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EE6603-POWER SYSTEM OPERATION AND CONTROL UNIT – I INTRODUCTION

P aavai I n sti t u ti o n s De p a r tm e nt of E E E. EE6603-POWER SYSTEM OPERATION AND CONTROL UNIT – I INTRODUCTION. UNIT-I. 1. 1.

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EE6603-POWER SYSTEM OPERATION AND CONTROL UNIT – I INTRODUCTION

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  1. PaavaiInstitutions DepartmentofEEE EE6603-POWER SYSTEM OPERATION AND CONTROL UNIT – I INTRODUCTION UNIT-I 1. 1

  2. PaavaiInstitutions DepartmentofEEE CONTENTS TECHNICAL TERMS 1. INTRODUCTION 1.1. SYSTEM LOAD VARIATION 1.1.1. System load characteristics 1.1.1.1. Connected Load 1.1.1.2. Maximum Demand 1.1.1.3. Demand Factor 1.1.1.4. Average Load 1.1.1.5. Load Factor 1.1.1.6. Diversity Factor 1.1.1.7. Plant Capacity Factor 1.1.1.8. Plant Use Factor 1.1.2. Load curves 1.1.3. Load-duration curve 1.1.4..load factor 1.1.5. Diversity factor 1.2. RESERVE REQUIREMENTS 1.2.1. Installed reserves 1.2.2. Spinning reserves 1.2.3. Cold reserves 1.2.4. Hot reserves 1.3. OVERVIEW OF SYSTEM OPERATION 1.3.1. Load forecasting 1.3.2. Unit commitment 1.3.3. Load dispatching 1.4. OVERVIEW OF SYSTEM CONTROL 1.4.1. Governor Control 1.4.2. Load frequency control 1.4.3. Economic dispatch control UNIT-I 1. 2

  3. PaavaiInstitutions DepartmentofEEE 1.4.4. Automatic voltage regulator 1.4.5. System voltage control 1.4.6. Security control QUESTION BANK UNIT-I 1. 3

  4. PaavaiInstitutions DepartmentofEEE TECHNICAL TERMS Load curve: The curve drawn between the variations of load on the power station with Reference to time Dailyloadcurve:Thecurvedrawnbetweenthevariationsofloadwithreferencetovarious time period of day Monthly load curve: The obtained from daily load curve. Yearlyloadcurve:Theobtainedfrommonthlyloadcurvewhichisusedtofindannualload factor. Connectedload:Thesumofcontinuousratingsofalltheequipmentsconnectedtosupply systems. Maximum demand: The greatest demand of load on the power station during a given period. Demand factor: The ratio of maximum demand to connected load. Average demand: The average of loads occurring on the power station in a given period (day or month or year). Load factor: The ratio of average load to the maximum demand during a given period. Diversity factor: The ratio of the sum of individual maximum demand on power station. Capacityfactor:Theratioofactualenergyproducedtothemaximumpossibleenergythat could have been produced during a given period. Plant use factor: The ratio of units generated to the product of plant capacity and the number of hours for which the plant was in operation. Load duration curve: When the load elements of a load curve are arranged in the order of descending magnitudes the curve then Load management: As generator capacity has increased in price (to as much as $1000 per kilowatt) and as the fuel shortages put an extra squeeze on them, many electric utilities are finding it worthwhile to try to „slave‟ the load peaks. This is referred to as load management. Function of AVR: The basic role of the AVR is to provide constancy of the generator terminal voltage during normal, small and slow changes in the load. Optimal dispatch: Optimal dispatch is the state that the power system is in prior to any contingency UNIT-I 1. 4

  5. PaavaiInstitutions DepartmentofEEE 1. INTRODUCTION: Power system operations have the responsibility to ensure that adequate power is deliveredtotheloadreliablyandeconomically,inordertoensureadequatedeliveryofpower demand. The electric energy system can be operated at the desired operating level by maintaining frequency, voltage and security. The real and reactive power generated is controlled automatically. Power stations: 1. Steam plant 2. Hydro power plant 3. Nuclear power plant 4. Diesel power plant Objectives of a power system Operation Operational objectives ofapower system havebeen to providea continuous quality servicewith minimumcost to the user. Theseobjectives are:  First Objective: Supplying the energy user with quality service, i.e., at acceptable voltage and frequency Second Objective: Meeting the first objective with acceptable impact upon the environment. Third Objective: Meeting the first and second objectives continuously, i.e., with adequate security and reliability. Fourth Objective: Meeting the first, second, and third objectives with optimum economy, i.e., minimum cost to the energy user. The term “continuous service” can be translated to mean “secure and reliable service”    1.1. SYSTEM LOAD VARIATION The variation of load on the power station with respect to time. SYSTEM LOAD • From system‟s point of view, there are 5 broad category of loads: 1. 2. 3. Domestic Commercial Industrial UNIT-I 1. 5

  6. PaavaiInstitutions DepartmentofEEE 4. Agriculture 5. Others - street lights,traction. Domestic: Lights, fans, domestic appliances like heaters, refrigerators, air conditioners, mixers, ovens, small motors etc. Demand factor = 0.7 to 1.0; Diversity factor = 1.2 to 1.3; Load factor = 0.1 to 0.15 Commercial: Lightings for shops, advertising hoardings, fans, AC etc. Demand factor = 0.9 to 1.0; Diversity factor = 1.1 to 1.2; Load factor = 0.25 to 0.3 Industrial: Small scale industries: 0-20kW Medium scale industries: 20-100kW Large scale industries: above 100kW Industrial loads need power over a longer period which remains fairly uniform throughout the day For heavy industries: Demand factor = 0.85 to 0.9; Load factor = 0.7 to 0.8 Agriculture: Supplying water for irrigation using pumps driven by motors Demand factor = 0.9 to 1; Diversity factor = 1.0 to 1.5; Load factor = 0.15 to 0.25 Other Loads: Bulk supplies, street lights, traction, government loads which have their own peculiar characteristics 1.1.1. System load characteristics  Connected load  Maximum demand  Average load  Load factor  Diversity factor  Plant capacity factor  Plant use factor 1.1.1.1. Connected Load: It is the sum of continuous rating so fall the equipment connected to supply system UNIT-I 1. 6

  7. PaavaiInstitutions DepartmentofEEE 1.1.1.2. Maximum Demand: It is the greatest demand of load on the power station during a given period 1.1.1.3. Demand Factor: It is the ratio of maximum demand on the powerstation to its connected load. Demand factor =Maximum demand connected load 1.1.1.4. Average Load: The averageof loads Occurringon thepower station in a given period(dayormonth oryear) DailyAverageLoad= �� �� ����� ��������� �� � ��� 24 ����� Weeklyload=�� �� ����� ��������� �� � � ��� � ������ �� � ���� � Yearly Load =�� �� ����� ��������� �� � ���� 8760 ����� 1.1.1.5. Load Factor: The ratio of average load to the maximum demand during a given period LoadFactor=Average load Maximum demand If the plant is in operation for T hours LoadFactor=�������� ������𝑇 ������� ��������𝑇 1.1.1.6. Diversity Factor: Theratioofthesumofindividualmaximumdemandstothemaximumdemandonpower station. Diversityfactor= ��� �� ��� ���������� ��� ��� ������� ������ 1.1.1.7. Plant Capacity Factor: Itis theratio ofactual energyproducedto themaximum possible energythat could havebeen produced during a given period. Plant CapacityFactor=������� ������� 𝑃���� ��� ������� ������� ���� ����� �������� �������� 1.1.1.8. Plant Use Factor: ItistheratioofkWhgeneratedtotheproductofplantcapacityandthenumberofhoursfor which the plant was in operation. StationoutputinkWh Plant use factor Plant capacity Hoursof use When the elements of a load curve are arranged in the order of descending magnitudes. 1.1.2. Load curves The curve showing the variation of load on the power station with respect to time UNIT-I 1. 7

  8. PaavaiInstitutions DepartmentofEEE Figure.1.1 Load curves Types of Load Curve: Daily load curve–Load variations during the whole day Monthly load curve–Load curve obtained from the daily load curve Yearly load curve-Load curve obtained from the monthly load curve Base Load: The unvarying load which occurs almost the whole day on the station Peak Load: The various peak demands so load of the station Figure.1.2. Daily load curve 1.1.3. Load duration curve: When the elements of a load curve are arranged in the order of descending magnitudes. UNIT-I 1. 8

  9. PaavaiInstitutions DepartmentofEEE Figure.1.3. Load Duration Curve The load duration curve gives the data in a more presentable form  The area under the load duration curve is equal to that of the corresponding load curve  The load duration curve can be extended to include any period of time 1.1.4. Load factor Theratioofaverageloadtothemaximumdemandduringagivenperiodisknownas load factor. Load factor = (average load)/ (maximum demand) 1.1.5. Diversity factor Theratioofthesumofindividualmaximumdemandonpowerstationisknownas diversity factor. Diversity factor = (sum of individual maximum demand)/(maximum demand). 1.2. RESERVE REQUIREMENTS 1.2.1 Installed reserve Installedreserveisthatgeneratingcapacitywhichisconnectedtothebusandisreadytotake load. 1.2.2 Spinning reserve The spinning reserve is the extra generating capacity that is available by increasing the power output of generators that are already connected to the power system. For most generators, this increase in power output is achieved by increasing the torque applied to the turbine's rotor UNIT-I 1. 9

  10. PaavaiInstitutions DepartmentofEEE 1.2.3. Cold reserve: Coldreserveisthatgeneratingcapacitywhichisavailableforservicebutisnotin operation. 1.5.4. Hot reserve: Hotreserveisthatgeneratingcapacity whichisavailableforoperationbutisnotin service. 1.3. OVER VIEW OF SYSTEM OPERATION 1.3.1 Load Forecasting Theloadon theirsystemshould be estimatedin advance.Theestimation inadvanceis known as load forecasting. Load forecasting based on the previous experience without any historical data.  Very short time: Minutes to ½ hour  Short time: ½ to few hours  Medium term: Few days to few weeks  Long time: Few months to few years Need for Load Forecasting  Very short time: generation & distribution  Short time: maintaining the spinning reserve  Medium term: Predicted monsoon acting & hydro availability & allocating Spinning reserve.  Long time: Maintenance schedule for generating units, planning for future 1.3.2. Unit Commitment:  A short term load forecast  System reserve requirements  System security  Startup costs for all units  Minimum level fuel cost  Incremental fuel cost  Maintenance cost UNIT-I 1. 10

  11. PaavaiInstitutions DepartmentofEEE 1.3.3. Load dispatching: Thermal scheduling: Loading of steam units are allocated to serve the objective of minimum fuel cost. Hydro thermal scheduling: 1.Loadingofhydroandthermalunitsareallocatedtoservetheobjectiveofminimumfuel cost. 2.Schedulingofhydrounitsarecomplexbecauseofnaturaldifferencesinthewatersheds, manmade storage. 3.Duringrainyseason,wecanutilizehydrogenerationtoamaximum&theremaining period its depends on water availability. 4.Ifavailabilityofwaterisnotenoughtogeneratepower,wemustutilizeonlythermal power generation. Types: 1. Long range hydro –scheduling 2. Short range hydro scheduling 1.7. OVERVIEW OF POWER SYSTEM CONTROL:  Speed regulation of the governor  Controls the boiler pressure, temperature & flows  Speed regulation concerned with steam input to turbine  Load is inversely proportional to speed  Governor senses the speed & gives command signal  Steam input changed relative to the load requirement. 1.4.1. Governor Control Governor is A device used to control the speed of a prime mover. A governor protects the prime mover from overspeed and keeps the prime mover speed at or near the desired revolutionsperminute.Whenaprimemoverdrivesanalternatorsupplyingelectricalpower at a given frequency, a governor must be used to hold the prime mover at a speed that will yield this frequency. An unloaded diesel engine will fly to pieces unless it is under governor control. 1.4.2. Load frequency control 1. Sense the bus bar frequency & compare with the tie line power frequency 2. Difference fed to the integrator & to speed changer 3. Tie line frequency maintained constant UNIT-I 1. 11

  12. PaavaiInstitutions DepartmentofEEE 1.4.3. Economic dispatch control 1. When load distribution between a number of generator units considered optimum schedule affected when increase at one replaces a decreases at other. 2.Optimumuseofgeneratorsateachstationatvariousloadisknownaseconomicdispatch control. 1.4.4. Automatic voltage regulator 1. Regulate generator voltage and output power 2. Terminal voltage & reactive power is also met 1.4.5. System voltage control Controlling the voltage within the tolerable limits. Devices used are 1. Static VAR compensator 2. Synchronous condenser 3. Tap changing transformer 4. Switches 5. Capacitor 6. Reactor 1.4.6. Security control 1. Monitoring & decision 2. Control Monitoring & decision: 1. Condition of the system continuously observed in the control centers by relays. 2. If any continuous severe problem occurs system is in abnormal condition. Control: 1. Proper commands are generated for correcting the abnormality in protecting the system. 2. If no abnormality is observed, then the normal operation proceeds for next interval. 3. Central controls are used to monitor the interconnected areas 4. Inter connected areas can be tolerate larger load changes with smaller frequency deviations 5.Centralcontrolcentremonitorsinformationaboutfrequency,generatingunitoutputsand tie line power flows to interconnected areas. 6. This information is used by automation load frequency control in order to maintain area frequency at its scheduled value. UNIT-I 1. 12

  13. PaavaiInstitutions DepartmentofEEE Frequency tie flows generator power System generator control Load frequency control, Economic dispatch schedule System voltage control Prime mover and control Excitation system and control Field current Generator Other generating units and associated controls Voltage Speed/power Electrical Power Transmission controls, reactive power and voltage controls, HVDC, Transmission & Associated cnotrols Frequency tie flows generator power Figure.1.4. Overview of system operation and control UNIT-I 1. 13

  14. PaavaiInstitutions DepartmentofEEE PROBLEMS 1. A power supplyishavingthe followingloads: Type of load Maximum demand(kw) Diversity factor of group Demand factor Domestic 10,000 1.2 0.8 Commercial 30,000 1.3 0.9 Industrial 50,000 1.35 0.95 If the overall system diversity factor is 1.5, determine (a) the maximum demand, (b) connected load of each type. Solution: (a)Total maximum demand of loads=10000+30000+50000=90000 kw System diversity factor=1.5 Maximumdemand=Total demand/system diversity factor =90000/1.5=60000 kw (b)Connected load of each type Domestic load: Diversity factor of domestic load=Maximum domestic demand/maximum domestic load demand =12000/0.8=15000 kw (c)Commercial load: Connected commercial demand=Maximum demand/demand factor for commercial load =39000/0.9=43333.33 kw (d)Industrial load: Connected industrial load=Maximum demand/demand factor of industrial load =67500/0.95=71052.63 kw 2. A generatingstation hasamaximum demand of400 MW.The annual loadfactor is 60% and capacity factor is 50%.Find the reserve capacity of the plant. Solution: Energy generated per annum=Maximum demand*load factor*hours in a year =400*0.6*8760 =2102.4*103 MWhr Plant capacity =Unit generated per annum/capacity factor hours in a year =2102.4*103/0.5 UNIT-I 1. 14

  15. PaavaiInstitutions DepartmentofEEE QUESTION BANK PART A What is the objectiveof power system operation and control? What is load curve and load duration curve? Define load factor & diversity factor. Define spinning reserve, Cold reserve & hot reserve. Define Maximum Demand & demand factor. State the purpose of system generation control. State the differences between P-f and Q-|V| controls. What is meant by load frequency control? What is daily, Weekly, Annual load curve? 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Define load and list out the types of loads. 11. What is Average demand? 12. What is Capacity factor? PART-B 1. A generating station has the following daily load cycle: Time (hours) 0-6 6-10 10-12 12-16 16-20 20-24 Load(M 20 25 30 25 35 20 Draw the Load curve and load duration curve and find Maximum demand, Units generated per day, Average Load&Load Factor. 2. Explain the following: (i) Load forecasting, (ii) Economic dispatch control (EDC) 3. A Power station has to meet the following demand. Group A: 200kW between 8 A.M and 6 P.M Group B: 100kW between 6 A.M and 10 A.M Group C: 50kW between 6 A.M and 10 A.M Group D: 100kW between 10 A.M and 6 P.M and 6 P.M and 6 A.M Plot the daily load cure and load duration curve and determine (i) Diversity factor,(ii) Units generated per day,(iii) Load factor. 4. Discuss about the recent trends in real timeoverview ofsystem operation&control of power system. UNIT-I 1. 15

  16. PaavaiInstitutions DepartmentofEEE 5. Briefly discuss the classification of loads and list out the important Characteristics of various types of loads. 6. Explain the need for voltage and frequency regulation in power system. 7. Explain the system voltage control and security control. UNIT-I 1. 16

  17. PaavaiInstitutions DepartmentofEEE UNIT –II SYSTEM OPERATION UNIT-II 2. 1

  18. PaavaiInstitutions DepartmentofEEE CONTENTS TECHNICAL TERMS 2. INTRODUCTION 2.1. SYSTEM LOAD FORECASTING 2.1.1. Important Factors for Forecasts 2.1.2. Forecasting Methods 2.1.3. Medium- and long-term load forecasting methods 2.2. ECONOMIC DISPATCH 2.2.1. Economic operation of power systems 2.2.2. Performance curves 2.2.3. Solution Methods 2.2.4. Economic dispatch problem 2.2.5. Thermal system dispatching with network losses considered 2.2.6. lambda-iteration method 2.2.7. Base point and participation factors 2.2.8. Economic dispatch controller added to LFC: 2.3. UNIT COMMITMENT 2.3.1. Constraints in Unit Commitment 2.3.2. Spinning Reserve 2.3.3. Thermal Unit Constraints 2.3.4 Other Constraints 2.3.4.1 Hydro-Constraints 2.3.4.2 Must Run 2.3.4.3 Fuel Constraints 2.3.5. Unit commitment solution methods 2.3.5.1. Priority-List Methods 2.3.5.2. Dynamic-Programming Solution 2.3.5.3. Forward DP Approach 2.3.4. Lagrange Relaxation Solution UNIT-II 2. 2

  19. PaavaiInstitutions DepartmentofEEE TECHNICAL TERMS Btu (British thermal unit): A standard unit for measuring the quantity of heat energy equal to the quantity of heat required to raise the temperature of 1 pound of water by 1 degree Fahrenheit. Capacity: The amount of electric power delivered or required for which a generator, turbine, transformer, transmission circuit, station, or system is rated by the manufacturer. Combined Cycle Unit: Anelectricgeneratingunitthatconsistsofoneormorecombustionturbinesandone ormoreboilers with aportion of therequiredenergyinputto theboiler(s) provided by the exhaust gas of the combustion turbine(s). Demand: The rate at which energy is delivered to loads and scheduling points by generation, transmission, and distribution facilities. Demand (Electric): The rate at which electric energy is delivered to or by a system, part of a system, or piece of equipment, at a given instant or averaged over any designated period of time. Demand-Side Management: The planning, implementation, and monitoring of utility activities designed to encourage consumers to modify patterns of electricity usage,includingthetimingandlevelofelectricitydemand.Itrefersonlytoenergy and load-shape modifying activities that are undertaken in response to utility- administeredprograms.Itdoesnotrefertoenergyandload-shapechangesarising from the normal operation of the marketplace or from government-mandated energy- efficiency standards.Demand-SideManagement(DSM)coversthecompleterangeof load-shape objectives, including strategic conservation and load management, as well as strategic load growth. Deregulation: The elimination of regulation from a previously regulated industry or sector of an industry. Electric Service Provider: An entity that provides electric service to a retail or end- use customer. Energy: The capacity for doing work as measured by the capability of doing work (potential energy) or the conversion of this capability to motion (kinetic energy). Energy has several forms, some of which are easily convertible and can be changed to another form useful for work. Most of the world's convertible energy comes from UNIT-II 2. 3

  20. PaavaiInstitutions DepartmentofEEE fossil fuels that are burned to produce heat that is then used as a transfer medium to mechanical or other means in order to accomplish tasks. Electrical energy is usually measured in kilowatthours, while heat energy is usually measured in British thermal units. Energy Charge: That portion of the charge for electric service based upon the electric energy (kWh) consumed or billed Outage:Theperiod duringwhichageneratingunit, transmission line, or other facility is out of service. Forced Outage: The shutdown of a generating unit, transmission line or other facility, for emergency reasons or a condition in which the generating equipment is unavailable for load due to unanticipated breakdown. Fuel: Any substance that can be burned to produce heat; also, materials that can be fissioned in a chain reaction to produce heat. UNIT-II 2. 4

  21. PaavaiInstitutions DepartmentofEEE 2. INTRODUCTION Accurate models for electric power load forecasting are essential to the operation and planning of a utility company. Load forecasting helps an electric utility to make important decisionsincludingdecisionsonpurchasingandgeneratingelectricpower,loadswitching, and infrastructure development. Load forecasts are extremely important for energy suppliers,ISOs, financial institutions, and other participants in electric energy generation, transmission, distribution, and markets. Load forecasts can be divided into three categories: short-term fore-casts which are usually from one hour to one week, medium forecasts which are usually from a week to a year, and long-term forecasts which are longer than a year. Theforecastsfordifferenttimehorizonsareimportantfordifferentoperationswithin a utility company. The natures of these forecasts are different as well. For example, for a particular region, it is possible to predict the next day load with an accuracy of approximately 1-3%. However, it is impossible to predict the next year peak load with the similar accuracy since accurate long-term weather forecasts are not available. For the next year peak forecast, it is possible to provide the probability distribution of the load based on historical weather observations. It is also possible, according to the industry practice, to predict the so-called weather normalized load, which would take place for average annual peak weather conditions or worse than average peak weather conditions for a given area. Weather normalized load is the load calculated for the so-called normal weather conditions which are the average of the weather characteristics for the peak historical loads over a certain period of time. The duration of this period varies from one utility to another. Most companies take the last 25-30 years of data. Load forecasting has always been important for planning and opera-tional decision conducted by utilitycompanies. However, with the deregulation of the energy industries, load forecasting is even more important. With supply and demand fluctuating and the changes of weather conditions and energy prices increasing by a factor of ten or more during peak situations, load forecasting is vitally important for utilities. Short-term load forecasting can help to estimate load flows and to make decisions that can prevent overloading. Timely implementations of such deci-sions lead to the improvement of network reliability and to the reduced occurrences of equipment failures and blackouts. Load forecasting is also important for contract evaluations and evaluations of various so- phisticated financial products on energy pricing offered by the market. In the deregulated economy, decisions on capital expenditures based on long-term forecasting are also more UNIT-II 2. 5

  22. PaavaiInstitutions DepartmentofEEE important than in a non-deregulated economy when rate increases could be justified by capital expenditure projects. Most forecasting methods use statistical techniques or artificial intelligence algorithms such as regression, neural networks, fuzzy logic, and expert systems. Two of the methods,so-calledend-useandeconometricapproacharebroadlyusedformedium-and long-term forecasting. A variety of methods, which include the so-called similar day approach, various regression models, time series, neural networks, statistical learning algorithms, fuzzy logic, and expert systems, have been developed for short-term forecasting. As we see, a large variety of mathematical methods and ideas have been used for load forecasting. The development and improvements of appropriate mathematical tools will lead to the development of more accurate load forecasting techniques. The accuracy of load forecasting depends not only on the load forecasting techniques, but also on the accuracy of forecasted weather scenarios. Weather forecasting is an important topic which is outside of the scope of this chapter. 2.1. SYSTEM LOAD FORECASTING 2.1.1. Important Factors for Forecasts For short-term load forecasting several factors should be considered, such as time factors, weatherdata,andpossiblecustomers’classes.Themedium-andlong-termforecaststake into account the historical load and weather data, the number of customers in different categories, the appliances in the area and their characteristics including age, the economic and demographic data and their forecasts, the appliance sales data, and other factors. The time factors include the time of the year, the day of the week, and the hour of the day. There are important differences in load between weekdays and weekends. The load on different weekdays also can behave differently. For example, Mondays and Fridays being adjacenttoweekends,mayhavestructurallydifferentloadsthanTuesday throughThursday. Thisisparticularly trueduringthesummertime.Holidaysaremoredifficulttoforecastthan non-holidays because of their relative infrequent occurrence. Weather conditions influence the load. In fact, forecasted weather parameters are the most important factors in short-term load forecasts. Various weather variables could be considered for load forecasting. Tem-perature and humidity are the most commonly used load UNIT-II 2. 6

  23. Paavai Institutions Department of EEE predictors. Among the weather variables listed above, two composite weather variable functions, the THI (temperature-humidity index) and WCI (wind chill index), are broadly used by utility companies. THI is a measure of summer heat discomfort and similarly WCI is cold stress in winter. Most electric utilities serve customers of different types such as residential, commercial, andindustrial.Theelectricusagepatternisdifferentforcustomersthatbelongtodifferent classes but is somewhat alike for customers within each class. Therefore, most utilities distinguish load behavior on a class-by-class basis. 2.1.2. Forecasting Methods Over the last few decades a number of forecasting methods have been developed. Two of themethods,so-calledend-useandeconometricap-proacharebroadly usedformedium-and long-term forecasting. A variety of methods, which include the so-called similar day approach,variousregressionmodels,timeseries,neuralnetworks,expertsystems,fuzzy logic, and statistical learning algorithms, are used for short-term forecasting. The development, improvements, and investigation of the appropriate mathematical tools will lead to the development of more accurate load forecasting techniques. Statistical approaches usually require a mathematical model that rep-resents load as function of different factors such as time, weather, and customer class. The two important categories of such mathematical models are: additive models and multiplicative models. They differ in whether the forecast load is the sum (additive) of a number of components or the product (multiplicative) of a number of factors. For example, presented an additive model that takes the form of predicting load as the function of four components: L = Ln + Lw + Ls + Lr, -------------------------------------------- (1) where L is the total load, Ln represents the “normal” part of the load, which is a set of standardized load shapes for each “type” of day that has been identified as occurring throughout the year, Lw represents the weather sensitive part of the load, Ls is a special event UNIT-II 2. 7

  24. PaavaiInstitutions DepartmentofEEE component that create a substantial deviation from the usual load pattern, and Lr is a completely random term, the noise. Naturally, price decreases/increases affect electricity consumption. Large cost sensitive industrial and institutional loads can have a significant effect on loads.. A multiplicative model may be of the form L = Ln+ Fw +Fs+ Fr, -------------------------------------------------- (2) where Ln is the normal (base) load and the correction factors Fw , Fs, and Fr are positive numbers that can increase or decrease the overall load. These corrections are based on current weather (Fw ), special events (Fs), and random fluctuation (Fr ). Factors such as electricity pricing (Fp) and load growth (Fg ) can also be included. Weather variables and the base load associated with the weather measures were included in the model. 2.1.3. Medium- and long-term load forecasting methods The end-use modeling, econometric modeling, and their combinations are the most often used methods for medium- and long-term load fore-casting. Descriptions of appliances used by customers, the sizes of the houses, the age of equipment, technology changes, customer behavior, and population dynamics are usually included in the statistical and simulation models based on the so-called end-use approach. In addition, economic factors such as per capita incomes, employment levels, and electricity prices are included in econometric models. These models are often used in combination with the end-use approach. Long-term fore-casts include the forecasts on the population changes, economic development, industrial construction, and technology development. End-use models. The end-use approach directly estimates energy consumption by using extensiveinformationonenduseandendusers,suchasappliances,thecustomeruse,their age, sizes of houses, and so on. Statistical information about customers along with dynamics of change is the basis for the forecast. End-use models focus on the various uses of electricity in the residential, commercial, and industrial sector. These models are based on the principle that electricity demand is derived from customer’s demand for light, cooling, heating, refrigeration, etc. UNIT-II 2. 8

  25. PaavaiInstitutions DepartmentofEEE Ideally this approach is very accurate. However, it is sensitive to the amount and quality of end-usedata.Forexample,inthismethodthedistributionofequipmentageisimportantfor particular types of appliances. End-use forecast requires less historical data but more in- formation about customers and their equipment. Econometric models. The econometric approach combines economic theory and statistical techniques for forecasting electricity demand. The approach estimates the relationships between energy consumption (de-pendent variables) and factors influencing consumption. The relation-ships are estimated by the least-squares method or time series methods. One of the options in this framework is to aggregate the econometric approach, when consumption in different sectors (residential, commercial, industrial, etc.) is calculated as a function of weather, economic and other variables, and then estimates are assembled using recent historical data. Integration of the econometric approach into the end-use approach introduces behavioral components into the end-use equations. Statistical model-based learning. The end-use and econometric methods require a large amount of information relevant to appliances, customers, economics, etc. Their application is complicatedandrequireshumanparticipation. Inadditionsuchinformationisoftennot available regarding particular customers and a utility keeps and supports a pro-file of an “average” customer or average customers for different type of customers. The problem arises if the utility wants to conduct next-year forecasts for sub-areas, which are often called load pockets. In this case, the amount of the work that should be performed increases proportion- ally with the number of load pockets. In addition, end-use profiles and econometric data for different load pockets are typically different. The characteristics for particular areas may be different from the average characteristics for the utility and may not be available. We compared several load models and came to the conclusion that the following multiplicative model is the most accurate L(t) = F (d(t), h(t)) · f (w(t)) + R(t),--------------------------------------(3) where L(t) is the actual load at time t, d(t) is the day of the week, h(t) is the hour of the day, F (d, h) is the daily and hourly component, w(t) is the weather data that include the temperature UNIT-II 2. 9

  26. PaavaiInstitutions DepartmentofEEE and humidity, f (w) is the weather factor, and R(t) is a random error. In fact, w (t) is a vector that consists of the current and lagged weather variables. This reflects the fact that electric load depends not only on the current weather conditions but also onthe weatherduring theprevioushoursanddays.Inparticular,the well-knowneffectofthe so-called heat waves is that the use of air conditioners increases when the hot weather continues for several days. 2.2. ECONOMIC DISPATCH 2.2.1. Economic Operation of Power Systems One of the earliest applications of on-line centralized control was to provide a central facility, to operate economically, several generating plants supplying the loads of the system. Modernintegratedsystemshavedifferenttypes ofgeneratingplants,suchas coal fired thermal plants, hydel plants, nuclear plants, oil and natural gas units etc. The capital investment, operation and maintenance costs are different for different types of plants. The operation economics can again be subdivided into two parts. i)Problemofeconomicdispatch,whichdealswithdeterminingthepoweroutputofeach plant to meet the specified load, such that the overall fuel cost is minimized. ii)Problemofoptimalpowerflow,whichdealswithminimum–lossdelivery,whereinthe power flow, is optimized to minimize losses in the system. In this chapter we consider the problem of economic dispatch. During operation of the plant, a generator may be in one of the following states: i) Base supply without regulation: the output is a constant. ii) Base supply with regulation: output power is regulated based on system load. iii)Automaticnon-economicregulation:outputlevelchangesaroundabasesettingasarea control error changes. iv) Automatic economic regulation: output level is adjusted, with the area load and area control error, while tracking an economic setting. UNIT-II 2. 10

  27. PaavaiInstitutions DepartmentofEEE Regardless of the units operating state, it has a contribution to the economic operation, even though its output is changed for different reasons. The factors influencing the cost of generation are the generator efficiency, fuel cost and transmission losses. The most efficient generator may not give minimum cost, since it may be located in a place where fuel cost is high.Further,if theplant is located farfrom theload centers, transmission losses maybehigh and running the plant may become uneconomical. The economic dispatch problem basically determines the generation of different plants to minimize total operating cost. Moderngeneratingplantslikenuclearplants,geo-thermalplantsetc,mayrequire capital Investment of millions of rupees. The economic dispatch is however determined in terms of fuel cost per unit power generated and does not include capital investment, maintenance, depreciation, start-up and shut down costs etc. 2.2.2. Performance Curves Input-Output Curve This is the fundamental curve for a thermal plant and is a plot of the input in British thermal units (Btu) per hour versus the power output of the plant in MW as shown in Fig 2.1 Figure 2.1: Input – output curve Heat Rate Curve The heat rate is the ratio of fuel input in Btu to energy output in KWh. It is the slope of the input – output curve at any point. The reciprocal of heat – rate is called fuel –efficiency. The heat rate curve is a plot of heat rate versus output in MW. A typical plot is shown in Fig.2.2 UNIT-II 2. 11

  28. PaavaiInstitutions DepartmentofEEE Figure 2.2 Heat rate curve. Incremental Fuel Rate Curve The incremental fuel rate is equal to a small change in input divided by the corresponding change in output. Incremental fuel rate =∆Input/∆ Output The unit is again Btu / KWh. A plot of incremental fuel rate versus the output is shown in Figure 2.3: Incremental fuel rate curve Incremental cost curve The incremental cost is the product of incremental fuel rate and fuel cost (Rs / Btu or $ /Btu). The curve in shown in Fig. 4. The unit of the incremental fuel cost is Rs / MWh or $ /MWh. Figure 2.4: Incremental cost curve UNIT-II 2. 12

  29. PaavaiInstitutions DepartmentofEEE In general, the fuel cost Fi for a plant, is approximated as a quadratic function of the generated output PGi. Fi = ai + bi PGi + ci PG2 Rs / h --------------------------------- (4) The incremental fuel cost is given by 𝑑�𝑖 = 𝑏𝑖 + 2𝑖 𝑃�𝑖 Rs / MWh ------------------------------------ (5) 𝑑𝑝𝑖 The incremental fuel cost is a measure of how costly it will be produce an increment of power. The incremental production cost, is made up of incremental fuel cost plus the incremental cost of labour, water, maintenance etc. which can be taken to be some percentage of the incremental fuel cost, instead of resorting to a rigorous mathematical model. The cost curve can be approximated by a linear curve. While there is negligible operating cost for a hydel plant, there is a limitation on the power output possible. In any plant, all units normally operate between PGmin, the minimum loading limit, below which it is technically infeasible to operate a unit and PGmax, which is the maximum output limit. 2.2.3. Solution Methods: 1. Lagrange Multiplier method 2. Lamda iteration method 3. Gradient method 4. Dynamic programming 5. Evolutionary Computation techniques 2.2.4. The Economic Dispatch Problem Figure 2.5 shows the configuration that will be studied in this section. This system consists of N thermal-generating units connected to a single bus-bar serving a received electrical load Pload input to each unit, shown as FI,represents the cost rate of the unit. The output of each unit, Pi, is the electrical power generated by that particular unit. The total cost rate of this system is, of course, the sum of the costs of each of the individual units. The essential constraint on the operation of this system is that the sum of the output powers must equal the load demand.Mathematically speaking, the problem may be stated very concisely. That is, an objective function, FT, is equal to the total cost for supplying the indicated load. The problem is to minimize FT subject to the constraint that the sum of the UNIT-II 2. 13

  30. Department of EEE Paavai Institutions powers generated must equal the received load. Note that any transmission losses are neglected and any operating limits are not explicitly stated when formulating this problem. That is, ------------------------------------------ (6) Figure2.5. N thermal units committed to serve a load of Pload. This is a constrained optimization problem that may be attacked formally using advanced calculus methods that involve the Lagrange function. In order to establish the necessary conditions for an extreme value of the objective function, add the constraint function to the objective function after the constraint function has been multiplied by an undetermined multiplier. This is known as the Lagrange function and is shown in Eq(7) ------------------------------------------------ (7) The necessary conditions for an extreme value of the objective function result when we take the first derivative of the Lagrange function with respect to each of the independent variables and set the derivatives equal to zero. In this case,there are N+1 variables, the N valuesofpoweroutput,Pi,plustheundeterminedLagrangemultiplier,λ.Thederivativeof the Lagrange function with respect to the undetermined multiplier merely gives back the constraint equation. On the other hand, the N equations that result when we take the partial derivative of the Lagrange function with respect to the power output values one at a time give the set of equations shown as Eq. 8. ----------------------------------------------- (8) UNIT-II 2. 14

  31. PaavaiInstitutions DepartmentofEEE When we recognize the inequality constraints, then the necessary conditions may be expanded slightly as shown in the set of equations making up Eq. 9 --------------------------------------------- (9) Several of the examples in this chapter use the following three generator units. EXAMPLE 2.1 Supposethatwewishtodeterminetheeconomicoperatingpointforthesethreeunits when delivering a total of 850 MW. Before this problem can be solved,the fuel cost of each unit must be specified. Let the following fuel costs are in effect. Unit 1: Coal-fired steam unit: Max output = 600 MW Min output = 150 MW Input-output curve: Unit 2 Oil-fired steam unit: Max output = 400 MW Min output = 100 MW Input-output curve: Unit 3: Oil-fired steam unit: Max output = 200 MW, Min output = 50 MW Input-output curve: Unit 1: fuel cost = 1.1 P/MBtu Unit 2: fuel cost = 1.0 Jt/MBtu Unit 3: fuel cost = 1.0 Jt/MBtu Then UNIT-II 2. 15

  32. PaavaiInstitutions DepartmentofEEE Using Eq. 3.5, the conditions for an optimum dispatch are and then solving for, P1,P2,P3 P1 = 393.2 MW P2 = 334.6 MW P3 = 122.2 MW Note that all constraints are met; that is, each unit is within its high and low limit and the total output when summed over all three units meet the desired 850 MW total. EXAMPLE 2.2 Suppose the price of coal decreased to 0.9 P/MBtu. The fuel cost function for unit 1 becomes If one goes about the solution exactly as done here, the results are This solution meets the constraint requiring total generation to equal 850 MW, but units 1 and 3arenotwithinlimit.Tosolveforthemosteconomicdispatchwhilemeetingunitlimits, suppose unit 1 is set to its maximum output and unit 3 to its minimum output. The dispatch becomes UNIT-II 2. 16

  33. PaavaiInstitutions DepartmentofEEE we see that λ must equal the incremental cost of unit 2 since it is not at either limit. Then Next, calculate the incremental cost for units 1 and 3 to see if they meet the conditions. Note that the incremental cost for unit 1 is less than λ, so unit 1 should be at its maximum. However,theincrementalcostforunit3isnotgreaterthan,λsounit3shouldnotbeforced toits minimum. Thus,to findtheoptimaldispatch,allowtheincrementalcostatunits 2and3 to equal λ as follows. UNIT-II 2. 17

  34. PaavaiInstitutions DepartmentofEEE 2.2.5. Thermal System Dispatching With Network Losses Considered Figure 2.6. Shows symbolically an all-thermal power generation system connected to an equivalent load bus through a transmission network. The economic dispatching problem associated with this particular configuration is slightly more complicated to set up than the previous case. This is because the constraint equation is now one that must include the network losses. The objective function, FT, is the same as that defined for Eq.10 ------------------ (10) The same procedure is followed in the formal sense to establish the necessary conditions for a minimum-cost operating solution, The Lagrange function is shown in Eq.11. In taking the derivative of the Lagrange function with respect to each of the individual power outputs,Pi,itmustberecognizedthatthelossinthetransmissionnetwork,Plossisafunction of the network impedances and the currents flowing in the network. For our purposes, the currentswillbeconsideredonlyasafunctionoftheindependentvariablesPi andtheload Pload taking the derivative of the Lagrange function with respect to any one of the N values of Pi results in Eq. 11. collectively as the coordination equations. ----------------------------------- (11) It is much more difficult to solve this set of equations than the previous set with no losses since this second set involves the computation of the network loss in order to establish the validity of the solution in satisfying the constraint equation. There have been two general approaches to the solution of this problem. The first is the development of a mathematical expressionforthelossesinthenetworksolelyasafunctionofthepoweroutputofeachof the units. This is the loss-formula method discussed at some length in Kirchmayer’s Economic Operation of Power Systems. The other basic approach to the solution of this problem is to incorporate the power flow equations as essential constraints in the formal establishment of the optimization problem. This general approach is known as the optimal power flow. UNIT-II 2. 18

  35. PaavaiInstitutions DepartmentofEEE Figure.2.6.N thermal units serving load through transmission network 2.2.6. The Lambda-Iteration Method Figure 2.7.is a block diagram of the lambda-iteration method of solution for the all- thermal, dispatchingproblem-neglectinglosses.We canapproach thesolution to this problem by considering a graphical technique for solving the problem and then extending this into the area of computer algorithms. Suppose we have a three-machine system and wish to find the optimum economic operating point. One approach would be to plot the incremental cost characteristics for each of these three units on the same graph, such as sketched in Figure 3.4. In order to establish the operating points of each of these three units such that we have minimum cost and at the same time satisfy the specified demand, we could use this sketch and a ruler to find the solution. That is, we could assume an incremental cost rate (λ) and find the power outputs of each of the three units for this value of incremental cost. the three units for this value of incremental cost. Of course, our first estimate will be incorrect. If we have assumed the value of incremental cost such that the total power output is too low, we must increase the 3. value and try another solution. With two solutions, we can extrapolate (or interpolate) the two solutions to get closer to the desired value of total received power. By keeping track of the total demand versus the incremental cost, we can rapidly find the desired operating point. If we wished, we could manufacture a whole series of tables that would show the total power supplied for different UNIT-II 2. 19

  36. PaavaiInstitutions DepartmentofEEE incremental cost levels and combinations of units. That is, we will now establish a set of logicalrulesthatwouldenableustoaccomplishthesameobjectiveaswehavejustdonewith ruler and graph paper. The actual details of how the power output is established as a function of the incremental cost rate are of very little importance. Figure: 2.7. Lambda-iteration method We could, for example, store tables of data within the computer and interpolate between the stored power points to find exact power output for a specified value of incremental cost rate. Another approach would be to develop an analytical function for the power output as a function of the incremental cost rate, store this function (or its coefficients) in the computer, and use this to establish the output of each of the individual units. This procedure is an iterative type of computation, and we must establish stopping rules.Twogeneralformsofstopping rulesseemappropriateforthisapplication..Thelambda- iteration procedure converges very rapidly for this particular type of optimization problem. The actual computationalprocedureis slightlymorecomplexthan that indicated inFigure2.7 since it is necessary to observe the operating limits on each of the units during the course of thecomputation. The well-knownNewton-Raphson method maybe usedto project the incremental cost value to drive the error between the computed and desired generation to zero. UNIT-II 2. 20

  37. PaavaiInstitutions DepartmentofEEE Example: 2.3 Given the generator cost functions found in Example 2.1, solve for the economic dispatch of generation with a total load of 800 MW.Using α = 100 and starting from P10= 300 MW,P2 =200MW,andP3 =300MW,wesettheinitialvalueofλ.equaltotheaverageof the incremental costs of the generators at their starting generation values. This value is 9.4484.The progress of the gradient search is shown in Table 3.2. The table shows that the iterations have led to no solution at all. Attempts to use this formulation 0 0 will result in difficulty as the gradient cannot guarantee that the adjustment to the generators willresultinaschedulethatmeetsthecorrecttotalloadof800MW.Asimplevariationof this technique is to realize that one of the generators is always a dependent variable and remove it from the problem. In this case, we pick P3 and use the following: Then the total cost, which is to be minimized, is: Note that this function stands by itself as a function of two variables with no load-generation balanceconstraint(and noλ). The cost can beminimizedby agradient method and inthis casethegradient is: \ Notethatthisgradientgoestothezerovectorwhentheincrementalcostatgenerator3is equal to that at generators 1 and 2. The gradient steps are performed in the same manner as previously, where: UNIT-II 2. 21

  38. PaavaiInstitutions DepartmentofEEE ------------------------------------ (12) Each time agradient stepis made, thegeneration at generator 3is set to 800 minus thesum of the generation at generators 1 and 2. This method is often called the “reduced gradient” because of the smaller number of variables. 2.2.7. Base Point and Participation Factors This method assumes that the economic dispatch problem has to be solved repeatedly by moving the generators from one economically optimum schedule to another as the load changes by a reasonably small amount. We start from a given schedule-the base point. Next, theschedulerassumesaloadchangeandinvestigateshowmucheachgeneratingunitneeds to be moved (i.e.,“participate” in the load change) in order that the new load be served at the most economic operating point.Assume that both the first and second derivatives in the cost versus power output function are available (Le., both F; and Fy exist). The incremental cost curveofthe unitisgiveninFigure3.7.Astheunitloadischangedbyanamount,the system incremental cost moves from λ0toλ0 for a small change in power output on this single unit, ith ----------------------------------------- (13) This is true for each of the N units on the system, so that ---------------------------------------(14) The total change in generation (=change in total system demand) is, of course, the sum of the individual unit changes. Let Pd be the total demand on the generators (where then Pload+Ploss&), UNIT-II 2. 22

  39. PaavaiInstitutions DepartmentofEEE ---------------------------------------- (15) The earlier equation, 15, can be used to find the participation factor for each unit as follows --------------------------------------- (16) The computer implementation of such a scheme of economic dispatch is straightforward. It might be done by provision of tables of the values of FY as a function of the load levels and devising asimple schemeto taketheexistingload plus the projectedincreaseto lookup these data and compute the factors. somewhat less elegant scheme to provide participation factors would involve a repeat economic dispatch calculation at. The base-point economic generation values are then subtracted from the new economic generation values and the difference divided to provide the participation factors. This scheme works well in computer implementations where the execution time for the economic dispatch is short and will always give consistent answers when units reach limits, pass through break points on piecewise linear incremental cost functions, or have nonconvex cost curves. EXAMPLE 2.4 Starting from the optimal economic solution found in Example 2A; use the participation factor method to calculate the dispatch for a total load of 900 MW. UNIT-II 2. 23

  40. PaavaiInstitutions DepartmentofEEE 2.2.8. Economic dispatch controller added to LFC: Both the load frequency control and the economic dispatch issue commands to change the power setting of each turbine-governor unit. At a first glance it may seem that these two commandscanbeconflicting.Thishoweverisnottrue.Atypicalautomaticgeneration control strategy is shown in Fig. 5.5 in which both the objective are coordinated. First we computetheareacontrolerror.AshareofthisACE,proportionaltoαi,isallocatedtoeach of the turbine-generator unit of an area. Also the share of unit- i , γi X Σ( PDK - Pk ), for the deviation of total generation from actual generation is computed. Also the error between the economic power setting and actual power setting of unit- i is computed. All these signals are then combined control signal. and passed through a proportional gain Ki to obtain the turbine-governor Figure: 2.8. Economic dispatch controller added to LFC UNIT-II 2. 24

  41. PaavaiInstitutions DepartmentofEEE 2.3. UNIT COMMITMENT The life style of a modern man follows regular habits and hence the present society also follows regularly repeated cycles or pattern in daily life. Therefore, the consumption of electrical energy also follows a predictable daily, weekly and seasonal pattern. There are periods of high power consumption as well as low power consumption. It is therefore possible to commit the generating units from the available capacity into service to meet the demand. The previous discussions all deal with the computational aspects for allocating load to a plant in the most economical manner. For a given combination of plants the determination of optimal combination of plants for operation at any one time is also desired for carrying out the aforesaid task. The plant commitment and unit ordering schedules extend the period of optimization from a few minutes to several hours. From daily schedules weekly patterns can bedeveloped.Likewise,monthly, seasonal andannualschedules canbeprepared takingintoconsiderationtherepetitivenatureoftheloaddemandandseasonalvariations. Unitcommitmentschedulesarethusrequiredforeconomically committing theunitsinplants to service with the time at which individual units should be taken out from or returned to service. 2.3.1. Constraints in Unit Commitment Many constraints can be placed on the unit commitment problem. The list presented here is by no means exhaustive. Each individual power system, power pool, reliability council,andsoforth,may imposedifferentrulesonthescheduling ofunits,depending onthe generation makeup, load-curve characteristics, and such. 2.3.2. Spinning Reserve Spinning reserve is the term used to describe the total amount of generation available from all units synchronized (i.e., spinning) on the system, minus the present load and losses beingsupplied.Spinningreservemustbecarriedsothatthelossofoneormoreunitsdoes not cause too far a drop in system frequency. Quite simply, if one unit is lost, there must be ample reserve on the other units to make up for the loss in a specified time period.Spinning reserve must be allocated to obey certain rules, usually set by regional reliability councils (in the United States) that specify how the reserve is to be allocated to various units. Typical rules specify that reserve must be a given percentage of forecasted peak demand, or that reserve must be capable of making up the loss of the most heavily loaded unit in a given period of time.Others calculate reserve requirements as a function of the probability of not UNIT-II 2. 25

  42. PaavaiInstitutions DepartmentofEEE having sufficient generation to meet the load.Not only must the reserve be sufficient to make upforageneration-unitfailure,butthereservesmustbeallocatedamongfast-responding units and slow-responding units. This allows the automatic generation control system to restore frequency and interchange quickly in the event of a generating-unit outage. Beyond spinning reserve, the unit commitment problem may involve various classes of “scheduled reserves” or “off-line” reserves. These include quick-start diesel or gas-turbine units as well as most hydro-units and pumped-storage hydro-units that can be brought on-line, synchronized, and brought up to full capacity quickly. As such, these units can be “counted” in the overall reserve assessment, as long as their time to come up to fullcapacityistakenintoaccount.Reserves,finally,mustbespreadaroundthepowersystem to avoid transmission system limitations (often called “bottling” of reserves) and to allow various parts of the system to run as “islands,” should they become electrically disconnected. 2.3.3. Thermal Unit Constraints Thermal units usually require a crew to operate them, especially when turned on and turned off. A thermal unit can undergo only gradual temperature changes, and this translates into a timeperiodofsomehoursrequiredtobring theuniton-line.Asaresultofsuchrestrictionsin the operation of a thermal plant, various constraints arise, such as: 1. Minimum up time: once the unit is running, it should not be turned off immediately 2.Minimumdowntime:oncetheunitisdecommitted,thereisaminimumtimebeforeit can be recommitted. 3.Crewconstraints:ifaplantconsistsoftwoormoreunits,theycannotbothbeturnedon at the same time since there are not enough crew members to attend both units while starting up. In addition, because the temperature and pressure of the thermal unit must be moved slowly, a certain amount of energy must be expended to bring the unit on-line. This energy does not result in any MW generation from the unit and is brought into the unit commitment problem as astart-upcost.Thestart-upcost can varyfromamaximum “cold-start” valueto a much smaller value if the unit was only turned off recently and is still relatively close to operating temperature. There are two approaches to treating a thermal unit during its down period. The first allows the unit’s boiler to cool down and then heat back up to operating temperaturein timeforascheduledturn on. Thesecond (called banking) requires that sufficient energy be input to the boiler to just maintain operating temperature. The costs for the two can be compared so that, if possible, the best approach (cooling or banking) can be chosen. UNIT-II 2. 26

  43. PaavaiInstitutions DepartmentofEEE ��−��/𝛼 Start-up cost when cooling = Cc 1 − Where Cc = cold-start cost (MBtu) F = fuel cost × F+Cf------------------------------------------------- (17) Cf= fixed cost (includes crew expense, maintenance expenses) (in R) α = thermal time constant for the unit t = time (h) the unit was cooled Start-up cost when banking = Ct x t x F+Cf Where Ct = cost (MBtu/h) of maintaining unit at operating temperature Up to a certain number of hours, the cost of banking will be less than the cost of cooling, as is illustrated in Figure 5.3.Finally, the capacity limits of thermal units may change frequently, due to maintenance or unscheduled outages of various equipment in the plant; this must also be taken 2.3.4 Other Constraints 2.3.4.1 Hydro-Constraints Unit commitment cannot be completely separated from the scheduling of hydro-units. In this text, we will assume that the hydrothermal scheduling (or “coordination”) problem can be separated from the unit commitment problem. We, of course, cannot assert flatly that our treatment in this fashion will always result in an optimal solution. Figure 2.9 Hydro-Constraints UNIT-II 2. 27

  44. PaavaiInstitutions DepartmentofEEE 2.3.4.2 Must Run Someunitsaregivenamust-runstatusduringcertaintimesoftheyearforreasonofvoltage support on the transmission network or for such purposes as supply of steam for uses outside the steam plant itself. 2.3.4.3 Fuel Constraints We will treat the “fuel scheduling” problem system in which some units have limited fuel, or else have constraints that require them to burn a specified amount of fuel in a given time, presents a most challenging unit commitment problem. 2.3.5. Unit Commitment Solution Methods Thecommitmentproblemcanbeverydifficult.Asatheoreticalexercise,letuspostulatethe following situation. 1. Wemustestablish a loadingpatternforMperiods. 2. WehaveNunits to commitand dispatch. 3. TheMloadlevelsandoperatinglimitsontheNunitsaresuchthatanyoneunitcan supplytheindividualloadsandthatanycombinationofunitscanalsosupplythe loads. Next, assume we are going to establish the commitment by enumeration (brute force). The total number of combinations we need to try each hour is, C (N, 1) + C (N,2) + ... + C(N, N - 1) + C ( N , N ) = 2N – 1-----------------------------------(18) Where C (N, j) is the combination of N items taken j at a time. That is, -----------------------------------------(19) For the total period of M intervals, the maximum number of possible combinations is (2N - l)M, which can become a horrid number to think about. For example, take a 24-h period (e.g., 24 one-hour intervals) and consider systems with 5, 10, 20, and 40 units. The value of (2N - 1)24 becomes the following. UNIT-II 2. 28

  45. PaavaiInstitutions DepartmentofEEE N (2N - 1)24 5 6.2 ×1035 10 1.73×1072 20 3.12×10144 40 Too big These very large numbers are the upper bounds for the number of enumerations required. Fortunately, the constraints on the units and the load-capacity relationships of typical utility systems are such that we do not approach these large numbers. Nevertheless, the real practical barrier in the optimized unit commitment problem is the high dimensionality of the possible solution space. The most talked-about techniques for the solution of the unit commitment problem are: 1. Priority-list schemes, 2. Dynamicprogramming(DP), 3. Lagrange relation (LR). 2.3.5.1. Priority-List Methods The simplest unit commitment solution method consists of creating a priority list of units. As we saw in Example 5B, a simple shut-down rule or priority-list scheme could be obtained after an exhaustive enumeration of all unit combinations at each load level. The priority list of Example 5B could be obtained in a much simpler manner by noting the full- load average production cost of each unit, where the full-load average production cost is simply the net heat rate at full load multiplied by the fuel cost. Priority List Method: Prioritylistmethodisthesimplestunitcommitmentsolutionwhichconsistsofcreatinga priority list of units. Full load average production cost= Net heat rate at full load X Fuel cost Assumptions: 1. No load cost is zero 2. Unit input-output characteristics are linear between zero output and full load 3. Start up costs are a fixed amount UNIT-II 2. 29

  46. PaavaiInstitutions DepartmentofEEE 4. Ignore minimum up time and minimum down time Steps to be followed 1. Determine the full load average production cost for each units 2. Form priority order based on average production cost 3. Commit number of units corresponding to the priority order 4.AlculatePG1, PG2 ………….PGNfrom economicdispatchproblemforthefeasible combinations only 5. For the load curve shown Assumeloadisdroppingordecreasing,determinewhetherdroppingthenextunitwillsupply generation & spinning reserve. If not, continue as it is If yes, go to the next step 6. Determine the number of hours H, before the unit will be needed again. 7. Check H< minimum shut down time. If not, go to the last step If yes, go to the next step 8. Calculate two costs 1. Sumof hourly production for the next H hours with the unit up 2. Recalculate the same for the unit down + start up cost for either cooling or banking 9. Repeat the procedure until the priority list Merits: 1. No need to go for N combinations 2. Take only one constraint 3. Ignore the minimum up time & down time 4. Complication reduced Demerits: 1. Start up cost are fixed amount 2. No load costs are not considered. 2.3.5.2. Dynamic-Programming Solution Dynamic programming has many advantages over the enumeration scheme, the chief advantage being a reduction in the dimensionality of the problem. Suppose we have found units in a system and any combination of them could serve the (single) load. There would be UNIT-II 2. 30

  47. PaavaiInstitutions DepartmentofEEE a maximum of 24 - 1 = 15 combinations to test. However, if a strict priority order is imposed, there are only four combinations to try: Priority 1 unit Priority 1 unit + Priority 2 unit Priority 1 unit + Priority 2 unit + Priority 3 unit Priority 1 unit + Priority 2 unit + Priority 3 unit + Priority 4 unit The imposition of a priority list arranged in order of the full-load averagecost rate would result in a theoretically correct dispatch and commitment only if: 1. No load costs are zero. 2. Unit input-output characteristics are linear between zero output and full load. 3. There are no other restrictions. 4. Start-up costs are a fixed amount. In the dynamic-programming approach that follows, we assume that: 1. A state consists of an array of units with specified units operating and 2. The start-up cost of a unit is independent of the time it has been off-line 3. There are no costs for shutting down a unit. 4. There is a strict priority order, and in each interval a specified minimum the rest off-line. (i.e., it is a fixed amount).amount of capacity must be operating. A feasible state is one in which the committed units can supply the required load and that meets the minimum amount of capacity each period. 2.3.5.3. Forward DP Approach One could set up a dynamic-programming algorithm to run backward in time starting from the final hour to be studied, back to the initial hour. Conversely, one could set up the algorithm to run forward in time from the initial hour to the final hour. The forward approach hasdistinctadvantagesinsolvinggeneratorunitcommitment.Forexample,ifthestart-up costofaunitisafunctionofthetimeithasbeenoff-line(i.e.,itstemperature),thena forward dynamic-program approach is more suitable since the previous history of the unit can be computed at each stage. There are other practical reasons for going forward. The initial conditions are easily specified and the computations can go forward in time as long as UNIT-II 2. 31

  48. PaavaiInstitutions DepartmentofEEE required. A forward dynamic-programming algorithm is shown by the flowchart in Figure 2.11 The recursive algorithm to compute the minimum cost in hour K with combinati Fcost(K,I)=min[Pcost(K,I)+Scost(K-1,L:K,I)+Fcost(K-1,L)] ----------------------------------(20) Where Fcost(K, I ) = least total cost to arrive at state ( K , I ) Pcost(KI, ) = production cost for state ( K ,I ) Scost(K - 1, L: K , I)= transition cost from state (K - 1, L) to state ( K , I ) State (K, 1) is the Zth combination in hour K. For the forward dynamic programming approach,wedefineastrategyasthetransition,orpath,fromonestateatagivenhourtoa state at the next hour. Note that two new variables, X and N, have been introduced in Figure 2.11 X = number of states to search each period N = number of strategies, or paths, to save at each step These variables allow control of the computational effort (see below Figure).For complete enumeration, the maximum number of the value of X or N is 2n – 1 Figure: 2.10. Compute the minimum cost UNIT-II 2. 32

  49. PaavaiInstitutions DepartmentofEEE Figure: 2.11. Forward DP Approach UNIT-II 2. 33

  50. PaavaiInstitutions DepartmentofEEE 2.3.5.4. Lagrange Relaxation Solution The dynamic-programming method of solution of the unit commitment problem has many disadvantages for large power systems with many generating units. This is because of the necessity of forcing the dynamic-programming solution to search over a small number of commitment states to reduce the number of combinations that must be tested in each time period. Westart bydefiningthevariable��𝑙 as 𝑡 We shall now define several constraints and the objective function of the unit commitment problem: 1. Loading constraints: ----------------------- (21) 2. Unit limits: 3. Unit minimum up- and down-time constraints. Note that other constraints can easily be formulated and added to the unit commitment problem. These include transmission security constraints (see Chapter 1 l), generator fuel limit constraints, and system air quality constraints in the form of limits on emissions from fossil-fired plants, spinning reserve constraints,etc. The objective function is: 4. ------------------------- (22) WecanthenformtheLagrangefunctionsimilartothewaywedidintheeconomicdispatch problem: ---------------------------- (23) UNIT-II 2. 34

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