"Introduction to Power System Operation & Control Introduction The function of a power station is to deliver power to a large number of consumers. However, the power demands of different consumers vary in accordance with their activities. The result of this variation in demand is that load on a power station will never be constant; rather it varies from time to time. Most of the complexities of modern power plant operation arise from the inherent variability of the load demanded by the users. Unfortunately, electrical power cannot be stored and, therefore, the power station must produce power as and when demanded to meet the requirements of the consumers. On one hand, the power engineer would like that the alternators in the power station should run at their rated capacity for maximum efficiency and on the other hand, the demands of the consumers have wide variations. This makes the design of a power station highly complex. Variable Load on Power Station The load on a power station varies from time to time due to uncertain demands of the consumers and is known as variable load on the station. A power station is designed to meet the load requirements of the consumers. An ideal load on the station, from stand point of equipment needed and operating routine, would be one of constant magnitude and steady duration. However, such a steady load on the station is never realized in actual practice. The consumers require their small or large block of power in accordance with the demands of their activities. Thus the load demand of one consumer at any time may be different from that of the other consumer. The result is that load on the power station varies from time to time. Types of Loads A device which taps electrical energy from the electric power system is called a load on the system. The load may be resistive, inductive (e.g., induction motor), capacitive or some combination of them. The various types of loads on the power system are: (i) Domestic load. Domestic load consists of lights, fans, refrigerators, heaters, television, small motors for pumping water etc. Most of the residential load occurs only for some hours during the day (i.e., 24 hours) e.g., lighting load occurs during night time and domestic appliance load occurs for only a few hours. For this reason, the Load Factor is low (10% to 12%). (ii) Commercial load. Commercial load consists of lighting for shops, fans and electric appliances used in restaurants etc. This class of load occurs for more hours during the day as compared to the domestic load. The commercial load has seasonal variations due to the extensive use of air conditioners and space heaters.(iii) Industrial load. Industrial load consists of load demand by industries. The magnitude of industrial load depends upon the type of industry. Thus small scale industry requires load up to 25 kW, medium scale industry between 25kW and 100 kW and large-scale industry requires load above 500 kW. Industrial loads are generally not weather dependent. (iv) Municipal load. Municipal load consists of street lighting, power required for water supply and drainage purposes. Street lighting load is practically constant throughout the hours of the night. For water supply, water is pumped to overhead tanks by pumps driven by electric motors. Pumping is carried out during the off-peak period, usually occurring during the night. This helps to improve the Load Factor of the power system. (v) Irrigation load. This type of load is the electric power needed for pumps driven by motors to supply water to fields. Generally this type of load is supplied for 12 hours during night. (vi) Traction load. This type of load includes tram cars, trolley buses, railways etc. This class of load has wide variation. During the morning hour, it reaches peak value because people have to go to their work place. After morning hours, the load starts decreasing and again rises during evening since the people start coming to their homes. Effects of variable load The variable load on a power station introduces many perplexities in its operation. Some of the important effects of variable load on a power station are: (i) Need of additional equipment. The variable load on a power station necessitates having additional equipment. By way of illustration, consider a steam power station. Air, coal and water are the raw materials for this plant. In order to produce variable power, the supply of these materials will be required to be varied correspondingly. For instance, if the power demand on the plant increases, it must be followed by the increased flow of coal, air and water to the boiler in order to meet the increased demand. Therefore, additional equipment has to be installed to accomplish this job. As a matter of fact, in a modern power plant, there is much equipment devoted entirely to adjust the rates of supply of raw materials in accordance with the power demand made on the plant.(ii) Increase in production cost. The variable load on the plant increases the cost of the production of electrical energy. An alternator operates at maximum efficiency near its rated capacity. If a single alternator is used, it will have poor efficiency during periods of light loads on the plant. Therefore, in actual practice, a number of alternators of different capacities are installed so that most of the alternators can be operated at nearly full load capacity. However, the use of a number of generating units increases the initial cost per kW of the plant capacity as well as floor area required. This leads to the increase in production cost of energy. Important Terms and Factors The variable load problem has introduced the following terms and factors in power plant engineering: (i) Connected load. It is the sum of continuous ratings of all the equipments connected to supply system. A power station supplies load to thousands of consumers. Each consumer has certain equipment installed in his premises. The sum of the continuous ratings of all the equipments in the consumers premises is the connected load o f the consumer. For instance, if a consumer has connections of five 100-watt lamps and a power point of 500 watts, then connected load of the consumer is 5 × 100 + 500 = 1000 watts The sum of the connected loads of all the consumers is the connected load to the power station. (ii) Maximum demand: It is the greatest demand of load on the power station during a given period. The load on the power station varies from time to time. The maximum of all the demands that have occurred during a given period (say a day)is the maximum demand. Thus referring back to the load curve of Fig. 3.2, the maximum demand on the power station during the day is 6 MW and it occurs at 6 P.M. Maximum demand is generally less than the connected load because all the consumers do not switch on their connected load to the system at a time. The knowledge of maximum demand is very important as it helps in determining the installed capacity of the station. The station must be capable of meeting the maximum demand. Demand Factor ? Demand Factor = Maximum Demand of a system / Total connected load on the system ? Demand Factor is always less than one. ? Example: if a residence having 6000W equipment connected has a Maximum Demand of 3300W, than Demand Factor = 6000W / 3300W = 55%. ? The lower the Demand Factor, the less system capacity required to serve the connected load. ? Feeder-circuit conductors should have an ampere sufficient to carry the load; the ampere of the feeder-circuit need not always be equal to the total of all loads on all branches connected to it.? Remember that the Demand Factor permits a feeder-circuit ampere to be less than 100% of the sum of all branch-circuit loads connected to the feeder. Diversity factor / simultaneity factor (K ) s ? Diversity Factor = Sum of Individual Max. Demand. / Max. Demand on Power Station. ? Diversity Factor = Installed load. / Running load. ? Diversity Factor is usually more than one. (Since the sum of individual max. demands >Max. Demand) ? The load is time dependent as well as being dependent upon equipment characteristics. The Diversity Factor recognizes that the whole load does not equal the sum of its parts due to this time Interdependence (i.e. diverseness). ? When the Maximum Demand of a supply is being assessed it is not sufficient to simply add together the ratings of all electrical equipment that could be connected to that supply. If this is done, a figure somewhat higher than the true Maximum Demand will be produced. This is because it is unlikely that all the electrical equipment on a supply will be used simultaneously. ? The concept of being able to De-rate a potential maximum load to an actual Maximum Demand is known as the application of a Diversity Factor. ? 70% diversity means that the device in question operates at its nominal or maximum load level 70% of the time that it is connected and turned on. ? If total installed full load ampere is twice your running load ampere then the Diversity Factor is two. ? If total installed full load ampere is four times your load a ampere then the Diversity Factor is four. ? If everything (all electrical equipment) was running at full load at the same time the Diversity Factor is equal to One ? Greater the Diversity Factor, lesser is the cost of generation of power. ? Diversity Factor in a distribution network is the ratio of the sum of the peak demands of the individual customers to the peak demand of the network. ? This will be determined by the type of service, i.e., residential, commercial, industrial and combinations of such. Example I: One Machine Shop has Fluorescent fixtures=1 No, 5kw each, Receptacle outlets =15 No, 1500w each. Lathe=1No, 10 Hp, Air Compressor=1 No, 20 Hp, Fire Pump=1 No, 15 Hp. After questioning the customer about the various loads, the information is further deciphered as follows: 1. The shop lights are on only during the hours of 8 a.m. to 5 p.m.2. The receptacle outlets are in the office only, and will have computers and other small loads plugged into them. 3. The lathe is fully loaded for 5 minutes periods. The rest of the time is setup time. This procedure repeats every 15 minutes. 4. The air compressor supplies air to air tools and cycles off and on about half the time. 5. The fire pump only runs for 30 minutes when tested which is once a month after hours. ? Lighting Demand Factor = Demand Interval Factor x Diversity Factor. (15 minute run time/ 15 minutes) x1.0 = 1.0 Lighting Demand Load = 5 kW x 1.0 = 5 kW ? Receptacle Outlet Demand Factor = Demand Interval Factor x Diversity Factor (15 minute run time / 15 minutes) x0.1 = 0.1 Receptacle Outlet Demand Load = 15 x 1500 watts x 0.1 = 2.25 kW ? Lathe Demand Factor = Demand Interval Factor x Diversity Factor. (5minute run time / 15 minutes) x1.0 =0 .33 Lathe Demand Load = 10 hp x .746 x .33 = 2.46 kW ? Air Compressor Demand Factor = Demand Interval Factor x Diversity Factor. (7.5 minute run time / 15 minutes) x1.0 = 0.5 Air Compressor Demand Load = 20 hp x .746 x .5 = 7.46 kW ? Fire Pump Demand Factor = Demand Interval Factor x Diversity Factor. (15 minute run time/ 15 minutes) x0.0 = 0.0 Fire Pump Demand Load = 15 hp x .746 x 0.0 = 0.0 kW ? Summary of Demand Loads : Equipment kW D.F. Demand KW Lighting 5 1 5 Receptacle Outlets 22.5 .1 2.25 Lathe 7.5 .33 2.46 Air Compressor 15 0.5 7.46 Fire Pump 11.25 0.0 0.0 TOTAL 61.25 Kw 17.17 Kw Example II: A distribution feeder serves 5 houses, each of which has a peak demand of 5 KW. The feeder peak turns out to be 20 kw. The diversity is then 20/25 or 0.8. This results from the timing differences between the individual heating/cooling, appliance usages in the individual customers.? As supply availability decreases, the Diversity Factor will tend to increase toward 1.00. This can be demonstrated when restoring service after outages (called cold starts)as the system initial surge can be much greater than the historical Peak Loads. Example-III: A sub-station has three outgoing feeders: 1. feeder 1 has Maximum Demand 10 MW at 10:00 am, 2. feeder 2 has Maximum Demand 12 MW at 7:00 pm and 3. feeder 3 has Maximum Demand 15 MW at 9:00 pm, 4. While the Maximum Demand of all three feeders is 33 MW at 8:00 pm. ? Here, the sum of the Maximum Demand of the individual sub-systems (feeders)is 10 + 12 + 15 = 37 MW, while the system Maximum Demand is 33 MW. The Diversity Factor is 37/33 = 1.12. The Diversity Factor is usually greater than 1; its value also can be 1 which indicates the Maximum Demand of the individual sub-system occurs simultaneously. ? Diversity is the relationship between the rated full loads of the equipment downstream of a connection point, and the rated load of the connection point. To illustrate: 1. The building at these co-ordinates is fitted with a 100A main supply fuse. 2. The distribution board has 2no. 6A breakers, 1no. 20A breaker and 5no. 32A breakers, a total, potentially, of 192A. ? Not all these rated loads are turned on at once. If they were, then the 100A supply fuse would rupture, as it cannot pass 192A. So the Diversity Factor of the distribution board can be said to be 192A/100A, or 1.92, or 52%. ? Many designers prefer to use unity as the Diversity Factor in calculations for planning conservatism because of plant load growth uncertainties. Local experience can justify using a Diversity Factor larger than unity, and smaller service entrance conductors and transformer requirements chosen accordingly. ? The Diversity Factor for all other installations will be different, and would be based upon a local evaluation of the loads to be applied at different moments in time. Assuming it to be 1.0 may, on some occasions, result in a supply feeder and equipment rating that is rather larger than the local installation warrants. ? In the case of the example given above, achieving a diversity of 1.0 or 100% would require well over twice the cross-sectional area of copper cable to be installed in a deep trench underneath a field, the rebuild of a feeder cabinet to larger dimensions. ? Diversity Factor is mostly used for distribution feeder size and transformer as well as to determine the maximum Peak Load and Diversity Factor is always based on knowing the process. You have to understand what will be on or off at a given time for different buildings and this willsize the feeder. Note for typical buildings Diversity Factor is always one. Determine the Maximum Demand load for node then you can easily determine the feeder and transformer size. Diversity Factor in distribution Network Diversity Factors Elements of System General Large Residential Commercial Power Industrial Between individual users 2.00 1.46 1.45 Between transformers 1.30 1.30 1.35 1.05 Between feeders 1.15 1.15 1.15 1.05 Between substations 1.10 1.10 1.10 1.10 From users to transformers 2.00 1.46 1.44 From users to feeder 2.60 1.90 1.95 1.15 From users to substation 3.00 2.18 2.24 1.32 From users to generating station 3.29 2.40 2.46 1.45 Diversity Factor for distribution switchboards Diversity Factors Elements of System General Large Residential Commercial Power Industrial Between individual users 2.00 1.46 1.45 Between transformers 1.30 1.30 1.35 1.05 Between feeders 1.15 1.15 1.15 1.05 Between substations 1.10 1.10 1.10 1.10 From users to transformers 2.00 1.46 1.44 From users to feeder 2.60 1.90 1.95 1.15 From users to substation 3.00 2.18 2.24 1.32 From users to generating station 3.29 2.40 2.46 1.45 Diversity Factor for distribution switchboards Number of circuits Diversity Factor (KS) Assemblies entirely tested 2 and 3 0.9 4 and 5 0.8 6 to 9 0.7 10 and more 0.6Diversity Factor for according to circuit function (IEC 60439) Circuits Function Diversity Factor (ks) Lighting 0.9 Heating and air conditioning 0.8 Socket-outlets 0.7 Lifts and catering hoist 0.75 For the most powerful motor 1 For the second most powerful motor 0.75 For all motors 0.8 Load Factor ? Load Factor = Average load. /Maximum load during a given period. ? It can be calculated for a single day, for a month or for a year. ? Its value is always less than one. Because Maximum Demand is always more than avg. demand. ? It is used for determining the overall cost per unit generated. Higher the Load Factor, lesser will be the cost per unit. ? Load Factor = Load that a piece of equipment actually draws / Load it could draw (full load). ? Example: Motor of 20 hp drives a constant 15 hp load whenever it is on. ? The motor Load Factor is then 15/20 = 75%. ? Load Factor is term that does not appear on your utility bill, but does affect electricity costs. Load Factor indicates how efficiently the customer is using peak demand. ? Load Factor = ( energy (kWh per month)) / ( peak demand (kW)x hours/month ) ? A high Load Factor means power usage is relatively constant. Low Load Factor shows that occasionally a high demand is set. To service that peak, capacity is sitting idle for long periods, thereby imposing higher costs on the system. Electrical rates are designed so that customers with high Load Factor are charged less overall per kWh. ? For Example ? Customer AHigh Load Factor ? 82% Load Factor = (3000 kWh per month x 100%) / 5kW x 730 hours/month. ? Customer BLow Load Factor ? 41% Load Factor = (3000 kWh per month x 100%) / 10kW x 730 hours/month. ? To encourage the efficient use of installed capacity, electricity rates are structured so the price per kWh above a certain Load Factor is lower. The actual structure of the price blocks varies by rate.Utilization factor (K) u ? In normal operating conditions the power consumption of a load is sometimes less than that indicated as its nominal power rating, a fairly common occurrence that justifies the application of utilization factor (K ) in the estimation of realistic values. u ? Utilization Factor = The time that a equipment is in use./ The total time that it could be in use. ? Example: The motor may only be used for eight hours a day, 50 weeks a year. The hours of operation would then be 2000 hours, and the motor Utilization factor for a base of 8760 hours per year would be 2000/8760 = 22.83%. With a base of 2000 hours per year, the motor Utilization factor would be 100%. The bottom line is that the use factor is applied to get the correct number of hours that the motor is in use. ? This factor must be applied to each individual load, with particular attention to electric motors, which are very rarely operated at full load. In an industrial installation this factor may be estimated on an average at 0.75 for motors. ? For incandescent-lighting loads, the factor always equals 1. ? For socket-outlet circuits, the factors depend entirely on the type of appliances being supplied from the sockets concerned. Maximum demand ? Maximum Demand (often referred to as MD)is the largest current normally carried by circuits, switches and protective devices. It does not include the levels of current flowing under overload or short circuit conditions. ? Assessment of Maximum Demand is sometimes straightforward. For example, the Maximum Demand of a 240 V single-phase 8 kW shower heater can be calculated by dividing the power (8kW)by the voltage (240 V)to give a current of 33.3 A. This calculation assumes a power factor of unity, which is a reasonable assumption for such a purely resistive load. ? There are times, however, when assessment of Maximum Demand is less obvious. For example, if a ring circuit feeds fifteen 13 A sockets, the Maximum Demand clearly should not be 15 x 13 = 195 A, if only because the circuit protection will not be rated at more than 32 A. Some 13 A sockets may feed table lamps with 60 W lamps fitted, whilst others may feed 3 kW washing machines; others again may not be loaded at all. ? Lighting circuits pose a special problem when determining MD. Each lamp-holder must be assumed to carry the current required by the connected load, subject to a minimum loading of100 W per lamp holder (ademand of 0.42 A per lamp holder at 240 V). Discharge lamps are particularly difficult to assess, and current cannot be calculated simply by dividing lamp power by supply voltage. The reasons for this are: 1. Control gear losses result in additional current, 2. the power factor is usually less than unity so current is greater, and 3. Chokes and other control gear usually distort the waveform of the current so that it contains harmonics which are additional to the fundamental supply current. ? So long as the power factor of a discharge lighting circuit is not less than 0.85, the current demand for the circuit can be calculated from: ? current (A)= (lamp power (W)x 1.8) / supply voltage (V) ? For example, the steady state current demand of a 240 V circuit supplying ten 65 W fluorescent lamps would be: I = 10X65X1.8A / 240 = 4.88A ? Switches for circuits feeding discharge lamps must be rated at twice the current they are required to carry, unless they have been specially constructed to withstand the severe arcing resulting from the switching of such inductive and capacitive loads. Coincidence factor ? The coincidence factor =Max. demand of a system / sum of the individual Maximum Demands ? The coincidence factor is the reciprocal of the Diversity Factor Demand Factor & Load Factor according to Type of Industries Demand Load Utilization Type of Industry Factor Factor Factor (DF x LF) Arc Furnace 0.55 0.80 0.44 Induction Furnace 0.90 0.80 0.72 Steel Rolling mills 0.80 0.25 0.20 Mechanical/ Electrical a) Single Shift 0.45 0.25 0.11 b) Double Shift 0.45 0.50 0.22 Cycle Industry 0.40 0.40 0.16 Wire products 0.35 0.40 0.14 Auto Parts 0.40 0.50 0.20 Forgings 0.50 0.35 0.17Rice Shellers a) Working Season 0.70 0.80 0.56 b) Non-Working Season 0.05 0.30 0.01 Cotton Ginning a) Working Season 0.70 0.25 0.17 b) Non-Working Season 0.10 0.10 0.01 Spinning Mills 0.60 0.80 0.48 Textile Industry 0.50 0.80 0.40 Dyeing and Printing 0.40 0.50 0.20 Ghee Mills 0.50 0.50 0.25 Oil Mills 0.70 0.50 0.35 Plastic 0.60 0.25 0.11 Soap 0.50 0.25 0.12 Rubber (Foot Wear) 0.45 0.35 0.16 Distilleries 0.35 0.50 0.17 Chemical Industry 0.40 0.50 0.20 Gas Plant Industry 0.70 0.50 0.35 Sugar 0.30 0.45 0.13 Paper 0.50 0.80 0.40 Flour Mills(Single Shift) 0.80 0.25 0.20 Milk Plants 0.40 0.80 0.32 Printing Presses 0.35 0.30 0.10 Repair Workshops 0.40 0.25 0.10 Bottling Plants 0.40 0.35 0.14 Radio Stations 0.55 .0.45 0.25 Telephone exchange 0.50 0.90 0.45 Public Water Works 0.75 0.40 0.30 Medical Colleges 0.60 0.25 0.15 Hospitals 0.25 0.90 0.22 Nursing Homes 0.50 0.50 0.25 Colleges and Schools 0.50 0.20 0.10 Hotels and Restaurants 0.75 0.40 0.30Demand Factor & Load Factor according to Type of Buildings: Individual Facilities Demand Factor Load Factor Communicationsbuildings 60-65 70-75 Telephone exchange building 55-70 20-25 Air passenger terminal building 65-80 28-32 Chemistry and Toxicology Laboratory 70-80 22-28 Materials Laboratory 30-35 27-32 Electrical and electronics systems laboratory 20-30 3-7 Controlled humidity warehouse 60-65 33-38 Hazardous/flammable storehouse 75-80 20-25 Hospital 38-42 45-50 Laboratory 32-37 20-25 Medical Clinic 45-50 20-23 Single-family residential housing 60-70 10-15 Apartments 35-40 38-42 Fire station 25-35 13-17 Police station 48-53 20-25 Bakery 30-35 45-60 Laundry/dry cleaning plant 30-35 20-25 Schools 65-70 12-17 Churches 65-70 5-25 Post Office 75-80 20-25 Retail store 65-70 25-32 Bank 75-80 20-25 Supermarket 55-60 25-30 Restaurant 45-75 15-25 Auto repair shop 40-60 15-20 Hobby shop, art/crafts 30-40 25-30 Bowling alley 70-75 10-15 Gymnasium 70-75 20-45 Skating rink 70-75 10-15 Theatre 45-55 8-13Plant use factor. It is ratio of kWh generated to the product of plant capacity and the number of hours for which the plant was in operation i.e.=Units Generated per Annum It is often required to find the kWh generated per annum from maximum demand and Load Factor. The procedure is as follows: = =Units generated/annum = Average load (in kW) × Hours in a year Units generated/annum = Maximum demand (in kW) × L.F. × 8760 Load Curve A graphical plot showing the variation in demand for energy of the consumers on a source of supply with respect to time is known as the load curve. If this curve is plotted over a time period of 24 hours, it is known as daily load curve. If it is plotted for a week, month, or a year, then its named as the weekly, monthly or yearly load curve respectively. The load duration curve reflects the activity of a population quite accurately with respect to electrical power consumption over a given period of time. To understand the concept better it is important that we take the real life example of load distribution for an industrial load and a residential load, and have a case study on them, to be able to appreciate its utility from the perspective of an electrical engineer. The load on a power station is never constant; it varies from time to time. These load variations during the whole day (i.e., 24 hours)are recorded half-hourly or hourly and are plotted against time on the graph. The curve thus obtained is known as daily load curve as it shows the variations of load with respect to time during the day. The Figure shows the typical daily load curve of a power station. It is clear that load on the power station is varying, being maximum at 6 P.M. in this case. It may be seen that load curve indicates at a glance the general character of the load that is being imposed on the plant. Such a clear representation cannot be obtained from tabulated figures. The monthly load curve can be obtained from the daily load curves of that month. For this purpose, average* values of power over a month at different times of the day are calculated and then plotted on the graph. The monthly load curve is generally used to fix the rates of energy. The yearly loadcurve is obtained by considering the monthly load curves of that particular year. The yearly load curve is generally used to determine the annual Load Factor. Importance The daily load curves have attained a great importance in generation as they supply the following information readily: (i). The daily load curve shows the variations of load on power station for different hours of the day. (ii). The area under the daily load curve gives the number of units generated in the day. (iii). Units generated/day = Area (in kWh) under daily load curve. (iv). The highest point on the daily load curve represents the maximum demand on station that day. (v). The area under the daily load curve divided by the total number of hours gives the average load on the station in the day. ( ) = 24 (vi). The ratio of the area under the load curve to the total area of rectangle in which it is contained gives the Load Factor. =24 =24 Area(inkWh)underdailyloadcurve = Totalareaofrectangleinwhichtheloadcurveiscontained Case Study on Daily Industrial Load Curve The figure given below shows the load duration curve of an industrial load over a period of 24 hours. A closer introspection into the curve shows that the load demand starts to rise only after 5 hoursin morning as some of the machinery in the plant starts running perhaps for warming prior to operation of a few departments having to start early to synchronize the overall working of the plant in proper manner. By 8 hours in morning, the entire industrial load comes into play and remains constant up to shortly before noon, when it begins to fall off a bit because of lunch period. The morning shape of the curve is again restored from around 14 hrs and remains like that till about 18 hrs. In evening, most of the machineries start to shut down. Demand falls to minimum again by 21 to 22 hours in night and remains the same till 5 hours in morning next day. Case study on Daily Residential Load Curve In case of a residential load, as we can see from the diagram below, the minimum load is reached at about 2 to 3 hours at morning, when most people are asleep and during 12 noon, when most people are out at work. Whereas, the peak of the residential load demand starts at around 17 hrs and lasts up to 21 to 22 hrs at night, after which again the load drops rapidly, as most people retire to bed. Since, this residential load curve, is taken in a sub-continental continental country like India, we see that the load demand in summer is a bit higher in summer compared to a similar pattern of lower values during the winter season.Load Duration Curve When the load elements of a load curve are arranged in the order of descending magnitudes, the curve thus obtained is called a load duration curve. The load duration curve is obtained from the same data as the load curve but the ordinates are arranged in the order of descending magnitudes. In other words, the maximum load is represented to the left and decreasing loads are represented to the right in the descending order. Hence the area under the load duration curve and the area under the load curve are equal. The above figure (i)show the daily load curve. The daily load duration curve can be readily obtained from it. It is clear from daily load curve [See Fig. (i)],that load elements in order of descending magnitude are : 20 MW for 8 hours; 15 MW for 4 hours and 5 MW for 12 hours. Plotting these loads in order of descending magnitude, we get the daily load duration curve as shown in Fig. (ii). The following points may be noted about load duration curve: (i) The load duration curve gives the data in a more presentable form. In other words, it readily shows the number of hours during which the given load has prevailed. (ii) The area under the load duration curve is equal to that of the corresponding load curve. Obviously, area under daily load duration curve (in kWh)will give the units generated on that day. (iii) The load duration curve can be extended to include any period of time. By laying out the abscissa from 0 hour to 8760 hours, the variation and distribution of demand for an entire year can be summarized in one curve. The curve thus obtained is called the annual load duration curve.What is Operating Reserve? Having enough energy to meet demand is an important part of reliability. Although we always schedule sufficient generation to meet demand, unplanned events can upset the balance of supply and demand. Such contingencies include: A sudden, unexpected increase in demand, generation loss, or when several generators are unable to follow their dispatch instructions. The loss of a transmission element, which remove generation or result in a more restrictive operating limit that makes supply unavailable. To help manage situations such as these, we ensure that we have enough stand-by resources in the form of operating reserve (OR). Operating reserve provides us with a supply cushion that we can quickly call upon in the event of an unexpected energy shortfall. If a contingency occurs, operating reserve is activated, quickly re-establishing the balance between supply and demand. Classes of Operating Reserve There are three classes of operating reserve, determined by the time required to bring the energy into use and the physical behavior of the facilities that provide it:10-minute synchronized (spinning)10-minute non-synchronized (non-spinning)30-minute Total operating reserve is the sum of these three types of reserve. Spinning Reserve (10-minute reserve) We must have enough 10-minute reserve to cover the largest single contingency that can occur, given the current grid configuration. For example, this might be the loss of Ontarios largest single generation unit. In this case, if the largest generator on the grid is 900 megawatts (MW), we must schedule at least 900 MW of 10-minute operating reserve. A portion of our 10-minute reserve must be spinning or synchronized to the grid (referred to as 10S). The maximum amount of 10 -minute reserve that must be synchronized is 100%, but we are allowed to reduce this percentage (to a minimum of 25%), based on our performance in recovering from contingencies. We can reduce the synchronized portion of our reserve by 10% in any month that we successfully recover to our pre-contingency supply/demand balance following every reportable event (supply loss > 500 megawatts):Because we consistently recover to our pre-contingency supply/demand balance, we normally carry the minimum allowable synchronized reserve (25% of our 10-minute requirement).If we fail to successfully recover from a reportable event, our synchronized reserve requirement increases by 20% of the 10-minute reserve total (to 45%). It remains at that percentage until further recovery successes allow us to reduce it, or failures force us to increase it again. We continuously monitor this recovery performance. The remainder of the 10-minute reserve requirement is non-synchronized (referred to as 10NS). Our non-synchronized portion is normally set at 75%. 30-minute reserve The 30-minute reserve requirement is equal to the greater of: Half of the second largest single contingency, or the largest commissioning generating unit (this reflects the increased risk of tripping for a new generator that is still undergoing commissioning tests during initial operation). This type of reserve does not have to be synchronized and is referred to as 30R in our reports. SPINNING RESERVE Although the word spinning calls to mind a mechanical object, these reserves are for electrical power supplies and their practical applications. Demand for electrical power varies and that power level continuing all the time is called Base Load. The maximum power level during a day is called the Peak Load. Storage of electrical energy to be used during the peak periods has great economic advantages (see Storage of Electrical Energy). However, Spinning Reserves have different functions: they have spare power ready to be supplied at any moment, i.e. within few seconds in the case of forced outages, break down, disconnection and for frequency control. Generally they are close to the consumer and avoid complete blackout; those for frequency control are close to the generation units. To understand which power supplies are suitable for this purpose; they should be reviewed regarding their dynamic characteristics. The state characteristics, i.e. at which level and how long can the power be supplied continuously is of second order importance because the need for the Spinning Reserve is for a short time (10 seconds to 30 min.) until the operating or dispatching reserves started. As another state characteristic the running costs are not of primary importance for Spinning Reserves either. The dynamic characteristics of power supplies are related to their ability to be loaded or unloaded at a required rate. Nuclear power plants and conventional thermal (steam)plants have veryslow dynamic characteristics, i.e. they need more than an hour to reach full production rate. Gas turbine power plants need a few minutes to 15 minutes to produce full power. Hence they are suitable to be used as operational reserves. Diesel engines have start-up times in the range 10 seconds to a few minutes; hence they are preferred as operational reserves in comparison to gas turbines. Power supplies that need only a few seconds to produce full power and can last many minutes are preferred for Spinning Reserve applications. The Spinning Reserves have stored energy. This stored energy can be supplied at a rather low rate for, say 30 minutes, until an operational reserve reaches its full load or it can be supplied at a much higher rate only for a few minutes until a diesel generator starts up. For Spinning Reserve applications of tens of MW the combination of stored energy with a diesel generator unit should be preferred. Depending on the specific needs super capacitors and superconducting magnetic energy storage may have advantages. However these systems have not yet seen practical applications. Utility System as a Spinning Reserve: The three functions of the Spinning Reserves areTo supply power for frequency control,To compensate loss of power due to breakdown or forced outage of a generation unitTo supply power to a group of consumers in case of disconnection. For the first and second functions the required power rate is very high and it is economically not feasible to build very large electrical energy storage plants only for this purpose. However, the power units of the utility system that are already running can serve as Spinning Reserve by increasing their output within few seconds, at a slight sacrifice of efficiency. Power units have to run, even during the peak periods, at their design, or nominal, conditions. Satisfying all the safety regulations, the pressure, temperature and flow rate of working substance can be modulated to reach the maximum power of the generation unit. This power increase is in the range of 3-5 % of the nominal power and it can be achieved within few seconds. In large interconnected systems, this Spinning Reserve is distributed to different generation units.The total power can be increased by two means. Firstly the power rate of the running plants will be reduced 3-5 % and their number will be increased, without causing any remarkable loss of efficiency. Secondly the capacity of the electrical energy storage units which are installed for peak shaving, i.e. that of pumped hydro, compressed air and flywheel power systems will be increased. Although starting up these plants to supply power to the utility grid requires several minutes, the stopping of energy charging process to these systems can be very quick. Within a few seconds it releases the power, which is being consumed for charging, and this acts as a Spinning Reserve. Although the reliability of a utility power system securing which by means of Spinning Reserves is of primary importance, comparison of different alternatives considering economic factors is also important. The quality of the frequency control and the safety against unexpected loss of a generation unit will be evaluated with respect to the economics of the investment costs of new Spinning Reserve plants and the operating costs of manipulating the Load Factors of the running power plants. These evaluations and comparisons lead to the technical-economical solutions of utility power system Spinning Reserve problems. Electric Load Forecasting & Electric Demand Forecasting Electric load and demand forecasting involves the projection of peak demand levels and overall energy consumption patterns to support an electric utilitys future system and business operations. Quanta Technology is a global leader in research, development, and application of best practices in this field, with a staff of industry-recognized experts including: H. Lee Willis and Julio Romero-Aguero and an experience base of over 1000 projects spanning the past forty years. Quanta Technology provides completed and documented load forecasts, utility load forecasting projects, load forecast improvement projects, and load forecast benchmarking, support, training, and load forecast expert testimony in a wide range of specific load forecasting categories.Spatial Load ForecastingSmall Area ForecastingDistribution Load ForecastingTransmission Load ForecastingLoad Forecasting for Integrated Resource PlanningElectric Revenue ForecastingMulti-Scenario Load ForecastingWeather NormalizationSpatial Load Forecasting This involves the forecasting of peak load, forecasting of utility customer count, and forecasting of utility customer energy consumption needs of an area, or spatial basis, sufficient to support the planning of utility facilities that involve the sighting of T&D equipment to serve local regions. The overall growth of a utilitys peak demand might indicate that during the next decade it will need to add three substations to its system in order to meet growing demand. But to the planners and engineers who have to develop plans for those substations, a key element will be where? Where, within the utility system, will those new substations be required? A spatial electric load forecast, sometimes called a geographic forecast, provides a projection of Electric Peak, customer counts, and energy demand done with sufficient geographic resolution to answer this where question. Spatial electric load forecasts must cover a period into the future that provides a good lead time for planners, so they can arrange additions in a timely and efficient manner. In addition, the period must extend beyond that far enough that planners can evaluate if the additions being planned will have an economic and efficient service lifetime or need to be augmented/changed early in their service lifetimes, etc. Small Area Forecasting All spatial forecasts use the small area approach. The service area being studied is divided into a number of distinct areas and the load for each is fore cast.These areas might be the cells of a grid defined by a GIS system or a mapping coordinate system. They might be able to be the service areas of the feeders in a distribution system. Sometimes they are the irregular polygons defined by precinct boundaries or other geographic features and distinctions. Regardless, a distinct demand and energy forecast, and perhaps projections and analysis of customer types, etc., is done for each and every s mall area. The u se of small areas alone does not make a forecast spatial: all spatial forecasts are small area forecasts but not all small area forecasts are spatial. Spatial forecasts forecast load growth in each small area while taking into consideration to the extent needed information on load, trends, and condition s in all surrounding areas and for the mass of all small areas in the system, and forecast all areas in a unified simultaneous manner, as for example in a demo - economic simulation that allocates growth among all areas in the utility service territory. By contrast, a small area method that serially proceeds through each of several hundred feeders in a utility system, fitting a polynomial to eachs load history and projecting that trend into the future to produce a load forecast for that area, is a small area method but not a spatial method. This forecast doesnot analyze the interactions and patterns of growth among neighboring small areas, or look at how each fits into and is affected by the overall system growth. It produces several hundred essentially independent forecastseach done without consideration of trends and interactions among the total systems areas.Spatial r esolution of a load forecast refers t o the geographic detail it usesthe area size. Generally, a spatial resolution of at least 1/4th , and ideally, about 1/10th the size of the equipment service areas being planned is needed to provide effective planning of T&D systems. Distribution Load Forecasting This is a form of spatial load forecasting that focuses on providing the information necessary to support power distribution planning. Typically this means projecting peak loads of primary feeders for periods of three to ten years into the future.Best practice in distribution load forecasting includes projection of weather normalized peak demand on a feeder basis for five to ten years into the future, with spatial resolution (area detail)within each feeder area that meets planners needs to know how much load can be efficiently transferred between feeder areas, what load will be require along feeder reaches, etc. Transmission Load Forecasting This a form of spatial load forecasting that focuses on providing the information necessary to support power transmission system planning. Typically this also means projecting peak loads of primary feeders for periods of three to ten years into the future.Best practice in transmission load forecasting includes projection of weather normalized peak demand on a substation or substation bus basis for five to thirty years into the future, with spatial resolution (area detail)within each feeder area which meets planners needs to know how much load can be efficiently transferred between substation areas, what load would be in the area served by a bulk transmission line, or in an area assigned to a possible new substation, etc. Load Forecasting for Integrated Resource Planning (IRP) This involves projecting peak - load and demand - related trends in energy efficiency, conservation, load control, and demand response, as well as trends in the potential for as - yet unimplemented programs in those resources. Best practice methods use customer class analysis of energy consumption and end - use models and analysis of market penetration by appliance type, usually including hourly end use load curve models of power consumption by customer class and sub - class to analyze and project trends of future energy efficiency and demand response.Electric Revenue Forecasting This involves projecting revenues from electric sales expected in the future for an electric system. Typically this is done on a probabilistic basis (for weather and perhaps other scenarios)by customer class and segment and includes analysis of utility load growth, economics, and regulatory rates. This is not what Quanta Technology does, and we do not offer these services directly, but provide expertise and support on the forecasting of demand to partner companies who work with in these fields. Multi - Scenario Load Forecasting In many electric utility planning situations, a single forecast based on the expectation of outcomes cannot be used for effective planning: different outcomes would require far different plans, for which no average plan can be built. There is uncertainty as to the outcome of major events or load growth factors which cannot be resolved or averaged out of the forecast consideration. In such cases, planners require a multi - scenario, or what - if load forecasts, covering the different possibilities, so that they can study the system capability needs of the outcomes and develop contingency plans for all possible outcomes.Best practice in multi - scenario forecasting is to handle the uncertainty in the planning by providing planning resource in the T&D expansion plan through effective multi - scenario planning. Weather Normalization Weather Normalization of Electric Load Data is done for two reasons. First, it removes the effects of randomness of weather from historical trends in peak load and energy usage, so that they may be more accurately analyzed for trends due to customer and economic growth and changes in usage patterns.Second, it standardizes historical and forecast peak and energy values on standard weather conditions to which the utility plans. Most utilities do not plan their system s to accommodate average (50%) weather, but some reasonable extremes such as a 90% extreme (apower system designed to handle the electric demands of summer heat storms which will occur, on average, once every ten years)are accommodated.Optimal weather normalization involves determining both weather normalization formulae and factors, and coordinating these with equipment loading standards designed to fit the expected peak durations and stress levels of the probabilistic weather patterns the utility can expect as defined by that normalization.Unit Commitment The unit commitment involves in finding the least-cost dispatch of available generation resources to meet the electrical load. Generating resources can include a wide range of types: 1. Nuclear 2. Thermal (using coal, gas, other fossil fuels, or biomass) 3. Renewable (including hydro, wind, wave-power, and solar) The key decision variables that are decided by the computer program are: 1. Generation level (in megawatts) 2. Number of generating units on In addition, generating plants are subject to a number of complex technical constraints, including: 1. Minimum stable operating level 2. Maximum rate of ramping up or down 3. Minimum time period the unit is up and/or down These constraints have many different variants; all this gives rise to a large class of mathematical optimization problems. Unit commitment (UC)is an optimization problem used to determine the operation schedule of the generating units at every hour interval with varying loads under different constraints and environments. Many algorithms have been invented in the past five decades for optimization of the UC problem, but still researchers are working in this field to find new hybrid algorithms to make the problem more realistic. The importance of UC is increasing with the constantly varying demands. Therefore, there is an urgent need in the power sector to keep track of the latest methodologies to further optimize the working criterions of the generating units. What is economic dispatch? The operation of generation facilities to produce energy at lower cost to reliably serve consumers and recognizing any operation limits of generation and transmission facilities. Economic Dispatch - Power SystemMonitor load, generation and interchange (imports/exports) to ensure balance of supply and loadMonitor and maintain system frequency at 50 Hz during dispatch according to standards, using Automatic Generation Control (AGC) to change generation dispatch as neededMonitor hourly dispatch schedules to ensure that dispatch for the next hour will be in balanceMonitor flows on transmission systemKeep transmission flows within reliability limitsKeep voltage levels within reliability ranges Take corrective action, when needed, by:Limiting new power flow schedulesCurtailing existing power flow schedulesChanging the dispatchShedding load This monitoring is typically performed by the transmission operator Area Factors Limiting the Effectiveness of Dispatch in Minimizing Customer CostsGeographic area included The size of the geographic region over which the dispatch occurs affects the level of costs: that is, which generation resources and which transmission facilities are considered in planning and economic dispatch.Generation resources included Which generation resources in the area are included in the planning and economic dispatch, and whether they are included in the same manner, affects the level of costs.Tra nsmission facilities included The transmission facilities are included in the planning and economic dispatch, and reliability security limits of the transmission facilities are incorporated into the economic dispatch Factors Limiting Effectiveness of Dispatch in Minimizing Customer CostsFrequency of the dispatch Performing an economic dispatch more frequently (e.g., 5 or 15 minutes rather than each hour) affects the level of costs.Communication o f information Generation operators, transmission owners, and load serving entities must provide accurate and current information to those performing the planning and dispatch functions. Those performing planning and dispatch must provide accurate and current dispatch instructions to generation operators, transmission operators and load serving entities. Inadequate or incomplete communications affects the level of costs of the economic dispatch.Software tools for dispatch and information Reliable and secure computer software is essential for rapidly responding to system changes to maintain power system reliability, while selecting the lowest cost generators to dispatch. Obsolete software affects the level of costs achieved by the economic dispatch.Coordination of dispatch across regions Where there are multiple, independently performed, dispatches in a region, the effectiveness of coordination agreements and their implementation affect the level of costs of the economic dispatch.Governor ControlLoad Frequency Control A governor, or speed limiter, is a device used to measure and regulate the speed of a machine, such as an engine. A classic example is the centrifugal governor, also known as the Watt or fly-ball governor, which uses weights mounted on spring-loaded arms to determine how fast a shaft is spinning, and then uses proportional control to regulate the shaft speed. Turbine controls In steam turbines, the steam turbine governing is the procedure of monitoring and controlling the flow rate of steam into the turbine with the objective of maintaining its speed of rotation as constant. The flow rate of steam is monitored and controlled by interposing valves between the boiler and the turbine.In water turbines, the governors have been used since the mid-19th century to control the speeds of the turbines. A variety of fly ball systems were used during the first 100 years of water turbine governors. Fly ball component acted directly to the value of the turbine or the wicket gate to control the amount of water that enters the turbines. A newer system with mechanical governors started around 1880. An early mechanical governor is a servomechanism that comprises a series of gears that use the turbine's speed to drive the fly ball and turbine's power to drive the control mechanism. The mechanical governors were continued to be enhanced. By 1930, the mechanical governors had many parameters that could be set on the feedback system for precise controls. In the later part of the twentieth century, electronic governors and digital systems started to replace the mechanical governors. AUTOMATIC LOAD FREQUENCY CONTROL The control mechanism needed to maintain the system frequency. The topic of maintaining the system frequency constant is commonly known as AUTOMATIC LOAD FREQUENCY CONTROL (ALFC). It has got other nomenclatures such as Load Frequency Control, Power Frequency Control, Real Power Frequency Control and Automatic Generation Control. The basic role of ALFC is:To maintain the desired megawatt output power of a generator matching with the changing load.To assist in controlling the frequency of larger interconnectionTo keep the net interchange power between pool members, at the predetermined values The ALFC loop will maintain control only during small and slow changes in load and frequency. It will not provide adequate control during emergency situation when large megawatt imbalances occur. We shall first study ALFC as it applies to a single generator supplying power to a local service area.REAL POWER CONTROL MECHANISM OF A GENERATOR The real power control mechanism of a generator is shown in Figure. The main parts are:Speed changerSpeed governorHydraulic amplifierControl valve. They are connected by linkage mechanism. Their incremental movements are in vertical direction. In reality these movements are measured in millimeters; but in our analysis we shall rather express them as power increments expressed in MW or p.u. MW as the case may be. The movements are assumed positive in the directions of arrows. Corresponding to raise command, linkage movements will be: A moves downwards; C moves upwards; D moves upwards; E moves downwards. This allows more steam or water flow into the turbine resulting incremental increase in generator output power. When the speed drops, linkage point B mo ves upwards and again generator output power will increase. Corresponding to Lower command, linkage movements w ill be: A moves upwards; C moves downwards; D moves downwards; E moves upwards. This allows more steam or water flow into the turbine resulting incremental decrease in generator output power. When the speed increases, linkage point B move s downwards and again generator output power will decrease. Economic Dispatch and Operations of Electric Utilities Electricity is a unique commodity in that it cannot generally be stored at a large scale at reasonable cost, so the entities that operate the transmission grid need to make plans and take actions to keep supply and demand matched in "real-time" - from minute to minute and second to second. Except in circumstances where regulations have prohibited such actions, the electric utility industry has historically broken the process of meeting customer demands into three stages. Resource planning Days to years in advance, utilities have acquired stores of electric generation capacity through several mechanisms including the construction of new generation plants and supporting transmission lines, long-term forward contracting, and smaller quantities of spot-market purchases. Construction of new generation plants typically needs to happen years in advance, while forward and spot market contracts may be signed for periods varying from years in advance to a day or hour in advance. Utilities operating in states that have by and large retained the regulated and vertically-integrated structuresubmit resource plans to their respective state regulatory commissions through a process known as "integrated resource planning." Generation unit commitment Days to hours in advance, utilities make "commitment" decisions to have certain quantities of existing generation plant available to produce electricity when the need arises. In some cases (such as nuclear plants or hydroelectric facilities), the commitment decisions are made many weeks or months in advance. The decision to commit a generating unit to be able to produce electricity means that the utility is willing to incur fixed costs related to unit startup in order to have that generating plant ready and available to produce electricity in real time. Generators with large start-up costs or long minimum-run times (such as large combustion turbines and nuclear power plants)cannot run optimally if their output is determined using a single- period analysis (a"period" in the electric power industry usually refers to a length of time of about an hour). Instead, their operation must be scheduled over a longer time horizon of days or even weeks. A utility would need a forecast of demand weeks in advance before turning on a generator with a long minimum run time. They would need to look at the demand forecast over that period of weeks and decide the lowest-cost mix of generation plants that would meet the demand. This decision is referred to as the unit-commitment decision, and it is aptly named. The utility would, weeks in advance of consumption, have to commit to using a given mix of generation resources. If demand were to deviate wildly (and unexpectedly)from the utility's forecast, it would be faced with the decision of curtailing output from some of its generators (if it over-estimated demand)or utilizing generators with fast start times but high costs (if it under-estimated demand). Dispatch Close to the real-time point of consumption (i.e., minutes ahead of real time), LSEs issue dispatch orders to existing generation facilities, setting specific output levels for each. LSEs also utilize some generation facilities to provide "ancillary services," which represent very fast (sub-second to minutes) automatic adjustments to keep supply and demand in balance. The process of dispatching generation plants to meet customer demands within a specified control footprint is variously known as "economic dispatch" or "optimal power flow." The terminology here is suggestive that generation plants are dispatched in such a way as to minimize the total cost of delivered electricity. The economic dispatch algorithm actually implemented is conceptually pretty simple. Begin by turning on (or"dispatching")your generation source with the lowest "marginal" or operational costs. Have that generation source increase output until all load is met or the generation source hits its capacity constraint, whichever comes first. If the cheapest generation source hits its capacity constraintbefore all the demand is met, the second-cheapest generation source is turned on, and increases power until either it reaches its capacity constraint or all the demand is met. The process continues by successively turning on more expensive generation sources until the entire load is served. It is important to realize that the economic dispatch algorithm does not consider any fixed costs of power plants - only those costs directly associated with plant operation (for fossil-fired power plants, this would be primarily fuel). Economic dispatch is best illustrated using an example. Suppose that you were an electric utility that had three generators that could be used to meet electricity demand, as shown in Table 5.1. The fixed costs would represent land leases, fuel/transmission interconnections and any other costs that do not depend on the level of output. The marginal cost measures the amount of money that it costs each plant to produce one megawatt-hour of electric energy. Table: Fleet of power plants for economic dispatch example. Plant Name Capacity (MW) Fixed Costs ($/MWh) Marginal Cost ($/MWh) Colchester 100 50 10 Warren 75 25 30 Burke 20 10 60 Suppose that demand during some time period was 150 MWh. The process of determining economic dispatch would follow three steps. First, order the plants from lowest to highest marginal cost, which will tell you which plants would be utilized to produce electricity given some level of demand. This picture is called the "dispatch curve," shown in Figure 5.6. Each step in the dispatch curve represents one power plant. The height of the step represents the marginal cost of electricity production for each plant. The width of each step represents the capacity of each plant. Note that the x-axis represents total capacity for the entire utility, not the capacity for any individual power plant.In this case, to meet demand of 150 MWh, the utility would dispatch Colchester at its maximum output (100 MWh)and would meet the remaining 50 MWh of demand using the Warren plant. The Burke plant (the most expensive of the lot)is not dispatched. We can use the dispatch information to calculate several cost measures for our hypothetical electric utility. Total Cost is the sum of all costs incurred to meet electricity demand. To obtain total cost, we would multiply quantity produced times marginal cost for each plant, and then add in the fixed costs for all plants. Note that we need to add fixed costs even for plants that do not produce anything. Average Cost is the ratio of Total Cost to the total amount of electricity produced. System Marginal Cost is the marginal cost of the generating plant that meets the last MWh of electricity demanded. The system marginal cost is also referred to as the "system lambda." We can now calculate these cost measures for our example. The economic dispatch of all power plants in the system is: Colchester produces 100 MWh Warren produces 50 MWh Burke produces 0 MWh. Total cost = ($50 + $25 + $10) +$10/MWh × 100 MWh + $30/MWh × 50 MWh + $60/MWh × 0 MWh = $2,585. Average Cost = $2,585 ÷ 150 MWh = $17.23/MWh. System Lambda The "marginal generator" (the plant used to meet the last MWh of demand)is the Warren plant. So, the system lambda would just be the marginal cost of the Warren plant, which is $30/MWh. Note the different units for total cost ($) versus average cost and marginal cost ($/MWh). Here is an exercise that you can try on your own. Take the same three-generator example and suppose that demand was 190 MWh. Verify that: Total cost = $4,235 Average cost = $22.29/MWh System lambda = $60/MWhAUTOMATIC VOLTAGE REGULATOR The sections on AVR unit a. Sensing circuit Three-phase generator voltage sensing circuit is given in the PT, three-phase current and voltage output is derived from the PT and then rectified by diode circuit, and flattened by a series of capacitors and resistors and voltage can be adjusted by VR (variable resistance). The advantage of the sensing circuit is to have a fast response to the generator output voltage. Output voltage response is proportional to the generator output voltage is directly proportional b. Comparative amplifier Comparative amplifier circuit is used as a compares the voltage received from the sensing circuit with the set voltage. Voltage difference is called the error voltage. The error voltage is fed to the amplifier to produce a proportional large voltage. c. Exciter The Output of the amplifier is fed to the exciter and the exciter feeds the output voltage to the rotor field of the alternator which acts as the rotating transformer. The Power to operate the exciter is fed through a battery.d. Generator / Alternator The rotor part of the alternator is connected with shaft to the turbine to receive the mechanical power from the turbine. The Mechanical power is transferred from rotor as electrical Power to stator part of the alternator through the magnetic field produced by the excitation of rotor windings. The output voltage of the stator windings of the alternator varies accordingly to the rotor excitation according to the principle of transformer hence it is called as a rotating transformer."