IEEE Power & Energy Magazine - March/April 2021 - 66

different communication channels ranging from dedicated
platforms to emails and phone calls. It then is the task of
the operational planning team to verify the feasibility of the
received maintenance schedules based on the congestion
forecast and security analysis (at various time scales: year
ahead, week ahead, and day ahead).
In case of anticipated N or N−1 violations, three types
of measures are investigated: topological actions, generation
limiting and redispatch, and maintenance rescheduling. In
the latter case, coordination with the respective asset owner
is required until an alternative solution is found, and then
security analysis needs to be repeated to check the measure's effectiveness. This iterative process is the result of
the sequential coupling between maintenance planning and
congestion management. Notably, if anticipated congestion
can be avoided by either a real-time topological action or
by rescheduling the maintenance of a grid asset, the former
is often preferred due to the complexity in maintenance
rescheduling among several asset owners and their maintenance service providers.
To improve operational efficiency and security of supply,
we envision an integrated approach to optimize the maintenance schedules of a control area's transmission grid assets
while considering possible congested network elements in
system operation as well as the maintenance needs of generation and distribution grid assets. A comprehensive maintenance scheduling tool would comprise maintenance periods
as decision variables for four types of assets: 1) transmission assets of the control area, 2) DSO assets, 3) generation
assets, and 4) transmission assets of neighboring control
areas. Since the specific maintenance requirements of points
2)-4) are not known to the TSO of the given control area,
we propose that DSOs, generation companies, and neighboring TSOs submit a list of preferred maintenance windows
as well as blocking periods when no maintenance work is
possible for their assets.
As indicated in Figure 10, the submission of preferences
can be enabled by a portal that all involved parties can
access. The best maintenance window for each asset is then
determined while ensuring network security in case of contingencies and satisfying the submitted preferences as much
as possible. In this way, the TSO's operational planning team
automatically obtains a maintenance schedule that minimizes the need for remedial actions against grid insecurity.
This is a pragmatic approach placed halfway between today's
industrial practice where generation and distribution asset
owners submit fixed maintenance schedules to the TSO and
idealized academic approaches where generation and transmission assets with distinct ownerships are co-optimized.
Figure 11 presents an illustration of the envisioned approach
for integrated maintenance scheduling and congestion management and contrasts it with today's practice.
From a mathematical point of view, this is a complex
optimization problem due to the presence of integer decision variables (maintenance schedules, topological remedial
66

ieee power & energy magazine

actions, and so on) and various nonlinearities, especially if
an ac power flow model is used to capture voltage violations.
Moreover, it is a large-scale problem due to the hundreds or
thousands of buses and transmission lines and the consideration of many contingency scenarios. Further, as revealed
by the analysis of some historical grid events, it is sometimes important to include models for the distribution grid
in the study, which further increases the problem size. Such
a large-scale, mixed-integer, nonlinear, and nonconvex optimization problem is practically impossible to solve to full
optimality in a reasonable amount of time and with realistic
computational resources. Nevertheless, for practical applications, a good feasible solution that satisfies time and computational constraints would be sufficient.
Various methods have been proposed in the scientific literature to optimize the maintenance scheduling of power grid
generation and transmission assets (in a separated, sequential,
or joint manner). The methods to solve the resulting mixedinteger program can be generally classified into mathematical programming, heuristic approaches, and combinations
of these. Early mathematical programming approaches were
based on dynamic programming that, however, turned out
not to be scalable due to the curse of dimensionality. More
recent approaches rely on branch and bound-based mixedinteger program models often enhanced with decomposition
techniques (mostly Bender's decomposition or Lagrangian relaxation). Such approaches typically use a linearized
dc power flow model, thus resulting in mixed-integer linear
programs. A large variety of heuristics has been applied in
the maintenance scheduling problem, including genetic algorithms, particle swarm optimization, simulated annealing,
cuckoo searches, electro search algorithms, and so on.
We believe that a hybrid approach is needed to efficiently
tackle this problem at scale, which combines elements from
mathematical optimization, heuristic optimization, artificial
intelligence, and customized approximations based on operational experience. An example of a hybrid approach would
be applying first a heuristic to provide a set of initial feasible solutions and then using these to initialize branch and
bound-based algorithms executed in parallel to obtain local
optima in the neighborhood of the initial feasible solutions.
Such an approach would combine the strength of heuristics
in efficiently exploring a vast and nonconvex search space
with the guarantee of mathematical programming to return
locally optimal solutions.
Another possibility would be to use heuristics for the
discrete variables and mathematical programming for the
continuous ones, which could be done either in two steps
or iteratively. For instance, one could use heuristic optimization until the discrete variables converge and then
switch to gradient-based optimization for the remaining
continuous variables. Alternatively, one could decompose
the problem into an outer loop optimizing over the integer maintenance decisions (solved with heuristics) and an
inner loop optimizing over remedial actions [basically, a
march/april 2021
IEEE Power & Energy Magazine - March/April 2021

Table of Contents for the Digital Edition of IEEE Power & Energy Magazine - March/April 2021
