Presentation on theme: "Least Cost System Operation: Economic Dispatch 1"— Presentation transcript:
1 Least Cost System Operation: Economic Dispatch 1 Smith College, EGR 325 March 3, 2006 some slides from T. Overbye, UIUC
2 Overview Complex system time scale separation Least cost system operationEconomic dispatch first viewGenerator cost characteristicsFour curves of generator performanceConstrained optimizationLinear programmingEconomic dispatch completed
3 Long term system planning: Production cost Decide what to buildHourly to monthly decisions: Unit commitmentDecide which plants to have warmed up and ready to goDifferent technologies have different requirementsMinutes to Hour: Economic dispatchDecide which plants to use to meet the expected load now5 minutes to 1 hourCycles to Minutes: Short term system operations and Load Flow ModelMaintain supply and demand balance moment to moment~17msec per cycle up to 5 minute control functions
4 Power System Economic Operation The installed generating capacity is greater than the load at any specific momentThis give us a lot of flexibility in deciding which generators to use to meet the load at any moment
5 What is “Economic Dispatch?” Economic dispatch (ED) determines the least cost dispatch of generation for a system.To dispatch ≡ To order to generate (more) energyEconomic Dispatch (from EPACT 1992)The operation of generation facilities to produce energy at the lowest cost to reliably serve consumers, recognizing any operational limits of generation and transmission facilities.
6 Economic Dispatch Formulation Focusing on our objectiveHow do we represent our objective mathematically?What mathematical tool do we use to obtain this objective?What does solving our (to be developed) set of equations help us to decide?
7 Economic Dispatch Formulation Therefore we need to understandHow to represent system generating costs mathematicallyCosts of operating (dispatching) generatorsIndirect costs associated with constraints on the systemHow to find the minimum system cost givenGenerator costs andSystem constraintsConstrained optimization via linear programming
9 Generator CostsMany fixed and variable costs are associated with power system operationThe major variable cost is associated with generationThe cost to generate a MWh can vary widelyFor thermal units we have well-defined equations to calculate generating costsFor other generating units (e.g., hydro and nuclear) the cost is difficult to quantify
15 To minimize total system generating costs we develop cost relationships between cost of power output and operating costs, inputSteamBody of waterStackThermal TurbineGGeneratorCoolingTowerCondenserPumpGasesBoilerCoal feederBurner
16 Mathematical Formulation of Costs Typically curves can be approximated usingquadratic or cubic functionspiecewise linear functionsRelying on the quadratic nature of HR, we will use a quadratic cost equationStandard quadratic representation is...?
17 Mathematical Formulation of Costs From total cost to marginal cost...The marginal cost is one of the most important quantities in operating a power systemMarginal cost = incremental cost: the cost of producing the next increment of power (the next MWh)How do we find the marginal cost?
18 Discussion QuestionsIf we have 3 generators, our first-pass system cost equation is...?We find the minimum system cost by ...?How do we then find values for PGi from each generator (our original goal)?What is missing for the actual problem of finding the minimum system operating cost?
19 Summary Formulated the economic dispatch problem conceptually Examined the mathematical origin for generator costsDefined heat rateBegan mathematical formulation of the economic dispatch problemTo be completed next Wednesday