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Modern electrical power utilities must maintain their electrical equipment and replace it when the end of its useful life arrives. The Transmission Maintenance Scheduling (TMS) problem consists in generating an annual maintenance plan for electric power transportation equipment while maintaining the stability of the network and ensuring a continuous power flow for customers. Each year, a list of equipment (power lines, capacitors, transistors, etc.) that needs to be maintained or replaced is available and the goal is to generate an optimal maintenance plan. This paper proposes a constraint-based scheduling approach for solving the TMS problem. The model considers two types of constraints: (1) constraints that can be naturally formalized inside a constraint programming model, and (2) complex constraints that do not have a proper formalization from the field specialists. The latter cannot be integrated inside the model due to their complexity. Their satisfaction is thus verified by a black box tool, which is a simulator that mimics the impact of a maintenance schedule on the real power network. The simulator is based on complex differential power-flow equations. Experiments are carried out at five strategic points of Hydro-Québec power grid infrastructure, and involve more than 200 electrical equipment and 300 withdrawal requests. Results show that the model is able to comply with most of the formalized and unformalized constraints. It also generates maintenance schedules within an execution time of only a few minutes. The generated schedules are similar to the ones proposed by a field specialist and can be used to simulate maintenance programs for the next 10 years.