Considering the power plants long term maintenance, the programmed outag= es must satisfy some (technical) constraints, and quite complex costs struc= ture e.g.

- demand, generation units availability, minimum reserve required by peri= od, risk levels
- man power such as availability for each period, requirements by mainten= ance tasks, sequence, incompatibility
- opportunities such as spot or balancing market prices opportunities, wi= nd or water availability
- possible (ToP, extra costs for anticipating or delay, etc.= ) options in the maintenances contracts with third parts.

Some of these constraints have an inherent uncertainty that should be ta= ken into account, while considering a closed form of the opportunity/cost s= tructure can be very difficult.

The respect of these constraints is a mixed responsibility, in fact we r= emark that in market based systems GenCos a common scheme is: GenCos commun= icate their maintenance schedules (at least of those above a certain size) = and TSO coordinates/approves/requires changes to all of them. The interacti= ons between these two actors have received intensive interest. This interac= tion can also be implemented in an iterative fashion giving birth to comple= x schemes. Iterative coordination methods based on rescheduling signals hav= e been proposed, for instance a coordination procedure where at every itera= tion the TSO indicates permissible and impermissible maximum power for the = maintenance of the generating units in each period. In the same way, other = approaches coordinate the decisions through corrective signals sent by the = TSO to the GenCOs, indicating the maximal capacities that can be in mainten= ance per each geographical area during critical periods. These signals are = calculated according to the responsibility of each GenCo for not supplying = the load. These capacity-based signals can be replaced by penalties and/or = incentive signals. The objective function associated with the GenCO problem= is modified at each iteration to represent the TSO's recommendations. In s= ome models GenCOs that adjust their maintenance plans are paid to (partiall= y) ofset their losses compared to their initial plans; the cost is paid by = the customers.

Lobato [4] shows how to schedule maintenance of single generator given a= deterministic prediction of future prices over 3 years. The generator has = 3 maintenace state variables. Each days operation and start ups accumulates= these variables and maintenace of one of the three must occur before its s= tate varaible reaches a limit. It is important how the plant is operated fr= om day to day (e.g. how many startups there are) affects the when maintenan= ce has to be done. There are times of the year where more profit can be mad= e from a generator (e.g. because prices are high), so there can be a confli= ct between what is optimal in the short term and when is the best time to d= o maintenance.

From an algorithmic point of view these business processes call for the =
use of Benders decomposition-like schemes to take into account the objectiv=
es of the TSO and the GenCOs in the long-term. The GenCOs' objective is cos=
t minimization rather than profit maximization. The master problem deals wi=
th the GenCOs' formulation of the problem, and the reliability checks of th=
e TSO are handled in the subproblems. Feasibility and optimality cuts gener=
ation allows the coordination of the decisions as in the standard Benders' =
general scheme.For instance [7] use =
this approach to design *mobile agent software* to coordinate the ac=
tors. However at the present time we do *not* have evidence that in =
real life TSO and GenCos actually coordinates in such a sophisticated manne=
r.

The complexity of the sole yearly thermal (notably nuclear) power plant = with only min cost goals, can be appreciated for instance taking a look at = the Rodaef contest of 2010 - organized together with Fre= nch GenCo EDF - and related solutions given by participants. In this contes= t very often the algorithmic approaches are based on some sort of problem-s= pecific heuristic or (Benders, Lagrangian or Column Generation) decompositi= on, possibly coupled with constraint or mathematical programming engines. T= he usage of these algorithmic "heavy weapons" somehow gives a = flavor of how complex this problem can be (indeed the posed problem has bee= n proved to be NP-hard).

[1] F. Brandt, "Solving a Large-Scale Energy Management Problem with Var= ied Constraints", Diploma Thesis At the Department of Informatics Institute= of Theoretical Informatics.

[2] Adam Wojciechowski, "On the optimization of opportunistic maintenanc= e activities", Department of Mathematical Sciences, Chalmers University of = Technology Department of Mathematical Sciences, University of Gothenburg SE= -412 96 G=C3=B6teborg, Sweden 2010.

[3] Salvador Perez Canto ,"Using 0/1 mixed integer linear programming to=
solve a reliability-centered problem of power plant preventive maintenance=
scheduling", Optimization and Engineering September 2011,

<= span class=3D"authorPreferredName prefNameLink">Sanchez-Martin, P. <= span class=3D"authorPreferredName prefNameLink">Saiz-Marin, E., "Lon= g Term Maintenance Optimization of CCGT Plants", Power and Energy Engineeri= ng Conference (APPEEC), 2012 Asia-Pacific, 27-29 March 2012, pp 1-4.

[5] Aur=C3=A9lien Froger, Michel Gendreau, Jorge E. Mendoza, Eric Pinson= , Louis Martin Rousseau, "Maintenance Scheduling in the Electricity Industr= y: A Literature Review", CIRRELT 2014 n. 53, October 2014.

[6] K. Dahal, K. Al-Arfa j, and K. Paudyal. Modelling generator maintena= nce scheduling costs in deregulated power markets. European Journal of Oper= ational Research, 240(2):551561, 2015.

[7] X. Xu and M. Kezunovic. Mobile agent software applied in maintenance= scheduling. In Proc. 2001 North American Power Symposium, 2001

Prof. Ken Mc Kinnon, University of Edinburgh