Modern communication mechanisms are at the heart of a smart grid system to ensure that the required information is transmitted within various components of the grid. Throughout this paper, we have studied how communication performance delays and smart grid controller delays effects the overall control system operation. The main goal of this paper is to propose and analyze resource allocation algorithm satisfying delay requirements of the communication infrastructure and the controller. Simulation of a communication network is implemented using OMNeT++ to study and record the corresponding delays. The collected data is used to train resource allocationlearning algorithm implemented in Matlab. The method will enable us to have a real number evaluation of time allocation for the communication network and the controller by taking into account constraints present on the syste

Kemal, Mohammed Seifu

Olsen, Rasmus Løvenstein

VBN (Videnbasen)  Aalborg Universitets forskningsportal

Aalborg UniversitetAnalysis of Timing Requirements for Data Aggregation and Control in Smart GridsKemal, Mohammed Seifu; Olsen, Rasmus LøvensteinPublished in:Telecommunications Forum (TELFOR), 2014DOI (link to publication from Publisher):10.1109/TELFOR.2014.7034380Publication date:2014Document VersionAccepted author manuscript, peer reviewed versionLink to publication from Aalborg UniversityCitation for published version (APA):Kemal, M. S., & Olsen, R. L. (2014). Analysis of Timing Requirements for Data Aggregation and Control in SmartGrids. In Telecommunications Forum (TELFOR), 2014 (pp. 162-165). IEEE (Institute of Electrical andElectronics Engineers). https://doi.org/10.1109/TELFOR.2014.7034380General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            - Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            - You may not further distribute the material or use it for any profit-making activity or commercial gain            - You may freely distribute the URL identifying the publication in the public portal -Take down policyIf you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access tothe work immediately and investigate your claim.Downloaded from vbn.aau.dk on: January 10, 2026Analysis of Timing Requirements for DataAggregation and Control in Smart GridsMohammed Kemal, Student Member, IEEE , Rasmus Olsen, Member, IEEE,Abstract—Modern communication mechanisms are at theheart of a smart grid system to ensure that the requiredinformation is transmitted within various components of thegrid. Throughout this paper, we have studied how communicationperformance delays and smart grid controller delays effects theoverall control system operation. The main goal of this paper isto propose and analyze resource allocation algorithm satisfyingdelay requirements of the communication infrastructure and thecontroller. Simulation of a communication network is imple-mented using OMNeT++ to study and record the correspondingdelays. The collected data is used to train resource allocationlearning algorithm implemented in Matlab. The method willenable us to have a real number evaluation of time allocationfor the communication network and the controller by taking intoaccount constraints present on the system.Keywords—Smart Grid, Data Collection, Timing Requirement,Control.I. INTRODUCTIONThe smart grid concept has widely been used in recentyears in different contexts and with different definitions [1].In this paper, smart grid is viewed as a network of electricgeneration units, transmission lines, distribution substationsand consumers with sensors and communication devices aspart of the communication infrastructure.Renewable energy sources such as solar energy and windenergy are significantly variable demanding highly sophisti-cated control mechanisms. This control mechanism requiresa faster and efficient communication system between highlydistributed energy sources and consumers. Recent improve-ments seen in communication technologies has opened thedoor in resolving restrictions on electrical grids caused bycommunication constraints.For complex controllers deployed on smart grid, the com-munication infrastructure must have the capacity to transfer theinformation within an optimal time frame. The performance ofcontrol operation is constrained by capacity of the communica-tion infrastructure. The main motive for this work is the needfor a method to optimize the communication and controllerdelays in-terms of minimizing the total operating time andmaximizing the capacity of the system. The communicationinfrastructure implemented for data collection under the sim-ulation platform is DSL access network.Mohammed Kemal is a recent graduate of Electronic Systems, AalborgUniversity, Aalborg, Denmark,e-mail: moseifu@gmail.com.Rasmus Olsen is an Associate Professor of the Department ofElectronic Systems, Aalborg University, Aalborg, Denmark,e-mail: (seehttp://kom.aau.dk/ rlo).II. BACKGROUNDA. Timing RequirementFor a control system studied, the timing require-ment(control loop back time) is constrained by communicationdelays for data collection, delays for data redistribution and de-lay for the control operation. This scenario is depicted as highlevel message sequence diagram shown on figure 1. Shownby the message sequence diagram is one step of the periodicmessage exchange performed by the control mechanism.Fig. 1. High Level Message Sequence DiagramThe control loop back time is constrained by,• Nc number of consumers• Na number of aggregators;• d distance;• B bandwidth;• β aggregation server capacity;• ξ Control complexity;δc(n), ξc(n) and δr(n) are T-collection, T-control and T-redistribution respectively(see figure 1). The total control loopback time Tt satisfies a relationship:Tt = δc(n) + ξc(n) + δr(n) (1)III. RELATED WORKSIn relation to smart grid timing requirements, [4] statesthe communication delivery times for different applications insmart grids. It has described a standard defining communica-tion delivery times of information to be exchanged within andexternal to substation integrated protection, control, and dataacquisition systems[4]. The idea of using mixture models is acommon practice in studying delay distributions of a communi-cation infrastructure. [5], [6], [7] all use Gaussian mixture dis-tribution with maximum likelihood expectation maximizationto model the distributions of communication network delaymeasurements. [8] Proposes penalized maximum likelihoodexpectation maximization (PML-EM) algorithm applied onadditive Gaussian mixture model. [9] is a paper to simulateboth the communication side and the control aspects of a smartgrid scenario where OMNeT++ is used to simulate powerline communication infrastructure. Our paper here differs fromother literatures because delay analysis and estimation methodsby Gaussian mixture model is used to implement resourceallocation algorithm. To the best of our knowledge, such amethod for resource allocation used in smart grid controller isnot considered on other literatures.IV. RESOURCE ALLOCATION USING DENSITYESTIMATION(RADE)Here we propose a resource allocation algorithm RADEto give us numerical evaluation of allocation of available timeresource for the control server and communication mechanism.The first phase is to estimate model of the system by usingrecorded data sets of the corresponding delays.1) Collection of data sets : {ξc(n), δr(n), δc(n)}, whereξc(n) is collected from the control algorithm,δr(n) and δc(n) are collected from the communica-tion network.2) Estimate the distribution of each collected(training)data by using parametric density estimation (EM-MLfor Gaussian mixture mode).ξc(n), δr(n), δc(n) ∼K∑i=1N (µi,Σi) (2)3) Compute the density function P (x)Pξc(ξc), Pδr (δr), Pδc(δc) =K∑i=1φiN (µi,Σi) (3)4) Estimate the joint PDFP =n∏i=1P i(x) = Pξc(ξc) ∗ Pδr (δr) ∗ Pδc(δc) (4)5) Estimate the joint CDF,FX(x)Now we have the system model, We use it to give usnumerical evaluation by setting ε. ε is the accepted threshold orconfidence bound our system satisfies according to the trainedmodel. In other words, its the required percentile coverage ofthe distribution in which the system should satisfy fulfillingthe delay requirements to perform in an acceptable manner.while test data : {x; ξct, δdt, δtc} doEstimate FX(x);if FX(x) > ε thenIt satisfies the system requirement;elseIt doesnt satisfy the system requirement;endendAlgorithm 1: Testing time allocationV. EXPERIMENT AND RESULTSA. Communication Scenario Description1) Network Topology: Digital subscriber lines(DSL) areknown to provide high-speed, low latency and secure in-frastructure to be used for smart grid applications. For ourimplementation as shown with figure 2, It is assumed thatthere is point to point connection from smart meters to theaggregator and distribution server. An aggregator located atcentral station will be used for collecting the data and forwardit to the controller and redistribution is done in the samemanner in which controller signals are sent back to the metersby using the same communication channel.Fig. 2. Network toplogy used for implementation2) Simulation: We have implemented the simulation bysetting the parameters for the simulation to create multiplescenarios and see the results by plotting the recorded delaydistributions. Since the DSL channel that we are using is ashared medium, We have generated four types of traffics to seehow it affects the end to end delay caused by the automaticmetering interface(AMI) traffic.TABLE I. Scenario parametersParameter ValueTCPapps 3UDPapps 1AMI packet size 200BAMI packet Idle interval 3600sAMI resource utilization 25%HTTP resource utilization 25%FTP resource utilization 25%Video streaming resource utilization 25%Number of client 100QOS Diff ServerDSL BW 10MbpsDSL propagation delay 20msBack-end BW 100MbpsBack-end propagation delay 10msHTTP and FTP traffics use TCP packets in which theyare sent to a specific TCP port on the server where theserver listens to those traffics on the specified ports. A normalscenario is tested by using droptail queuing policy in which thelast packets are randomly dropped during buffer overflow. Toimplement video streaming and burst data generation, UDPports are set for each traffic on the server and intelligentconsumer. QOS with queuing and priority scheduling policyis implemented by using differentiated services(diffserv) im-plementation in Inet. A scenario on table I is tested in whichQOS parameter with priority queuing policy is implemented.The message from intelligent consumers is a 200B TCP packettransmitted with an idle interval of every 10 minutes. The fullset of parameter is shown in table I. Data is collected for endto end delay( δc(n) + δr(n)) of the communication network.We can see from the histogram plot that the distributions hasa significant degree of randomness because of the queue onthe buffer.Fig. 3. Scenario delay distributionB. Controller RequirementHierarchical predictive control model [3] is used as a usecase for the analysis part and the rest of this work. It is chosenbecause of the prior work done to study computational burdensin relation to traffic caused by the consumers and other loadswhich presents a tested model to be used in relation to ourstudy. It is proposed for resource distribution to be deployedon smart grids. In smart grid control, consumers or energyconsuming units like heat pumps, car batteries, refrigeratorsand more, require power in a limited value within a specificset of time. This and other constraints add to the complexityof the control system. The high level controller[3] has to dealwith the aggregated value of the constraints mentioned. Forthis model, all distributed loads are seen as one big consumerby aggregating the constraints within.According to Hierarchical Control PredictiveModel(HCPM)[3], The main computational burdens arethe vertex generation, the top level distribution and theaggregator level distribution, all of which must be performedat each time step. Vertex generation is generation of avertex vector representing minimum or maximum powerconsumption rate at a specific moment for each consumer.Equation 6 taken from [3] is an example we use in this paperto illustrate the complexity of a controller. It is stated that thecomplexity of the quadratic programming of a distributiontask increases approximately with the square of the numberof receivers and approximately doubles with an increase inthe horizon length.Dc(Nd) = βd2NhNd2 + βo (5)Nd the number of associated consumers or aggregatorsin the layer directly below where βo is dependent on thecomputational power of computer and Horizon length Nhis the number of time steps of the prediction. It is alsoargued on [3] and shown on Equation 7 that the vertexcomputation burden is linear with the number of consumersand number of vertices. The total upper computational burdenis mainly affected by the vertex computational burden andthe distribution computational burden. This can be denotedas the aggregate of the two computational burdens as notedon Equation 8. The relationship is used for the estimationof the controller delay(ξc(Nd)) for the operation. We haveused this relationships to estimate the delay distributions forthe controller using Gaussian mixture model when testing themodels on the later section.Vc(Nd) = βvNh!2NhNd (6)ξc(Nd) = Vc(Nd) +Dc(Nd) (7)C. RADE Implementation and ResultsThe primary goal of RADE is to tell us if our allocation ofsmart grid time resource for the communication infrastructureand control server are appropriate. For this we have designed asystem that will give numerical evaluation of the choice. In thiswork we focused on time allocation problem where RADE isused to test if our allocation satisfies delay requirements for thecommunication network and the controller given N number ofintelligent consumers connected to the system. On the previoussections we have analyzed how we collect the features thatwill be used for RADE algorithm. The two features used arethe delay distributions collected from the network simulationdone on OMNeT++ and the distribution for the controller.Let us discuss the data preparation phase where the collecteddistributions are trained to model the best fit for the algorithm.D. Data Preparation and TrainingWe collected 100 samples from each intelligent con-sumers(meters) in total 10000 samples by the simulator. Thesame amount of data is generated from the controller distribu-tion by assuming a mixture of Gaussian distribution. The datais divided in to three namely, training data, validation data,and test data. The training data is used for RADE as inputfeatures which is used to train the learning algorithm. Thefirst step is using the method expectation maximization andmaximum likelihood method to parametrize the training datawith Gaussian mixture parameters. An example fit is shownon the fig 4 which shows the fitting of delay distribution ofthe tested scenario which was shown fig 3.The cross validation data is used to make the learningalgorithm work efficiently and improve if it doesnt satisfies theconfidence level that we want our fit to have. The confidencelevel is the percentage of coverage of the distribution thatour fit is able to cover. For this work we used confidencelevel of above 90%. We use the test data to confirm if thefit works as desired. The same procedure is taken to dividedthe delay distribution of the controller. Assumption is takenFig. 4. Fitting the distributionFig. 5. PDF plot of the Joint distributionthat the controller delay distribution can be modeled by usingGaussian mixture model.E. RADE TestOn previous sections we discussed what input datas weused for the model and how we prepared the data by fittingthem to a Gaussian mixture model using EM-ML. By usingthe method mentioned by RADE algorithm we get the jointdistribution of the input features. Fig 5 shows the multivariatedistribution function P(x) of the data. The delay distributionfor the communication network has a bigger peak value around150ms and a smaller peak value at 220ms. While the controllerdelay distribution is concentrated at around 300ms.The multivariate CDF(FX(x)) of the distributions is shownon Fig 6. It is found from the test that we can get 100%coverage if we set 220ms for the communication network and600ms for the controller.Another test taken to show how the proposed method canbe used to evaluate the time allocation problem and assist tomake proper allocation choices. It is a test performed to relatecommunication network mean delay with total processing timegiven the control distribution is fixed and taking differentconfidence bounds on the CDF(FX(x)). As shown on Table II,The test is taken for three confidence bounds 75% , 85% and95%. The mean for the Gaussian mixture distribution is variedby sliding the whole Gaussian components by its value.Fig. 6. CDF plot of the Joint distributionTABLE II. Confidence bound and Mean Communication NetworkMean Ntk Delay(s) 0.000 0.100 0.200 0.300 0.400 0.500Total Time(75%) 0.409 0.513 0.609 0.712 0.801 0.891Total Time(85%) 0.611 0.719 0.803 0.899 1.091 1.183Total Time(95%) 0.821 0.931 1.010 1.110 1.183 1.300VI. CONCLUSIONThroughout the course of this paper, We proposed and im-plemented Resource allocation algorithm(RADE) specificallyfor smart grid control timing requirements. RADE providesreal number evaluation of allocation of resources which willenable us to check fulfillment of confidence bounds by allocat-ing the proper processing time for smart grid communicationnetwork and controller.The training datas used for this model are communicationnetwork delay distribution and controller delay distribution. Toget a realistic distribution of the communication delay, we im-plemented a simulation network for DSL access network usingOMNeT++. Since access network is a shared medium, Thesimulation is tested by generating different network traffics.Controller using HPCM is used for this work for estimatingcontroller delay distributions. RADE Implementation is testedand got results to support our argument that this method canbe used for resource allocation problems on smart grids.REFERENCES[1] Energinet and DanskEnergy, Smart Grid in Denmark, May, 2010[2] Ali Keyhani,Muhammad Marwali, Smart Power Grids , 2011, Springer[3] Klaus Trangbaek, Mette Pedersen, Jan Bendtsen, Jakob Stoustrup, Pre-dictive smart grid control with exact aggregated power constraints, 2011,From the book Smart Power Grids 2011, -, 655-675[4] 1646TM IEEE Standard Communication Delivery Time PerformanceRequirements for Electric Power Substation Automation, 2004, IEEEPower Engineering Society,[5] Figueiredo M., Jain,, Unsupervised learning of finite mixture models,,Mar. 2002, IEEE Trans. on Pattern Analysis and Machine Intelligence,51 Issue: 8 , 381396[6] G. McLachlan and D. Peel, Finite mixture models,, Mar. 2000, NewYork: John Wiley & Sons,[7] G. Celeux, S. Chr‘etien, F. Forbes, and A. Mkhadri,, A component-wiseEM algorithm for mixtures,, 1999, INRIA Rhone-Alpes,France,[8] Meng-Fu Shih, Alfred O. Hero, Unicast-Based Inference of NetworkLink Delay Distributions with Finite Mixture Models, 2010, IEEETransactions on Signal Processing, 2219 - 2228[9] J.T.Madsen,T.l.F.Kristensen, R.L.Olsen, T.K.Madsen, K.Balachandran,Simulating Network Adapted Market Controller in a Smart Grid Sce-nario, 2013,

English

Analysis of Timing Requirements for Data Aggregation and Control in Smart Grids

Mohammed Kemal

Rasmus Olsen

Crossref

Analysis of timing requirements for data aggregation and control in smart grids

    Aalborg UniversitetAnalysis of Timing Requirements for Data Aggregation and Control in Smart GridsKemal, Mohammed Seifu; Olsen, Rasmus LøvensteinPublished in:Telecommunications Forum (TELFOR), 2014DOI (link to publication from Publisher):10.1109/TELFOR.2014.7034380Publication date:2014Document VersionPeer reviewed versionLink to publication from Aalborg UniversityCitation for published version (APA):Kemal, M. S., & Olsen, R. L. (2014). Analysis of Timing Requirements for Data Aggregation and Control in SmartGrids. In Telecommunications Forum (TELFOR), 2014 (pp. 162-165). IEEE.  (Telecommunications ForumProceedings). DOI: 10.1109/TELFOR.2014.7034380General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            ? Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            ? You may not further distribute the material or use it for any profit-making activity or commercial gain            ? You may freely distribute the URL identifying the publication in the public portal ?Take down policyIf you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access tothe work immediately and investigate your claim.Downloaded from vbn.aau.dk on: April 26, 2017Analysis of Timing Requirements for DataAggregation and Control in Smart GridsMohammed Kemal, Student Member, IEEE , Rasmus Olsen, Member, IEEE,Abstract—Modern communication mechanisms are at theheart of a smart grid system to ensure that the requiredinformation is transmitted within various components of thegrid. Throughout this paper, we have studied how communicationperformance delays and smart grid controller delays effects theoverall control system operation. The main goal of this paper isto propose and analyze resource allocation algorithm satisfyingdelay requirements of the communication infrastructure and thecontroller. Simulation of a communication network is imple-mented using OMNeT++ to study and record the correspondingdelays. The collected data is used to train resource allocationlearning algorithm implemented in Matlab. The method willenable us to have a real number evaluation of time allocationfor the communication network and the controller by taking intoaccount constraints present on the system.Keywords—Smart Grid, Data Collection, Timing Requirement,Control.I. INTRODUCTIONThe smart grid concept has widely been used in recentyears in different contexts and with different definitions [1].In this paper, smart grid is viewed as a network of electricgeneration units, transmission lines, distribution substationsand consumers with sensors and communication devices aspart of the communication infrastructure.Renewable energy sources such as solar energy and windenergy are significantly variable demanding highly sophisti-cated control mechanisms. This control mechanism requiresa faster and efficient communication system between highlydistributed energy sources and consumers. Recent improve-ments seen in communication technologies has opened thedoor in resolving restrictions on electrical grids caused bycommunication constraints.For complex controllers deployed on smart grid, the com-munication infrastructure must have the capacity to transfer theinformation within an optimal time frame. The performance ofcontrol operation is constrained by capacity of the communica-tion infrastructure. The main motive for this work is the needfor a method to optimize the communication and controllerdelays in-terms of minimizing the total operating time andmaximizing the capacity of the system. The communicationinfrastructure implemented for data collection under the sim-ulation platform is DSL access network.Mohammed Kemal is a recent graduate of Electronic Systems, AalborgUniversity, Aalborg, Denmark,e-mail: moseifu@gmail.com.Rasmus Olsen is an Associate Professor of the Department ofElectronic Systems, Aalborg University, Aalborg, Denmark,e-mail: (seehttp://kom.aau.dk/ rlo).II. BACKGROUNDA. Timing RequirementFor a control system studied, the timing require-ment(control loop back time) is constrained by communicationdelays for data collection, delays for data redistribution and de-lay for the control operation. This scenario is depicted as highlevel message sequence diagram shown on figure 1. Shownby the message sequence diagram is one step of the periodicmessage exchange performed by the control mechanism.Fig. 1. High Level Message Sequence DiagramThe control loop back time is constrained by,• Nc number of consumers• Na number of aggregators;• d distance;• B bandwidth;• β aggregation server capacity;• ξ Control complexity;δc(n), ξc(n) and δr(n) are T-collection, T-control and T-redistribution respectively(see figure 1). The total control loopback time Tt satisfies a relationship:Tt = δc(n) + ξc(n) + δr(n) (1)III. RELATED WORKSIn relation to smart grid timing requirements, [4] statesthe communication delivery times for different applications insmart grids. It has described a standard defining communica-tion delivery times of information to be exchanged within andexternal to substation integrated protection, control, and dataacquisition systems[4]. The idea of using mixture models is acommon practice in studying delay distributions of a communi-cation infrastructure. [5], [6], [7] all use Gaussian mixture dis-tribution with maximum likelihood expectation maximizationto model the distributions of communication network delaymeasurements. [8] Proposes penalized maximum likelihoodexpectation maximization (PML-EM) algorithm applied onadditive Gaussian mixture model. [9] is a paper to simulateboth the communication side and the control aspects of a smartgrid scenario where OMNeT++ is used to simulate powerline communication infrastructure. Our paper here differs fromother literatures because delay analysis and estimation methodsby Gaussian mixture model is used to implement resourceallocation algorithm. To the best of our knowledge, such amethod for resource allocation used in smart grid controller isnot considered on other literatures.IV. RESOURCE ALLOCATION USING DENSITYESTIMATION(RADE)Here we propose a resource allocation algorithm RADEto give us numerical evaluation of allocation of available timeresource for the control server and communication mechanism.The first phase is to estimate model of the system by usingrecorded data sets of the corresponding delays.1) Collection of data sets : {ξc(n), δr(n), δc(n)}, whereξc(n) is collected from the control algorithm,δr(n) and δc(n) are collected from the communica-tion network.2) Estimate the distribution of each collected(training)data by using parametric density estimation (EM-MLfor Gaussian mixture mode).ξc(n), δr(n), δc(n) ∼K∑i=1N (µi,Σi) (2)3) Compute the density function P (x)Pξc(ξc), Pδr (δr), Pδc(δc) =K∑i=1φiN (µi,Σi) (3)4) Estimate the joint PDFP =n∏i=1P i(x) = Pξc(ξc) ∗ Pδr (δr) ∗ Pδc(δc) (4)5) Estimate the joint CDF,FX(x)Now we have the system model, We use it to give usnumerical evaluation by setting ε. ε is the accepted threshold orconfidence bound our system satisfies according to the trainedmodel. In other words, its the required percentile coverage ofthe distribution in which the system should satisfy fulfillingthe delay requirements to perform in an acceptable manner.while test data : {x; ξct, δdt, δtc} doEstimate FX(x);if FX(x) > ε thenIt satisfies the system requirement;elseIt doesnt satisfy the system requirement;endendAlgorithm 1: Testing time allocationV. EXPERIMENT AND RESULTSA. Communication Scenario Description1) Network Topology: Digital subscriber lines(DSL) areknown to provide high-speed, low latency and secure in-frastructure to be used for smart grid applications. For ourimplementation as shown with figure 2, It is assumed thatthere is point to point connection from smart meters to theaggregator and distribution server. An aggregator located atcentral station will be used for collecting the data and forwardit to the controller and redistribution is done in the samemanner in which controller signals are sent back to the metersby using the same communication channel.Fig. 2. Network toplogy used for implementation2) Simulation: We have implemented the simulation bysetting the parameters for the simulation to create multiplescenarios and see the results by plotting the recorded delaydistributions. Since the DSL channel that we are using is ashared medium, We have generated four types of traffics to seehow it affects the end to end delay caused by the automaticmetering interface(AMI) traffic.TABLE I. Scenario parametersParameter ValueTCPapps 3UDPapps 1AMI packet size 200BAMI packet Idle interval 3600sAMI resource utilization 25%HTTP resource utilization 25%FTP resource utilization 25%Video streaming resource utilization 25%Number of client 100QOS Diff ServerDSL BW 10MbpsDSL propagation delay 20msBack-end BW 100MbpsBack-end propagation delay 10msHTTP and FTP traffics use TCP packets in which theyare sent to a specific TCP port on the server where theserver listens to those traffics on the specified ports. A normalscenario is tested by using droptail queuing policy in which thelast packets are randomly dropped during buffer overflow. Toimplement video streaming and burst data generation, UDPports are set for each traffic on the server and intelligentconsumer. QOS with queuing and priority scheduling policyis implemented by using differentiated services(diffserv) im-plementation in Inet. A scenario on table I is tested in whichQOS parameter with priority queuing policy is implemented.The message from intelligent consumers is a 200B TCP packettransmitted with an idle interval of every 10 minutes. The fullset of parameter is shown in table I. Data is collected for endto end delay( δc(n) + δr(n)) of the communication network.We can see from the histogram plot that the distributions hasa significant degree of randomness because of the queue onthe buffer.Fig. 3. Scenario delay distributionB. Controller RequirementHierarchical predictive control model [3] is used as a usecase for the analysis part and the rest of this work. It is chosenbecause of the prior work done to study computational burdensin relation to traffic caused by the consumers and other loadswhich presents a tested model to be used in relation to ourstudy. It is proposed for resource distribution to be deployedon smart grids. In smart grid control, consumers or energyconsuming units like heat pumps, car batteries, refrigeratorsand more, require power in a limited value within a specificset of time. This and other constraints add to the complexityof the control system. The high level controller[3] has to dealwith the aggregated value of the constraints mentioned. Forthis model, all distributed loads are seen as one big consumerby aggregating the constraints within.According to Hierarchical Control PredictiveModel(HCPM)[3], The main computational burdens arethe vertex generation, the top level distribution and theaggregator level distribution, all of which must be performedat each time step. Vertex generation is generation of avertex vector representing minimum or maximum powerconsumption rate at a specific moment for each consumer.Equation 6 taken from [3] is an example we use in this paperto illustrate the complexity of a controller. It is stated that thecomplexity of the quadratic programming of a distributiontask increases approximately with the square of the numberof receivers and approximately doubles with an increase inthe horizon length.Dc(Nd) = βd2NhNd2 + βo (5)Nd the number of associated consumers or aggregatorsin the layer directly below where βo is dependent on thecomputational power of computer and Horizon length Nhis the number of time steps of the prediction. It is alsoargued on [3] and shown on Equation 7 that the vertexcomputation burden is linear with the number of consumersand number of vertices. The total upper computational burdenis mainly affected by the vertex computational burden andthe distribution computational burden. This can be denotedas the aggregate of the two computational burdens as notedon Equation 8. The relationship is used for the estimationof the controller delay(ξc(Nd)) for the operation. We haveused this relationships to estimate the delay distributions forthe controller using Gaussian mixture model when testing themodels on the later section.Vc(Nd) = βvNh!2NhNd (6)ξc(Nd) = Vc(Nd) +Dc(Nd) (7)C. RADE Implementation and ResultsThe primary goal of RADE is to tell us if our allocation ofsmart grid time resource for the communication infrastructureand control server are appropriate. For this we have designed asystem that will give numerical evaluation of the choice. In thiswork we focused on time allocation problem where RADE isused to test if our allocation satisfies delay requirements for thecommunication network and the controller given N number ofintelligent consumers connected to the system. On the previoussections we have analyzed how we collect the features thatwill be used for RADE algorithm. The two features used arethe delay distributions collected from the network simulationdone on OMNeT++ and the distribution for the controller.Let us discuss the data preparation phase where the collecteddistributions are trained to model the best fit for the algorithm.D. Data Preparation and TrainingWe collected 100 samples from each intelligent con-sumers(meters) in total 10000 samples by the simulator. Thesame amount of data is generated from the controller distribu-tion by assuming a mixture of Gaussian distribution. The datais divided in to three namely, training data, validation data,and test data. The training data is used for RADE as inputfeatures which is used to train the learning algorithm. Thefirst step is using the method expectation maximization andmaximum likelihood method to parametrize the training datawith Gaussian mixture parameters. An example fit is shownon the fig 4 which shows the fitting of delay distribution ofthe tested scenario which was shown fig 3.The cross validation data is used to make the learningalgorithm work efficiently and improve if it doesnt satisfies theconfidence level that we want our fit to have. The confidencelevel is the percentage of coverage of the distribution thatour fit is able to cover. For this work we used confidencelevel of above 90%. We use the test data to confirm if thefit works as desired. The same procedure is taken to dividedthe delay distribution of the controller. Assumption is takenFig. 4. Fitting the distributionFig. 5. PDF plot of the Joint distributionthat the controller delay distribution can be modeled by usingGaussian mixture model.E. RADE TestOn previous sections we discussed what input datas weused for the model and how we prepared the data by fittingthem to a Gaussian mixture model using EM-ML. By usingthe method mentioned by RADE algorithm we get the jointdistribution of the input features. Fig 5 shows the multivariatedistribution function P(x) of the data. The delay distributionfor the communication network has a bigger peak value around150ms and a smaller peak value at 220ms. While the controllerdelay distribution is concentrated at around 300ms.The multivariate CDF(FX(x)) of the distributions is shownon Fig 6. It is found from the test that we can get 100%coverage if we set 220ms for the communication network and600ms for the controller.Another test taken to show how the proposed method canbe used to evaluate the time allocation problem and assist tomake proper allocation choices. It is a test performed to relatecommunication network mean delay with total processing timegiven the control distribution is fixed and taking differentconfidence bounds on the CDF(FX(x)). As shown on Table II,The test is taken for three confidence bounds 75% , 85% and95%. The mean for the Gaussian mixture distribution is variedby sliding the whole Gaussian components by its value.Fig. 6. CDF plot of the Joint distributionTABLE II. Confidence bound and Mean Communication NetworkMean Ntk Delay(s) 0.000 0.100 0.200 0.300 0.400 0.500Total Time(75%) 0.409 0.513 0.609 0.712 0.801 0.891Total Time(85%) 0.611 0.719 0.803 0.899 1.091 1.183Total Time(95%) 0.821 0.931 1.010 1.110 1.183 1.300VI. CONCLUSIONThroughout the course of this paper, We proposed and im-plemented Resource allocation algorithm(RADE) specificallyfor smart grid control timing requirements. RADE providesreal number evaluation of allocation of resources which willenable us to check fulfillment of confidence bounds by allocat-ing the proper processing time for smart grid communicationnetwork and controller.The training datas used for this model are communicationnetwork delay distribution and controller delay distribution. Toget a realistic distribution of the communication delay, we im-plemented a simulation network for DSL access network usingOMNeT++. Since access network is a shared medium, Thesimulation is tested by generating different network traffics.Controller using HPCM is used for this work for estimatingcontroller delay distributions. RADE Implementation is testedand got results to support our argument that this method canbe used for resource allocation problems on smart grids.REFERENCES[1] Energinet and DanskEnergy, Smart Grid in Denmark, May, 2010[2] Ali Keyhani,Muhammad Marwali, Smart Power Grids , 2011, Springer[3] Klaus Trangbaek, Mette Pedersen, Jan Bendtsen, Jakob Stoustrup, Pre-dictive smart grid control with exact aggregated power constraints, 2011,From the book Smart Power Grids 2011, -, 655-675[4] 1646TM IEEE Standard Communication Delivery Time PerformanceRequirements for Electric Power Substation Automation, 2004, IEEEPower Engineering Society,[5] Figueiredo M., Jain,, Unsupervised learning of finite mixture models,,Mar. 2002, IEEE Trans. on Pattern Analysis and Machine Intelligence,51 Issue: 8 , 381396[6] G. McLachlan and D. Peel, Finite mixture models,, Mar. 2000, NewYork: John Wiley & Sons,[7] G. Celeux, S. Chr‘etien, F. Forbes, and A. Mkhadri,, A component-wiseEM algorithm for mixtures,, 1999, INRIA Rhone-Alpes,France,[8] Meng-Fu Shih, Alfred O. Hero, Unicast-Based Inference of NetworkLink Delay Distributions with Finite Mixture Models, 2010, IEEETransactions on Signal Processing, 2219 - 2228[9] J.T.Madsen,T.l.F.Kristensen, R.L.Olsen, T.K.Madsen, K.Balachandran,Simulating Network Adapted Market Controller in a Smart Grid Sce-nario, 2013,

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Analysis of Timing Requirements for Data Aggregation and Control in Smart Grids

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