Dr Jacob Klimstra explains how the proper choice of the number of generating units in a decentralized power plant can help to mitigate the negative impact of downtime.
A 56 MW power plant in Ghana, based on 36 1.56 MW generating units Credit: Rolls-Royce Friedrichshafen |
Decentralized power plants find many interesting applications, such as cogeneration in a hospital, flexible backup for intermittent renewable electricity sources, power supply for chemical process plants or as elements in district heating systems.
There are situations where temporary unavailability of a decentralized generator due to, e.g., maintenance is not a problem. In a greenhouse application, where decentralized generation supplies electricity for assimilation lighting, heat for optimum growth temperature and CO_{2} for fertilization, a stop of a few hours for minor-scale maintenance is not detrimental. A complete overhaul taking a few days might be scheduled at a time when the crop is changed. However, in the case of a major breakdown or a long logistical delay for spare parts, which fortunately happens rarely, unavailability of the generating unit can give rise to high costs.
A local utility often charges high fees for electricity that is only occasionally drawn from the public grid. A hospital that uses its cogeneration installation for emergency power in case of grid failure might need to hire mobile diesel-fuelled generators to ensure its electricity supply when its generating system breaks down.
For cogenerators which have to deliver peaking power that has been contractually agreed, failure to do so might result in substantial fines. This is the reason that some owners of decentralized power plants not only insure the repair costs of a major breakdown, but also the associated costs of not being able to produce output.
The proper choice of the number of generating units in a decentralized power plant can help to mitigate the negative impact of the unavailability of one or more units.
Problems that can cause downtime
The following examples, where owners of a decentralized installation suffered from an incorrect approach in choosing or operating an installation, are fortunately not common practice. They are rather used as illustrations of how things can go wrong.
A tomato grower had decided to install a single 4 MW gas-fired generating unit to cover the heat and electricity needs of his greenhouse. A catalytic exhaust gas cleaning system was used to supply the required CO_{2} to the greenhouse in order to optimize the conditions for maximum growth of his crop.
Unfortunately, no burst disks had been installed in the lengthy exhaust system for preventing damage caused by an explosion. When the ignition system of the installation showed a hiccup at full load, a combustible mixture entered the exhaust system and an explosion occurred that damaged the installation.
Controversies about the cause of the problem and discussions about the nature and costs of preventative measures to avoid damage in future caused a few months of delay before the unit could run again. This resulted in substantial financial losses for the owner.
In another example, a hospital had five identical generating units in parallel while they tried to ensure that all units were making close to the same operating hours. Sometimes, operators have the idea that ensuring that all units in parallel get close to the same amount of running hours is the best strategy.
Due to a design error in the cooling system, a slowly developing fouling of the machines resulted in a major breakdown of all five units within a time span of only a few weeks. Notwithstanding a clever design consisting of multiple units in parallel for optimum output flexibility and redundancy, their cogeneration capacity and emergency power capacity was completely lost. The only option was to hire a number of diesel generators to ensure reliable electricity generation during the repair time. Fortunately, a boiler was available to produce the required heat and steam.
Availability and reliability
A previous article (Issue 2, pp 27-30) discussed the operational availability of power plants. This is the percentage of time over an extended period that a unit is available when scheduled maintenance time and logistical delay of the required spare parts are subtracted from the total time. An operational availability of 97.5% is a good approximation for electricity generators, ranging from reciprocating engine-driven units to large-scale power plants.
Next to the time required for scheduled maintenance, outage can occur due to breakdown of components or nuisance trips from incorrect operator actions or sensor signals. The unavailability caused by such events, commonly called the unreliability, might be the cause of an additional standstill during, on average, 1% of the time. This can mean that a generating unit might experience an event once in its 80,000 hour lifetime that results in an unscheduled stop of one month. It might also mean that the unit has unforeseen stops of 30 minutes roughly twice a month.
A combination of some short events and a few problems of longer duration is of course also possible. Increasing the number of units in parallel can reduce the impact of downtime. The following will show how to determine the consequences of having multiple units in parallel.
Installing a second unit of the same capacity
In a case where, e.g., a nominal electrical output of 10 MW is required at a site, one can accept the consequences of having only one generator and live with the scheduled maintenance intervals and occasional outages caused by a less-than-100% reliability. To mitigate financial risks, the owner can decide to take breakdown insurance as well as loss of production insurance.
In a case, however, where a loss of output from the decentralized unit is unacceptable, one might choose to arrange backup from the utility grid, which has a reliability of 99.99% to 99.999%, depending on the location. Such backup is often not cheap, since the utility has to ensure a supply that occurs maybe only 3% to 4% of the time.
If such an arrangement with the utility is not possible or is too costly, one might decide to install another 10 MW unit in combination with a battery-based uninterruptible power supply. If the running unit fails or requires maintenance, the other unit can immediately be started up and can take over the electricity production. The consequence is that the capital expenditure in local generation will double in this case. However, since the two units have to run only 50% of the time, the combined technical life of the installation will double from, say, 20 years to 40 years.
It is not wise to run both units in parallel at each 50% load, since the fuel efficiency will be low and the maintenance costs per kWh will double.
The question is how much the electricity costs go up when you install a spare generator. The fixed charge rate (FCR) for an estimated discount rate of 6% and 20 years depreciation is 8.7%, while for a 40-year lifetime it is 6.6%. The result of having two installations of 10 MW each instead of one is that the annual capital costs will be 2 • 6.6% = 13.2% of the investment capital of one unit. That is a factor 13.2/8.7 ≈ 1.5 times the cost of having one unit. The costs of the no-break set have not been taken into account here.
The question is, of course, if the installation is really needed for a timespan of 40 years. A public utility might consider such a timespan reasonable, but most private companies have a shorter lifespan.
For an investment price per generator set of €500/kW, the capital costs would be around 0.5 €cent/kWh in case of a single unit and 0.75 €cent/kWh in case of two units. This only applies if the installation can run for the aforementioned 40 years. If the units will only be used for 20 years, having an extra unit will turn the capital costs to 1.0 €cent/kWh.
In case of operation and maintenance costs of 1 €cent/kWh and fuel costs of 5 €cent/kWh, the total cost per kWh would rise from 6.5 €cents/kWh to 6.75 €cent/kWh for the 40-year timespan. Even if both units would be written off in 20 years, the total cost per kWh would only go up from 6.5 € cent/kWh to 7.0 €cent/kWh with two units instead of one. The actual costs of capital, maintenance and fuel depend on the local situation and will even vary over time.
Since maintenance can be carried out on one unit when the other is running, the operational availability will be practically 100%. The probability that an unforeseen problem will occur because of a reliability of 99% is again 1%. This applies for both units.
However, this is only an issue during the time that one of the units is undergoing maintenance. Since the time for maintenance in our example is 2.5% of the time, the time that, on average, no power output is available is only 0.025 • 1 = 0.025% of the time.
Therefore, the supply reliability of electricity where there is one spare unit able to provide the full output is about 99.975%.
Three 5 MW units in parallel
Having three 5 MW units available to fulfil a demand of maximum 10 MW is a cheaper option, and a more flexible one than having two 10 MW units. If all three units are running in parallel and taking an equal share of the load, they will each have an output of 3.33 MW. This might still be acceptable from a fuel efficiency point of view, although the specific maintenance costs in €/kWh will be a factor 5/3.33 = 1.5 higher than when running at full output. We presume here that the investment costs per kW are the same for a 5 MW unit as for a 10 MW unit. With three units running with a reliability of 99% each, the probability P that all three are running can be determined with the so-called product rule (as discussed in part one of this article):
P (all running) = 0.99 • 0.99 • 0.99 = 0.97 or 97%
Therefore, one of the units will not be running due to unreliability at least 3% of the time. This is the logical consequence of having a number of units running. The probability that exactly a certain number of units are running can be calculated with the binomial distribution discovered by the Swiss scientist and mathematician James Bernoulli (1654-1705). This distribution gives the probability that an event will happen exactly m times out of n trials. In case of a power station with n units ready for running with a unit reliability of R, one can write:
where n! = 1 • 2 • 3 • …. • n and 0! = 1.
In case m = n, the distribution equation turns into the simple product rule. Table 1 gives the result of this equation for m ranging from 0 to 3 while n = 3.
Table 1 shows that the probability that at least two units are running equals 0.970299 + 0.029403 = 0.9999707 ≈ 99.997%. That means that, in the case of three 5 MW units in parallel, failure to produce the required 10 MW is 100 – 99.997 = 0.003% of the time. This is, on average, about 16 minutes per year. The probability that at least one unit is running is even much higher, and in that case the available output is still 5 MW. Therefore, this solution of having three units of 5 MW nominal output to produce 10 MW delivers a higher combined reliability than having one spare unit of 10 MW. The total capital will also be lower than investing in two 10 MW units.
However, these three units also need maintenance, which takes about 2.5% of the time per unit. The maintenance can, of course, be carried out sequentially. Therefore, during 3 • 2.5 = 7.5% of the time, only two units will be available. If we follow the reasoning of the three units in parallel for determining the combined reliability of only two units, we would end up with a probability of 0.99 • 0.99 = 0.98 that two units will run during the time that maintenance is carried out. That would temporarily drastically lower the probability to deliver 10 MW, compared with two 10 MW units in parallel. However, the probability of having problems with a machine increases when the moment for maintenance approaches.
The risk of experiencing a problem is also high directly after maintenance actions. The best option is to let an engine run for at least 24 hours after maintenance and then tackle one of the other units. It is also good to use one of the three units as a forerunner with a higher accumulated number of running hours than the others. This machine is then acting as a learning case which facilitates the detection of emerging problems. With such an approach, reliability in the case of two units temporarily in parallel during maintenance is much higher than 98%.
Two 5 MW units in parallel with one 5 MW spare unit
It is also possible to determine whether running two 5 MW units in parallel with one spare 5 MW unit will be viable. This will at least reduce the specific maintenance costs and improve the fuel efficiency.
The previous section showed that having two 5 MW units running in parallel gives a probability of 98% that the two units will run. However, when one fails, the spare unit can be activated. Statistically, this is the same situation as having three units running in parallel. The resulting reliability in producing 10 MW is again 99.997%. One has to bear in mind that if a unit fails, there will be a short timespan required for starting up the spare unit. A no-break set can cover that time if absolutely necessary. If the three units were already running in parallel, as in the previous example, a short hiccup in output will also occur when one of them fails. If one of the three machines fails, the remaining two units have to increase their output and that takes some time. In practice, a good starting reliability is required for the option with two units running in parallel and one standby unit.
In conclusion
If high reliability is required for the output of a decentralized energy plant, opting for a reserve machine offers large improvements. This is especially the case if a dedicated maintenance strategy is chosen, where the unit used for reserve has been properly tested after maintenance actions. A reserve machine does not necessarily have the power capacity to cover the full load. An option of, e.g., three units, where each unit can carry half of the load, is more effective and more economical than having one spare unit that can carry the full load. Having three generating units also offers more flexibility in case of a variable load.
For large installations with a power output in the 100 MW range, multiple units in parallel can be chosen to improve flexibility and output reliability. Having many identical units in parallel also helps to simplify the maintenance process. Further, since the multiple machines use identical spare parts, such parts can be stored locally, thus ensuring that the logistical delay is minimized.
Dr Jacob Klimstra is Managing Editor of Decentralized Energy This article is available on-line. Please visit www.decentralized-energy.com