CHAPTER 4 RELIABILITY CONSTRAINTS The reliability constraints
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1. 1 Appendix I These equations are found in Appendix VII Section 26 and is called Equation Energy AF a b c RSA d e f MOZ It is only for illustrative purposes the base runs do not include this constraint 84 Long Term Model USER MANUAL June 19 2000 4 2 The Treatment of Capacity and Energy Trading and Firm and Non firm Power in the Model In an ideal world with no limits on computer memory and running time models such as ours would distinguish in the optimization between two types of power Firm power as defined in section 2 17 Article 1 of SAPP s ABOM and economy energy as defined in section 2 11 of the same document To conserve on memory and running time Purdue s model does not distinguish between the two power flows during the optimization but does allow users to distinguish between them after the optimization A Splitting up power flows into firm and non firm components The characteristic of firm power flow is that the exporting country must have on hand either in the form of its own generating capacity or capacity available from other countries sufficient capacity to always provide such power to the importing country In our model this capacity commitment or as section 2 27 puts it the lease of a specific generating unit or units or a portion of such unit s is the variable Fmax ty z zp representing country z s leasing of capacity in ty to country zp Once Fmax ty z zp i2. Long Term Model USER MANUAL June 19 2000 CHAPTER 4 RELIABILITY CONSTRAINTS The reliability constraints insure that a proper reserve margin is maintained between installed MW capacity and peak period MW demand in every period PeakD z dgr z ty Reliability requirements enter the model in two ways Requirement 1 Each country must maintain a SAPP specified reserve margin for each of the major sources of supply thermal plants including pumped storage Parameter RESTHM in Appendix VI Section 12 default value 19 and hydro plants Parameter RESHYD 10 default value in Appendix V Section 12 Since the model as in the real world allows trade in reserves imports held by others and exports held for others to enter into the equation they must be added Fimax ty zp z imports of reserves and subtracted Fmax ty z zp exports of reserves from the left hand side of the reserve equation Exports of reserves are simply subtracted but imports of reserves need to be adjusted downward by the line loss between z and zp no adjustment for forced outage is necessary according to SAPP definitions of reserve requirements As in the case of the demand equation a country can choose not to meet the reserve constraint by choosing a positive value for unsatisfied reserve requirements variable UM z ty and a cost MW set by the user parameter UMcost found in Section 1 of Appendix II The nominal values set at 10 000 KW in the model Thi
3. UAL June 19 2000 HOinit z ih 1 DecayHO HOV exp step z ih gt HOV exp t z ih 1 DecayHO t 1 a Se ty ty PAING HNinit z nh X Yh t z nh 1 DecayHN HN exp step z nh Y HNV exp t z nh 1 DecayHN hydro ET ar capacity PGPSOinit z 1 DecayPHO 9 gt PHNinit z phn ph z z phn 1 DecayPHN phh t 1 1 RESHYD z reserves held in ty by country zp for Be country z adjusted for loss and Fmax ty zp z 1 PFOloss zp z transmission forced zp outage rates UM z ty unsatisfied reserve requirements peak demand in year ty reserves in 4 PeakD z dgr z ty LM z th DLC z Ay Fmax ty Zy zj ty held by country z J zp J for use by country zp This reserve margin constraint as stated in GAMS notation is equation ResvREG2 and is shown in Appendix VI Section 14 4 1 The Autonomy Constraint In addition to system reliability considerations non technical political and economic factors may require that domestic capacity be maintained at some prescribed fraction of domestic peak demand regardless of the economic advantages of importing cheap power or reserve capacity This will be the function of the country autonomy constraint which reflects the level of autonomy each country wishes to maintain by specifying a country autonomy factor AF z ty 2 0 found in Section 1 of Appendix VD which reflects each country s desire to be c
4. chases Firm Power Sales Since firm power purchases sales are not variables in the model we use leased capacity purchases sales Fmax ty z zp in the equation the purchases suitably adjusted for line loss and outage rates Thermal rain in ty k Hydro a in ty y y Fma i ielo s zp gt Peak Demand ty z 2 Fmax ty z zp zp To summarize e Power flows between countries can after the fact be broken down into firm and non firm power e Both the transmission and load balance constraints consider only the total flows of firm and non firm power 87
5. ompletely self sufficient AF 2 1 willing to depend completely on firm imports during peak if it is economic to do so AF 0 or something in between 0 lt AF z ty lt 1 83 Long Term Model USER MANUAL June 19 2000 Available Installed Thermal plus hydro capacity in period ty gt AF z ty JD peak y z DSM peak y 2 DLC V ty z peak These equations are found in Appendix VII Section 16 for e all but RSA and MOZ Equation ResvREG4 e RSA ResvREG4 a b c e MOZ ResvREG4 d e f In addition to each country requiring that domestic production capacity not involving any reliance upon reserves held by others always be large enough to satisfy a given fraction of domestic peak demand a country might also require that a certain fraction of demand in all periods be met by domestic production This is a far more costly to SAPP constraint because it prevents any trade beyond that allowed by the constraint taking place in a given year This constraint when added would enter the demand supply constraint by requiring that x of domestic production over a year be met by domestic generation e g gt PG ty ts td th z i gt PGN ty ts td th z ni H ty ts td th z ih gt Hnew ty ts td th z nh Enaf z ty Demand ih nh in all hours days seasons and years where Enaf z ty is the fraction of demand in country z during year ty which must be met by domestic production Table Enaf z ty Section
6. p and the current capacity of the old lines connecting z to zp e g for old lines ignoring decay and forced outages PF ty ts td th z zp lt PFinit z zp X PFOVexp tye zp tye 1 a similar equation holds for new lines In addition a constraint requiring that there be sufficient transmission capacity at all times to handle the import export of reserves must be added e g the sum of current new and old transmission capacity derated by decay and forced outage Fimax ty z zp C Treatment in the Load Balance Constraints The hourly load balances which require that supplies must equal demands involve only domestic generation power imports power exports and demand Ignoring both unserved and dumped energy the load balance equation for the time slice ty ts td th is simply 86 Long Term Model USER MANUAL June 19 2000 Sum of all Domestic Generation f Jin ty ts td th Jok gt PF ty ts td th Zp z 1 lineloss in ty ts td zp Demand in ty ts td th z zp gt PF ty ts td th z zp zp No distinction is made between firm and non firm power in meeting demand nor should there be both can interchangeably satisfy the load balance equation D Treatment in the Reliability Constraints According to section 2 33 and Appendix I of the SAPP ABOM the reserve capacity obligation of each country can be expressed as Thermal Capacity X Hydro Capacity SPee Denard Bian Dower 1 19 1 10 Pur
7. s cost should reflect the actual capacity cost of a backstop technology used in emergencies to generate electricity or equivalently the actual cost of a demand side management program put in place to shave peaks by load shedding during peak periods 81 Long Term Model USER MANUAL June 19 2000 Available Installed Thermal Capacity m Available Installed Hydro Capacity 1 RESTHM 2z 1 RESHYD z Reserves held by others to back up firm imports to z 1 lineloss UM z ty Re serves held by z to back up firm exports to others PeakD z dgr z ty LM z th DLC Note that the choice of RESTHM and RESHYD are behavioral choices values can be entered to reflect each SAPP member s attitudes The choice of FORICN and FORICO however are set by the reliability of the lines connecting zp and z The full equation is as follows ty PGOinit z i 1 DecayPGO PGOexpstep z i PGOexp t z i 1 DecayPGO t 1 ty N Texpstep z ni gt PGNTexp T z i 1 DecayNT t 1 NSCexpstep z ni gt PGNSCexp t z ni 1 DecayNSC t 1 existing ty thermal PGNCCinit z ni YCC t z ni 1 DecayNCC capacity T l ty NCCexpstep zni Y PGNCCexp t z ni 1 DecayNCC t 1 ty PGNLCinit z ni YLC t z ni 1 DecayNLC t 1 ty NLCexpstep z ni gt PGNLCexp t z ni 1 DecayNLC ty 1 1 RESTHM 2 82 Long Term Model USER MAN
8. s known along with the flow variables PF ty ts td th z zp and PFnew ty ts td th z zp the following rules can be used to split up the flows between z and zp into firm and economy trade Case A power flows exceed Fmax If PF ty ts td th z zp PFnew ty ts td th z zp gt Fmax ty z zp J Firm Fmax ty z zp J economy PF ty ts tdt th z zp PFnew ty ts td th z zp Fmax ty z zp Case B Power flows less than or equal to Fmax If PF ty ts td th z zp PFnew ty ts td th z zp Fmax ty z zp then Firm PF ty ts td th z zp PFnew ty ts td th z zp J Economy 0 85 Long Term Model USER MANUAL June 19 2000 Thus all power flows are firm unless power flows exceed the capacity commitment represented by Fmax ty z zp only the excess if any of power flows over Fmax ty z zp should be considered economy sales since such sales are not backed up by any committed capacity in the exporting country e g non capacity non firm transactions SAPP ABOM service schedule e B Treatment in the Transmission Capacity Constraint The flow variables for old and new lines PF ty ts td th z zp and PFnew ty ts td th z zp power flows from country z to country zp in a given time slice give the total flow between two countries consisting of the sum of all firm and non firm power trades Thus the transmission capacity flow constraints for old lines involve only PF ty ts td th z z
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