CHAPTER 4 RELIABILITY CONSTRAINTS The reliability constraints
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1. 2001 HOinit 1 DecayHO HOV exp step HOV exp T z ih 1 DecayHo T 1 existing hydro capacity HNinit Yh t z nh 1 DecayHN t 1 HN exp step gt HNV exp t z nh 1 DecayHN t 1 PGPSOinit z 1 DecayPHO ty gt PHNinit z phn Y ph t z phn 1 DecayPHN phn t 1 1 RESHYD z held in ty b t reserves held in ty by country zp for 5 F max ty zp Z 1 PFOloss zp z country z adjusted zp for loss unsatisfied reserve UM zty gt requirements peak demand in year ty plus reserves in ty PeakD z dgr zty LM z th DLC z 2 Fmax ty z held by country z for use by country zp zp This reserve margin constraint as stated in GAMS notation is equation ResvREG2 and is shown in Appendix VII Section 14 4 1 The Autonomy Constraints 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 self sufficiency each country wishes to maintain by specifying a country autonomy factor AF zty 0 found in Section 1 of Appendix VI which reflects each country s desire to be compl2. ignoring decay and forced outages ty PF ty ts td th z zp lt PFinit z zp gt PFOVexp tye z zp tye 1 a similar equation holds for new lines In addition since firm power trade can be much less than its maximum Fmax a constraint requiring that there be sufficient transmission capacity at all times to handle the maximum promised import export of reserves must be added e g the sum of current new and old transmission capacity derated by decay and forced outage must be greater then or equal to Fmax ty z zp 98 Long Term Model USER MANUAL February 2001 ty Fmax ty z zp lt PFinit z zp gt PFOVexp tye z zp PFnew z zp tye 1 ty 9 PFNVexp tye z zp tye 1 This equation Equation FmaxTcapAj is found in Appendix VII Section 13 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 aS PF ty ts td th zp z 1 lineloss zp Sum of all Domestic Generation in ty ts td th Demand in ty ts d th z zp PF ty ts td th z zp p 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
3. set by the user parameter UMcost found in Section 1 of Appendix II The nominal value is set at 1000 KW in the model This cost should reflect SAPP penalty costs to be imposed on SAPP members when these agreed upon reserve requirements are violated for a given year 93 Long Term Model USER MANUAL February 2001 Available Installed Thermal Capacity n Available Installed Hydro Capacity 1 RESTHM z 1 RESHYD z Reserves held by others to back up firm imports to z J lineloss UM z ty 2 Reserves held by z to back up firm exports to others PeakD z dgr z ty LM z th DLC z Note that the choice of RESTHM and RESHYD are behavioral choices values can be entered to reflect each SAPP member s attitudes The full equation is as follows the expressions for installed capacity in year ty were explained in Chapter 3 PGOinit 1 DecayPGO ty PGO exp step gt PGO exp T z i 1 DecayPGO J t 1 y NT exp step DA PGNT exp T z i 1 DecayNT t 1 ty NSC exp step DA PGNSC exp T z ni 1 DecayNSC t 1 oe T existing thermal o ty a capacity PGNCCinit gt YCC t z ni 1 DecayNCC Tel NCC exp step X PGNCC exp T z ni 1 DecayNCC J t 1 ty PGNLCinit gt YLC T zni X1 DecayNLC JOE t 1 NLC exp step 9 PGNLC exp T z ni 1 DecayNLC ty 1 1 RESTHM z 94 Long Term Model USER MANUAL February
4. 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 Hydro Capacity 1 19 1 10 gt Peak Demand Firm Power Purchases Firm Power Sales Since firm power purchases sales are not variables in the model we use capacity purchases sales Fmax ty z zp in the equation the purchases suitably adjusted for line loss 99 Long Term Model USER MANUAL February 2001 m ie ermal Capacity in 1y Hydro Capacity nD S Emax zp 2 I linelos f 5 zp gt Peak Demand ty z gt 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 the total flows of firm and non firm power e A separate constraint must be added to insure that at all times sufficient transmission capacity is available to handle reserve power flows between countries 100
5. Long Term Model USER MANUAL February 2001 CHAPTER 4 RELIABILITY CONSTRAINTS The reliability constraints insure that a proper reserve margin is maintained between domestic and imported 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 VI Section 13 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 imports must be added Fmax ty zp z imports of reserves and exports subtracted Fmax ty z zp exports of reserves from the supply side of the reserve equation Alternatively exports of reserves can be added and imports subtracted from domestic peak demand to create the peak responsibility of a region 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 at a cost MW
6. etely self sufficient AF 1 95 Long Term Model USER MANUAL February 2001 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 zty lt 1 Available Installed Thermal plus hydro capacity in period ty adjusted for forced outage gt AF z D peak y z DSM peak y z DLC z V y z peak These equations are found in Appendix VII Section 16 for e all but RSA DRC and MOZ Equation ResvREG4 e RSA ResvREG4 a b c e MOZ ResvREG4 d e f e DRC A single autonomy constraint for RSA DRC and MOZ which covers both nodes in the three countries requires an autonomy equation of a different form for these two countries In addition to each country requiring that domestic production capacity 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 all time slices 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 PGN ty ts td th z ni p2 H ty ts td th z ih 2 Hnew ty ts td th z nh Enaf z ty Demand where Enaf z ty is the f
7. raction of demand in country z during year ty which must be met by domestic production Table Enaf z ty Section 1 Appendix VI These equations are 96 Long Term Model USER MANUAL February 2001 found in Appendix VII Section 26 and are called Equation Energy AP a b c RSA d e f MOZ 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 is the variable Fmax ty z zp representing country z s leasing of capacity in ty to country zp Once Fmax ty z zp is known along with the flow variables PF ty ts td th z zp and PFnew ty ts td th z
8. 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 Firm Fmax ty z zp economy PF ty ts td th z zp PFnew ty ts td th z zp Fmax ty z zp 97 Long Term Model USER MANUAL February 2001 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 lt Fmax ty z zp then ce PF ty ts td th z zp PFnew ty ts td th z zp Economy 0 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 zp and the current capacity of the old lines connecting z to zp e g for old lines
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