Traditionally, Norwegian hydroelectric power plants have been designed and built to maintain the highest possible levels of continuous power generation with only a limited number of start/stop sequences. However, in recent years many hydroelectric power plants have undergone modifications to their operational procedures resulting in several start/stop sequences and more frequent load changes than previously. This development must of necessity entail increased wear and tear on the plant's engineering components. Few analytical studies have been carried out to investigate what bearing this increased wear and tear has on the plant's engineering lifetime, and the need this creates for increased maintenance resulting in increased costs for the power plant owner.

The report deals with issues related to the specification of start/stop costs for hydroelectric power aggregates in an overall perspective. Instead of employing a detailed technical review of the different hydroelectric power plant components and their wear and tear¬mechanisms, general mathematical approaches are developed based on statistics combined with audit costs and intervals. General methods of this type require few input parameters, and probably provide equally accurate results.

Three major topics are considered:

• Financial methods for describing how start/stop sequences influence a given aggregate's audit intervals, thus resulting in increased operational and maintenance costs. Both theoretical and more practical methods are considered.
• Failure statistics for hydroelectric power aggregates for the period 1987 - 97, for which start/stop sequences were the cause of failure.
• Methods for calculating lost revenues resulting from unplanned operational shutdown (breakdown).

The methods for the calculation of start/stop costs incorporate both average and marginal considerations. If a plant is in the process of evaluating a long-term contract or operational profile which incorporates frequent start/stop sequences, it will be important to be able to calculate the average ¬start/stop costs in order to ensure that costs are budgeted for during the term of the contract. In a short-term market for, for example, regulating power, we will on the contrary be interested in knowing what price we must ask in order to cover the costs linked to a single start/stop sequence. In addition, models simulating short-term production planning processes will be based on marginal start/stop costs.

In general, running costs will increase with the age of the plant as is illustrated in Figure 1. If we assume that the wear and tear incurred as a result of a start/stop sequence is equivalent to a given number of operational hours, this results in an immediate increase in the costs curve as shown in Figure 2. This means that the start cost is dependant on the age of the power plant.

Figure 1: Increased running costs as a function of the age of the plant.

Figure 2: Costs as a function of cumulative time in operation.

Norwegian failure stastistics demonstrate that it is the turbine and generator among the plant's components which exhibit the greatest probablity of failure during the start sequence. As demonstrated in Figure 3, these plant components accounted for 50% and 29% respectively of all failures recorded during the start sequence in the period 1987 - 1997. If we examine "permanent failures" (breakdowns) it is the circuit breaker and generator which exhibit the greatest periods of inactivation totalling 116 and 60 hours respectively.

Figure 3: Reciprocal distribution of failures incurred by different plant components.

The breakdown of an aggregate may result in financial loss firstly because we lose an opportunity to generate power at high prices, and secondly in cases where the reservoir is not large enough to receive the run-off which is produced during the shutdown period. However, the outage of an aggregate also influences other stations within the same drainage basin, such that the entire affected basin must be analysed in order to quantify any costs incurred as a result of a breakdown. Added to this of course will be the repair costs for the damaged equipment. Figur 4 shows an example of the calculated financial consequences resulting from a breakdown during the weeks 6-14 for 60 different run-off years. In some years run-off conditions and reservoir capacity are such that we actually obtain a more favourable result than in the reference scenario.

 
Figure 4: Variations in revenues in the event of total breakdown of a station within a large drainage basin during weeks 6-14 for 60 different run-off years.

The report is prepared as part of a colloboration between SINTEF Energy Research and SINTEF Technology Management.