces as a set of n observations which is a sample realization, from an infinite population of such samples: y1 , y2 , ..., yn . To model the SCN data flow, we consider the number of packets pass in between a pair of IEDs: PV and load unit. Load transmits its reactive power absorption to the PV unit through the frames of data. The reactive power variation as the load consumption is sent from the load and received by PV. The aim is to model the cumulative number of packets transmitted according to the reactive power curve in Fig. 2. Time-series analyzing methods detect and explore the linear relationship existing through the current values, historical data and exogenous factors, (Ngo 2013). Among the different time-series analysis methods, Box-Jenkins and exponential smoothing methods are the most widely used to obtain a mathematical model, (Ding 2012). In this work, the Box-Jenkins method has been applied based on ARMA model which is a popular identification model in the automatic control domain. There are different model structures as Auto Regressive (AR), Moving Average (MA), Auto Regressive Moving Average (ARMA), Auto Regressive Integrated Moving Average (ARIMA), and Fractional Auto Regressive Integrated Moving Average (FARIMA). Here ARMA is used which outputs a time series in response at a sequence of white Gaussian noise, (Box
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et al. 1976). To look at the system as a linear filter is likely to serve for control purposes, and ARMA as a simple linear class has been selected to be able to apply all the linear analyzing methods. 3.1 ARMA Modelling Box-Jenkins methodology is implemented within five steps as below, (Pankratz 1983): 1. Data preprocessing, 2. Model identification, 3. Estimation of the model parameters, 4. Diagnostic verification of model, 5. possibly Forecasting. ARMA(p,q) polynomial expression is written as below: wt = ϕ1 wt−1 + ϕ2 wt−2 + ... + ϕp wt−p + at + θ1 at−1 + θ2 at−2 + ... + θq at−q , (1) where wt is the data sampled periodically and preprocessed if necessary, at is the white noise sequence. ϕi and θj are respectively the process and noise coefficients which can be written as polynomial functions of a delay operator, z −1 , as below: ϕ(z −1 ) = 1 + ϕ1 z −1 + ϕ2 z −2 + ... + ϕp z −p θ(z −1 ) = 1 − θ1 z −1 − θ2 z −2 − ... − θq z −q (2) −k where z wt = wt−k , such that the transfer function of a discrete-time filter is obtained: θ(z −1 ) ψ(z −1 ) = (3) ϕ(z −1 ) 4. APPLICATION TO THE CONSIDERED CASE STUDY In this section, the implementation of ARMA model over the data traffic obtained by simulation is explained. Load reactive power variations in Fig. 2 are sent through a communication channel described in Appendix A, referred to as the nominal case. Data should be first prepared and smoothed over time. So, any trend (linear, cyclic) through the sampled data should be removed. Then, applying a proper type of ARMA model with the best orders (p,q) will give the stochastic model of data in a simple polynomial form. Finally, the model accuracy is evaluated by diagnostics tools: Residuals, Mean Squared Error (MSE), and Goodness of Fit (GFit). ARMA model can be used as a predictive model to forecast the future behavior of data, (Wang 2013). 4.1 Data preparation ARMA model should be applied on a special class of time series which is stationary. They are assumed to be in a specific form of statistical equilibrium, and in particular, vary over time in a stable manner about a fixed mean (constant mean, constant variance). Since many real-world time series have nonstationary characteristics, the non-stationarity behavior is removed by special tools. One way to detect different trends is to plot data and find them visually. In addition, the autocorrelation curve over the series can also be used. There are different nonstationarity factors and removal tools, as follows. Detrending – sometimes, there is a linear time trend which increases or decreases through time. Since any dependence to time should not exist, it can be removed by a simple difference method. Thus, a new time series is obtained by differencing each value from its previous value, which has more stable 446
variation around its mean. By noting yt the original, directly measured, time series, then the simple difference is: (4) yt = z −1 yt = yt − yt−1 The simple difference gives the cumulative number of packets being transmitted in each sampling period. Zero mean – the mean value of the time series is removed to have data variations around zero. y¯ t = yt − mean(yt ), (5) ¯ where y t is the zero-mean series. Desimilarity – while modelling the SCN traffic, a different behavior to the Internet traffic may be found. Internet traffic shows only Short Range Dependence (SRD), but in the SCN traffic depending on the communication protocol, also a Long Range Dependence (LRD) characteristic could exist, (Kolbusz et al. 2006). ARMA can precisely model the SRD characteristics but not LRD. Hence, to be able to use ARMA for the SCN traffic as well, we could apply a fractional difference over data to eliminate the LRD characteristics, (Markakis et al. 2012). From practical modelling point of view, such processes may exhibit certain features that could give the impression of the need for differencing to achieve stationarity. To evaluate the selfsimilarity and LRD through the data, the Hurst parameter (H) can be used. H can be evaluated by three different methods; R/S analysis, variance-time analysis, and periodogram analysis. Here, R/S method was used, (Cano 2000). If H is such that 0.5 < H < 1, then some LRD characteristic through the traffic may be identified. Closer to 1, stronger LRD characteristic exists. To obtain time series with only SRD characteristic, the fractional difference is applied as many times as needed to get H closer to 0.5, (Jensen et al. 2014). Note that the presence of H greater than 0.5 is not necessarily indicative of long-term dependence, not being sufficient reason to apply the fractional difference. So, models of different orders (with and without fractional difference application) may be fitted to the data and if the best model fits well for not fractioned series, the conclusion is that the time series contains no long-term dependence. Deseasonality – a seasonal pattern may exist through the time series. These fluctuations are usually due to the measuring period and the behavior of data which is transmitted through the considered traffic. For series with seasonal periodicity, as for the linear trend, it is necessary to remove this periodic trend over time. Like the simple difference, to smooth the seasonal behavior, a seasonal difference may be used. In a seasonal process, the mean value for each season will vary from the others, which leads to a nonstationary series. Considering the sampling process, the seasonal period, s, can be found out. To seasonally differentiate, we subtract from each observation the observation occurring s sampling times earlier: −s D ¯ ∆D ) y t, (6) s wt = (1 − z
where wt is the preproccesed series (stationary, detrended, deseasonalized), and D is the number of seasonal difference required to apply, s is the seasonal period. If D = 1: wt = y¯ t − y¯ t−s . 4.2 Model identification At the identification stage, two graphical tools may help to find out the proper type of ARMA model by measuring the correlation through the observations within the series itself. These plots are called an estimated Auto Correlation Function
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(ACF) and an estimated Partial Auto Correlation Function (PACF). ACF and PACF measure the statistical relationships within a series, (Brockwell et al. 2016). The ACF and PACF plots can provide an indication about the best p and q. In order to find the proper model orders, p and q, here the MSE value has been considered. The best orders are selected for which the estimated model results in its minimum value.
residual test. By selection of p and q, the ARMA coefficients will result as the final step of the process. In this work, we have used the first four steps of Box-Jenkins methodology, i.e. no forecasting. For the nominal case, the best estimation model has GFit = 89.96% and MSE = 0.4497 for ARMA(6,4). The polynomial coefficients of ARMA model are given in (A-1) in the Appendix.
4.3 Parameter estimation
4.5 Mathematical Expression
Box-Jenkins method suggests some diagnostic checks to help determining if an estimated model is statistically adequate. A model that fails these diagnostic tests is rejected. Furthermore, the results at this stage may also indicate how a model could be improved. This leads us back to the identification stage. The cycle of identification, estimation, and diagnostic checks is repeated until a good final model is found out. The ARMA model coefficients are estimated and model is validated through the diagnostics concerning MSE and GFit. Fitting a proper model results in a sequence of uncorrelated residuals. The residual ACF is plotted and if it shows significant autocorrelation in the residuals, the model should be modified to include more auto regressive or moving average orders. A satisfactory model may be used to forecast the future behavior of series, (Yaffee et al. 2000).
As we have the ARMA model of the stochastic data behavior, by adding all the previously removed trends, we will reconstruct the original measured traffic. To do so, inverse operations of all the differences (simple difference, mean difference and seasonal difference) are applied to the ARMA model output. Through the inversion, the data traffic can be mathematically expressed as below, beginning from the stochastic behavior (white Gaussian noise), then adding the deterministic behavior: - Estimated ARMA output: a sequence of white Gaussian noise at is passed through the ARMA(p,q) already identified and estimated. θ(z −1 ) at (7) wt = ϕ(z −1 ) - Add the seasonality: the periodical trend subtracted by seasonal difference is added here to the ARMA output.
4.4 Model implementation The ARMA model is applied to the sampled data over our simulated network. The first step is to find a proper sampling period. GOOSE protocol has no hand shaking topology as TCP/IP protocol, so to ensure the arrival of the packets, the messages are retransmitted four times at each data change. As the cosimulation of this work has a minimum retransmission period equal to 10 ms, so any changes in the number of packets will be at least on this time. Sampling period selection is an important step to have a series following the data changes properly. Since the minimum transmission period of GOOSE messages in this simulation is equal to 10 ms, a reasonable choice for the sampling time would be less than 12 . 10 ms (according to the Shannon’s theorem, (Marks 1991)). The sampling period has been chosen as Ts = 2 ms, and gives 7500 samples. The modelling procedure is illustrated by the flowchart in Fig. 3, in which related processed data for each step is assigned. There is a linear upward trend over time in the original sampled data, so to remove the trend we have applied the firstorder simple difference. Next, a mean value of data has been removed to achieve a zero-mean process. As explained previously, model identification has been applied with and without a fractional difference. These models have been evaluated by their GFit and MSE models without fractional difference lead to a more accurate result. By applying the seasonal difference with s = 3 s/Ts = 1500 sample times, the seasonal trend is removed. Now, data is preprocessed completely and could be modelled by a properly selected ARMA model. The way we decided to select a proper ARMA model, was to find the minimum MSE value for all the possible pairs of p and q up to some values from where no significant increase in accuracy is obtained. We will have the best GFit while its MSE is minimized. Final step is to check the whiteness of the model residuals. If residuals are mostly close to zero, then p and q are the best model parameters. If not, we should increase p and q to pass the 447
1 θ(z −1 ) at , (8) ϕ(z −1 ) (1 − z −s ) where x¯ t denotes the series including the seasonal trend. - Add the mean value: x¯ t =
1 θ(z −1 ) at + mean(yt ), = (9) −1 ϕ(z ) (1 − z −s ) where x t is the series after adding the mean value which was removed by the zero-mean process. - Inversion of simple difference (equivalent to integration): x t
1 1 + mean(y ) t (1 − z −s ) (1 − z −1 ) (10) Fig. 4 shows the estimated time series against the original one, that is, the number of packets transmitted over the communication channel under the considered scenario, in the nominal case (see the Appendix). xt =
θ(z −1 ) at ϕ(z −1 )
5. PARAMETRIC ANALYSIS To go further, we have studied how the communication channel parameters affect the traffic model. Thus, three main network channel characteristics were studied: packet loss, channel speed and cable length. For each factor, different values have been selected and set as new channel characteristics (all other parameters are constant at their nominal values), then simulation has been re-run and related traffic was sampled. So, the achieved series were modelled by a proper ARMA model. To assess the changes, we studied the identified model frequency response, so Bode plots are drawn in each case of parameter variation.
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Select an approprate time scale
yes
ACF = 0 & PACF = 0? no Plot sampled data
yes
Time Linear Trend?
no Simple Difference
Zero-Mean Seasonal Trend?
yes
Seasonal no Difference parameter estimation Identify p & q with min MSE
Residual = 0?
no
yes yes ARMA
0.8
Fig. 3. Flowchart of the ARMA model implementation and model validation steps for the considered case study in the nominal case described in Appendix A.
Fig. 4. The estimated time series in comparison with the original measured data traffic for the considered case study in the nominal case. - Packet loss: The probability of packet loss (PL) has been set to four different values. In the nominal case, there is no packet loss (PL = 0%). As shown in Fig. 5 of related Bode plots for each case, by increasing PL from 5% to 20% the ARMA orders increase too so adds up the number of poles and zeros. Variability exhibited in low frequency is more obvious in the 448
Fig. 5. Estimated ARMA model Bode plots for PL = 5%, 10%, 15%, and 20%, the nominal case corresponding to PL = 0%. Bode gain plot, whereas the Bode phase plots differs mainly in high frequency, which suggests that, the more intense the traffic is, the more sensitive the delays are to the variation of this parameter. - Channel rate or channel speed: In the same way as for PL, this time the channel transfer rate (CHR, nominal rate in this cosimulation is defined as 106 bytes/s) has been changed. Fig. 6
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Fig. 6. Estimated ARMA model Bode plots for CHR = 0.3 . 106 , 0.4 . 106 , and 0.5 . 106 bytes/s, the nominal case corresponding to CHR = 106 bytes/s. clearly shows the changes on the traffic model. If the channel capacity decreases to half, the traffic still flows close to the nominal status, but as CHR is tightened more than a half, the estimated model differs significantly from the nominal case, corresponding to somehow ill-configured communication network. In this way, limits for improper configuration of the channel capacity may be identified. - Cable Length: Variation of the length of the connecting cable in between the IEDs indicated no considerable effect on the traffic stochastic model. 6. CONCLUSION This paper has investigated a data-driven approach of modelling data traffic through communication networks within smart grids. The case of a distribution grid with two renewable energy sources which exchange reactive power information for voltage regulation purposes by means of IEC 61850 GOOSE protocol has been considered. A time-series-based identification procedure has been presented. A sensitivity study has been conducted to assess how the parameters of identified ARMA models vary in relation to variations of some communication network parameters. Further works will consider the potential of the proposed identification procedure of being applied on line, for control purposes – possibly in a linearparameter-varying framework – in order to formally take account of interactions between the energy layer and the communication layer in smart grids. REFERENCES Andrén, F., Bründlinger, R., and Strasser, T. (2014). IEC 61850/61499 Control of Distributed Energy Resources: Concept, Guidelines, and Implementation. IEEE Transactions on Energy Conversion, Chapter 2, 29(4), 1008-1017. Box, G. E. P., Jenkins, G. M., Reinsel, G. C., and Ljung G. M. (1976). Time-series analysis: forecasting and control. Wiley, New Jersey. Brockwell, P. J., Davis, R. A. (2016). Introduction to time series and forecasting. Springer International Publishing, Springer Texts in Statistics, Switzerland, Chapter 3, 73-97. Cano, J.C., Manzoni, P. (2000). On the Use and Calculation of the Hurst Parameter with MPEG Videos Data Traffic. IEEE in Euromicro Conference 26th, 1, 448-455. 449
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Ding, N. (2012). Load models for operation and planning of electricity distribution networks with smart metering data. HAL, Doctoral dissertation, Univ. Grenoble Alpes. Hong, W. C. (2013). Intelligent energy demand forecasting. Springer Science and Business Media, Chapter 2, 21-40. Jensen, A., Nielsen, M. (2014). A fast fractional difference algorithm. Journal of Time Series Analysis, 35(5), 428-436. Kolbusz, J., Paszczyn, S., and Wilamowski, B. M. (2006). Network Traffic Model for Industrial Environment. IEEE Transactions on Industrial Informatics, 2(4), 213-220. Li, W., et al (2014). Cosimulation for Smart Grid Communications. IEEE Transactions on Industrial Informatics, 10(4), 2374-2384. Mackiewicz, R. E. (2006). Overview of IEC 61850 and Benefits. IEEE In Power Systems Conference and Exposition PSCE 06, 57, 623-630. Manbachi, M., et al. (2014). Real-Time Adaptive VVO/CVR Topology Using Multi-Agent System and IEC 61850-Based Communication Protocol. IEEE Transactions on Sustainable Energy, 5(2), 587-597. Marks, R. J. I. (2012). Introduction to Shannon Sampling and Interpolation Theory. Springer Science and Business Media. Ngo, T. H. D. (2013). The Box-Jenkins methodology for timeseries models. SAS Global Forum Conference, 6, 454-2013. Pankratz, A. (1983). Forecasting with Univariate Box-Jenkins Models. Wiley, New Jersey, 6. Peirelinck, T., Bratcu, A. I., and Bésanger, Y. (2016). Impact of IEC 61850 GOOSE Communication Quality on Decentralized Reactive Power Control in Smart Distribution Grids – a Cosimulation Study. IEEE Electrical Power and Energy Conference (EPEC), Ottawa, Canada, 1-6. Sharma, E., Bratcu A. I., Chiculit˛ă, C., and Bésanger, Y. (2015). Co-simulation of a Low-Voltage Utility Grid Controlled over IEC 61850 protocol. International Conference on Electric Utility Deregulation and Restructuring and Power Technologies (DRPT), Changsha, China, 5, 2365-2372. Yaffee, R. A., McGee, M. (2000). An introduction to time-series analysis and forecasting: with applications of SAS and SPSS. Academic Press, Inc. Orlando, FL, USA, 222-244. Yang, T., Zhao, R., Zhang, W., and Yang, Q. (2017). On the Modelling and Analysis of Communication Traffic in Intelligent Electric Power Substations. IEEE Transactions on Power Delivery, 32(3), 1329-1338. Zhang, Z., Huang, X., Keune, B., Cao, Y., and Li, Y. (2017). Modelling and simulation of data flow for VLAN-based communication in substations. IEEE Systems Journal, 11(4), 2467. Appendix A. THE NOMINAL CASE PROPERTIES The nominal case considered through this work, has been sampled by a sampling period Ts = 2 ms without any packet loss. The channel speed is set to 106 bytes/s, and the cable length is equal to 1 km. The ARMA(6,4) polynomial model estimated for the nominal case is as below: wt = 1.758wt−1 − 0.06078wt−2 − 0.7888wt−3 − 0.2517wt−4 + 0.3021wt−5 + 0.04102wt−6 + at − 0.8397at−1 − 0.6358at−2 + 0.1521at−3 + 0.3345at−4 (A.1)
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Time-series Modelling of IEC 61850 GOOSE Time-series Time-series Modelling Modelling of of IEC IEC 61850 61850 GOOSE GOOSE Communication Traffic between IEDs in smart Time-series Modelling of IEC 61850 GOOSE Communication Traffic between IEDs Communication Traffic between IEDs in in smart smart grids a parametric analysis Communication Traffic between IEDs in smart grids a parametric analysis grids - a parametric analysis grids - a parametric analysis R. Feizimirkhani ∗,∗∗ A. I. Bratcu ∗ Y. Bésanger ∗∗
∗ ∗∗ R. Feizimirkhani ∗,∗∗ Bésanger ∗,∗∗ A. I. Bratcu ∗ ∗∗ ∗ Y. ∗∗ R. A. I. Bratcu Y. Bésanger R. Feizimirkhani Feizimirkhani ∗,∗∗ A. I. Bratcu Y. Bésanger ∗,∗∗ ∗ ∗∗ A. I. Bratcu Y. Bésanger ∗R. Feizimirkhani Univ. Grenoble Alpes, CNRS, Grenoble INP*, GIPSA-lab, ∗ Grenoble Alpes, CNRS, Grenoble INP*, GIPSA-lab, ∗ ∗ Univ. Univ. Grenoble Alpes, CNRS, Grenoble Grenoble INP*, GIPSA-lab, GIPSA-lab, 38000 Grenoble, France CNRS, INP*, ∗ Univ. Grenoble Alpes, 38000 Grenoble, France Univ. Grenoble Alpes, CNRS, Grenoble INP*, GIPSA-lab, 38000 Grenoble, France (e-mail: [email protected]), 38000 Grenoble, France (e-mail: [email protected]), 38000 Grenoble, France (e-mail: [email protected]), ([email protected]) (e-mail: [email protected]), ([email protected]) ∗∗ (e-mail: [email protected]), ([email protected]) Univ. Grenoble Alpes, CNRS, Grenoble INP*, G2Elab, ([email protected]) ∗∗ Grenoble Alpes, CNRS, INP*, ∗∗ ([email protected]) ∗∗ Univ. Univ. Grenoble Alpes, CNRS, Grenoble Grenoble INP*, G2Elab, G2Elab, 38000 Grenoble, France, Univ. Grenoble Alpes, CNRS, Grenoble INP*, G2Elab, ∗∗ 38000 Grenoble, France, Univ. Grenoble Alpes, CNRS, Grenoble INP*, G2Elab, 38000 Grenoble, France, (e-mail: [email protected]) 38000 Grenoble, France, (e-mail: [email protected]) 38000 Grenoble, France, (e-mail: (e-mail: [email protected]) [email protected]) (e-mail: [email protected]) Abstract: Nowadays Nowadays power power grids grids are are intelligent intelligent since since their their protection, protection, supervision supervision and and control control are are Abstract: Abstract: Nowadays power grids are intelligent since their protection, supervision and control are held by a communication network through which different Intelligent Electronic Devices (IEDs) Abstract: Nowadays power grids are intelligent since their protection, supervision and control are held by a communication network through which Intelligent Electronic Devices (IEDs) Abstract: grids intelligent sincedifferent their protection, supervision and control are held by communication network through different Intelligent Electronic Devices (IEDs) are interoperating. interoperating. Topower design and are maintain anwhich efficient Substation Communication Network (SCN) held by aa Nowadays communication network through which different Intelligent Electronic Network Devices (IEDs) are To design and maintain an efficient Substation Communication (SCN) held by a communication network through which different Intelligent Electronic Devices (IEDs) are interoperating. To design and maintain an efficient Substation Communication Network (SCN) with high transmission quality, developing a unitary mathematical model of the SCN data traffic as are interoperating. To design and maintain an efficient Substation Communication Network (SCN) with high transmission quality, developing aaan unitary mathematical model of the SCN data traffic as are interoperating. Toofdesign and maintain efficient Substation Communication Network (SCN) with high transmission quality, developing unitary mathematical model of the SCN data traffic as underlying paradigm any control design approach is an important issue. In this paper, a stochastic with high transmission quality, developing a unitary mathematical model of the SCN data traffic as underlying paradigm of quality, any control design approach is an important issue. In this paper, aa stochastic with high transmission developing a aunitary model the data traffic as underlying paradigm any design is an important issue. In this paper, representation of data dataof traffic is derived, derived, andapproach parametric analysis over theof communication channel underlying paradigm oftraffic any control control design approach ismathematical an analysis importantover issue. Incommunication thisSCN paper, a stochastic stochastic representation of is and a parametric the channel underlying paradigm oftraffic any control design is anisanalysis important issue. Incommunication this paper, distribution a stochastic representation of data traffic is derived, derived, andapproach a parametric parametric analysis over thean communication channel characteristics is presented. The identification method illustrated on electrical representation of data is and a over the channel characteristics is presented. identification method is illustrated electrical distribution representation data traffic The is derived, and a parametric overon thean channel characteristics is presented. The identification method is illustrated on an grid containing containingof two renewable sources which are exchanging information byelectrical means of ofdistribution IEC 61850 characteristics istwo presented. The identification method isanalysis illustrated on ancommunication electrical distribution grid renewable sources which are exchanging information by means IEC 61850 characteristics is presented. The identification method is illustrated on an electrical distribution grid containing two renewable sources which are exchanging information by means of IEC 61850 GOOSE (Generic Object-Oriented Substation Event) communication protocol in the context of aa grid containing two renewable sources which are exchanging information by means of IEC 61850 GOOSE (Generic Object-Oriented Substation Event) communication protocol in the context of grid containing two renewable sources which are exchanging information byofmeans of IEC 61850 GOOSE (Generic Object-Oriented Substation Event) communication protocol in the context of simple distributed reactive power control. The co-simulation and code process both electrical andaa GOOSE (Generic Object-Oriented Substation Event) communication protocol in the context of simple distributed reactive power control. The co-simulation code process of both electrical and ® and ® protocol GOOSE (Genericconfigurations Object-Oriented Substation Event) communication in the context of a simple distributed reactive power control. The co-simulation and code process of both electrical and communication are performed in MATLAB /Simulink environment. simple distributed reactive power control. The co-simulation and code process of both electrical and ® ® /Simulink environment. communication configurations are performed in MATLAB ® ® simple distributed reactive power control. The co-simulation and code process of both electrical and ® ® /Simulink environment. environment. communication configurations configurations are are performed performed in in MATLAB MATLAB /Simulink communication © 2018, IFAC (International Federation of Automatic Control)® /Simulink Hosting by® Elsevier Ltd. All rights reserved. environment. communication configurations are performed in MATLAB Keywords: Smart Grid, Time Series, IEC 61850 GOOSE, Communication Traffic, ARMA Keywords: Smart Grid, Time Series, IEC 61850 GOOSE, Communication Traffic, ARMA Keywords: Keywords: Smart Smart Grid, Grid, Time Time Series, Series, IEC IEC 61850 61850 GOOSE, GOOSE, Communication Communication Traffic, Traffic, ARMA ARMA Keywords: Smart Grid, Time Series, IEC 61850 GOOSE, Communication Traffic, ARMA 1. INTRODUCTION nectivity between central management and individual bays 1. INTRODUCTION INTRODUCTION nectivity between central management and individual bays 1. nectivity between central management and individual bays and also connects different bays among themselves and 1. INTRODUCTION nectivity between central management and individual bays and also connects different bays among themselves and bays 1. INTRODUCTION nectivity between central management and individual and also connects different bays among themselves and bays with Supervisory, Control and Data Acquisition (SCADA) sysand also connects different bays among themselves and bays The energy sector as a whole is standing on the frontier of big Supervisory, Control and Data Acquisition (SCADA) sysThe energy energy sector sector as as aa whole whole is is standing standing on on the the frontier frontier of of big big with and also connects different bays among themselves anda bays with Supervisory, Control and Data Acquisition (SCADA) tem. On the other hand, process bus connects within bay, The with Supervisory, Control and Data Acquisition (SCADA) syschanges. An important challenge to enable all these changes The energy sector as a whole is standing on the frontier of big tem. On the other hand, process bus connects within a sysbay, changes. An important challenge to enable all these changes with Supervisory, Control and Data Acquisition (SCADA) sysThe energy sector as a whole is standing on the frontier of big tem. On the other hand, process bus connects within aaflowbay, primary equipment to IED, (Mackiewicz 2006). Messages changes. An important challenge to enable all these changes tem. On the other hand, process bus connects within bay, is the integration of multiple Distributed Energy Resources changes. An important challenge to enable all these changes primary equipment to IED, (Mackiewicz 2006). Messages flowis the integration of multiple Distributed Energy Resources tem. On equipment the the other hand, process bus connects within aflowbay, changes. Anthis important challenge to enable all theseResources changes primary to IED, (Mackiewicz 2006). Messages ing through IEC 61850 SCN (Substation Communication is the integration of multiple Distributed Energy primary equipment to IED, (Mackiewicz 2006). Messages flow(DERs). For union to be successful, Information and Comis the integration of multiple Distributed Energy Resources through the IEC 61850 SCN (Substation Communication (DERs). For this this union union to be be successful, successful, Information and ComCom- ing primary equipment to IED, (Mackiewicz 2006). Messages flowis the integration of multiple Distributed Energy Resources ing through the IEC 61850 SCN (Substation Communication Network) correspond to electrical information generated by (DERs). For to Information and through the IEC 61850 SCN (Substation Communication munication Technology (ICT) will have have Information to be be extensively extensively used ing (DERs). For this union to(ICT) be successful, and ComNetwork) correspond to electrical information generated by munication Technology will to used ing through the IEC 61850 SCN (Substation Communication (DERs). For this union to be successful, Information and ComNetwork) correspond to electrical information generated by various electrical devices. Messages can further be classified munication Technology (ICT) will have to be extensively used Network) correspond to electrical information generated by by the system operators. Only this combination of electrical munication Technology (ICT) will have to be extensively used various electrical devices. Messages can further be classified by the system operators. Only this combination of electrical Network) correspond to electrical information generated by munication Technology (ICT) will have to be extensively used various electrical devices. Messages can further be classified into three categories according to their distribution over time: by the system operators. Only this combination of electrical various electrical devices. Messages can further be classified grids and communication networks will allow challenges to by the system operators. Only this combination of electrical into three categories according to their distribution over time: grids and communication networks will allow challenges to various electrical devices. Messages can further be classified by the system operators. Only this combination of electrical into three categories according to their distribution over time: periodic, and burst. During operation of power grids and networks allow challenges to threerandom, categories according to theirthe distribution over time: be overcome and the the "smart "smart grid" to towill be truly truly smart (Andrén grids and communication communication networks will allowsmart challenges to into and burst. During the operation of power be overcome and grid" be (Andrén into threerandom, categories according to their distribution over time: grids and communication networks will allowsmart challenges to periodic, periodic, random, and burst. During the operation of power substation, the states of individual substation IEDs colbe overcome and the "smart grid" to be truly (Andrén periodic, random, and burst. During the operation ofare power et al. 2014). The inter-dependency of electrical dynamics and be overcome and the "smart grid" to be truly smart (Andrén substation, the states of individual substation IEDs are colet al. 2014). The The inter-dependency of electrical dynamics and periodic, random, and burst. During the operation of power be overcome and the "smart grid" to be truly smart (Andrén substation, the states of individual substation IEDs are collected periodically and sent to the control center. Such peet al. 2014). inter-dependency of electrical dynamics and substation, the states of individual substation IEDs are colcommunication systems is a challenge in its own right that et al. 2014). The inter-dependency of electrical dynamics and lected periodically and sent to the control center. Such pecommunication systems is aa challenge challenge in its its own own right that that substation, the states ofsent individual substation IEDsSuch are colet al. 2014). Thelightly. inter-dependency of electrical dynamics and lected periodically and to the control center. periodical data acquisition is required for decision-making, in communication systems is in right lected periodically and sent to the control center. Such pecannot be taken Since the communication network will communication systems is a challenge in its own right that riodical data acquisition is required for decision-making, in cannot be taken lightly. Since the communication network will lected periodically and sent to the control center. Such pecommunication systems is a challenge in its own right that riodical data acquisition is required for decision-making, in order to maintain the stability of the overall power system cannot be taken lightly. Since the communication network will riodical data acquisition is required for decision-making, in always be prone to unexpected errors, there will be a need to cannot be taken lightly. Since the communication network will order to maintain the stability of the overall power system always be prone to unexpected errors, there will be a need to riodical data acquisition is required for decision-making, in cannot be taken lightly. Since the communication network will order to maintain the stability of the overall power system operation. Burst data flow consists of protection action inforalways be prone to unexpected errors, there will be a need to order to maintain the stability of the overall power system simulate the effect of these malfunctions on the electrical grid. always be prone to unexpected errors, there will be a need to operation. Burst data flow consists of protection action inforsimulate the effecttoof ofunexpected these malfunctions malfunctions on the the electrical grid. order toswitch-changing maintain theflow stability of the overall power system always be prone errors, there will be a need to operation. Burst data flow consists of protection action information, information and record information simulate the effect these on electrical grid. operation. Burst data consists of protection action inforThis is why co-simulation of both networks is a very important simulate theco-simulation effect of theseofmalfunctions onisthe electrical grid. mation, switch-changing information and record information This is why why both networks networks very important operation. Burst dataofflow consists of bay protection action inforsimulate the effect of these electrical grid. mation, switch-changing information and record information about the sequence events in the is generThis of both is aaa very important mation, switch-changing information and level, recordand information factor in theco-simulation further implementation of on smart grids. If done done This is is in why co-simulation ofmalfunctions both networks isthe very important about the sequence of events in the bay level, and is generfactor the further implementation of smart grids. If mation, switch-changing information and record information This is why co-simulation of both networks is a very important about the sequence of events in the bay level, and is generated only when any fault occurs. During normal operation, factor implementation If the sequence offault events in the bay level, andoperation, is genercorrectly, this further will benefit benefit the stability stability of (Li,smart W., et etgrids. al. 2014). 2014). factor in in the the further implementation of smart grids. If done done about ated only when any occurs. During normal correctly, this will the (Li, W., al. about the sequence events inand the bay level, andoperation, is generfactor in the further implementation of smart grids. If done ated only when any occurs. During normal monitoring and control devices, protection devices, do not correctly, this will benefit the stability (Li, W., et al. 2014). ated only when anyoffault fault occurs. During normal operation, IEC 61850 is a communication standard playing the role of a correctly, this will benefit the stability (Li, W., et al. 2014). monitoring and control devices, and protection devices, do not IEC 61850 is a communication standard playing the role of a ated only when any fault occurs. During normal operation, correctly, this will benefit the stability (Li, W., et al. 2014). monitoring and control devices, and protection devices, do not change their states. IEDs connected to these electrical primary IEC 61850 is a communication standard playing the role of a monitoring and control devices, and protection devices, do not common language which makes it possible for IEDs of difIEC 61850language is a communication standard playing the role of a change their states. IEDs connected to these electrical primary common which makes it possible for IEDs of difmonitoring and control devices, andto protection devices, do not IEC 61850 is a communication standard playing the role of a change their states. IEDs connected these electrical primary devices at the bay level, periodically send their state inforcommon language which makes it possible for IEDs of difchange their states. IEDs connected to these electrical primary ferent manufacturers to communicate with each other. IEC common language which makes it possible for IEDs of difdevices at the bay level, periodically send their state inforferent manufacturers to communicate communicate with for eachIEDs other. IEC change their states. IEDs connected to these electrical primary common language which makes it possible of difdevices at the bay level, periodically send their state information through GOOSE messages. SCN data flow is mainly ferent manufacturers to with each other. IEC at the bay level, messages. periodically send their state infor61850 architecture includes three protocols: protocols: GOOSE (Generic ferent architecture manufacturers to communicate with GOOSE each other. IEC devices mation through GOOSE SCN data flow is mainly 61850 includes three (Generic at the the bay level, messages. periodically send their inforferent manufacturers to communicate with GOOSE each other. IEC devices mation through GOOSE SCN data flow is periodic while power and communication grid are stable. 61850 architecture includes three protocols: (Generic mation through GOOSE messages. SCN data flowstate is mainly mainly Object-Oriented Substation Event) messaging, MMS (Manu61850 architecture includes three protocols: GOOSE (Generic periodic while the power and communication grid are stable. Object-Oriented Substation Event) messaging, MMS (Manumation through GOOSE messages. SCN data flow is mainly 61850 architecture includes three protocols: GOOSE (Generic periodic while while the power and communication communication grid are are stable. Occurrence of aa fault distributes burst messages, while the Object-Oriented Substation Event) messaging, MMS (Manuthe power and grid stable. facturing Message Specification) and SV (Sampled (Sampled measured Object-Oriented Substation Event) messaging, MMS (Manu- periodic Occurrence of distributes burst messages, while the facturing Message Specification) and SV measured periodic while the power and communication grid are stable. Object-Oriented Substation Event) messaging, MMS (ManuOccurrence of aathefault fault distributes burst messages, while the random flow is minor part, (Zhang et al. 2017). facturing Message Specification) and SV (Sampled measured Occurrence of fault distributes burst messages, while the Values) with two interface buses: process bus and station bus. facturing Message Specification) and SV (Sampled measured random flow is the minor part, (Zhang et al. 2017). Values) with two interface buses: process bus and station bus. Occurrence of a fault distributes burst messages, while the facturing Message Specification) and SV (Sampled measured random flow is the minor part, (Zhang et al. 2017). In this paper, the power grid is assumed to be stable, so the Values) with two interface buses: process bus and station bus. random flow is the minor part, (Zhang et al. 2017). Station bus interconnects the whole substation, provides conValues) with two interface buses: process bus and station bus. In this paper, power is assumed to be stable, so the Station bus interconnects the whole substation, provides conrandom flowdata isthe the minorisgrid part, (Zhang et is al. 2017). Values) with two interface buses: process bus and station bus. In this paper, the power grid is assumed to be stable, so major SCN traffic periodic; this considered as the Station bus interconnects the whole substation, provides conIn this paper, the power grid is assumed to be stable, so Station bus interconnects the whole substation, provides con- major SCN data traffic is periodic; this is considered as the this SCN paper, the poweris is assumed toconsidered be stable, so the Station bushas interconnects wholebysubstation, provides con- In major SCN data traffic isgrid periodic; thistois isdescribe considered as the nominal case. Sometimes it is possible mathematThis work been financiallythe supported Grenoble Institute of Technolmajor data traffic periodic; this as nominal case. Sometimes it is possible to describe mathematThis work has been financially supported by Grenoble Institute of Technol major SCN data traffic is periodic; this is considered as the nominal case. Sometimes it is possible to describe mathematogy in the framework of AGIR project CY-PHY-GRID. This work has been financially supported by Grenoble Institute of Technolically aa deterministic physical phenomenon based on physinominal case. Sometimes it is possible to describe mathematThis work has been of financially supported by Grenoble Institute of Technology in the framework AGIR project CY-PHY-GRID. ically deterministic physical phenomenon based on physi nominal case. Sometimes it is possible to describe This work has been of financially supported by Grenoble Institute of Technol*Institute offramework Engineering Univ. project Grenoble Alpes ogy in AGIR CY-PHY-GRID. ically physical phenomenon based on ogy in the the of AGIR CY-PHY-GRID. ically aa deterministic deterministic physical phenomenon basedmathematon physiphysi*Institute offramework Engineering Univ. project Grenoble Alpes ogy in the framework of AGIR project CY-PHY-GRID. *Institute of Engineering Univ. Grenoble Alpes ically a deterministic physical phenomenon based on physi*Institute of Engineering Univ. Grenoble Alpes
*Institute Univ. Grenoble Alpes 2405-8963of©Engineering 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright © 2018 IFAC 444 Peer review©under of International Federation of Automatic Copyright 2018 responsibility IFAC 444Control. Copyright © 2018 IFAC 444 Copyright © 2018 IFAC 444 10.1016/j.ifacol.2018.11.743 Copyright © 2018 IFAC 444
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Fig. 2. Reactive power over time (kVAR) as the transmitted electrical load profile.
(a) Simulation block diagram of the communication architecture, (Sharma et al. 2015).
(b) Power grid configuration inside the block distribution grid, (Peirelinck et al. 2016).
Fig. 1. The co-simulation performed on an electrical distribution grid containing two renewable sources, and a load in interaction with its communication network. cal laws, which lead us to calculate the exact values of some time-dependent variable at any time instant. However, no phenomenon is totally deterministic, and random events can disturb the process. In power grids, load variations are typically unknown, and there is randomness through the data behavior, (Hong 2013). A model allowing to calculate the probability of the related values between two specified limits is called a probability model or a stochastic model, (Box et al. 1976). Data traffic has such a stochastic behavior and needs to be described by its probability model. There are different stochastic methods to fit a model to the SCN traffic. Most of the previous work on modelling and characterizing the network traffic has either focused on the TCP/IP based communication network, e.g. Internet, or evaluating the static amount of the SCN traffic, (Yang et al. 2017). In this paper, traffic is characterized and modelled by time-series methods, namely Auto Regressive Moving Average (ARMA) models, within a data-driven approach. This paper is organized as follows. Section 2 introduces a brief information of the overall case study in this work. Section 3 presents a detailed description of time-series analysis and ARMA modelling. In Section 4, the considered model is implemented over the IEC 61850 GOOSE data traffic in the considered case study. Section 5 evaluates the effects of some communication channel parameters on traffic model parameters. Finally, key facts are summarized and conclusions are derived in Section 6. 2. CASE STUDY DESCRIPTION One of the properties different nodes could independently control, without the need of a centralized supervisor, is the 445
reactive power absorbed or injected in the grid. Communication network in the smart grid enables implementation of some distributed and cooperative algorithms, such as voltage and/or reactive power control of a distribution grid based on the load prediction methods, in a way that local energy resources cooperate to guarantee a voltage within the defined boundaries, (Manbachi et al. 2014). This change is expected to continue; therefore the communication network, and the devices connected to it, should be able to adapt to this changing nature. The case study considered here includes two renewable generating units, Photovoltaic (PV) and Wind Turbine (WT), committed to compensate the reactive power of a load unit supposed known. Each unit is equipped with an IED and communicates through a Virtual Local Area Network (VLAN). A co-simulation model of electrical and communication grid implemented in MATLAB® /Simulink® (Electrical grid: PowerSim toolbox, Communication grid: SimEvents toolbox) has been used to obtain the data traffic flow, namely the reactive power variation transmitted over IEC 61850 GOOSE (Peirelinck et al. 2016). The focus is here on modelling the variation of number of data packets flowing through the communication channel over time, exchanging information about how much reactive power is able to provide each of them at a given time. Fig. 1 illustrates (a) the IEC 61850 communication network by which (b) a Low Voltage distribution network including the PV, WT and load unit are interconnected. 3. TIME-SERIES MODELLING Time series is a sequence of equispaced data over time. Data will be measured over equal time spaces as a set of n observations which is a sample realization, from an infinite population of such samples: y1 , y2 , ..., yn . To model the SCN data flow, we consider the number of packets pass in between a pair of IEDs: PV and load unit. Load transmits its reactive power absorption to the PV unit through the frames of data. The reactive power variation as the load consumption is sent from the load and received by PV. The aim is to model the cumulative number of packets transmitted according to the reactive power curve in Fig. 2. Time-series analyzing methods detect and explore the linear relationship existing through the current values, historical data and exogenous factors, (Ngo 2013). Among the different time-series analysis methods, Box-Jenkins and exponential smoothing methods are the most widely used to obtain a mathematical model, (Ding 2012). In this work, the Box-Jenkins method has been applied based on ARMA model which is a popular identification model in the automatic control domain. There are different model structures as Auto Regressive (AR), Moving Average (MA), Auto Regressive Moving Average (ARMA), Auto Regressive Integrated Moving Average (ARIMA), and Fractional Auto Regressive Integrated Moving Average (FARIMA). Here ARMA is used which outputs a time series in response at a sequence of white Gaussian noise, (Box
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et al. 1976). To look at the system as a linear filter is likely to serve for control purposes, and ARMA as a simple linear class has been selected to be able to apply all the linear analyzing methods. 3.1 ARMA Modelling Box-Jenkins methodology is implemented within five steps as below, (Pankratz 1983): 1. Data preprocessing, 2. Model identification, 3. Estimation of the model parameters, 4. Diagnostic verification of model, 5. possibly Forecasting. ARMA(p,q) polynomial expression is written as below: wt = ϕ1 wt−1 + ϕ2 wt−2 + ... + ϕp wt−p + at + θ1 at−1 + θ2 at−2 + ... + θq at−q , (1) where wt is the data sampled periodically and preprocessed if necessary, at is the white noise sequence. ϕi and θj are respectively the process and noise coefficients which can be written as polynomial functions of a delay operator, z −1 , as below: ϕ(z −1 ) = 1 + ϕ1 z −1 + ϕ2 z −2 + ... + ϕp z −p θ(z −1 ) = 1 − θ1 z −1 − θ2 z −2 − ... − θq z −q (2) −k where z wt = wt−k , such that the transfer function of a discrete-time filter is obtained: θ(z −1 ) ψ(z −1 ) = (3) ϕ(z −1 ) 4. APPLICATION TO THE CONSIDERED CASE STUDY In this section, the implementation of ARMA model over the data traffic obtained by simulation is explained. Load reactive power variations in Fig. 2 are sent through a communication channel described in Appendix A, referred to as the nominal case. Data should be first prepared and smoothed over time. So, any trend (linear, cyclic) through the sampled data should be removed. Then, applying a proper type of ARMA model with the best orders (p,q) will give the stochastic model of data in a simple polynomial form. Finally, the model accuracy is evaluated by diagnostics tools: Residuals, Mean Squared Error (MSE), and Goodness of Fit (GFit). ARMA model can be used as a predictive model to forecast the future behavior of data, (Wang 2013). 4.1 Data preparation ARMA model should be applied on a special class of time series which is stationary. They are assumed to be in a specific form of statistical equilibrium, and in particular, vary over time in a stable manner about a fixed mean (constant mean, constant variance). Since many real-world time series have nonstationary characteristics, the non-stationarity behavior is removed by special tools. One way to detect different trends is to plot data and find them visually. In addition, the autocorrelation curve over the series can also be used. There are different nonstationarity factors and removal tools, as follows. Detrending – sometimes, there is a linear time trend which increases or decreases through time. Since any dependence to time should not exist, it can be removed by a simple difference method. Thus, a new time series is obtained by differencing each value from its previous value, which has more stable 446
variation around its mean. By noting yt the original, directly measured, time series, then the simple difference is: (4) yt = z −1 yt = yt − yt−1 The simple difference gives the cumulative number of packets being transmitted in each sampling period. Zero mean – the mean value of the time series is removed to have data variations around zero. y¯ t = yt − mean(yt ), (5) ¯ where y t is the zero-mean series. Desimilarity – while modelling the SCN traffic, a different behavior to the Internet traffic may be found. Internet traffic shows only Short Range Dependence (SRD), but in the SCN traffic depending on the communication protocol, also a Long Range Dependence (LRD) characteristic could exist, (Kolbusz et al. 2006). ARMA can precisely model the SRD characteristics but not LRD. Hence, to be able to use ARMA for the SCN traffic as well, we could apply a fractional difference over data to eliminate the LRD characteristics, (Markakis et al. 2012). From practical modelling point of view, such processes may exhibit certain features that could give the impression of the need for differencing to achieve stationarity. To evaluate the selfsimilarity and LRD through the data, the Hurst parameter (H) can be used. H can be evaluated by three different methods; R/S analysis, variance-time analysis, and periodogram analysis. Here, R/S method was used, (Cano 2000). If H is such that 0.5 < H < 1, then some LRD characteristic through the traffic may be identified. Closer to 1, stronger LRD characteristic exists. To obtain time series with only SRD characteristic, the fractional difference is applied as many times as needed to get H closer to 0.5, (Jensen et al. 2014). Note that the presence of H greater than 0.5 is not necessarily indicative of long-term dependence, not being sufficient reason to apply the fractional difference. So, models of different orders (with and without fractional difference application) may be fitted to the data and if the best model fits well for not fractioned series, the conclusion is that the time series contains no long-term dependence. Deseasonality – a seasonal pattern may exist through the time series. These fluctuations are usually due to the measuring period and the behavior of data which is transmitted through the considered traffic. For series with seasonal periodicity, as for the linear trend, it is necessary to remove this periodic trend over time. Like the simple difference, to smooth the seasonal behavior, a seasonal difference may be used. In a seasonal process, the mean value for each season will vary from the others, which leads to a nonstationary series. Considering the sampling process, the seasonal period, s, can be found out. To seasonally differentiate, we subtract from each observation the observation occurring s sampling times earlier: −s D ¯ ∆D ) y t, (6) s wt = (1 − z
where wt is the preproccesed series (stationary, detrended, deseasonalized), and D is the number of seasonal difference required to apply, s is the seasonal period. If D = 1: wt = y¯ t − y¯ t−s . 4.2 Model identification At the identification stage, two graphical tools may help to find out the proper type of ARMA model by measuring the correlation through the observations within the series itself. These plots are called an estimated Auto Correlation Function
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(ACF) and an estimated Partial Auto Correlation Function (PACF). ACF and PACF measure the statistical relationships within a series, (Brockwell et al. 2016). The ACF and PACF plots can provide an indication about the best p and q. In order to find the proper model orders, p and q, here the MSE value has been considered. The best orders are selected for which the estimated model results in its minimum value.
residual test. By selection of p and q, the ARMA coefficients will result as the final step of the process. In this work, we have used the first four steps of Box-Jenkins methodology, i.e. no forecasting. For the nominal case, the best estimation model has GFit = 89.96% and MSE = 0.4497 for ARMA(6,4). The polynomial coefficients of ARMA model are given in (A-1) in the Appendix.
4.3 Parameter estimation
4.5 Mathematical Expression
Box-Jenkins method suggests some diagnostic checks to help determining if an estimated model is statistically adequate. A model that fails these diagnostic tests is rejected. Furthermore, the results at this stage may also indicate how a model could be improved. This leads us back to the identification stage. The cycle of identification, estimation, and diagnostic checks is repeated until a good final model is found out. The ARMA model coefficients are estimated and model is validated through the diagnostics concerning MSE and GFit. Fitting a proper model results in a sequence of uncorrelated residuals. The residual ACF is plotted and if it shows significant autocorrelation in the residuals, the model should be modified to include more auto regressive or moving average orders. A satisfactory model may be used to forecast the future behavior of series, (Yaffee et al. 2000).
As we have the ARMA model of the stochastic data behavior, by adding all the previously removed trends, we will reconstruct the original measured traffic. To do so, inverse operations of all the differences (simple difference, mean difference and seasonal difference) are applied to the ARMA model output. Through the inversion, the data traffic can be mathematically expressed as below, beginning from the stochastic behavior (white Gaussian noise), then adding the deterministic behavior: - Estimated ARMA output: a sequence of white Gaussian noise at is passed through the ARMA(p,q) already identified and estimated. θ(z −1 ) at (7) wt = ϕ(z −1 ) - Add the seasonality: the periodical trend subtracted by seasonal difference is added here to the ARMA output.
4.4 Model implementation The ARMA model is applied to the sampled data over our simulated network. The first step is to find a proper sampling period. GOOSE protocol has no hand shaking topology as TCP/IP protocol, so to ensure the arrival of the packets, the messages are retransmitted four times at each data change. As the cosimulation of this work has a minimum retransmission period equal to 10 ms, so any changes in the number of packets will be at least on this time. Sampling period selection is an important step to have a series following the data changes properly. Since the minimum transmission period of GOOSE messages in this simulation is equal to 10 ms, a reasonable choice for the sampling time would be less than 12 . 10 ms (according to the Shannon’s theorem, (Marks 1991)). The sampling period has been chosen as Ts = 2 ms, and gives 7500 samples. The modelling procedure is illustrated by the flowchart in Fig. 3, in which related processed data for each step is assigned. There is a linear upward trend over time in the original sampled data, so to remove the trend we have applied the firstorder simple difference. Next, a mean value of data has been removed to achieve a zero-mean process. As explained previously, model identification has been applied with and without a fractional difference. These models have been evaluated by their GFit and MSE models without fractional difference lead to a more accurate result. By applying the seasonal difference with s = 3 s/Ts = 1500 sample times, the seasonal trend is removed. Now, data is preprocessed completely and could be modelled by a properly selected ARMA model. The way we decided to select a proper ARMA model, was to find the minimum MSE value for all the possible pairs of p and q up to some values from where no significant increase in accuracy is obtained. We will have the best GFit while its MSE is minimized. Final step is to check the whiteness of the model residuals. If residuals are mostly close to zero, then p and q are the best model parameters. If not, we should increase p and q to pass the 447
1 θ(z −1 ) at , (8) ϕ(z −1 ) (1 − z −s ) where x¯ t denotes the series including the seasonal trend. - Add the mean value: x¯ t =
1 θ(z −1 ) at + mean(yt ), = (9) −1 ϕ(z ) (1 − z −s ) where x t is the series after adding the mean value which was removed by the zero-mean process. - Inversion of simple difference (equivalent to integration): x t
1 1 + mean(y ) t (1 − z −s ) (1 − z −1 ) (10) Fig. 4 shows the estimated time series against the original one, that is, the number of packets transmitted over the communication channel under the considered scenario, in the nominal case (see the Appendix). xt =
θ(z −1 ) at ϕ(z −1 )
5. PARAMETRIC ANALYSIS To go further, we have studied how the communication channel parameters affect the traffic model. Thus, three main network channel characteristics were studied: packet loss, channel speed and cable length. For each factor, different values have been selected and set as new channel characteristics (all other parameters are constant at their nominal values), then simulation has been re-run and related traffic was sampled. So, the achieved series were modelled by a proper ARMA model. To assess the changes, we studied the identified model frequency response, so Bode plots are drawn in each case of parameter variation.
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Select an approprate time scale
yes
ACF = 0 & PACF = 0? no Plot sampled data
yes
Time Linear Trend?
no Simple Difference
Zero-Mean Seasonal Trend?
yes
Seasonal no Difference parameter estimation Identify p & q with min MSE
Residual = 0?
no
yes yes ARMA
0.8
Fig. 3. Flowchart of the ARMA model implementation and model validation steps for the considered case study in the nominal case described in Appendix A.
Fig. 4. The estimated time series in comparison with the original measured data traffic for the considered case study in the nominal case. - Packet loss: The probability of packet loss (PL) has been set to four different values. In the nominal case, there is no packet loss (PL = 0%). As shown in Fig. 5 of related Bode plots for each case, by increasing PL from 5% to 20% the ARMA orders increase too so adds up the number of poles and zeros. Variability exhibited in low frequency is more obvious in the 448
Fig. 5. Estimated ARMA model Bode plots for PL = 5%, 10%, 15%, and 20%, the nominal case corresponding to PL = 0%. Bode gain plot, whereas the Bode phase plots differs mainly in high frequency, which suggests that, the more intense the traffic is, the more sensitive the delays are to the variation of this parameter. - Channel rate or channel speed: In the same way as for PL, this time the channel transfer rate (CHR, nominal rate in this cosimulation is defined as 106 bytes/s) has been changed. Fig. 6
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Fig. 6. Estimated ARMA model Bode plots for CHR = 0.3 . 106 , 0.4 . 106 , and 0.5 . 106 bytes/s, the nominal case corresponding to CHR = 106 bytes/s. clearly shows the changes on the traffic model. If the channel capacity decreases to half, the traffic still flows close to the nominal status, but as CHR is tightened more than a half, the estimated model differs significantly from the nominal case, corresponding to somehow ill-configured communication network. In this way, limits for improper configuration of the channel capacity may be identified. - Cable Length: Variation of the length of the connecting cable in between the IEDs indicated no considerable effect on the traffic stochastic model. 6. CONCLUSION This paper has investigated a data-driven approach of modelling data traffic through communication networks within smart grids. The case of a distribution grid with two renewable energy sources which exchange reactive power information for voltage regulation purposes by means of IEC 61850 GOOSE protocol has been considered. A time-series-based identification procedure has been presented. A sensitivity study has been conducted to assess how the parameters of identified ARMA models vary in relation to variations of some communication network parameters. Further works will consider the potential of the proposed identification procedure of being applied on line, for control purposes – possibly in a linearparameter-varying framework – in order to formally take account of interactions between the energy layer and the communication layer in smart grids. REFERENCES Andrén, F., Bründlinger, R., and Strasser, T. (2014). IEC 61850/61499 Control of Distributed Energy Resources: Concept, Guidelines, and Implementation. IEEE Transactions on Energy Conversion, Chapter 2, 29(4), 1008-1017. Box, G. E. P., Jenkins, G. M., Reinsel, G. C., and Ljung G. M. (1976). Time-series analysis: forecasting and control. Wiley, New Jersey. Brockwell, P. J., Davis, R. A. (2016). Introduction to time series and forecasting. Springer International Publishing, Springer Texts in Statistics, Switzerland, Chapter 3, 73-97. Cano, J.C., Manzoni, P. (2000). On the Use and Calculation of the Hurst Parameter with MPEG Videos Data Traffic. IEEE in Euromicro Conference 26th, 1, 448-455. 449
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Ding, N. (2012). Load models for operation and planning of electricity distribution networks with smart metering data. HAL, Doctoral dissertation, Univ. Grenoble Alpes. Hong, W. C. (2013). Intelligent energy demand forecasting. Springer Science and Business Media, Chapter 2, 21-40. Jensen, A., Nielsen, M. (2014). A fast fractional difference algorithm. Journal of Time Series Analysis, 35(5), 428-436. Kolbusz, J., Paszczyn, S., and Wilamowski, B. M. (2006). Network Traffic Model for Industrial Environment. IEEE Transactions on Industrial Informatics, 2(4), 213-220. Li, W., et al (2014). Cosimulation for Smart Grid Communications. IEEE Transactions on Industrial Informatics, 10(4), 2374-2384. Mackiewicz, R. E. (2006). Overview of IEC 61850 and Benefits. IEEE In Power Systems Conference and Exposition PSCE 06, 57, 623-630. Manbachi, M., et al. (2014). Real-Time Adaptive VVO/CVR Topology Using Multi-Agent System and IEC 61850-Based Communication Protocol. IEEE Transactions on Sustainable Energy, 5(2), 587-597. Marks, R. J. I. (2012). Introduction to Shannon Sampling and Interpolation Theory. Springer Science and Business Media. Ngo, T. H. D. (2013). The Box-Jenkins methodology for timeseries models. SAS Global Forum Conference, 6, 454-2013. Pankratz, A. (1983). Forecasting with Univariate Box-Jenkins Models. Wiley, New Jersey, 6. Peirelinck, T., Bratcu, A. I., and Bésanger, Y. (2016). Impact of IEC 61850 GOOSE Communication Quality on Decentralized Reactive Power Control in Smart Distribution Grids – a Cosimulation Study. IEEE Electrical Power and Energy Conference (EPEC), Ottawa, Canada, 1-6. Sharma, E., Bratcu A. I., Chiculit˛ă, C., and Bésanger, Y. (2015). Co-simulation of a Low-Voltage Utility Grid Controlled over IEC 61850 protocol. International Conference on Electric Utility Deregulation and Restructuring and Power Technologies (DRPT), Changsha, China, 5, 2365-2372. Yaffee, R. A., McGee, M. (2000). An introduction to time-series analysis and forecasting: with applications of SAS and SPSS. Academic Press, Inc. Orlando, FL, USA, 222-244. Yang, T., Zhao, R., Zhang, W., and Yang, Q. (2017). On the Modelling and Analysis of Communication Traffic in Intelligent Electric Power Substations. IEEE Transactions on Power Delivery, 32(3), 1329-1338. Zhang, Z., Huang, X., Keune, B., Cao, Y., and Li, Y. (2017). Modelling and simulation of data flow for VLAN-based communication in substations. IEEE Systems Journal, 11(4), 2467. Appendix A. THE NOMINAL CASE PROPERTIES The nominal case considered through this work, has been sampled by a sampling period Ts = 2 ms without any packet loss. The channel speed is set to 106 bytes/s, and the cable length is equal to 1 km. The ARMA(6,4) polynomial model estimated for the nominal case is as below: wt = 1.758wt−1 − 0.06078wt−2 − 0.7888wt−3 − 0.2517wt−4 + 0.3021wt−5 + 0.04102wt−6 + at − 0.8397at−1 − 0.6358at−2 + 0.1521at−3 + 0.3345at−4 (A.1)