Adaptive prediction model accuracy in the control of residential energy resources

Transcription

1 Delft Univerity of Technology Delft Center for Sytem and Control Technical report Adaptive prediction model accuracy in the control of reidential energy reource R.R. Negenborn, M. Houwing, B. De Schutter, and H. Hellendoorn If you want to cite thi report, pleae ue the following reference intead: R.R. Negenborn, M. Houwing, B. De Schutter, and H. Hellendoorn, Adaptive prediction model accuracy in the control of reidential energy reource, Proceeding of the 17th IEEE International Conference on Control Application, San Antonio, Texa, pp , Sept Delft Center for Sytem and Control Delft Univerity of Technology Meelweg 2, 2628 CD Delft The Netherland phone: (ecretary) fax: URL: Thi report can alo be downloaded viahttp://pub.dechutter.info/ab/08_013.html

2 Adaptive Prediction Model Accuracy in the Control of Reidential Energy Reource Rudy R. Negenborn, Michiel Houwing, Bart De Schutter, and Han Hellendoorn Abtract With the increaing ue of ditributed energy reource and intelligence in the electricity infratructure, the poibilitie for minimizing cot of houehold energy conumption increae. Technology i moving toward a ituation in which automated energy management ytem could control dometic energy generation, torage, and conumption. In previou wor we have propoed a controller baed on model predictive control for controlling an individual houehold uing a micro combined heat and power plant in combination with heat and electricity torage. Although the controller provide adequate performance in computer imulation, the computational time required to determine which action to tae can be ignificant, due to the precie prediction made over a long prediction horizon. In thi paper we propoe to mae the computation le time conuming by coarening the quality of the prediction made over the prediction horizon by decreaing their time reolution. In imulation tudie we illutrate the performance of the propoed approach. I. INTRODUCTION A. Ditributed energy reource Ditributed energy reource, compriing ditributed power generation, ditributed energy torage, and load management option, can play a crucial role in upporting policy objective a electricity maret liberalization, mitigating climate change, increaing the amount of electricity generated from renewable ource and enhancing energy aving [1], [2]. A wide body of literature tate that ditributed generation of electricity, e.g., via photo-voltaic, wind turbine, or micro combined heat and power plant (µchp), ha a good chance of pervading the electricity infratructure in the future (ee, e.g. [3], [4]). Alo, everal electricity torage technologie are under development (uch a lithium-ion batterie, plug-in hybrid electric vehicle [5], and demandide management option are foreeen for the future power ytem [6]. Applying ditributed generation and torage technologie at cutomer ite ha ey economic and environmental potential. Specific potential lie in the opportunity to locally Thi wor i upported by the BSIK project Next Generation Infratructure (NGI), by the project Multi-agent control of large-cale hybrid ytem (DWV.6188) of the Dutch Technology Foundation STW, the European 6th Framewor Networ of Excellence HYbrid CONtrol: Taming Heterogeneity and Complexity of Networed Embedded Sytem (HYCON), contract number FP6-IST , and the Delft Reearch Center Next Generation Infratructure. R.R. Negenborn, B. De Schutter, and J. Hellendoorn are with the Delft Center for Sytem and Control of the Delft Univerity of Technology, Meelweg 2, 2628 CD Delft, The Netherland. B. De Schutter i alo with the Marine and Tranport Technology department of the Delft Univerity of Technology. M. Houwing i with the Faculty of Technology, Policy and Management of the Delft Univerity of Technology, Jaffalaan 5, 2628 BX Delft, The Netherland. (Correponding author R.R. Negenborn; r.r.negenborn@tudelft.nl; phone: ; fax: ). utilize the wate heat from the converion of primary fuel into electricity by combined heat and power ytem. Conequently, there ha been ignificant progre toward developing mall combined heat and power ytem (Wcale), o-called micro-chp or µchp ytem, baed on a Stirling engine, an internal combution engine, a ga turbine, or fuel cell converion technology [7]. E.g., Stirling µchp ytem are expected to pervade the Dutch maret ubtantially in the hort- to mid-term [8]. In The Netherland, thee Stirling ytem target the houing maret egment of ytem replacement and are probably not meant for newly built houe a thee have too little heat demand. The matured Dutch maret i expected to comprie of around unit per year. For everal other countrie (e.g., UK, Germany, and Japan) µchp technology i alo expected to play a ignificant role [7]. The introduction of uch ditributed energy reource together with the introduction of more information and communication technology in the electricity ytem provide intereting and novel automated demand repone opportunitie at the dometic uer level. Houehold thereby become more active end-uer of electricity. They can devie new contractual arrangement with upplier and/or networ manager, thereby becoming more independent in term of energy uage. B. Model predictive control In order to exploit the increaed operational freedom of houehold, in [9] we propoed a controller for houehold energy flow optimization. The controller control a houehold that ha the capability of generating it own power with a µchp unit, that can tore heat and electricity, and that can trade electricity with an external energy upplier. The controller ue the control technique Model Predictive Control (MPC) [10] and ha the ta to automatically determine which action hould be taen in order to minimize the operational cot of fulfilling reidential electricity and heat requirement ubject to operational contraint. The controller ue an MPC trategy uch that it can: tae into account the deciion freedom due to heat and electricity torage poibilitie; incorporate prediction on reidential electricity and heat demand; incorporate model of the dynamic and contraint of intalled generator and torage. MPC i baed on olving at each control tep an optimization problem over a prediction horizon ubject to ytem dynamic, an objective function, and contraint on tate,

3 action, and output. At each control tep the optimization yield a equence of action optimizing expected ytem behavior over the prediction horizon. Action (control input) are implemented by the controller on the ytem until the next control tep, after which the procedure i repeated with new ytem meaurement. Due to the prediction horizon an MPC controller can tae benefit of nowledge that it may have over the future, uch a predicted energy demand baed on hitorical data of energy conumption pattern. C. Aim and outline of thi paper Although the MPC controller propoed in [9] chooe action that optimize the energy cot for the houehold in imulation tudie, the time that i required to find thee action can be coniderable. The large amount of time required i due to the large amount of computation required to olve the MPC optimization problem at each control tep. The aim of thi paper i to reduce the computational burden of the approach preented in [9]. In thi paper we propoe an approximation of the original MPC optimization problem which yield a ignificant reduction in required computation time, while eeping the performance lo due to thi reduction limited. Thi paper i organized a follow. In Section II we hortly decribe the main component and aumption of the ytem under tudy. In Section III we propoe the control objective and contraint of the approximation of our MPC formulation. In Section IV the performance of the propoed approach i illutrated through imulation tudie. II. SYSTEM DESCRIPTION The analyi in thi paper focue on the ytem a hown in Fig. 1. The ytem conit of a houehold that interact with it energy upplier. Energy trading flow are preent between the houehold and the upplier a hown. The houehold ha full control over it ditributed energy reource and there i no interaction with other houehold regarding electrical energy trade. The houehold fulfill it electricity and heat conumption requirement through everal alternative energy upply and conumption mean. The µchp unit intalled in the houehold i baed on Stirling technology [7]. The unit conit of a Stirling engine prime mover, converion 1, and an auxiliary burner, converion 2, which can provide additional thermal power. The Stirling engine convert natural ga ( f 1 ) into electrical energy (g) and heat (h 1 ). The heat i upplied to a central heat torage in the form of hot water, of which the energy content i indicated by h. The auxiliary burner alo convert natural ga ( f 2 ) in providing the additional heat (h 2 ). Heat conumption (h c ) i taen from the heat torage. Electrical energy can be tored in a battery (e ) (e.g., a lithium-ion battery). In addition, electrical energy can flow to and from the battery, repreented in Fig. 1 by ( i ) and ( o ) repectively. Locally generated electrical energy can be ued directly by the houehold (e c ), it can be tored, or it can be old to the upplier (e ext ). Electrical energy can alo be imported from the upplier (i ext ). The upplier thu ell f f f 1 2 houehold g converion 1 converion 2 (aux. burner) Fig. 1. (Stirling) i µ CHP Energy upplier ext h 2 e ext e h 1 h c = power flow = heat flow = natural ga flow i e torage h torage h o e c Electricity conumption Heat conumption ytem boundary Conceptual overview of the ytem under tudy. primary fuel ( f = f 1 + f 2 ) for fueling the µchp unit a well a additionally required import electrical energy for the houehold. The upplier buy any electrical energy that the houehold would lie to feed bac for a feed-bac tariff. Note that we conider one large heat torage from which all heat, for dometic hot water a well a for pace heating purpoe, can be extracted. Such a heat torage ytem i currently being mareted by a manufacturer in the UK, ee [11]. One torage allow u to combine pace heating and dometic hot water demand, which i more convenient for the ytem modeling. Note alo that we conider only a ingle heat conumption bloc. Building exhibit dynamic heat conumption behavior, depending on, among other, olar radiation, occupancy, the in-houe heating ytem configuration and building characteritic. By maing ue of the heat torage from which the needed heat for the houehold i extracted, the exact heat demand pattern a repreented by the ingle heat conumption bloc doe not have to be nown and it can therefore be aggregated into time bloc of relatively low reolution (15 min) compared to the actual dynamic change in heat demand. A decription of additional aumption can be found in [1], [9]. III. MPC FORMULATION In [9], an MPC controller i propoed for control of the houehold jut decribed. The objective of the MPC controller i to minimize the daily operational cot of reidential energy ue. The MPC controller employ a control tep ize of 15 minute, meaning that every 15 minute the controller determine which action to tae next. To determine which action to tae, the controller mae prediction over a number of imulation tep, referred to a the prediction

4 horizon. At each control tep the controller perform the following tep: 1) Mae a meaurement of the current tate of the houehold, involving meaurement of the current energy level in the heat and electricity torage. 2) Solve the MPC optimization problem, which involve finding over a prediction horizon of N imulation tep of 15 minute the action that lead to the bet predicted performance over the prediction horizon. 3) Implement the action found until the next control tep. The MPC controller mae prediction and determine which action to tae at each control tep in the prediction horizon. In a ene the controller of [9] perform long-term detailed planning of it action at each deciion tep. Although thi give at each control tep the bet deciion over the full prediction horizon, the computation involved in finding thi deciion can be coniderable. To decreae the computational load, intead of computing an action for each time imulation time tep of the prediction horizon, in thi paper we propoe the combination of hort-term detailed planning and longterm le detailed planning. Thi i expected to increae computational peed, while till providing adequate control performance. A. Short-term detailed and long-term rough prediction The idea i to decreae the computational requirement by uing a more abtract model of the ytem for prediction made further in the future. The abtract model are obtained by decreaing the reolution of the imulation time tep conidered in the prediction horizon. Hence, wherea in the original approach equal imulation time tep of 15 minute are conidered over the complete prediction horizon, here we propoe to increae the duration of imulation time tep within the horizon. Such an approach yield a reduction in the number of equation and variable involved in the optimization problem (in particular in term of integervalued variable), and i therefore expected to yield fewer computation. Under the aumption that event appearing further away in the future have a maller influence on control performance than event appearing oon, the performance lo hould be mall. In order to obtain a combination of hort-term detailed planning and long-term, le-detailed, planning, the prediction horizon i divided into two part, and in each part of the horizon a different prediction model i ued. For the firt part a detailed, exact model i ued. For the econd part a le detailed model i ued. In the following, we refer to the two part of the prediction horizon a Phae I and Phae II. In Phae I, a imulation time tep ize of 15 minute i taen, which give an exact repreentation of the dynamic of the modeled ytem. In Phae II, a imulation time tep ize of 1 hour i taen. Fig. 2 illutrate the decreaing imulation time tep reolution further in the prediction horizon. The ytem accept new action every 15 minute. Below we dicu how to formulate the prediction model and the control objective for the different phae within the prediction horizon. +1 PhaeI... PhaeII... +N 1 Fig. 2. Illutration of the different imulation time tep reolution conidered over a prediction horizon. The top part of the figure indicate the tep ued in the original approach, i.e., equiditant imulation time tep over the full prediction horizon. The bottom part indicate how in our approach for Phae I mall imulation time tep are conidered, while for Phae II everal imulation time tep are aggregated to form larger imulation time tep. B. Sytem model formulation In principle, there are variou way in which the more abtract model for Phae II could be derived from the detailed model. We develop the abtract model baed on expert nowledge of the ytem. A will be hown, the prediction model deigned in thi way for Phae II give good ytem performance and provide a bai for future comparion with poible other model. Our tarting point i the model developed previouly in [1, 9]. In Phae I the model that exactly repreent the houehold i ued. For Phae II, a pointed out, larger imulation time tep are ued. The model for Phae II i obtained by adapting ome of the equation of the model for Phae I. The adaptation mainly entail the removal of binary variable to continuou variable, the rewriting of ome contraint a to preent ytem behavior when conidering the larger imulation time tep and aggregating and averaging of imulation input data (decribed below). We firt decribe the model for Phae I and then decribe how the model for Phae II differ from thi model. 1) Model for Phae I: The model for Phae I that we have ued in thi paper i imilar to the model decribed in [9]. It i worthwhile to decribe it here a well, a then the difference in modeling the ytem in the different phae of the prediction horizon can be made clear. Define the binary variable v CHP and v aux, which indicate whether the intalled µchp prime mover and auxiliary burner are in operation at a pecific time tep. In addition, the binary variable up,, uchp down, and uaux up,, uaux down, are tart-up and hut-down indicator for the µchp prime mover and auxiliary burner, repectively, at time tep. An electric energy balance ha to be atified relating the power output of the Stirling engine, the input and output power flow of the electricity torage, the electricity conumption, and electricity exchanged with the energy upplier. Thi power balance i given by: g + i ext, + o, e ext, i, e c, = 0, (1) where g = η e f 1,, with η e the electric efficiency of the Stirling engine. The power output of the Stirling engine can be modulated between part load and full load, which

5 i modeled by the contraint: f 1, v CHP f 1,max (2) f 1, v CHP f 1,part, (3) where f 1,max and f 1,part are the fuel conumption at part and full load. For the Stirling engine there i alo a minimal operation time and a minimum down time. The contraint that force the prime mover to tay in operation until thi minimum ha been reached are: v CHP +n uchp up,, n=0,...,t up 1, (4) where t up i the minimum number of imulation time tep that the prime mover ha to tay in operation. The contraint that force the prime mover to tay out of operation during down-time are: 1 v CHP +r uchp down,, r=0,...,t down 1, (5) where t down i the minimum number of imulation time tep that the prime mover ha to tay out of operation. The fuel conumption of the auxiliary burner i retricted to lie within: v aux f 2,min f 2, v aux f 2,max, (6) where f 2,min and f 2,max are the minimal and maximum fuel conumption of the auxiliary burner. The electrical energy and heat tored hould be between minimum and maximum value: e,min e, e,max (7) h,min h, h,max, (8) where e,min and e,max are minimum and maximum energy level of the battery, and h,min and h,max are minimum and maximum energy level of the heat torage. The electricity flow to and from the battery are limited by an aumed battery charge or dicharge time of half an hour [5]. Hence, in 15 minute the battery can be maximally charged or dicharged with an amount equal to half the total torage capacity. Therefore, the contraint limiting the flow to and from the battery i given by: i, + o, 0.5 e,max, (9) where e,max i the maximum energy that can be tored in the battery. At each time tep electrical energy can either only be imported from or only be exported to the external energy upplier. Contraint on the import and export power flow are therefore: e ext, η e f 1, + o, (10) e ext, x e, P max (11) i ext, e c, + i, (12) i ext, x i, P max (13) x i, + x e, 1, (14) where P max i the maximum power flow allowed (2 W) through the phyical connection between the houehold and the external networ, x e, and x i, are auxiliary binary variable indicating whether electrical energy i imported or exported. The heat in the heat torage change over time depending on the heat conumption and generation. The dynamic of the heat torage are modeled by: h,+1 = h, + h 1, + h 2, h cp,, (15) where h 1, =(η tot η e ) f 1,,h 2, = η tot f 2,, and η tot i the total efficiency of the µchp unit. Similarly, the dynamic of the electricity torage are modeled by: e,+1 = e, + i, o,. (16) In order to let the modeled energy converion unit function a they hould, the binary variable v CHP, up,, and down, on the one hand, and vaux, u aux up,, and uaux down, on the other, have to be lined. The relation between thee variable are: v CHP v CHP 1 = uchp up, uchp down, (17) v aux v aux 1 = uaux up, uaux down, (18) up, + uchp down, 1 (19) u aux up, + uaux down, 1. (20) 2) Model for Phae II: The prediction model ued for Phae II i derived from the detailed model for Phae I. The main difference between the original prediction model and the model for Phae II are the following: The tart-up and hut-down behavior of the Stirling engine and the auxiliary burner i modeled differently and therefore contraint (4) and (5) are not preent. We treat the auxiliary burner power output a a continuou variable. The binary variable v aux, therefore become unneceary. Becaue the imulation time tep pan longer time interval, there can now be import and export of power in the ame imulation time tep. Hence, contraint (11), (13), and (14) are abent. In the energy balance equation, aggregated electricity and heat demand value are ued, obtained by aggregating the 15-minute demand data to obtain data per hour for Phae II. Due to the above abtraction the integer variable down,, uaux up,, uaux down,, vaux up,,, x i,, x e, become obolete and are removed from the model. The equation of the ytem model that change ubtantially for Phae II are decribed below. Since if the Stirling engine run, it energy output hould be between the output value correponding with the minimal up-time and the maximum value, intead of equation (2) and (3) for the Stirling engine operation, the following contraint are ued: f 1, t up v CHP f 1,part (21) f 1, r II v CHP f 1,max, (22)

6 where r II i the number of time tep that are conidered aggregated in the model of Phae II. The auxiliary burner contraint (6) i changed to: r II f 2,min f 2, r II f 2,max. (23) The contraint on the power flow to and from the battery change from (9) to: i, + o, r II 0.5 e,max. (24) Finally, the contraint on the power import and export change from (11), (13), and (14) to: e ext, + i ext, r II P max. (25) The prediction model for Phae I and II are coupled to each other. The model for Phae I require the meaurement of the current tate. Uing the model for Phae I, prediction are made for N I prediction tep of 15 minute. From that moment, the model of Phae II i ued to mae N II prediction tep of 60 minute. C. Control objective 1) Objective for Phae I: For Phae I, cot are computed for each imulation time tep of 15 minute. The operational cot depend on the price p f for ga conumption, the price p i,ext for importing electricity and the price p e,ext at which electricity can be old. The cot function for control tep with a prediction horizon of N I i therefore defined a: J( )= N 1 1( ( f1,+m + f 2,+m ) p f + i ext,+m p i,ext,+m m=0 ) e ext,+m p e,ext. (26) 2) Objective for Phae II: For Phae II the control objective function i imilar to (26). The electricity price differ, however, a in Phae II, average price for electricity import and export are taen over the aggregated imulation time tep. IV. SIMULATIONS In thi ection we illutrate the performance of the propoed approach with imulation experiment. We focu on the relation between the reduction in the computational load for the MPC controller and the accompanying change in ytem performance. A. Implementation We have implemented the decribed ytem and MPC controller in Matlab 7.4. The optimization problem that ha to be olved at each deciion tep i a mixed-integer linear programming problem, due to the preence of continuouvalued and binary-valued variable in combination with the linear objective function and contraint. We ue the tate-ofthe-art mixed-integer olver CPLEX v10 through the Tomlab interface to Matlab to olve the problem. mean computation time () level of detail Fig. 3. Mean computation time required () over all control tep for varying level of detail conidered in the prediction horizon. B. Simulation etup We conider a imulation period of one wee in a winter eaon. Heat demand and electricity demand pattern, a well a price for ga and electricity are aumed given on a per quarter bai, imilarly a in [9]. The import and export price are taen equal to each other and vary per hour. The tarting value for the imulation of the ytem are for =1 taen a: v CHP 1 = v aux 1 = up,1 = uchp down,1 = uaux up,1 = uaux down,1 = 0, e,1 = e,min, h,1 = h,min, We are intereted in oberving the reduction in computational load a the prediction made over the prediction horizon are made le preciely. We do thi by varying for a pecific prediction horizon length the number of imulation tep that i conidered in detail (modeled with the Phae I model) a well a the number of imulation tep that i conidered in le detail (modeled with the Phae II model). A a prediction horizon we tae two day, i.e., 192 imulation tep of 15 minute. We tart with computing the time required and performance obtained when maing 192 detailed imulation tep and thu do not employ aggregated imulation tep in the prediction horizon. We then gradually decreae the detailed part of the prediction horizon by replacing the detailed imulation tep with aggregated imulation tep. C. Reult Fig. 3 illutrate the mean computational time required at each control tep, when imulating for one full wee, and while varying the degree of detail conidered by the controller over the prediction horizon. We define thi degree of detail a the number of prediction tep conidered in detail with the Phae I model divided by the total number of prediction tep in the prediction horizon, i.e., 192. We clearly oberve that a the degree of detail i decreaed, the mean computational time required decreae ignificantly. Fig. 4 how the maximum computational time required over all control tep for varying degree of detail. For

7 maximum computation time () level of detail Fig. 4. Maximum computation time required () over all control tep for varying level of detail conidered in the prediction horizon. total performance level of detail Fig. 5. Total cot over full imulation of one wee for varying level of detail conidered in the prediction horizon. larger degree of detail, the computational time required i ignificantly larger than the control tep length. Fig. 5 illutrate the change in the total performance, i.e., the performance over the full imulation of one wee in term of operational cot of energy ue, a we vary the degree of detail conidered over the prediction horizon. We oberve that the total performance decreae only lightly with the decreae in detail. Hence, thee imulation clearly illutrate that the approach propoed in thi paper ha the potential to yield a ignificant reduction in computational time required, while only giving a light reduction in performance. reduction in computational requirement and the relatively low reduction in performance. Future reearch hould focu on more tructured approache of etting up the approximation of the detailed model, determining if it i beneficial to include a further coarening of the prediction horizon, and analyzing the effect of the horizon length on the performance. In addition, the robutne of the MPC controller againt uncertainty in meaurement and prediction of energy conumption patter hould be invetigated. Furthermore, the implementability of the propoed approach uing embedded hardware hould be addreed to mae the tep to a practical implementation. REFERENCES [1] M. Houwing, A. Ajah, P. W. Heijnen, I. Bouwman, and P. M. Herder, Uncertaintie in the Deign and Operation of Ditributed Energy Reource: The Cae of Micro-CHP Sytem. To appear in Energy - The International Journal, [2] M. Houwing, P. W. Heijnen, and I. Bouwman, Socio-Technical Complexity in Energy Infratructure - Conceptual Framewor to Study the Impact of Dometic Level Energy Generation, Storage and Exchange. In Proc. of the IEEE International Conference on Sytem, Man and Cybernetic, Taipei, Taiwan, October [3] A. Chamber, S. Hamilton, and B. Schnoor, Ditributed Generation: A Nontechnical Guide. Tula, Olahoma, US: Penn Well Corporation, [4] N. Jenin, R. Allan, P. Croley, D. Kirchen, and G. Strbac, Embedded Generation. London, UK: The Intitution of Electrical Engineer, [5] E. Lyen, S. Van Egmond, and S. Hagedoorn, Oplag van eletriciteit: Statu en toeomtperpectief voor Nederland (in Dutch). Utrecht Centrum voor Energieonderzoe - SenterNovem NEO , September [6] S. D. Braithwait, Real-Time Pricing and Demand Repone Can Wor within Limit. In Natural Ga & Electricity, vol. 21, [7] M. Pehnt, M. Came, C. Ficher, B. Praetoriu, L. Schneider, K. Schumacher, and J. Vob, Micro Cogeneration: Toward Decentralized Energy Sytem. Berlin: Springer, [8] A. De Jong, E. J. Baer, J. Dam, and H. Van Wolferen, Technich energie- en CO2-beparingpotentieel van micro-w in Nederland ( ) (in Dutch). Wergroep Decentraal, onderdeel van Platform Nieuw, July [9] M. Houwing, R. R. Negenborn, P. W. Heijnen, B. De Schutter, and J. Hellendoorn, Model predictive, leat cot control of reidential energy reource when applying µchp. In Proc. of IEEE PowerTech 2007, Lauanne, Switzerland, July [10] J. M. Maciejowi, Predictive Control with Contraint. Harlow, England: Prentice Hall, [11] Gledhill water torage - UK, V. CONCLUSIONS AND FUTURE RESEARCH In thi paper we have dicued reduction of computational requirement of a model predictive control (MPC) controller for houehold optimization. We have propoed to reduce the computational requirement of the controller by coarening the prediction made over the prediction horizon. Our approach relie on uing a prediction model that mae prediction at more coare time interval a prediction tep further in the prediction horizon are conidered. In experiment uing a imulation tudy we have illutrated the