CHAPTER 2 LOAD BALANCE The load balance, or demand/supply
Contents
1. enter the supply side of the demand supply balance equation The variable UE ty ts td th z gives the MW value of the amount The scalar UEcost Section 1 of Appendix II sets the cost MWh of unserved energy The nominal value is 140 MWh but it can be set at whatever value users want to adopt As will be explained later the model also allows the reserve requirements constraints to be violated by setting the variable UM z ty unsatisfied MW reserve requirements to some positive level at a cost MW set by the user Finally since it is possible that the presence of must run constraints may force supply generation plus imports to be greater than demand consumption plus exports 50 Long Term Model USER MANUAL September 5 2000 without the user recognizing the fact a new dummy variable dumped energy DumpEn ty ts td th z is added and the inequality converted to an equality e g generation imports unmet demand consumption exports dumped energy Thus if there is insufficient generation to meet demand unmet demand is greater than zero if because of must run constraints generation exceeds demand then dumped energy is greater than zero In all cases the load balance is just that a balance of demand and supply 2 3 The Full System Load Balance Equation The load balance equation Equation Demand in the model requires that for all time periods for each country z the sum of MW generation from e e2. ts td th z 1 PSOloss th th The GAMS format equation o dpumped is shown in Appendix VII Section 25 the same equation type holds for new pumped sites when constructed There are additional constraints described in Chapter 3 which limit the instantaneous generation rate and the total storage volume available per day The GAMS equation indicates this is always an equality at an optimum solution since it was decided not to include the possibility of longer term storage in the model The model enters pumped storage into the load balance equation on the supply side hence PGPSO ty ts td th z enters with a positive sign while PUPSO h ts td th z enters with a negative sign e g Generation plus net imports PGPSO ty ts td th z PUPSO ty ts td th z Demand Pumped storage from new sites indexed phn enters into the model in a similar fashion except the variables are PGPSN ty ts td th z phn and PUPSN ty ts td th z phn Data Tables for PSNloss phn are found in Section 9 of Appendix V In GAMS format equation Newpumped is shown in Appendix VII Section 25 f Net Imports Figures 1 2 and 1 3 in Chapter 1 and Tables PFOinit z zp and PFNinit z zp in Sections 1 and 7 respectively of Appendix III list the initial MW capacities of the existing and proposed lines respectively linking the 14 nodes which make up SAPP in the model The tables are symmetric so that power flow capacity from country A to B is the same as B to A even f
3. values e enter hourly load data for a representative week in per unit values in Table Uhour found in Appendix I Section___ 24 x 7 values e enter peak hour in MW for the base year in Table Upeak e enter total MWh in the base year entered into parameter DMWh z 41 Long Term Model USER MANUAL September 5 2000 Then model then automatically converts this data into Table Base ts td th z Appendix VIII Section ___ which gives the base year demand data for the 36 representative hourly demands the model uses to drive the model as explained below Table Yper ty sets the number of periods in the planning horizon If the user wishes to consider say a 5 period horizon then the user enters in the table for perl to per5 and 0 thereafter The model also allows the user to decide how many years each period will represent every year every other year every third year etc by selecting the value for scalar n in the model See Appendix I The model automatically adjusts the yearly growth rates and the cost function to insure the model fully adjusts to the period and years period selection made by the user allowing a wide range of planning horizons In all cases no capacity expansion is allowed in the initial year those construction projects SAPP indicated would be completed by the initial year are included as installed capacity Thus the first year s optimization involves only dispatch of existing capacity against the first y
4. 5 2000 and south to recognize the reality of the split supply situation in Mozambique and the split demand situation in RSA The site index i follows the column index stat 1 Power generation in period ty season ts day type td hour th at old site 7 in country z is given by the continuous non negative variable PG ty ts td th z i Thus PG 1 1 1 1 1 1 is the MW contribution of Angola z 1 site 1 stat 1 during period 1 2002 in season 1 winter in day type 1 off peak during hour 1 summer peak avnt b New Thermal Sites Table 1 3 in Chapter 1 lists the capacities of new or recommissioned thermal plants under consideration by SAPP The new sites have been grouped into five categories depending on their size fuel type and technology e Simple cycle combustion turbines NSA and Angola power generation from such sites is given by the variable PGNT ty ts td th z ni where ni is the site index for combustion turbines in country z proposed capacities can be found in Table 1 3 listed as T GT e Combined cycle combustion turbines Namibia and Tanzania power generation from such sites is given by the variable PGCC ty ts td th z ni proposed capacities for these units can be found in Table 1 3 listed as T CC e Small lt 500 MW coal fuel plants Botswana NSA and Zimbabwe power generation is given by PGSC ty ts td th z ni proposed capacities for these units can be found in Table 1 3 listed as T SC e Large g
5. Long Term Model USER MANUAL September 5 2000 CHAPTER 2 LOAD BALANCE The load balance or demand supply equations which ensures that user specified demands are met for each of the hours in the six representative day types in the model summer winter peak off peak and average days are described in this chapter see also Appendices I If and VII 2 1 The Demand for Electricity The model is driven by the typical hour day season year chronological demand approach taken by many of the latest commercial models rather than the load duration curve methodology used in earlier approaches Appendices I and H give all the input files necessary to create the demand drivers for the model Demands and supplies are for the utilities in SAPP rather than for the SAPP countries Thus municipalities or others in the SAPP countries which generate and use their own electricity are not considered in calculating either the forecast demand or the power available to meet such demands The model is set up to model demand in a user specified number of representative periods up to 10 in the future by selecting the parameter Yper ty found in Appendix II Section 2 starting in a user specified year 2000 is the default value Base year demand data are entered into the model using the SAPP specified format as of February 2000 e enter weekly peak load in per unit values for the base year in Table Uweek found in Appendix I Section___ 52
6. Minimum and maximum run levels for new plants minT z ni maxT z ni minSC z ni maxSC z ni minCC z ni maxCC z ni minLC z ni maxLC z ni minHN z nh maxHN z ni and old plants PGmin z i PGmax z i minH z ih and maxH z ih can be set by users they are found in Section 19 of Appendix IV for thermal units and Section 9 of Appendix V for hydro units Both the minimum and maximum utilization levels are entered as capacity factors that is minimum and maximum percent utilization of whatever the current capacity is for the unit in question Note that this method does not require the unit to be built since x of zero is still zero Users should use the At_ _ z ni Bef_ _ z ni or Aft_ _ z ni options described in Chapter 3 to force the model to build a unit at before or after a user specified year The equations which insure these constraints are met are found in Section 26 of Appendix VII names are Equation Tmin Equation SCmin etc a Existing Thermal Sites Table 1 1 in Chapter 1 and Table PGOinit z i in Section 13 of Appendix IV both list the year 2000 current MW capacities of the existing thermal sites in the model including Nuclear Koeberg SSA The rows in Table PGOinit z i are the locations listed in order of the z index assigned e g Ang Angola is z 1 Bot Botswana is z 2 etc Zimbabwe is z 14 Note Mozambique and RSA are divided into two regions north 45 Long Term Model USER MANUAL September
7. ear s demand Yearly demand growth rates which differ by time period n and by country z can be specified by the user parameter dgrowthI z dgrowth2 z dgrowth3 z etc in Appendix II Sections 2 3 and 4 The program automatically converts the yearly growth rates entered in the tables dgrowthI1 z into dgr z ty the proper growth rates for the periods of varying length in the model as indicated in Section 1 of Appendix VII In creating the base year demand drivers for the model from the SAPP input data format the model first selects within each year two seasons summer and winter The summer period contains nine months 273 days while the winter contains three months 91 days Within each season three days a peak day an off peak day and an average day are modeled Within the summer season there are 39 peak days 78 off peak days and 156 average days Within the winter season there are 13 peak 26 off peak and 52 average days Within each day type six hours are modeled one off peak hour taken to be hour 9 three peak hours hours 19 20 and 21 two average hours one average night hour 42 Long Term Model USER MANUAL September 5 2000 avnt representing 8 night hours and one average day hour avdy representing 12 average day hours peaks excluded Users can select other weights by entering desired weights in Table Mtod th found in Section 1 of Appendix I but should select such weights to insure the hou
8. inimization PF ty ts td th zp z competing with imports from other countries and domestic generation to satisfy power demands in country z Fmax ty zp z competing with domestic reserves to satisfy country z s reserve requirements After the optimal values of PF ty ts td th zp z and Fmax ty zp z are determined a calculation can be made to separate PF ty ts td th zp z into firm and non firm power by recognizing that the excess if any of PF ty ts td th zp z over Fmax ty zp z is non firm power the rest is firm See the detailed discussion of this and related points at the end of Chapter 4 The model does this calculation automatically and the results are reported in the Trade out file MW power flows from country z to zp on old lines are given by the variables PF ty ts td th z zp while flows on the new lines are given by the variables PFnew ty ts td th z zp Using this notation and accounting for line losses reducing the amount of power arriving at country z net imports for country z in a given hour would be imports arriving on old lines exports sent on old lines gt PF ty ts td th zp z 1 PFOloss zp z PF ty ts td th z zp zp imports arriving on new lines exports sent on new lines mm TA N TA T X PFnew ty ts td th zp z 1 PFNloss zp z PFnew ty ts td th z zp zp 49 Long Term Model USER MANUAL September 5 2000 Note that the assumption that line losses reduce the amount of p
9. need to be met beyond the horizon 2 2 The Supply Side The demand in a given region can be met from a variety of energy sources a existing thermal sites b new thermal sites c existing hydro sites d new hydro sites e pumped storage f net imports imports less exports g paying an unserved energy cost Within each region generating sites are identified which contain generating plants For purposes of dispatch all plants at a site are collectively dispatched Generation variables in MW for the sites are PG ty ts td th z i generation from existing thermal site 7 PGNT ty ts td th z ni generation from new gas turbines at site ni 44 Long Term Model USER MANUAL September 5 2000 PGNSC ty ts td th z ni generation from new small coal plants at site ni PGNCC ty ts td th z ni generation from new combined cycle plants at site ni PGNLC ty ts td th z ni generation from new large coal plants at site ni H ty ts td th z ih generation from existing hydro site ih Hnew ty ts td th z nh generation from new hydro site nh PGPSO ty ts td th z PUPSO ty ts td th z net generation from old pumped hydro sites PGPSO is generation supply PUPSO is pump demand PGPSWN ty ts td th z phn PUPSN ty ts td th z phn net generation from new pumped hydro sites PGPSN is generation supply PUPSN is pump demand Default value characteristics of new and old plants are based on data furnished by SAPP members
10. or DC lines see below Transmission losses on the lines are given in tables PFOloss z zp for existing lines and PFNloss z zp for new lines in Sections 3 and 5 respectively in Appendix III Uni directional DC lines in the model are modeled by assuming infinite loss in the counter flow direction Recalling that there are two types of power flows in the model firm power flows power flows from export country capacity held in reserve to insure power availability at all times during the period covered by the capacity commitment and non firm power 48 Long Term Model USER MANUAL September 5 2000 flows flows from export country capacity which does not have the guaranteed continuous availability feature of firm power one would expect the model to contain two sets of power flow variables one firm one non firm In fact the model contains only the total of firm and non firm power flows since in reality there is no way before the fact to label some flow firm and some non firm In the model as in the real world there is just a single decision flow variable PF ty ts td th zp z which measures flow from country zp to country z and a single capacity reservation decision variable Fmax ty zp z which represents capacity that country zp reserves for possible use by country z The optimization proceeds with no explicit connection between the two decision variables They independently seek the level that is consistent with SAPP wide cost m
11. ower arriving at country z implies that the importer bears the line loss alternatively the exporter could have borne the loss or the loss split 50 50 All this will alter only the cost MWh but not the real cost to SAPP of the transaction As in the case of generating units yearly minimum and maximum use levels for new and old lines can be set by the user by entering in Tables minPFO z zp maxPFO z zp minPFN z zp and maxPFN z zp the minimum and maximum yearly power flows in MWh found in Section 7 of Appendix III the equations are found in Section 26 of Appendix VII named PFmin PFmax PF Nmin and PFNmax As in the case of minimum and maximum utilization levels for generating units minimum and maximum flow levels for lines are entered as line capacity factors expressed as a percent of the current capacity Thus if a user wished to bound the use of a line between 20 and 80 of its maximum yearly KWh capacity the user would enter 20 in minPF__ z zp and 80 in maxPF_ _ z zp These constraints are particularly useful when testing the impact of forced exports on the optimal solution To prevent the model from immediately sending back forced exports during the re optimization the program automatically sets maxPFO zp z to zero whenever minPFO z zp is greater than zero and sets maxPFN zp z to zero whenever minPFN z zp is greater than zero g Unserved Energy Each region can choose not to meet hourly demand by allowing unserved energy to
12. r specified LM options to fractionally adjust up or down the load shapes of the representative days in the model It should be emphasized that the model in its current form does not compete LM against normal supply side options to obtain the least cost mix of LM and capacity expansion It simply allows various LM options with known costs to be entered into the model to see off line if they are cost effective when 43 Long Term Model USER MANUAL September 5 2000 compared to supply alternatives It is planned to add LM to the optimization formulation at a later date Combining the period growth assumptions with the DLC and LM data allows the specification of the right hand side of the load balance equation which specifies for each hour in each day in each season in each year the demand at the generating station that must be met inclusive of the effect of distribution line loss and LM programs Dyr ty ts td th z LM z th DLC z The choice of the number of periods in the planning horizon Yper ty governs the demand side of the equation in that the demand side is multiplied by Yper ty Yper ty Dyr ty ts td th z LM z th DLC z This is the right hand side of the load balance equation Equation Demand found in Appendix VII Section 26 Since Yper ty 1 for all periods within the planning horizon and O for all periods beyond the horizon the model only optimizes within the planning horizon no demands
13. rs total to 24 All this comes together in creating the demand driver for the model parameter Dyr ty ts td th z Section 2 of Appendix VII which is country z s MW demand in year ty in season fs ts winter summer in day td td peak off peak average in hour th th hr9 avnt hr19 hr20 hr21 and avdy Combining the yearly growth assumptions with the base year day type demand data found in Table Base ts td th z we have Dyr ty ts td th z Base ts td th z dgr z ty The GAMS notation is shown in Appendix VII Section 2 If the total GWh in the base year as calculated by this method does not equal the total GWh as reported in parameter DMWh z the program scales up or down the data in Base ts td th z by multiplying it by a correction factor Correction z which equates the base year MWh as calculated by the program to that reported by users in Parameter z Next the impact on these demands of domestic distribution loss and demand side management must be considered Table DLC z in Appendix II Section 5 the domestic loss coefficient in the model is applied to the demand value to allow for electricity loss within each SAPP region it converts demand at the customer meter into demand at the generating station If users enter sent out demand at the generating stations into the base year demand tables DLC z should be set to 1 0 The load management parameter LM z th in Appendix VI Section 12 allows SAPP membe
14. t 500 MW coal fuel plants NSA only power generation is given by PGLC ty ts td th z ni proposed capacities for those units can be found in Table 1 3 listed as T LC e Nuclear plants in RSA only listed as T NUC Users can add additional projects in each of the categories for consideration by entering the necessary cost and performance data into the data tables in the thermal data section either directly or through the interface described in Chapter 7 Once the data are entered the model automatically adds the proposed project to the list of projects under consideration 46 Long Term Model USER MANUAL September 5 2000 The model can have a total of eight new projects per technology per country including those listed in Table 1 3 allowing the user substantial flexibility in the specification of new thermal options for consideration c Existing Hydro Sites Table 1 2 in Chapter 1 and Table HOinit z ih z the row country index ih the column site index in Section 4 of Appendix V list the year 2000 current MW capacities of the existing hydro sites in the model A complete description of the sites will be given later in the report MW output from the existing sites is given by the variable H ty ts td th z ih d New Hydro Sites Table 1 3 in Chapter 1 and Table HNinit z nh in Section 1 of Appendix V again z the row country index nh the column new site index list the hydro sites under considera
15. tion by SAPP members The options as expected are dominated by the expansions of DRC s Grand Inga hydro site which accounts for over two thirds of planned hydro capacity MW output from the new sites is given by the variable Hnew ty ts td th z nh e Pumped Storage At least two SAPP members RSA and Tanzania either have or are planning to add pumped storage as a means of peak shaving valley filling their 24 hour demand profiles Table 1 3 contains data on the four known pumped storage projects planned by RSA Pump storage uses electricity off peak to pump water up to reservoirs which are then discharged during peak periods The hourly MW amount of on peak generating at the two existing pump storage sites in RSA will be indicated by the non negative variable PGPSO ty ts td th z while the hourly MW amount of off peak pumping will be indicated by the non negative variable PUPSO ty ts td th z The power available for generation must be less than the power used to pump because of pump storage system loss given by the parameter PSOloss in Section 9 of Appendix V Default value is 0 3 Pumped storage facilities are assumed to operate on a 24 hour cycle e g what is pumped up in a night must come 47 Long Term Model USER MANUAL September 5 2000 down in the same day Thus the sum over all hours in a day of PGPSO ty ts td th z cannot exceed the sum overall hours of PUPSO less loss PGPSO ty ts td th z lt X PUPSO ty
16. xisting thermal sites PG ty ts td th z i e new _ thermal sites PGNT ty ts td th z ni PGNCC ty ts td th z ni PGNSC ty ts td th z ni PGNLC ty ts td th z ni e net firm and non firm imports over existing transmission lines PF ty ts td th zp z 1 PF Oloss zp z PF ty ts td th z zp e net firm and non firm imports over new transmission lines PFnew ty ts td th zp z 1 PF Nloss zp z PFnew ty ts td th z zp e existing hydro sites H ty ts td th z ih e new hydro sites Hnew ty ts td th z nh e old pumped storage PGPSO ty ts td th z PUPSO ty ts td th z e new pumped storage PGPSN ty ts td th z phn PUPSN ty ts td th z phn plus unserved energy e UE ty ts td th z must equal Yper ty DLC z Dyr ty ts td th z LM z th e plus dumped energy DumpEn ty ts td th z all this is entered into the model using GAMS notation as equation Demand ty ts td th z and found listed in Appendix VII Section 26 51
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