Sažetak. Unutar vremenskog razdoblja od jedne godine Operator prijenosnog sustava određuje termine u kojima se prijenosni vodovi mogu isključiti iz pogona zbog potrebe za njihovim održavanjem. Za rješavanje predmetnog problema u tržišnim uvjetima u disertaciji je predložen dvorazinski pristup. U problemu gornje razine određuje se optimalan raspored održavanja poštivajući ograničenja sigurnosti prijenosne mreže. Navedeni problem gornje razine ograničen je skupom problema donje razine koji predstavljaju tržište, a time i proizvodnju svake elektrane u sustavu, za svaki vremenski period. Ovakav dvorazinski problem pretvoren je u nelinearni matematički problem s ograničenjima ekvilibrijuma koji se može linearizirati te na taj način riješiti dostupnim računalnim alatima. Sljedeći problem koji je potrebno riješiti je problem određivanja optimalnih termina održavanja agregata. Budući da su agregati u vlasništvu različitih proizvodnih tvrtki potrebno je na transparentan i nediskriminirajući način odrediti optimalne termine njihovog održavanja uzimajući u obzir želje za povećanjem profita proizvodnih tvrtki, ali uz ograničenja sigurnosti sustava. U ovoj je disertaciji za rješavanje predmetnog problema predložen također dvorazinski model koji ima oblik matematičkog problema s ograničenjima ekvilibrijuma. S obzirom da se predmetni problem iteracijski rješava za svaki agregat, cjelokupni problem okarakteriziran je
kao problem ekvilibrijuma s ograničenjima ekvilibrijuma.

Ključne riječi: dvorazinski problem, matematičko programiranje, optimizacija, planiranje održavanja, preventivno održavanje, problemi s ograničenjima ekvilibrijuma, tržišno okruženje.

Summary. Within a yearly horizon, a transmission system operator needs to schedule the maintenance outages of the set of transmission lines due for maintenance. Facing this task, two conflicting objectives arise: on one hand, the system security should be preserved as much as possible, and, on the other hand, market operation should be altered in the least possible manner. To address this scheduling problem, a bilevel
model is proposed whose upper-level problem schedules line maintenance outages seeking maximum system security. This upper-level problem is constrained by a set of lower-level problems that represent the clearing of the market for all the
time periods considered within the yearly planning horizon. This bilevel model is conveniently converted into a nonlinear mathematical program with equilibrium constraints (MPEC) that can be recast as a mixed-integer linear programming problem
solvable with currently available branch-and-cut techniques. After setting the maintenance schedule for transmission lines, the Transmission System Operator needs to set the maintenance schedule for all generators in the power system. Since generators are owned by different power producers, the optimal schedules for generators preventive maintenance has to be transparent and nondiscriminatory. Profit maximization objectives of each power producer have to be taken into account, but constraining these objectives by technical security requirements. To solve this problem, a bilevel mathematical model in the MPEC form is proposed. The upper-level problem contains generating unit scheduling constraints, while the lower-level problem simulates the market clearing process. Since each MPEC corresponds to a single generator maintenance scheduling problem, MPECs for each generator are solved cyclicly in order to achieve equilibrium, making this problem an equilibrium problem with equilibrium constraints (EPEC). The equilibrium, which may or may not exist, is achieved if non of the producers is able to increase its profit by changing the maintenance time periods of its generating units. This is known as the diagonalization procedures which often leads to local optimal point. The characterization of these local optimal points is the important issue of this doctoral thesis.

Key words: bilevel problem, maintenance planning, market environment, mathematical program with equilibrium constraints, mathematical programming, optimization, preventive maintenance.