INTRO 18 _____________________Welcome to ROSE-HULMAN RESOURCES__________________________ ..............a Thriving Electric Utility in Terre Haute, Indiana.............. RHR has a number of small turbine generators producing electricity for the campus. The load at Rose-Hulman must be served on demand. That is, the electricity demand is high during air conditioning season and quite small at 3:00 AM when only the double majors are studying. Your assignment is to correctly dispatch the generators to minimize the overall cost of electric energy delivered to Rose-Hulman. This small computer program will help you learn the basics of this important job. You will have opportunities to change data, respond to questions & etc. The ESCAPE key will get you out of what you are doing. While editing data, you may use CTRL Right or Left Arrow to move to the next field. The editing is set up in typeover mode. GENPOLY1 16 ______________________FITTING DATA TO A POLYNOMIAL_____________________________ This program uses a cubic polynomial to represent the heat rate function. That is: H(P) = h_3*P^3 + h_2*P^2 + h_1*P + h_0 Where H(P) is the heat input in Million BTU per hour. The polynomial coeffecients are h_3, h_2, h_1, and h_0. The power output of the generator is designated as P in megawatthours per hour. Typically, utilities run heat rate tests on generators on a regular basis. Then, somebody will fit that data into an economic dispatch program. Your next screen will give you opportunity to create your own data, or use suggested data. You may edit the suggested data however you like. THECOSTOF1 12 _________________________ THE COST OF GENERATION ______________________________ In order to properly dispatch large electric generators, we need to know how the energy input varies with output. This relationship is: Heat In = H(P) This is a handy relationship because it is strictly based on generator characteristics. Generators require a considerable amount of heat input just to get the machine spinning without producing any output. From there, cost increases with output. THECOSTOF2 8 _________________________ THE COST OF GENERATION ______________________________ Once we know how the heat input varies with power output it is a simple matter to multiply the heat input by the fuel cost. Cost = F(P) = H(P) * Fuel Cost THECOSTOF3 13 _________________________ THE COST OF GENERATION ______________________________ The final part of generation cost is the system losses. Generators far away must be penalized for the extra loss incurred moving electrical energy over transmission lines. This introduces a penalty factor. Cost = F(P) * 1 / Penalty_Factor This completes the cost equations for finding the cost as a function of generators output. GENERAL1 8 ________________GENERAL REQUIREMENTS FOR FINDING MINIMUM COST_________________ To find the minimum cost, we must meet certain constraints. First, the generator may not run below its minimum output. It also will not run above its maximum output. That is: P_min < P_out < P_max GENERAL2 8 ________________GENERAL REQUIREMENTS FOR FINDING MINIMUM COST_________________ The second requirement is that all dispatchable generators, have the same incremental cost. In other words the first derivitave of the cost function of all dispatchable generators is equal. The incremental cost or lambdas of each generator equals all the other units. dF(Cost)/dPi = lambda GENERAL3 7 ________________GENERAL REQUIREMENTS FOR FINDING MINIMUM COST_________________ Now we have the key constraints. Find an incremental cost where the net output is just what we need. Make sure generators are working within their limits. We have minimum cost for a given set of generators on line when we meet these conditions. EQUALLAMBDA1 8 -------------------- Learning About Finding the MIMIMUM COST ------------------ This section introduces you to the concept minimum output cost occurs when all dispatchable generators are operating at EQUAL INCREMENTAL cost. That is, the first derivative the cost function, the incremental cost or LAMBDA, of all dispatchable generators is equal. Let's try a simple two generator system ..... EQUALLAMBDA2 14 ---------------------- More About Finding the MIMIMUM COST ------------------- To visualize the equal incremental cost concept, we will take a simple two generator system. Each generator has it's own cost function, but both units have the same minimum and maximum output levels. The specific data are: UNIT MIN_LOAD MAX_LOAD COST EQUATION Unit 1 Unit 2 Let's look at two graphs while we try to meet a system load of 800 MW. The left graph is the total energy cost and the right graph is the incremental output cost for each unit. You will be asked to try finding the minimum cost by guessing the output of Unit 1. MAKEAGUESS 12 ---------------------------- Finding the Right Lambda ------------------------- Let's summarize what we have learned with a ten generator system. We need to dispatch all ten for minimum cost while meeting our system load of 3,000 MW. We know minimum cost is achieved when all dispatchable generators have equal incremental costs (lambdas). We also know that we must not run the generators below their minimum or above their maximum output. With this information, we can guess a lambda and graphically estimate the output of each generator. After you guess a lambda, watch how that guess affects the output of each generator. Then see how well you met the load. LOSSES1 8 ___________________________ Accounting For Losses _____________________________ So far we have neglected losses. Actually a generator that is many ohms away from the load must be peanalized because of the extra losses. To do this, we introduce a loss factor, dPloss/dP. Typically this data comes from load flow data. This program reads the data from a separate file and uses Stevenson's method to calculate loss peanalties. BINARY1 1 Sorry, Prof. Grigg wants you to figure this out. BINARY2 1 This is normally the first page of code. BINARY3 1 This is normally the second page of code. BINARY4 1 This is normally the third page of code. BINARY5 1 This is normally the fourth page of code.