Load Characteristics and Economic Aspects
For any developing country, the energy sector plays very important role in its growth. The progress of the country is indicated by its strong economic position which is highly dependent on its energy policy. The electrical supply company supplying power to consumers is a commercial enterprise which should have strong foundation to stay in competative business market and to get capital for meeting additional demands.
The electrical supply company is however different from the usual business enterprise in the following aspects,
i) Even though the supply company is public utility service they do not have direct competition. Mostly this sector comes under state governments and hence limits the earnings that can be made.
ii) There is obligation on the supply company to provide the service to whatsoever applies for it.
iii) The service provided by the supply company can not be withdraw from the consumers without regulatory approval.
Considering the above aspects, there is big responsibility on utility system to achieve economy in such a way that the cost per unit is as low as possible and at the same time the supply company gains profit and ensure reliable service while designing and building the power station.
The calculation of cost of electrical energy is a complex task. There are several factors affecting this cost. Few of this factors are land and equipment cost, the interest on the capital investment, depreciation on the equipment etc. Hence while deciding per unit cost a thorough study of various economic aspects of electric supply is to be made.
To understand this fact, let us consider an example. Suppose that an electric supply company has to provide power to particular area. For this purpose correct idea of load requirements must be known for that area. After this the next equation is how to get this power. There are various types of generation stations. The important stations are thermal hydral and nuclear stations. Number of factors are to be considered like suitable site, cost of fuel and its availability, nature of load to be supplied, environment cleanliness etc. While selecting the generating station.
The next important factor is the load on the power station is never constant but keeps on changing with time as demands are different. The variation in load are to be predicated initially and based on the maximum demand on the station, that much maximum capacity of the generating station is selected. Only selection is not sufficient but it has to maintain its constant service and reliability. Only one unit can not serve this purpose as it is not practical and economical too.
To solve this problem, an alternative is to be select size and number of generating sets in such a way as to fit in the load curve or in the load demands as closely as possible. But again the problem is increase in operational problems and maintenance costs with large number of generating units. Similarly the capital cost of the system also increase which will not lead to lower per unit cost of electricity. Hence there must be compromise on selecting the size and number of generating units for a station.
The above example shows the importance of economics of power generation and its study.
Before studying the economics of generation let us see few terms which are commonly used in system operation.
1) Connected load : The sum of continues ratings of all the equipments which are connected to the supply system is called connected load.
The load of thousands of consumers is supplied by a power station. The load means various equipments and apparatus present in consumer premises. If the summation of these continuous ratings of all the equipments is made then it forms the connected load of that consumer. The sum of connected loads of all the consumers is the connected load to the power station.
2) Maximum Demand : It is defined as the largest demand of load on the generating station during a specified period. The load on the generating station is never constant but keeps on varying from time to time. The demand of load which is maximum of all, during a given period, forms maximum demand.
Maximum demand is normally less than the connected load because the connected load to the system of various consumers is not switched on at the same time. The installed capacity of the station is decided from the maximum demand. It is quite obvious that the power station must be able to supply the maximum demand.
3) Demand factor : It is defined as the ratio of maximum demand to its connected load Mathematically it is given as
We have seen that the maximum demand is generally less than its connected load hence the demand factor is less than unity. This factor is an important consideration in deciding the capacity of the plant equipment.
Consider for example a building with following connected load.No. of lamps = 200 each of 4 W = 8 KW
Power points = 150 each of 500 W = 75 KW
Lift = 10 KW
Pump = 10 KW
Total connected load = 8 + 75 +10 +10 = 103 KW
This is the total connected load of the building but it is not switched on at the same time. Consider that 100 lamps, 100 power points, lift and pump are on at the same time which is say maximum possible condition of the load for that building. All the other load demands are less than this peak.
Maximum demand = 100 x 40 + 100 x 500 +10 +10= 4 KW + 50 KW + 20 KW
= 74 KW
Hence the demand factor for this building is
Demand factor = (Maximum demand)/(Connected load) = 74 kW/103 kW = 0.7184
At is ratio of two similar quantities it is not having any unit.
Similarly the demand factor of the generating station is also calculated from the knowledge of maximum demand and the connected load on that power station.
4) Average load or Average demand : It is defined as the average of the loads occurring on the power system or generating station in a given period. The period may be day or month or year. Mathematically it is given by as,
5) Load factor : It is defined as the ratio of average load to the maximum demand during a given period. Mathematically it is given as,
Depending upon the consideration of time, the load factor may be daily, monthly or yearly. Suppose the operation time of plant is say T hours.
Load factor = (Average load x T)/(Maximum demand x T)
The yearly load factor is defined as
Yearly load factor = (No.of units supplied in a year)/(Maximum number of units that can be supplied)
The load factor is always less than 1 as average load is similar than maximum demand. This is the key factor in deciding the overall cost per unit generated. With increases in load factor, maximum demand on the station will be less. We have already seen that the plant must supply its maximum demand. Thus with lower maximum demand, the capacity of the plant also lowers which reduces cost of plant with ultimate effect of reduction in cost per unit generated.
Monthly load power factor is given by,
The load factor defined as above corresponds to the supplier and may sometimes referred as undertaking load factor.
6) Delivery factor : To improve the working of the generating station the loads must be diversed or staggered. The maximum demand of various type of consumers which is supplied by a power station dose not occur at the same time. Hence the maximum demand on the generation station is always less than the sum of individual maximum demands.
The diversity factor is thus defined as the ratio of sum of individual maximum demands to the maximum demand on power station. Mathematically it is defined as,
The diversity factor is always greater than 1 if defined in above way. Greater the diversity factor, lesser is the cost of generation since more diversity factor means less maximum demand which corresponds to lesser plant capacity which reduces cost of plant and hence that of generation.
For understanding this factor, let us consider an example. Let us consider that a generating station is supplying power to follow various consumers.
= (6000 + 1000 + 2000 + 500 + 400 + 100)/(600)
Diversity factor = 10000/6000 = 1.66
The maximum demand of each category of load is not occurring at the same time. If it is occurring at the same time then the station has to supply this demand for short duration. The average load on the station is around 50%. Hence the plant generators will remain idle in the remaining time after supplying this peak demand and this will not be economical operation of the plant. Under such case the consumers are advised to diverse their loads or advised to ask their maximum demands at different times then the operation of station will be economical. In case of industrial load or municipal load such diversification of load is possible. So if the maximum demand is made smaller then it will be economical operation
In the above example if instead of 6000 kW, the maximum demand is made 5000 kW by diversification of load then the new diversity factor is calculated as
New diversity factor = (Sum of individual maximum demands) / (Maximum demand)= 10000/5000 = 2
Note : In summery, we can say that by diversing the load, the capital cost of the plant and hence cost per unit can be reduced. Similarly the alternators in the plant can be operated to their maximum capacity.
7) Capacity factor : It is defined as the ratio of actual energy produced to the maximum possible energy that could have been reduced during a given period.
Capacity factor = (Average demand x T) / (Maximum demand x T)
= Average demand/ plant capacity
For a period of one year,
Thus it can be seen that plant capacity factor indicates the reverse capacity of the plant. A power station should have some reverse capacity for increased load demand in the future. Hence the installed capacity of the plant is greater than the maximum demand.
Reversed capacity = Plant capacity - maximum demand.
If plant is not having any reversed capacity then plant capacity is equal to maximum demand which indicates that capacity factor and load factor are same.
Some important terms related to this factor are as given belowi) Firm power : It is the power which is available always even under emergency condition.
ii) Cold reverse : It is the reverse generation capacity which is available for service but not in operation.
iii) Hot reserve : It is the reverse generation capacity which is in operation but is not in service.
iv) Spinning reverse : It is that generating capacity which is connected to the bus and ready to take load.
8) Plant use factor : It is defined as the ratio of units generated (kWh) to the product of plant capacity and the number of hours for which the plant was in operation.
This factor is an indication of best possible and effective utilization of generating station. But it does not indicate the idle time of the plant.
Variable Load on Power Station
We have already seen that the load on the generating station is never constant but varies from time to time as thje demands from the consumers are available. Ideally it is required that the load should be of constant magnitude and for fixed duration which is not possible in practice. Thus as the load demand of various consumers goes on changing continuously, the load on the power station is always variable which has its own effects which are discussed below.
The first effect of variable load is the necessary of additional equipment for meeting the changing load demand. With increase in power demand, the output of the generating station must be increased which requires corresponding increase in supply of raw materials. Thus additional equipments are required to perform this task.
The second effect of variable load is increase in cost of production of electrical energy. Generally the alternator has its maximum efficiency near its rated capacity. Now if alternator is lightly loaded during periods of low demand then its efficiency will be poor. In such cases alternators of different capacities are to be installed in the plant so that they can be operated at their maximum efficiency. This increase cost per kW of the plant capacity as well as area required. This also increases production of cost energy.
Load Curve
We have already seen that the load on the power station goes on changing with respect to time. So if these variations are plotted then curve obtained is called load curve. From the load curve following information is obtained,
1. The variation of load on the plant during different hours of a day.
3. The maximum and minimum values of load during a day.
3. Maximum and minimum values of load during a year.
4. Average load on the station during a year.
5. It gives the indication whether the station is working efficiently or not.
The load curve may be a daily, monthly or yearly on the basis of whether the load variation are plotted during a day, month or a year.
In a daily load curve, the load variations are plotted against time on graph after recording their values on half-hourly or hourly basis. Fig.1 Shows a typical load curve on the plant. From this figure the general character of the load can be obtained which is not possible with tabulated values.
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| Fig. 1 Typically daily load curve |
It can be seen from the above curve that the maximum load occurs during the period between 6 p.m. to 8 p.m. whereas it is minimum in the afternoon period.
The monthly load curve can be obtained from daily load curve of that month. The average values of load at different periods of the day for the month is calculated and then the curve is plotted on the graph. This curve helps in determining the rates of energy.
The yearly load curve can be obtained from monthly load curve of that year. The annual load factor can be determined from this curve.
Now consider the above daily load curve. The area under this curve gives the number of units generated in the day.
Units generated in a day = Area under daily load curve.
The highest point on the load curve indicates the maximum demand on the station for that day.
If the area under this curve is divided by total number of hours gives the average load on the station.
The load factor can also be calculated by taking a ratio of area under load curve to the total area of the rectangular in which the curve is contained.
The size and generating units cab be obtained from the load curve. The number of generating units are such as to fit the load curve. This aids in operating the generating units near or at maximum efficiency.
Depending on load demands obtained from the load curve, the generating units can be put in operation. This sequence and time for which units are operated can be decided from the information obtained from load curve. Thus the operating schedule of the plant can be operated from load curve.
1.1 Plotting of Load Curve
Before plotting the load curve, the load is divided into number of categories. The load is classified into following different categories.
1) Public places load
2) Private or residential load
3) Cinema hall load
4) Shops, hostels and hospital load
5) Railway load
6) Water works load
7) Industrial load
8) Street light.
The load sheet is prepared for each locality. Then the total of each type of load in different hours in a day are obtained.
The reading taken for each types of load during different hours of a day are plotted on a graph which gives the load curve.
The load curve goes on changing from summer to winter. In the summer season, there is a load of refrigerators, fan and air conditioning. As the light load comes up after sunset the maximum demand of load will be between 8.00 p.m. to 10.0 p.m. In winter the load conditions are different and correspondingly peak demand are different.
The typical load curves for Delhi in summer, winter and monsoon season are shown in following Fig.2, 3, and 4.
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| Fig. 2 Winter season |
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| Fig. 3 Summer season |
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| Fig. 4 Monsoon season |
For each category of load, the load curve may be plotted. The summation of all these points gives the total load curve.
The maximum demand on the generating station can be obtained from the load curve for the given period. The maximum demand is nothing but the maximum load on the station during a given period. The peak load obtained from thew load curve is not the maximum demand. The maximum demand is the largest average load on the station for specified period. If the load readings are monitored continuously then the greatest load will be represent instantaneous maximum demand.
It is stated that the maximum demand is x kW, then it is meaningless unless it is specified by the time duration. The accuracy of this will dependent on how accurately the readings are obtained from load curves, scale of the curve and the number of ordinates taken within the specified period. The capacity of generating units can be decided from this information.
Load Duration Curve
The curve obtained by arranging the load elements of a load curve in order of decreasing magnitudes is called load duration curve. No extra data or information is required for plotting this curve as it can be plotted with the same data as that for load curve.
The ordinates from the load curve arranged in order of deceasing magnitudes. The peak load is shown to the left while the decreasing loads are arranged to the right in the descending order. It is quite obvious that the area under load curve and load duration curve is same.
The area under load duration curve indicates the total number of units that are consumed in that time. The load factor of the station can be determined from this. It also suggests the division of load between various generating units (alternators) of the plant to operate them near their maximum efficiency points.
Fig. 1(a) shows the daily load curve. The correspondingly daily load duration curve is shown in the Fig. 1(b).
The load elements of 3 kW, 6 kW, 9 kw, 12 kW, 15 kW and 18 kW are arranged in decreasing order for the respective time duration on the load duration curve. The total load supplied can be divided into various sections (sections I to VI in this case). Let us say that there are 6 alternators corresponding ti these sections.
The alternator which supplies load of 3 kW will be in operation almost continuously with high load factor. When the load is increased to 6 kW, then the second alternator will be put in service which will have comparatively low load factor. Likewise the alternators will be put in operation with decreasing load factors.
The important points that can be observed from the load duration curve are summarized as given below
1.The data obtained from load duration curve is in more presentable from as it shows te number of hours for which the load was present on the station.
2. It gives number of units generated after finding the area under that curve.
3. The load duration curve cab be plotted for entire year by considering time period of 8760 hours (hours of a year 24 hours x 365 days = 8760 hours) on x-axis. Thus the variation and corresponding distribution of load cab be obtained.
Integrated Load Duration Curve
A plot of number of units generated (kWh) for a given demand (kW) is called integration load duration curve on Y-axis, load demand in kW or MW is plotted while on z-axis corresponding number of units generated are obtained. Such a curve corresponding to load duration curve shown in Fig1.
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| Fig. 1 Integrated Load Duration Curve |
This curve is obtained from load duration curve. Let the load demand be 3 kW from the load duration curve in section I. The number of units generated corresponding to this demand will be area under section I which is shown as U1 in integrated load duration curve. Similarly the other pints are also obtained to get a total curve.
The number of units consumed by a load upto a particular time of a day can also be shown on a curve which is called as mass curve.
Selection of Size and Number of Generating Units
For deciding the size and number of generator units, firstly the load curve and other relevant parameter and factors from the load curve are to be determined. In order to calculate the size of the units, the station auxiliary load and the line losses should be considered. It can be approximately taken as 20 % of the consumer load.
The minimum number of units will be one. But there drawbacks in selecting a single unit to meet maximum demand are as given below
1. The rating of the unit should be such as to meet the maximum demand. But as the load on station is variable and load factor is less than 100 % there considerable time during which the load will be much less than maximum demand. During this period the unit may run at half load or even practically at no load. Hence it is not running all time to give maximum efficiency. It is also not economical to run the set at light load as fuel consumption will be more.
2. With only one unit, reliability of operation is reduced even though power can be obtained at cheaper rate. If the same unit is under repair or maintenance then continuity of supply is lost unless there is second unit present which may increase capital cost. Thus in the environment of variable load where reliability of supply is important it is neither practical nor economical to use a single unit.
The number of units are to be selected in such a way as to fit in the load curve as closely as possible. Then each unit can be made to operate in such a way that it runs almost at full load or at a load which gives maximum efficiency. The reverse capacity required in this case will only be a single largest unit which would be much smaller than the maximum reverse capacity that would be required with a single unit case. Thus plant capacity and plant use factor is improved. But there are following shortcomings of this system.
1. With increase in number of units, the floor area required is more and so corresponding cost is also more.
2. The cost for maintenance also increased.
3. With increase of number of units, there will be frequent starting, stopping and parallel operation of units which needs increased persons for handling the equipments.
4. Capital cost for large number of units is more than that of same capacity with smaller number of units of large size.
Thus selection of number of units is a critical task as a single unit as well as large number of smaller units would be unreliable and uneconomical. Thus a compromise is made in selection of these units. The best compromise between plant capacity and plant capacity factor also gives choice for selecting the units.
The following points should be considered for selecting of units for various stations
i) The load factor of the units should be high.
ii) The minimum number of units selected should be two.
iii) The plant must have some reverse capacity under abnormal conditions.
iv) With two units selected, both must be able to supply maximum demand or load.
v) The future demand and expansion should also be considered as the load on the station always increases.
vi) For large number of small units, the space and capital cost required is more.
As far as possible, the units of equal capacities are selected which will have following advantages.
i) The parts can be interchanged.
ii) The maintenance will be easier.
iii) The working time of each plant regulated.
iv) The spare parts required to be stored are less.
In summary, the selected units should work at high efficiency as the capital cost and running cost will then be minimum.
Interconnection of Power Stations
The connection of various generating stations is parallel is called interconnection of power stations or also called interconnected grid system. There are several advantages of this grid system and the cost associated with the interconnection through extra comparable to the benefits obtained from it.
Before studying the advantages of this grid system let us consider the concept of base load and peak load.
We have seen that the load on the power station is never constant but keeps on changing with time. This load can be subdivided into two parts viz i) Base load ii) Peak load
The unvarying load or fixed load which occurs almost whole day on the plant is called base load. The various peak demands of the load over and above base load of the power plant is called peak load.
Consider the load curve with base load and peak load shown in the Fig.1.
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| Fig. 1 |
Now if such load curve is to be met by a single unit then is installed capacity should be equal to peak load demand or even more. As peak load occurs for short duration such solution is not economical that we have seen earlier. The other way is to divide the load into base load and peak load. Thus by interconnection of various power stations of different types, some station will supply base load while some other stations will supply peak load. Thus the co-ordination of operation of different power stations is essential which is shown in the Fig.2.
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| Fig. 2 |
The power plant which are working as base load should be capable of working continuously for long periods. It should have low operating cost. Its repair should be economical and speedy.
The peak load power plants should be capable of quick start, fast synchronization, quick taking of load and fast response to load variations.
The hydro power plant serves as base load or peak load efficiency. They are normally employed as base load plants as their capital cost is high. When water is not abundantly available then the hydro power plant works as peak load.
The cost of generation per unit steam power plant is minimum. Hence it can be employed as base load. Nuclear power plants are also employed as base load. Diesel, gas and pumped storage plants are used as peak load plants.
The advantages of interconnected system are as given below
1) With interconnected grid system the peak load can be exchanged between the generation stations. From load curve if there is peak load demand which is more than related capacity of the plant then the excess load can be shared by other interconnected stations.
2) It is possible to use the older and inefficient plants with grid system for short duration to supply peak demands. These units may not operate independently but with grid system they can sustain peak loads. Thus older plants can be effectively used with this system.
3) With interconnected grid system the economical operation of the plant is possible. The total load is arranged in such a way that more efficient plants can be used as base load stations which can work continuously throughout the year at high load factor. The less efficient plants can be made to operate as peak load plants. Also larger generator units can be employed to reduce capital cost per kW.
4) Various interconnected plants have their load curves different due to which maximum demand on the system is reduced as compared to sum of individual maximum demands on various stations. Thus the effective capacity of the system increased as their is improvement in diversity factor.
5) It can be seen that the load curves of the two different stations are not identical. In worst conditions the peak loads may occur at a time different by few minutes. Thus the maximum demands on individual stations are not occurring simultaneously, it is possible to work with lesser installed capacity with interconnected grid system.
6) In abnormal conditions every station should have reverse standby unit to be put in operation. With grid system the reverse capacity is reduced which increases efficiency of the system.
7) The reliability and continuity of the supply is improved with interconnected grid system. With fault condition occurring in any one station, the supply can be maintained with the help of other stations.
Electrical Equipment Used in Power Station
A power station generates an electrical energy by using one of the energy sources. A modern power station contains number of electrical equipments. The important electrical equipments are,
1. Alternator : This is most important equipment. It is coupled to the turbine, whichever type of the station it may be i.e. steam, gas, nuclear etc. The turbine acts as a prime mover of alternator. The alternator converts the mechanical energy received from the turbine into an electrical energy.
Alternators are generally hydrogen cooled or air cooled. The necessary excitation to the alternators is provided by the main and pilot exciters directly connected to the alternator shaft.
2. Transformer : This is another important electrical equipment which is used to raise or lower available voltage levels as per the equipment. In a power station, different types of transformers are used, which are :
i) Main step up transformer which steps up the generated voltage for the further transmission.
ii) Station transformer which is used for the general service in the power station itself.
iii) Auxiliary transformers which supply to individual auxiliary unit.
3. Switchgear : This includes such a equipment which locates the fault on the power system and isolates the faulty part from the system. It contains circuit breakers, relays, isolation switches, fuses and other controlling devices.
Alternator gives its output to the busbar through the transformer and proper switchgear equipments.
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