Power Dispatching at Old DominionThe demand for electricity varies greatly during the day. Because large amounts of electricitycannot be stored economically, electric power companies cannot manufactureelectricity and hold it in inventory until it is needed. Instead, power companies mustbalance the production of power with the demand for power in real time. One of thegreatest uncertainties in forecasting the demand for electricity is the weather. Mostpower companies employ meteorologists who constantly monitor weather patterns andupdate computer models that predict the demand for power over a rolling, seven-dayplanning horizon. This forecasted seven-day window of demand is referred to as thecompany’s load profile. Typically it is updated every hour.Every power company has a baseload demand that is relatively constant. To satisfythis baseload demand, a power company uses its most economical, low-cost power generatingassets and keeps them running continuously. To meet additional demands forpower above the baseload, a power company must dispatch (or turn on) other generators.These other generators are sometimes called “peakers,” as they help the powercompany meet the highest demands or peak loads. It costs differing amounts of moneyto bring different types of peakers online. And because different peakers use differenttypes of fuel (e.g., coal, gas, biomass), their operating costs per megawatt (MW) generatedalso differ. Thus, dispatchers for a power company continually have to decidewhich generator to bring online or turn off to meet their load profile with the least cost.The Old Dominion Power (ODP) Company provides electrical power throughoutVirginia and the Carolinas. Suppose ODP’s peak-load profile (that is the estimated loadabove baseload) in MWs is currently estimated as follows: Day 2 3 4 5 6 7 Load (in MWs) 4,300 3,700 3,900 4,000 4,700 4,800 3,600 ODP currently has three peakinggenerators offline that are available to help meet this load. The generators have the following operatingcharacteristics: Generator Maximum MW Location Startup Cost Cost per Day Capacity per Day N… Show more… Show moreTo get an offline generator up and running, a startup cost must be paid. Once a generatoris running, it can continue to run indefinitely without having to pay this startupcost again. However, if the generator is turned off at any point, the setup cost must bepaid again to get it back up and running. Each day that a generator runs, there is both afixed and variable cost that must be paid. For example, any day that the New River generatoris online, it incurs a fixed cost of $200 plus $5 per MW generated. So even if thisgenerator is not producing any MWs, it still costs $200 per day to keep it running (soas to avoid a restart). When they are running, each generator can supply up to themaximum daily MWs listed in the final column of the table.a. Formulate a mathematical programming model for ODP’s power dispatching problem.b. Implement your model in a spreadsheet and solve it.c. What is the optimal solution?d. Suppose ODP can buy power sometimes from a competitor. How much should ODPbe willing to pay to acquire 300 MW of power on day 1? Explain your answer.e. What concerns, if any, would you have about implementing this plan?292Chapter 6 Integer Linear ProgrammingMathStatistics and Probability QANT 620

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