Optimization of transformer loading based on hot-spot temperature using a predictive health model

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1 Delft Unversty of Technology Delft Center for Systems and Control Techncal report Optmzaton of transformer ng based on hot-spot temperature usng a predctve health model G. Bajracharya, T. Koltunowcz, R.R. Negenborn, D. Djaram, B. De Schutter, and J.J. Smt If you want to cte ths report, please use the followng reference nstead: G. Bajracharya, T. Koltunowcz, R.R. Negenborn, D. Djaram, B. De Schutter, and J.J. Smt, Optmzaton of transformer ng based on hot-spot temperature usng a predctve health model, roceedngs of the 2010 Internatonal Conference on Condton Montorng and Dagnoss CMD 2010), Tokyo, Japan, pp , Sept Delft Center for Systems and Control Delft Unversty of Technology Mekelweg 2, 2628 CD Delft The Netherlands phone: secretary) fa: URL: Ths report can also be downed vahttp://pub.deschutter.nfo/abs/10_037.html

2 Optmzaton of Transformer Loadng Based on Hot-Spot Temperature usng a redctve Health Model G. Bajracharya 1, T. Koltunowcz 1, R. R. Negenborn 2, D. Djaram 1, B. De Schutter 2 and J. J. Smt 1 1 Dept. of Hgh-Voltage Components and ower Systems, Delft Unversty of Technology, The Netherlands 2 Delft Center for Systems and Control, Delft Unversty of Technology, The Netherlands *E-mal: g.bajracharya@tudelft.nl Abstract In the future grd, power equpment wll need to work wth dstrbuted generaton, deregulaton, and accelerated agng. To ths end, a model-based framework for the optmzaton of usage of power equpment s proposed. The framework uses a predctve health model of the equpment n order to optmze the usage of the equpment. In partcular, the predctve health model predcts the hot-spot temperature of the transformers n a network over a future tme wndow based on the epected ng. The allowed ng lmts of the transformers are based on the hot-spot temperature. Therefore, the optmal ng of the transformers s mantaned by performng an optmal power flow OF) computaton of the network that takes nto account hot-spot temperature dynamcs. The optmzaton determnes values for the tap poston of the transformers and the actve and reactve power of generators n the network. Moreover, sheddng of the s n the network s consdered when the aforementoned optons are not suffcent to control the ng of the transformers. A case study usng the IEEE 14-bus benchmark system s presented. The sheddng of the s s mnmzed by usng ths technque. Inde Terms transformer ng; predctve health model; hot-spot temperature; thermal ng; optmal power flow I. INTRODUCTION The electrcal power system has been changng drastcally n recent years, especally due to the ntroducton of deregulaton of the power ndustry n most parts of the world. Not only the structure of electrcal grds, but also the ways of fnancng generaton, transmsson, and dstrbuton have changed from the tradtonal state-owned utlty approach nto an nvestment-orented approach of power companes 1, 2]. Moreover, a sgnfcant porton of the electrcal nfrastructure wll be reachng the end of ts operatonal age wthn the comng few decades. There s a need for mamum utlzaton of equpment wthout degradng the relablty of the system. In order to optmze the operaton and mantenance of power system equpment, whle assurng a predefned level of relablty, a model descrbng the evoluton of ts health state, has to be ncorporated nto the asset management 3]. In 3], a framework was proposed for modelng the health state of power system equpment. The framework has been Ths research s supported by the SenterNovem Snerge project EOSLT04034, the BSIK project Net Generaton Infrastructures NGI), the Delft Research Center Net Generaton Infrastructures, and the European STRE project Herarchcal and dstrbuted model predctve control HD- MC). used n optmzng the ng of a sngle transformer usng temperature predctons n 4]. The hot-spot temperature s used to determne the ng lmts. Ths hot-spot temperature can be predcted usng the of the transformer 5]. In ths paper, ng of several transformers n a network s consdered. The optmal lmts of ng depend on the hot-spot temperature of the transformers. Therefore the optmal ng of the transformers s determned by performng an optmal power flow OF) computaton of the network that takes nto account the hot-spot temperature dynamcs. The outlne of ths paper s as follows. In Secton II, the predcted health model for the predcton of the hot-spot temperature s presented. Secton III proposes the control of transformers n a network based on the hot-spot temperature predcton. A case study of the IEEE 14 bus network s presented n Secton IV. Conclusons and future work are ncluded n Secton V. II. REDICTIVE HEALTH MODEL Our framework conssts of a predctve health model that can be used to predct the effects of dfferent mantenance actons and usage patterns 3]. The predctons can then be used for the optmzaton of mantenance actons and the equpment usage. The predctve health model n the framework ncludes a dynamc stress model. As equpment ages, varous stresses, such as electrcal, thermal, mechancal, and envronmental stresses, weaken the strength of the equpment. As the cumulatve stresses ncrease over tme, the relablty and the remanng lfe of the equpment decrease. The cumulatve stresses of the equpment are affected by the usage patterns e.g., the ng) and the mantenance actons e.g., the replacement of parts) performed on the equpment. The health state of the equpment s represented by the cumulatve stresses. The dynamcs of the cumulatve stresses can be descrbed usng a dynamc stress model gven by: ˆk+ 1)=fˆk),uk)), 1) where at dscrete tme step k, wth uk)= u T a k) u T d k)] T, the functon f descrbes the future cumulatve stresses ˆk+ 1) based on the usage of the equpment u d k), the mantenance actons u a k), and the current cumulatve stresses ˆk).

3 A. redctve health model of a transformer The temperature rse due to the ng of a transformer degrades the paper nsulaton of the transformer. Ths degradaton process reduces the delectrc and mechancal strength of the nsulaton paper and hence reduces ts lfe tme. In order to determne the allowed ng lmt of a transformer, the hot-spot temperature s consdered. Ths temperature s used for determnng the level of the paper degradaton. The hot-spot temperature can be predcted wth a thermal model. The thermal model of a transformer conssts of the top-ol model and a hot-spot model 5]. The dfferental equatons of the top-ol model and the hot-spot model are dscretzed by usng the forward Euler appromaton. The dscretzed top-ol model s then gven by: 1+R u I k) ) 2 µpu k) ) n θol,rated 1+R = µ pu k) ) n θ,ol k+ 1) θ,ol k) τol,rated h θ,ol k) u θ,amb k) ) n+1 + ) n, 2) θol,rated where θ,ol s the top-ol temperature, u θ,amb s the ambent temperature, u I s the factor, R s the rato of losses at the rated current and no- losses, θ ol,rated s the topol temperature rse over the ambent temperature at the rated, µ pu k) s the varable ol vscosty n per unt pu), τ ol,rated s the rated top-ol tme constant, n s a constant that depends on the type of coolng, and h s the tme step for dscretzaton 4]. The change n vscosty of ol at the top-ol temperature µ pu k) s gven by 5]: ep / θ,ol k)+273 )) µ pu k)= ep / θ ol,rated )). The dscretzed hot-spot model s as follows: ui k) ) 2 cu,pu k) µ pu k) ) n θhs,rated = µ pu k) ) n k+ 1) k) τwdg,rated h k) θ,ol k) ) n+1 + θ hs,rated ) n 3) where s the hot-spot temperature, θ hs,rated s the rated hot-spot temperature rse over the top-ol temperature, cu,pu k) are the varable losses n pu, and τ wdg,rated s the rated hot-spot tme constant 4]. The varable losses cu,pu k) are gven by 5]: cu,pu k)= cu,dc,pu 235+ k) 235+θ hs,rated + cu,eddy,pu 235+θ hs,rated 235+ k), where cu,dc,pu are the DC losses n pu, cu,eddy,pu are the eddy current losses n pu, and θ hs,rated s the rated hot-spot temperature. Together the top-ol model 2) and the hot-spot model 3) form the dynamc stress model 1) of the model-based optmzaton framework. III. CONTROL OF TRANSFORMER LOADING IN A NETWORK Typcally, the ng lmts of transformers n a network are fed at constant levels by the manufacturers and/or utltes. However, the mamum allowable ng of a transformer manly depends on the thermal lmts of the transformer. The hot-spot temperature of the transformer can be used to determne the mamum allowable ng. In ths paper, normal lfe epectancy ng defned n IEEE C ] s consdered. The mamum hot-spot temperature allowed for ths type of ng s 120 C. The predctve health model descrbed n the prevous secton s used to predct the hot-spot temperature. The predcted hot-spot temperature has to be mantaned below the allowed lmt by controllng the ng of the transformers u I. The ng of the transformers u I can be controlled by controllng the actve and reactve power of generators and s. The ng u I can also be controlled by controllng network parameters, such as transformer tap settngs. Actve and reactve power generaton, control sheddng or transfer of s), and the tap poston of transformers are therefore consdered as control nputs. A. Optmal power flow of the network wth the dynamcs of the hot-spot and top-ol temperatures In order to determne the optmal control nputs, an OF of the network s calculated. The dynamcs of the hotspot temperature 2) and the top-ol temperature 3) are consdered n ths OF. The dynamc OF problem s formulated as follows: subject to: mn J total k+ 1), zk),ũk)) 4) ũk) k+ 1)=f k), zk),ũk)) g k), zk),ũk))=0 g k), zk),ũk)) 0 where the tlde over a varable represents a vector wth the values of ths varable over a predcton horzon of N steps, e.g., ũk)= u T k),...,u T k+ N 1) ] T. The OF s consdered for a predcton horzon of N steps n the future. The three sets of varables consdered n the OF 2] are: The algebrac state vector zk) ncludes the varables for whch no dynamcs are consdered, zk)= z 1 θ k),z 1 v k),...,z b,n θ k),z b,n v k)] T, 5) wth I bus = { 1,..., b,n } the set of ndces of buses n the network, where z θ k) and z vk) are the angle and the voltage magntude of bus, respectvely. The dynamcs for the varables are neglected because t s too fast compare to the dynamcs of the hot-spot temperature and the top-ol temperature.

4 The dynamc state vector k) ncludes the varables for whch dynamcs are defned, ] k)= j 1 θ,ol k),j 1 k),...,j t,n θ,ol k),j t,n T k) 6) wth I tr ={ j 1,..., j t,n } the set of ndces of transformers n the network, where j θ,ol k) and j k) are the top-ol temperature and the hot-spot temperature of transformer j, respectvely. The control vector uk) conssts of the control nputs of the network, uk)= u 1,gen k),u 1 Q,gen k),u j 1 tapk),u k 1 shed k),..., u g,n,gen k),u g,n Q,gen k),uj t,n tapk),u k s,n shed k)] T, 7) wth I gen = { } 1,..., g,n the set of ndces of generators n the network, I tr ={ j 1,..., j t,n } the set of ndces of transformers n the network, and I ={m 1,...,m s,n } the set of ndces of s n the network, where u,gen k) and u Q,gen k) are the actve and the reactve power generaton at bus, utapk) j s the tap poston of transformer j, and u m shed k) s the sheddng of the at bus m. Sheddng of the actve and the reactve s gven by: m,actual k)=1 um shed k))m,demand k) Q m,actual k)=1 um shed k))qm,demand k) for u m shed k) 1, where m,demand k) and Q m,demand k) are the real power and the reactve power demand at bus m, respectvely, and where,actual m k) and Qm,actual k) are the real power and the reactve power delvered at bus m, respectvely. Nodal power balances between the nodes n the network g are consdered as constrants for the optmzaton. The predctve health model f, whch descrbes the dynamcs of the hot-spot temperature 2) and the top ol temperature 3), are constrants of the optmzaton problem. The branch flow lmts are gven by h. For transformers, the mamum hotspot temperature lmt s gven by: k+ 1) ma 8) Allowable voltage magntudes n the network are taken nto account by the varable lmts. Mamum and mnmum generaton capactes of generators are also consdered n the varable lmts. The total cost functon over the predcton horzon N s gven by: J total k+ 1), zk),ũk)) N l=0 J gen u,gen k+ l),u Q,gen k+ l)) I gen + J tap u j tapk+ l) ) + J shed u m shed k+ l) ) j I tr m I where J gen, J tap, and J shed gve the cost of generaton, the cost of tap and the cost of sheddng, respectvely. ] 9) Fg. 1. IEEE 14 bus network whch conssts of 3 transformers 7]. A. IEEE 14 bus network IV. CASE STUDY The IEEE 14 bus network 7], llustrated n Fgure 1, s used as case study. The network ncludes transmsson and dstrbuton systems. The network conssts of three transformers T 1, T 2, and T 3. Three generators are consdered at buses 1, 2, and 3. Two reactve power compensators are located at buses 6 and 8. The s of the dstrbuton system are assumed to be controllable. Sheddng s allowed at buses 6, 9, 10, 11, 12, 13, and 14. Data of the network parameters and the lmts of the actve and the reactve power generaton are gven n 7]. The allowable lmt of voltage varaton n the buses s consdered to be ± 6%. The cost of generaton J gen s gven by: J gen u,gen k),u Q,gen k)) = C 1 u,genk)+c 2 u,gen k) ) 2, where C1 1 = 20, C2 1 = 20, C3 1 = 20, C6 1 = 40, C8 1 = 40, C1 2 = 0.043, C2 2 = 0.25, C3 2 = 0.01, C6 2 = 0.01, and C8 2 = The cost of tap changes s gven by: J tap u j tapk) ) = u j tapk)) 2. The cost of sheddng s chosen to be hgher than the cost of generaton to avod sheddng as much as possble. The cost of sheddng J shed s gven by: J shed u m shed k))=d 1u m shed k)m k)+d 2u m shed k)m k))2, where D 1 = 80 and D 2 = 0.5. The nomnal ratngs of transformers T 1, T 2, and T 3 are consdered to be 50 MVA, 17 MVA, and 40 MVA respectvely. The thermal parameters of transformers are taken from the medum and large power transformers ONAN) gven n 8]. For the smulaton purposes, an ambent temperature u θ,amb k) of 25 C s consdered. In order to emphasze the ng of transformers, the power flow n the network s not consdered to be constraned by the ng capactes of the transmsson and dstrbuton

5 lnes. In order words, the ng capactes of the transformers are consdered as the bottlenecks n the network. B. Loadng consderng the hot-spot temperature The optmal power flow computaton for a profle s calculated. A step tme h of 1 mnute s consdered. A predcton horzon N of 5 steps s chosen. Fgure 2 gves the demands n dotted lnes) and the actual s n sold lnes) at the dstrbuton buses. The hot-spot temperature and the top-ol temperature of the transformer are presented n Fgure 3. As llustrated n Fgure 3, the hot-spot temperature of transformer T 2 2 reaches the mamum lmt of 120 C at k = 169. The ng of transformer T 2 s mantaned such that ts hot-spot temperature stays at the lmt. At ths pont, s are not shed. At k=207, the hot-spot temperature of transformer T 1 1 also reaches the lmt. As the hot-spot temperature of transformer T 1 and T 2 reaches the lmt, the power flow cannot be controlled wth the generaton control and the tap control. As a result, the sheddng of at bus 9 starts. As seen n Fgure 2, the actual sold lne) s less than the demand dotted lne) for range of k between tme steps 207 and 252. As the demands decrease, the hot-spot temperature of transformer T 1 1 reduces after k = 252) and the sheddng s elmnated. V. CONCLUSIONS AND FUTURE WORK A predctve health model for the hot-spot temperature predcton of transformers has been developed. The hot-spot predcton has been used n determnng the ng lmts of transformers n a network. The ng of the transformers s controlled by changng the actve and the reactve power generaton and the tap settng of the transformers. The sheddng of the s done when the ng of the transformer cannot be lmted by controllng the generaton and the tap settngs. The hot-spot temperatures of the transformers are mantaned below the mamum allowed lmt. The hot-spot temperatures of the transformers wll be used for estmatng the degradaton of the transformers. The degradaton of the transformers wll be epressed n terms of degree of polymerzaton of the paper nsulaton. By consderng the degradaton, other ng regmes defned n IEEE C57.91 wll be ncluded. Actve ower MW] k Fg. 2. Demand of the real power dotted lnes) and Actual real power delvered sold lnes) at buses of the dstrbuton system. Hot-spot temperatures C] k Fg. 3. Hot-spot and top-ol temperatures of transformers T 1, T 2, and T 3. 5] D. Susa, M. Lehtonen, H. Nordman, Dynamc Thermal Modellng of ower Transformers, IEEE Transactons of ower Delvery, vol. 20, no. 1. pp , January ] IEEE Gude for Loadng Mneral-Ol-Immersed Transformers, IEEE Standard C , June ] IEEE 14 bus power flow test case, URL: research/pstca/pf14/pg tca14bus.htm. 8] ower transformers - art 7: Loadng gude for ol-mmersed power transformers, IEC Standard , December REFERENCES 1] J. J. Smt, Trends n emergng technologes n power systems, n roceedngs of the 2005 Internatonal Conference on Future ower Systems, Amsterdam, The Netherlands, pp. 1 7, November ] R.R. Negenborn, Z. Lukszo, and H. Hellendoorn Eds.). Intellgent Infrastructures, Sprnger, Dordrecht, The Netherlands, ] G. Bajracharya, T. Koltunowcz, R. R. Negenborn, Z. app, D. Djaram, and B. De Schutter, J. J. Smt, Optmzaton of Mantenance for ower System Equpment Usng a redctve Health Model, n roceedngs of the 2009 IEEE Bucharest owertech Conference, Bucharest, Romana, pp. 1 6, July ] G. Bajracharya, T. Koltunowcz, R. R. Negenborn, Z. app, D. Djaram, B. De Schutter, and J. J. Smt, Optmzaton of condton-based asset management usng predctve health model, n roceedngs of the 16th Internatonal Symposum on Hgh Voltage Engneerng 2009, Cape Town, South Afrca, August 2009.