In this section, a number of assumptions are presented and motivated in order to arrive at manageable model formulations for the GMS problem in which the objective is either to minimise the probability of PGU failure or to maximise the system-wide expected energy production. Some of these assumptions are aimed at decreasing the complexity of the problem, thereby making it possible to solve the model efficiently. The model complexity is, however, decreased in such a manner so as not to generate maintenance schedules that are unrealistic or unfit for use in practice.
1. Components of the PGUs. A number of components are required to generate electric power, including boilers, steam turbines and generators. Failure of any one of these components typically causes the power generation process to be interrupted until the component has been repaired or replaced. The combination of all of these components are together referred to as a PGU. Therefore, a failure in one of the components of the PGU typically leads to failure of the entire PGU. For modelling purposes, all the components of a PGU are considered as a whole in the sense that PGU failures are not attributed to any specific components.
2. Frequency of maintenance. A number of different types of planned maintenance procedures may be performed on PGUs, including complete overhauls of PGUs as opposed to mere
routine check-ups. Moreover, PGUs may require planned maintenance more than once over a GMS planning period, especially during long scheduling windows. For the purpose of the models considered in this dissertation, however, it is assumed that only one type of maintenance procedure is performed on the PGUs in a system. It is therefore implicitly assumed that the length of the scheduling window is short enough to justify the assumption that exactly one planned maintenance is required for each PGU during the scheduling window. The duration of planned maintenance may, however, vary from one PGU to another as dictated by the power system scenario.
3. Frequency of failure. A number of different fuel types (i.e. coal, gas or water) are required for power generation in different types of PGUs. The fuel type may influence the failure rates of PGUs. The failure rates may also differ over instances of the same type of PGU. These difference in failure rates of the PGUs may lead to some PGUs failing more often than others, especially during long scheduling windows. For the purpose of the models considered in this dissertation, it is, however, assumed that no PGU will fail more than once during a scheduling window. This assumption is again justified if the scheduling window is not too long.
4. Contiguity of maintenance procedures. In any specific GMS problem instance, the duration of maintenance performed in respect of any given PGU is assumed to be constant. The duration of the maintenance furthermore has to be performed without interruption. That is, when a PGU is scheduled for maintenance, the entire period of maintenance has to be completed during consecutive time periods.
5. Initial conditions. Planned maintenance of PGUs is only scheduled over one scheduling window at a time. It is furthermore assumed that no PGU failure has been observed since completion of the previous maintenance of a PGU up to the end of the previous scheduling window. It is therefore implicitly assumed that at the beginning of the scheduling window, all of the PGUs in the power system are in a working condition.
6. Reliability after maintenance. When maintenance is performed on a PGU, the aim is to increase the reliability of the PGU. This reliability can either be assumed to be increased to “as good as new” or to the level of reliability at which it was operating before performing the last maintenance procedure, as explained in §3.4. In this dissertation, it is assumed that after having performed maintenance on a PGU and placing it back into operation, the PGU starts to operate at 100% reliability.
7. Transmission line maintenance and constraints. The problem of transmission line main- tenance was described in some detail in §2.1.5. The maintenance of transmission lines in a power system typically depends on GMS as maintenance on transmission lines relaying power from a PGU is only possible during periods when maintenance is performed on the PGU in question. The reason for this is that maintenance cannot be performed on transmission lines while these lines are actively used for the transmission of electricity. Therefore, when the PGU providing electricity via a certain transmission line is scheduled for planned maintenance, that transmission line is typically also scheduled for mainte- nance. In the GMS model formulations in this dissertation, however, the focus is on GMS — the scheduling of planned maintenance on transmission lines in the power sys- tem is not taken into account. The transmission constraints concerned with transmission capabilities and the transmission network, as described in §2.2.2, are therefore excluded from the mathematical model formulation in this dissertation.
8. Resources required for maintenance. In a realistic power system, many resources are re- quired to perform planned maintenance on PGUs successfully. These resources include
maintenance personnel and spare parts. A model accommodating constraints on all the required resources for PGU planned maintenance is expected to be very complex. For the purposes of the mathematical model formulations in this dissertation, it is therefore assumed that the only resource required for PGU planned maintenance is the maintenance crew responsible for performing the planned maintenance. This is not an unrealistic as- sumption, since the type of maintenance being scheduled is planned maintenance, which means that it is known beforehand that maintenance of any particular PGU will occur during a certain period within the scheduling window. Provision can therefore be made well in advance of each maintenance event to ensure that the spare parts and maintenance equipment required to perform the maintenance successfully, are indeed available.
9. Varying maintenance crew requirements. The complexity of the model is slightly increased by assuming that the maintenance crew required during each time period of planned maintenance is not necessarily the same. It is assumed that during each time period of planned PGU maintenance, a possibly different number of maintenance crew members may be required in order to successfully complete the planned maintenance. In other words, the number of maintenance crew members required to perform planned maintenance successfully on any particular PGU may vary over the duration of such maintenance. 10. Nature of the generating system. Within the realm of reliability theory, two main types
of systems prevail, namely non-repairable systems and repairable systems, as described in §3.3 and §3.4, respectively. The type of system is typically determined by the trend existing in the failure data. Wang and McDonald [214], however, claim that the components of a PGU “are all repairable.” According to Assumption 1, the PGU is furthermore seen as a whole (that is, separate analyses of individual PGU component failures are not carried out). For this reason, it is assumed that each PGU as a whole is also a repairable system.
11. The failure rates of the PGUs. Wang and McDonald [214] also state that although it is thought that the failure rate functions of the components of a PGU follow a bath-tub curve, as explained in§3.1, these components spend most of their time in the “useful life” phase of this curve, thus exhibiting an approximately constant failure rate which follows an exponential distribution. In this dissertation, PGU reliability incorporated into the GMS objective functions is therefore formulated as an exponential function for a repairable system which is in its “useful life” stage. Under this assumption, it is also safe to assume that only one planned maintenance is to be performed for each PGU during the scheduling window, if this scheduling window is not too long, as explained in Assumption 2.
12. Independence of PGU failures. Failures that occur in a system of PGUs are assumed to be independent of one another. A PGU that is taken out of operation due to a failure is therefore assumed to have little or no effect on the timing of failures of the other PGUs in the power generating system.