DEMAND FORECASTING MODELS

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1 DEMAND FORECASTING MODELS Conens E-2. ELECTRIC BILLED SALES AND CUSTOMER COUNTS Sysem-level Model Couny-level Model Easside King Couny-level Model E-6. ELECTRIC PEAK HOUR LOAD FORECASTING Sysem-level Forecas Couny-level Forecass Easside King Couny-level Forecas E-11. GAS BILLED SALES AND CUSTOMER COUNTS E-14. GAS PEAK DAY LOAD FORECAST E-16. MODELING UNCERTAINTIES IN THE LOAD FORECAST E-17. HOURLY ELECTRIC DEMAND PROFILE Daa Mehodology for Disribuion of Hourly Temperaures Mehodology for Hourly Disribuion of Load This appendix describes he economeric models used in creaing he demand forecass for PSE s 2015 IRP analysis. E - 1

2 ELECTRIC BILLED SALES AND CUSTOMER COUNTS Sysem-level Model PSE esimaed he following use-per-cusomer (UPC) and cusomer coun economeric equaions using sample daes from a hisorical monhly daa series ha exends from January 1989 o December 2013; he sample daes varied depending on secor or class. The billed sales forecas is based on he esimaed equaions, normal weaher assumpions, rae forecass, and forecass of various economic and demographic inpus. The UPC and cusomer coun equaions are defined as follows: UPC c, = use (billed sales) per cusomer for class c, monh CC c, = cusomer couns for class c, monh ( k ) = he subscrip lag form in k periods from monh (k) denoes eiher a lag of k periods from or a polynomial disribued RR c, ( k ) = effecive real reail raes for class c in polynomial disribued lagged form W c, = class-appropriae weaher variable; cycle-adjused HDD/CDD using base emperaures of 65, 60, 45, 35 for HDD and 65 and 75 for CDD; cycle-adjused HDDs/CDDs are creaed o fi consumpion period implied by he class billing cycles E - 2

3 EcoDem = class-appropriae economic and demographic variables; variables include c, ( k ) income, household size, populaion, employmen levels or growh, and building permis in polynomial disribued lagged form MD i = monhly dummy variable ha is 1 when he monh is equal o i, and zero oherwise for i from 1 o 12 UPC is forecas monhly a a class level using several explanaory variables including weaher, reail raes, monhly effecs, and various economic and demographic variables such as income, household size and employmen levels. Some of he variables, such as reail raes and economic variables, are added o he equaion in a lagged, or polynomial lagged form o accoun for boh shor-erm and long-erm effecs of changes in hese variables on energy consumpion. Finally, depending on he equaion, an ARMA(p,q) srucure could be imposed o acknowledge ha fuure values of he prediced variables could be a funcion of is lag value or he lags of forecas errors. Similar o UPC, PSE forecass he cusomer coun equaions on a class level using several explanaory variables such as household populaion, building permis, oal employmen, manufacuring employmen or he reail rae. Some of he variables are also implemened in a lagged or polynomial disribued lag form o allow he impac of he variable o vary wih ime. Many of he cusomer equaions use monhly cusomer growh as he dependen variable, raher han oals, o more accuraely measure he impac of economic and demographic variables on growh, and o allow he forecas o grow from he las recorded acual value. ARMA(p,q) could also be imposed on cerain cusomer couns equaions. E - 3

4 The billed sales forecas for each cusomer class before new conservaion is he produc of he class UPC forecas and he forecased number of cusomers in ha class, as defined below. Billed Salesc, = UPCc, CCc, The billed sales and cusomer forecass are adjused for known, shor-erm fuure discree addiions and subracions no accouned for in he forecas equaions, such as major changes in energy usage by large cusomers. These adjusmens may also include fuel and schedule swiching by large cusomers. The forecas of billed sales is furher adjused for new programmaic conservaion by class using he opimal conservaion bundle from he mos recen IRP. Toal billed sales in a given monh are calculaed as he sum of he billed sales across all cusomer classes: c PSE esimaes oal sysem delivered loads by disribuing monhly billed sales ino each billing cycle for he monh, hen allocaing he billing cycle sales ino he appropriae calendar monhs using degree days as weighs, and adjusing each delivered sales for losses from ransmission Toal Billed Sales = and disribuion. This approach also enables compuaion of he unbilled sales each monh. Couny-level Model Billed Sales c, We use hisorical daa from PSE s billing sysem o generae cusomer forecass by couny by esimaing an equaion ha relaes cusomer couns by class and couny o populaion or employmen levels in ha couny. The srucure of he couny-level cusomer couns economeric equaion is similar o he sysem-level cusomer couns equaion. CC = f EcoDem, MD ) for each couny c, ( c, ( k ) m EcoDem = class-appropriae economic and demographic variables in lagged or polynomial c, ( k ) disribued lagged forms; variables include populaion for residenial equaion, and employmen levels or growh for non-residenial equaions wih AR or MA erms. The forecass of couny-level cusomers are furher adjused proporionally so ha he oal of all cusomer couns is scaled o he original service area forecas a he class level. E - 4

5 The class-level UPC forecas by couny is based on he sysem-level UPC forecas by class, bu adjused o he couny level using he raio of he couny o he sysem-level hisorical weaheradjused UPC by class. Couny-level billed sales forecass by class are he produc of cusomer couns and use-per-cusomer, which are furher proporionally adjused so ha he oal billed sales across all counies is equal o he sysem-level billed sales by class. Known discree addiions or deleions o he couny-level billed sales are accouned for in he forecas. Finally, projeced conservaion savings by class are proporionally allocaed o counylevel class billed sales using he raio of class-level billed sales for each couny o he sysemlevel billed sales. This amoun is deduced from he before conservaion billed sales forecas by class for each couny. Easside King Couny Model The approach used o develop he forecas of billed sales for he Easside area of King Couny is similar o ha used for he couny-level billed sales forecas. Hisorical cusomer couns on a monhly basis are used o esimae cusomer couns economeric equaions by class for jus he Easside area. Again, he srucure of he cusomer couns equaion is CC = c, f ( EcoDemc, ( k ), MDm ) EcoDem = class-appropriae economic and demographic variables in lagged or polynomial c, ( k ) disribued lagged forms; variables include populaion for residenial equaion, and employmen levels or growh for non-residenial equaions wih AR or MA erms. The hisorical and projeced economic and demographic variables such as populaion and employmen are based on Puge Sound Regional Council jurisdicion populaion and employmen daabases and Vision 2040 forecass. The class-level UPC forecas for he Easside area is based on King Couny-level UPC forecas by class bu adjused using he raio of he Easside area o he King Couny-level hisorical weaher-adjused UPC by class. Again, billed sales is adjused for known block loads, as well as for fuure conservaion savings apporioned using he raio of billed sales for Easside o King Couny-level conservaion savings. E - 5

6 ELECTRIC PEAK HOUR LOAD FORECASTING Peak load forecass are developed using economeric equaions ha relae observed monhly peak loads o weaher-sensiive delivered loads for boh residenial and non-residenial secors. They accoun for deviaions of acual peak hour emperaure from normal peak emperaure for he monh, day of he week effecs, and unique weaher evens such as a cold snap or an El Niño season. Sysem-level Forecas Based on he forecased delivered loads, we use hourly regressions o esimae a se of monhly peak loads for he sysem based on hree specific design emperaures: Normal, Power Supply Operaions (PSO), and Exreme. The Normal peak is based on he average emperaure a he monhly peak during a hisorical ime period, currenly 30 years. The winer peaks are se a he highes Normal peak, which is currenly he December peak of 23 degrees Fahrenhei. We esimaed he PSO peak design emperaures o have a 1-in-20 year probabiliy of occurring. These emperaures were esablished by examining he minimum emperaure of each winer monh. An exreme value disribuion funcion relaing he monhly minimum emperaure and he reurn probabiliy was esablished. The analysis revealed he following design emperaures: 15 degrees Fahrenhei for January and February, 17 degrees Fahrenhei for November, and 13 degrees Fahrenhei for December. Finally, he Exreme peak design emperaures are esimaed a 13 degrees Fahrenhei for all winer monhs. Weaher dependen loads are accouned for by he major peak load forecas explanaory variable, he difference beween acual peak hour emperaure and he average monhly emperaure muliplied by sysem loads. The equaions allow he impac of peak design emperaure on peak loads o vary by monh. This permis he weaher-dependen effecs of sysem delivered loads on peak demand o vary by season. The sample period for his forecas uilized monhly daa from January 2002 o December E - 6

7 In addiion o he effec of emperaure, peak load esimaes accoun for he effecs of several oher variables, among hem he porion of monhly sysem delivered loads ha affecs peak loads bu is non-weaher dependen; a dummy variable ha accouns for large cusomer changes; and a day of he week variable. The funcional form of he elecric peak hour equaion is where: 1, Monh = 6,7,8 χ1 = 0, Monh 6,7,8 1, Monh = i MDi = i 0, Monh i { 1,2, 12} PkMW = monhly sysem peak hour load in MW S = sysem delivered loads in he monh in amw MD i = monhly dummy variable Δ T = deviaion of acual peak hour emperaure from monhly normal emperaure DD d = day of he week dummy LT d = lae hour of peak dummy, if he peak occurs in he evening χ 1= dummy variables used o pu special emphasis on summer monhs o reflec growing summer peaks. To clarify he equaion above, when forecasing we allow he coefficiens for loads o vary by monh o reflec he seasonal paern of usage. However, in order o conserve space, we have α employed vecor noaion. The Greek leers m, β, and δ are used o denoe coefficien vecors; here are also indicaor variables ha accoun for air condiioning load, o reflec he growing summer elecriciy usage caused by increased sauraion of air condiioning. d d E - 7

8 The peak load forecas is furher adjused for he peak conribuion of fuure conservaion based on he opimal bundle derived from he 2013 IRP. Couny-level Forecass The couny-level peak forecass are based on he following economeric specificaion of sysem monhly peaks as a funcion of monhly weaher and non-weaher sensiive loads, and accouning for he deviaion of peak emperaure from he monhly normal emperaure on a seasonal basis, o esimae a sysem coinciden peak forecas. The esimaed economeric equaion using hisorical daa from January 2002 o December 2012 is represened by Where: PkMW = monhly sysem peak-hour load in MW R = residenial delivered loads in he monh in amw NR = commercial plus indusrial delivered loads in he monh in amw Δ T = deviaion of acual peak-hour emperaure from monhly normal emperaure Ws = residenial plus a % of commercial delivered loads Seas = ( Winer if Monh = 11,12,1,2; Summer if Monh = 7,8; Oher if Monh = 3,4,5,6,9,10) AR(1) = auoregressive erm of order 1 for ime series funcions The Greek leers r α m and are used o denoe coefficien vecors. E - 8

9 The couny-level sysem coinciden peak forecas before conservaion is projeced by supplying he above equaion wih he couny s projeced residenial and non-residenial beforeconservaion loads, and using he design normal peak emperaure of 23 degrees Fahrenhei in he Δ T. Each couny s normal peak forecas is furher adjused so ha he sum of all couny peak forecass is equal o he sysem peak forecas. Peak conservaion savings are apporioned o each couny using he raio of each couny s peak load o he sysem peak loads, which is used in adjusing each couny s peak load forecas. E - 9

10 Easside King Couny Level Forecas The Easside King Couny coinciden peak load forecas based on he normal design emperaure of 23 degrees Fahrenhei was developed in a similar manner as he couny-level peak forecass. In he case of he sub-couny-level forecas, hisorical sysem coinciden peak load daa for subsaions serving he area from January 2008 o March 2014 were colleced, in addiion o he number of cusomers and billed sales by cusomer class. The esimaed economeric equaion for peak loads has he following form: Where: PkMW = monhly Easside peak-hour load in MW R = Easside residenial delivered loads in he monh in amw NR = Easside commercial plus indusrial delivered loads in he monh in amw Δ T = deviaion of acual peak-hour emperaure from monhly normal emperaure Ws = Easside residenial plus a % of commercial delivered loads Seas = ( Winer if Monh = 11,12,1,2; Summer if Monh = 7,8; Oher if Monh = 3,4,5,6,9,10) Trend = ime rend saring from 2008, afer he housing recession MA (1) = moving average erm of order 1 for ime series funcions The Greek leers and β are used o denoe coefficiens o be esimaed. The coinciden normal peak hour load forecas is developed using he forecass of Easside residenial and non-residenial loads, using 23 degrees Fahrenhei as he designed normal emperaure. The developmen of he load forecass by cusomer class was previously described above. This peak load forecas is furher adjused for conservaion by using he raio of Easside o King Couny peak loads as he share of he Easside in peak conservaion wihin King Couny. E - 10

11 GAS BILLED SALES AND CUSTOMER COUNTS A he gas sysem level, PSE forecass use-per-cusomer (UPC) and cusomer couns for each of he cusomer classes i serves. The gas classes include firm classes (residenial, commercial, indusrial, commercial large volume and indusrial large volume), inerrupible classes (commercial and indusrial) and ranspor classes (commercial firm, commercial inerrupible, indusrial firm and indusrial inerrupible). Energy demand from firm and inerrupible classes is summed o form he 2015 IRP Gas Base Demand Forecas. PSE esimaed he following UPC and cusomer coun economeric equaions using sample daes from a hisorical monhly daa series ha exends from January 1990 o December 2013; he sample daes varied depending on secor or class. The gas billed sales forecas is based on he esimaed equaions, normal weaher assumpions, rae forecass, and forecass of various economic and demographic inpus. The UPC and cusomer coun equaions are defined as follows: UPC, c = use (billed sales) per cusomer for class c, monh CC c, = cusomer couns for class c, monh ( k ) = he subscrip lag form in k periods from monh (k) denoes eiher a lag of k periods from or a polynomial disribued RR c, ( k ) = effecive real reail raes for class c in polynomial disribued lagged form E - 11

12 W c, = class-appropriae weaher variable; cycle-adjused HDDs using he base emperaure of 65; cycle-adjused HDDs are creaed o fi consumpion period implied by he class billing cycles EcoDem = class-appropriae economic and demographic variables; variables include c, ( k ) unemploymen rae, household size, non-farm employmen levels and growh, manufacuring employmen levels and growh, and building permis. Economic and demographic variables may be used in lag form or in polynomial disribued lag form. MD i = monhly dummy variable ha is 1 when he monh is equal o i, and zero oherwise for i from 1 o 12 UPC is forecas monhly a a class level using several explanaory variables including weaher, reail raes, monhly effecs, and various economic and demographic variables such as unemploymen rae, non-farm employmen and manufacuring employmen. Some of he variables, such as reail raes and economic variables are added o he equaion in a lagged, or polynomial lagged form o accoun for boh shor-erm and long-erm effecs of changes in hese variables on energy consumpion. Finally, depending on he equaion, an ARMA(p,q) srucure could be imposed o acknowledge ha fuure values of he prediced variables could be a funcion of is lag value or he lags of forecas errors. Similar o UPC, PSE forecass he gas cusomer coun equaions on a class level using several explanaory variables such as household size, building permis, oal employmen and manufacuring employmen. Some of he variables are also implemened in a lagged or polynomial disribued lag form o allow he impac of he variable o vary wih ime. Many of he cusomer equaions use monhly cusomer growh as he dependen variable, raher han oals, o more accuraely measure he impac of economic and demographic variables on growh, and o allow he forecas o grow from he las recorded acual value. ARMA(p,q) could also be imposed on cerain cusomer couns equaions. In addiion, some of he smaller cusomer classes are no forecas using equaions; insead, hose curren cusomer couns are held consan hroughou he forecas period. This is done for he ranspor classes, indusrial inerrupible class and indusrial large volume class. These classes have low cusomer couns and are no expeced o change significanly over he forecas period. E - 12

13 The billed sales forecas for each cusomer class, before new conservaion, is he produc of he class UPC forecas and he forecased number of cusomers in ha class, as defined below. Billed Salesc, = UPCc, CCc, The gas billed sales and cusomer forecass are adjused for known, shor-erm fuure discree addiions and subracions no accouned for in he forecas equaions, such as major changes in energy usage by large cusomers. These adjusmens may also include fuel and schedule swiching by large cusomers. The forecas of billed sales is furher adjused for new programmaic conservaion by class using he opimal conservaion bundle from he mos recen IRP. Toal billed sales in a given monh are calculaed as he sum of he billed sales across all cusomer classes: Toal Billed Sales = Billed Sales c, c PSE esimaes oal gas sysem delivered loads by disribuing monhly billed sales ino each billing cycle for he monh, hen allocaing he billing cycle sales ino he appropriae calendar monhs using heaing degree days as weighs, and adjusing each delivered sales for losses from ransmission and disribuion. This approach also enables compuaion of he unbilled sales each monh. E - 13

14 GAS PEAK DAY LOAD FORECAST Similar o he elecric peaks, he gas peak day is assumed o be a funcion of weaher-sensiive delivered sales, he deviaion of acual peak day average emperaure from monhly normal average emperaure and oher weaher evens. The following equaion used monhly daa from Ocober 1993 o December 2013 o represen peak day firm requiremens: 1, Wi n= 0, 1, Smr = 0, Mon h= 1, 2,11,12 Mon h 1, 2,11,12 Mon h = 6,7,8,9 Mon h 6,7,8,9 where: PkDThm = monhly sysem gas peak day load in dekaherms Fr = monhly delivered loads by firm cusomers Δ T g = deviaion of acual gas peak day average daily emperaure from monhly normal emperaure EN = dummy for when El Niño is presen during he winer M = dummy variable for monh of he year CSnp = indicaor variable for when he peak occurred wihin a cold snap period lasing more han one day, muliplied by he minimum emperaures for he day As before, he Greek leers are coefficien vecors as defined in he elecric peak secion above. This formula uses forecased billed sales as an explanaory variable, and he esimaed model weighs his variable heavily in erms of significance. Therefore, he peak day equaion will follow a similar rend as ha of he billed sales forecas wih minor deviaions based on he impac of oher explanaory variables. An advanage of his process is ha i helps esimae he conribuion of disinc cusomer classes o peak loads. E - 14

15 The design peak day used in he gas peak day forecas is a 52 heaing degree day (13 degrees Fahrenhei average emperaure for he day), based on he coss and benefis of meeing a higher or lower design day emperaure. In he 2003 LCP, PSE changed he gas supply peak day planning sandard from 55 heaing degree days (HDD), which is equivalen o 10 degrees Fahrenhei or a coldes day on record sandard, o 51 HDD, which is equivalen o 14 degrees Fahrenhei or a coldes day in 20 years sandard. The Washingon Uiliies and Transporaion Commission (WUTC) responded o he 2003 plan wih an accepance leer direcing PSE o analyze he benefis and coss of his change and o defend he new planning sandard in he 2005 LCP. As discussed in Appendix I of he 2005 LCP, PSE compleed a deailed, sochasic cos-benefi analysis ha considered boh he value cusomers place on reliabiliy of service and he incremenal coss of he resources necessary o provide ha reliabiliy a various emperaures. This analysis deermined ha i would be appropriae o increase our planning sandard from 51 HDD (14 degrees Fahrenhei) o 52 HDD (13 degrees Fahrenhei). PSE s gas planning sandard relies on he value our naural gas cusomers aribue o reliabiliy and covers 98 percen of hisorical peak evens. As such, i is unique o our cusomer base, our service erriory and he chosen form of energy. Thus, we use projeced delivered loads by class and his design emperaure o esimae gas peak day load. E - 15

16 MODELING UNCERTAINTIES IN THE LOAD FORECAST Load forecass are inherenly uncerain, and o acknowledge his uncerainy, high and low load forecass are developed. There are many sources of uncerainies in he load forecass including weaher and modelling errors, bu a key driver in loads are he assumpions on economic and demographic growh wihin he service erriory. Since he IRP focuses on long-erm uncerainy, he high and low load forecass are based on uncerainies relaed o long-erm economic and demographic growh. The economeric load forecas equaions depend on cerain ypes of economic and demographic variables; hese may vary depending on wheher he equaion is for cusomer couns or use-percusomer, and wheher he equaion is for residenial or non-residenial cusomer class. In PSE s load forecas models, he key service area economic and demographic inpus are populaion, employmen, unemploymen rae, personal income and building permis. These variables are inpus ino one or more load forecas equaions. The high and low load forecass are defined in he IRP as he 95h and 5h percenile, respecively, of he sochasic simulaion of he loads based on uncerainies in he economic and demographic inpus. To develop he sochasic simulaions of loads, a sochasic simulaion of PSE s economic and demographic elecric and gas models is performed o produce he disribuion of PSE s economic and demographic forecas variables. The forecass of PSE s economic and demographic variables are also a funcion of key U.S. macroeconomic variables such as populaion, employmen, unemploymen rae, personal income, personal consumpion expendiure index and long-erm morgage raes. We uilize he sochasic simulaion funcions in EViews, a popular economeric, forecasing and simulaion ool, by providing he sandard errors of he quarerly growhs of key U.S. macroeconomic inpus ino he PSE s economic and demographic models. These sandard errors were based on hisorical acuals from 1980 o The sochasic simulaion of PSE s economic and demographic models from 1,000 draws provides he basis for developing he disribuion of he relevan economic and demographic inpus for he load forecas models over he forecas period. Based on hese disribuions, sandard errors were esimaed for PSE service area populaion, employmen, unemploymen rae, personal income and building permis for each year over he forecas horizon. In a similar manner, hese sandard errors were used in producing he 250 sochasic simulaions of PSE s load forecass wihin EViews. The 5h and 95h percenile of hese sochasic simulaions were used as he low and high load forecass in he 2015 IRP. E - 16

17 HOURLY ELECTRIC DEMAND PROFILE Because emporarily soring large amouns of elecriciy is cosly, he minue-by-minue ineracion beween elecriciy producion and consumpion is very imporan. For his reason, and for purposes of analyzing he effeciveness of differen elecric generaing resources, an hourly profile of PSE elecric demand is required. We use our hourly (8,760 hours) load profile of elecric demand for he IRP for he sochasic analysis in he Resource Adequacy Model (RAM), for our power cos calculaion and for oher AURORA analyses. The esimaed hourly disribuion is buil using saisical models relaing acual observed emperaures, recen load daa and he laes cusomer couns. Daa PSE developed a represenaive disribuion of hourly emperaures based on daa from January 1, 1950 o December 31, Acual hourly delivered elecric loads beween January 1, 1994 and December 31, 2014 were used o develop he saisical relaionship beween emperaures and loads for esimaing hourly elecric demand based on a represenaive disribuion of hourly emperaures. Mehodology for Disribuion of Hourly Temperaures The above emperaure daa were sored and ranked o provide wo separae daa ses: For each year, a ranking of hourly emperaures by monh, coldes o warmes, over 60 years was used o calculae average monhly emperaure. A ranking of he imes when hese emperaures occurred, by monh, coldes o warmes, was averaged o provide an expeced ime of occurrence. Nex PSE found he hours mos likely o have he coldes emperaures (based on observed averages of coldes-o-warmes hour imes) and mached hem wih average coldes-o-warmes emperaures by monh. Soring his informaion ino a radiional ime series hen provided a represenaive hourly profile of emperaure. E - 17

18 Mehodology for Hourly Disribuion of Load For he ime period January 1, 1994 o December 31, 2014, PSE used he saisical hourly regression equaion: r ( Lh 2 + Lh 3 + Lh 4 % r = β, d DDd + α1lh 1 + α 2 & # + 3, m h 4, m h 2, d + ' 3 $ r r 2 (1 ( α T + α T ) + β Hol α P ( ) L ˆ ) h 1 5 h for hours from one o 24 o calculae load shape from he represenaive hourly emperaure profile. This means ha a separae equaion is esimaed for each hour of he day. Lˆh = Esimaed hourly load a hour h L h = Load a hour h Lh k = Load k hours before hour h T h = Temperaure a ime h 2 T h = Squared hourly emperaure a ime h P (1) ( h) = 1s degree polynomial Hol = NERC holiday dummy variables All Greek leers again denoe coefficien vecors. E - 18

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