Origen del proyecto

The power system consists of three functional zones: generation facilities, trans-mission facilities and distribution. From the reliability point of view, it can be looked at in three hierarchical levels. The generation facilities, the generation and transmission and the third hierarchical level of the generation, transmission and distribution [1].

The adequacy of the generating system is the most important aspect in system planning to ensure the system-function performance. A shortage in the ability of generating facilities to meet demand can cause serious and sometimes widespread supply interruptions, particularly during peak demand. This leads to immense Table 11.1 Rural network protection costs

Scheme Protection Cost Probable consumer-hours per annum

Hours per consumer 1 Expulsion fuses £500 24 h 500 cons. ¼ 12 000 24

2 Auto reclose £3 500 4 h 500 ¼ 2 000 4

3 Auto sectionalise £5 500 1 300 þ 4  200 ¼ 1 100 2.2 Note: Probable consumer-hours interrupted per annum are calculated based on experience of annual interruption duration for such networks.

financial losses, inconvenience and disturbance to consumer welfare. Therefore, the adequacy of generation is paramount in power-system reliability. Adequacy of the bulk transmission network is also important. However, its reliability is usually much higher than that of other parts of the electrical power system. Although faults and inadequacies in this network can cause serious interruptions, they are less frequent than those of the other facilities of the system. Distribution system dis-turbances and inadequacy cause only localised interruptions, which are less serious than generation and transmission inadequacies.

11.4.2 Assessment and economics of generation adequacy

Sufficient reserve is essential to ensure the adequacy of the generating system. This reserve was determined, in the past, by methods such as ensuring that the gen-erating system had enough percentage reserve, usually not less than 10–15 per cent of system peak, depending on the size of the system and regional interconnections, in order to meet maintenance requirements, unscheduled breakdowns of generating facilities or higher demand than anticipated. In small systems, generation reserve was assessed to be equal to the largest or the two largest sets out of commission.

Such deterministic methods cannot ensure the optimisation of investment in the system nor can they determine to a fair degree of accuracy the extent of system adequacy, and that this is the economically optimum adequacy. Correspondingly, simulation utilising probabilistic methods, which can more faithfully predict sys-tem performance and assist in the economical evaluation of investment, have become common in planning most large generating systems. The introduction of new generation facilities into the system reduces expected shortages and has system results that affect the whole economics of generation and the cost per unit of electricity produced. Such system effects can only be assessed through probabilistic simulation techniques.

The most widely utilised methods of assessing adequacy of generation are: the loss-of-load expectancy (LOLE) index, percentage energy loss index, and the fre-quency and duration method. These indices are used to assess probabilistic generation adequacy by convolution of the generating capacity model with the load model [8].

11.4.2.1 Loss-of-load expectation (LOLE) method

The LOLE may be the most widely used probabilistic index for generation relia-bility assessment. It is based on combining the probarelia-bility of generation capacity states with the daily peak probability so as to assess the number of days during the year in which the generation system may be unable to meet the daily peak:

LOLE¼X

L

nLAG

where nLis the number of occurrences of peak demand L during the year, and AGis the cumulative probability of being in capacity state j, such that C_j
1 L > Cj.

The reciprocal of the above equation is the LOLE in years per day. This means the probable number of years, or fraction of a year, during which the generation system will be unable to meet the peak demand of that day.

Economics of reliability of the power supply 167

The LOLE index has gained recognition because it provides a probabilistic figure that can be computed and employed in system planning. It combines a generation and a load model. It is relatively simple to compute, understand and apply. However, this index suffers from the following shortcomings:

● It gives no indication of the extent of load shedding in megawatt (MW) or percentage wise, nor does it give any indication of its duration or frequency regarding the average consumer, which is what reliability assessment should be mainly concerned with.

● The LOLE, in days per year, mainly indicates the number of days in the year in which the generating system would not be able to meet the load. The frequency of load shedding may be higher than this figure in case of double peaked daily load curves and in systems that employ units with high failure rates but short repair duration.

● Since such an index is not capable of assessing the actual damage, it is not very useful for comparing the reliabilities of different utilities or national systems, particularly if they have different shapes of the load curve and peak durations.

The above arguments, particularly the first one, have been recognised by the many users of this index. However, it is argued that for the same system, the use of the LOLE index would be adequate and correct for investigating different expansion plans and annual maintenance scheduling. This is correct only if the duration of peak demand is static over the years of study. This is not the case in many systems, with the continuous increase in the middle of the day load being experienced in most cases, particularly in developing economies.

To give an example, suppose that for a certain system with a typical daily load curve and annual load duration curves ‘A’ and ‘a’, respectively in Figure 11.3. The LOLE would be associated with the probably curtailment of the portion of the energy higher than the line ‘C’. If over a few years, the shape of the load curve changes to that of ‘B’ and ‘b’, while the LOLE is maintained constant, then the probable amount of energy curtailment, area cþ c⁰⁰, increases faster than the growth of peak demand. This signifies a disutility to the consumer and an actual

C

B A

Load

Time Time

c

a C

b c″

Figure 11.3 Effect of change of load curve on electricity curtailment

increase (probably small) in the unreliability of supply, which the LOLE cannot measure and defeats the purpose of maintaining the LOLE constant.

The effects of the change in the shape of the load curve and pattern of con-sumption, although they take place slowly over years, may change significantly from one season to another in the same year.

Besides the significant arguments against the LOLE mentioned above, it can be misleading in long-term planning and annual maintenance scheduling in systems of non-stationary load curves where significant changes in the duration of the peak load are expected to be encountered between seasons and over years.

11.4.2.2 Frequency and duration method with a load model

The theory of the frequency and duration analysis of the generation states with a load model is detailed in reference [8].

The generation frequency and duration approach, when coupled with the proper load model, will lead to the computation of a comprehensive reliability data.

It will indicate the probable existence of all possible negative margin states, their frequency of occurrence, cycle time and mean duration.

However, the model does not yield a single reliability index. Two indices are calculated: an availability index and another frequency index. Here also the fre-quency index is of similar value to that of the LOLE and the sound arguments against its application for system expansion and medium-term operation can be applied. The availability index will account for the duration of load shedding but not its extent and magnitude.

This was recognised by the developers of this method and the following index of percentage energy loss (PEL) [9] was suggested as being more representative of the actual reliability of the system for planning purposes.

11.4.2.3 Percentage energy loss (PEL) index

The method involves the generation capacity states availability table and the daily load curve. The probable energy curtailment, during one year, divided by the energy requirement of the load and multiplied by 100, yields the PEL index:

PEL¼probable energy curtailment energy requirement  100

The probable energy shedding is obtained by combining the generation states availability table with the segments of the load curve. By summing up all load segments, the probable energy curtailment will be computed.

The percentage energy loss index comes nearer than any other single index to assessing the true reliability of generation, because it reflects the ratio of energy curtailment (disutility) to the consumer to his consumption (utility) [5]. Hence, it can measure the amount of inconvenience and loss to the consumer, which is the principal concern of any reliability criterion. However, it also suffers from the fact that it is not useful in a dynamic load curve. If the generation expansion scheme is aimed towards maintaining the index constant, then with the load factor improve-ment with time, owing to an increase in base load (say by an increase in off-peak Economics of reliability of the power supply 169

space heating), the amount of energy permitted curtailment, which usually occurs during peak hours, would increase in proportion more than the growth in peak demand. This indicates deterioration in the ‘actual’ reliability of the supply and an increase in consumers’ disutility and inconvenience, which defeats the purpose of maintaining the index constant.

We have demonstrated the computational methods of various reliability indi-ces that are widely utilised for power system projects planning. What is important is how to use them intelligently. This calls for a better assessment of the social costs of power system unreliability, particularly those caused by the generating system.

11.5 Financial and economic evaluation of quality