Presentation on theme: "EE 369 POWER SYSTEM ANALYSIS"— Presentation transcript:
1 EE 369 POWER SYSTEM ANALYSIS Lecture 16Economic DispatchTom Overbye and Ross Baldick
2 AnnouncementsRead Chapter 12, concentrating on sections 12.4 and 12.5.Read Chapter 7.Homework 12 is 6.43, 6.48, 6.59, 6.61, 12.19, 12.22, 12.20, 12.24, 12.26, 12.28, 12.29; due Tuesday Nov. 25.Homework 13 is 12.21, 12.25, 12.27, 7.1, 7.3, 7.4, 7.5, 7.6, 7.9, 7.12, 7.16; due Thursday, December 4.
3 Economic Dispatch: Formulation The goal of economic dispatch is to determine the generation dispatch that minimizes the instantaneous operating cost, subject to the constraint that total generation = total load + lossesInitially we'llignore generatorlimits and thelosses
4 Unconstrained Minimization This is a minimization problem with a single equality constraintFor an unconstrained minimization a necessary (but not sufficient) condition for a minimum is the gradient of the function must be zero,The gradient generalizes the first derivative for multi-variable problems:
5 Minimization with Equality Constraint When the minimization is constrained with an equality constraint we can solve the problem using the method of Lagrange MultipliersKey idea is to represent a constrained minimization problem as an unconstrained problem.
9 Lambda-Iteration Solution Method The direct solution using Lagrange multipliers only works if no generators are at their limits.Another method is known as lambda-iterationthe method requires that there to be a unique mapping from a value of lambda (marginal cost) to each generator’s MW output:for any choice of lambda (marginal cost), the generators collectively produce a total MW outputthe method then starts with values of lambda below and above the optimal value (corresponding to too little and too much total output), and then iteratively brackets the optimal value.
16 Thirty Bus ED ExampleCase is economically dispatched (without consideringthe incremental impact of the system losses).
17 Generator MW LimitsGenerators have limits on the minimum and maximum amount of power they can produceTypically the minimum limit is not zero.Because of varying system economics usually many generators in a system are operated at their maximum MW limits:Baseload generators are at their maximum limits except during the off-peak.
21 Back of Envelope Values $/MWhr = fuelcost * heatrate + variable O&MTypical incremental costs can be roughly approximated:Typical heatrate for a coal plant is 10, modern combustion turbine is 10, combined cycle plant is 7 to 8, older combustion turbine 15.Fuel costs ($/MBtu) are quite variable, with current values around 2 for coal, 3 for natural gas, 0.5 for nuclear, probably 10 for fuel oil.Hydro costs tend to be quite low, but are fuel (water) constrained.
22 Inclusion of Transmission Losses The losses on the transmission system are a function of the generation dispatch.In general, using generators closer to the load results in lower lossesThis impact on losses should be included when doing the economic dispatchLosses can be included by slightly rewriting the Lagrangian:
28 Thirty Bus ED Example Now consider losses. Because of the penalty factors the generator incrementalcosts are no longer identical.
29 Area Supply Curve The area supply curve shows the cost to produce the next MW of electricity, assuming area is economicallydispatchedSupplycurve forthirty bussystem
30 Economic Dispatch - Summary Economic dispatch determines the best way to minimize the current generator operating costs.The lambda-iteration method is a good approach for solving the economic dispatch problem:generator limits are easily handled,penalty factors are used to consider the impact of losses.Economic dispatch is not concerned with determining which units to turn on/off (this is the unit commitment problem).Basic form of economic dispatch ignores the transmission system limitations.
31 Security Constrained ED or Optimal Power Flow Transmission constraints often limit ability to use lower cost power.Such limits require deviations from what would otherwise be minimum cost dispatch in order to maintain system “security.”
32 Security Constrained ED or Optimal Power Flow The goal of a security constrained ED or optimal power flow (OPF) is to determine the “best” way to instantaneously operate a power system, considering transmission limits.Usually “best” = minimizing operating cost, while keeping flows on transmission below limits.In three bus case the generation at bus 3 must be limited to avoid overloading the line from bus 3 to bus 2.
33 Security Constrained Dispatch Need to dispatch to keep linefrom bus 3 to bus 2 from overloading
34 Multi-Area OperationIn multi-area system, areas with direct interconnections can transact according to rules:In Eastern interconnection, in principle, up to “nominal” thermal interconnection capacity,In Western interconnection there are more complicated rulesActual power flows through the entire network according to the impedance of the transmission lines, and ultimately determine what are acceptable patterns of dispatch.Economically uncompensated flow through other areas is known as “parallel path” or “loop flows.”Since ERCOT is one area, all of the flows on AC lines are inside ERCOT and there is no uncompensated flow on AC lines.
35 Seven Bus Case: One-line System hasthree areasTop areahas fivebusesNo netinterchangebetweenAny areas.Left areahas onebusRight area has onebus
36 Seven Bus Case: Area View ActualflowbetweenareasSystem has40 MW of“Loop Flow”ScheduledflowLoop flow can result in higher losses
37 Seven Bus - Loop Flow? Note that Top’s Losses have increased from 7.09MW to9.44 MWTransaction has actually decreasedthe loop flow100 MW Transactionbetween Left and Right