Economics of reliability of the power supply
10.3 Reliability in system planning
In order to understand the value of this approach, it is advantageous to review the exist- ing methods that guide reliability planning and are applied by most of the electricity supply utilities worldwide. These can be summarised as follows [5]:
• empirical planning rules, • supply design standards,
• simplified cost–benefits analysis, and • detailed financial and economic evaluation.
The first three methods will be discussed in Sections 10.3.1–10.3.3, and the fourth method will be discussed in detail in Section 10.4.
10.3.1
Empirical planning rules
In this case, the planner, based on his experience and practice in dealing with similar situations, decides on the desired reliability level. This is achieved through the evalu- ation of the importance of the system and network and correspondingly the extent of redundancy to be incorporated, taking into account the following: the part of the sys- tem it is dealing with, voltage level and nature of the network, number and category of consumers, financial constraints, and past reliability records and past experience in handling a similar situation.
Almost all systems that do not have drawn out and written supply design standards, or probabilistic planning, employ such criteria. The empirical rules for generation involve a percentage reserve-margin method, without a loss of load expectation (LOLE) calculation; or for a small system, a firm generating capacity with the biggest set(s) out-of-commission. For the main network the ‘n− 1’ rule is employed, which
means that the loss of a main line from n parallel lines, or a transformer of n trans- formers, should not affect continuity of supply, with more emphasis being placed on important networks. In the distribution, and lower-voltage networks, ‘rules of thumb’ are employed in accordance with the consumer category and investment constraints mentioned earlier.
10.3.2
Supply design standards
Supply design standards are a step forward from the empirical approach, where the amount of past experience, performance, economical limitations and individual sep- arate rules are reduced to a set of detailed guidelines for utilisation by planners to reliably design the system.
In generation, this involves a LOLE target, which stipulates that in any year the probability of capacity shortage should not exceed a certain value; usually a fraction of a day. Correspondingly, plans are drawn out in advance for the generation system strengthening so that LOLE would not exceed a certain standard. In the network, consumer groups and supply areas are classed in accordance with their demand, the minimum number of circuits available, and the target time for restoration of supply is specified. For interruption duration not to exceed a certain level, the network may need strengthening.
10.3.3
Cost–benefit analysis
Generally, not all cost–benefit analysis of the power system should necessarily involve monetary valuation of the cost of interruption. An increasing amount of work is being undertaken to evaluate the cost of different schemes and the probable amount of interruption. Further engineering judgement is used to choose the right plan, within the constraints mentioned, utilising empirical rules.
A simple actual example commonly encountered is that of choosing the method of protection of rural single feeders (Figure 10.2). Three methods are discussed and costed: expulsion fuses (EF), autoreclose circuit breakers (AR) and AR with automatic-sectionaliser (AS), in the middle of the line. The cost and predicted con- tinuity performance of these schemes when applied to a particular rural network are summarised in Table 10.1.
Cost–benefit engineering judgement can now be applied. The employment of EF with an expenditure of only £500 on network protection will involve 12 000
× EF
AR
AS
5× 100 kVA p.m. transformers
Table 10.1 Rural network protection costs
Scheme Protection Cost Probable cons. h per consumer h per annum
1 Expulsion fuses £500 24 h× 500 cons. = 12 000 24 2 Autoreclose £3500 4 h× 500 = 2000 4 3 Autosectionalise £5500 1× 300 + 4 × 200 = 1100 2.2
Note: probable consumer-hours (cons. h) interrupted per annum are calculated based on experience of annual interruption duration for such networks.
consumer-hours lost and an interruption of 24 h per consumer per annum (plus main network interruptions). An expenditure of £3500 will save 10 000 consumer-hours; an extra £2000 investment can still reduce interruptions by a further 1.8–2.2 h and consumer-hours lost by 900. The problem is which plan to choose? The estimation of interruption length is obtained through experience in operating such systems.
It is doubtful if any system planning will accept scheme 1 in Table 10.1 (except if there is acute capital shortage). The question is whether the extra cost of scheme 3 justifies the expenditure. In a mature supply the engineer will empirically decide that the 4 h are excessive and its reduction to 2.2 h justifies the expenditure.
Proper cost–benefit evaluation involves valuing the social cost of interruption to the consumers over the next 20–30 years, also the cost of the fuses repair, the AR and AS maintenance over the same period, and discounting these costs to their present value. If with scheme 2 the present value of the social cost of interruptions plus the discounted cost of maintenance is higher than £3500, then scheme 3 is chosen. Alternatively, in case of a lower cost, then scheme 2 is adopted. If the cost of interruptions is much higher, then a more reliable supply should be provided through an alternative source. This, of course, necessitates detailed evaluation of the cost to the consumer of aborted energy (curve (B) in Figure 10.1).
One interesting feature of this simple example is how the marginal cost per consumer-hour saved, increased considerably after making the first step, from £0.30 to £2.22. Thus, the dominant feature is the accelerating cost of higher reliability (curve (A) in Figure 10.1).