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Which sensitivity factors are commonly used, and in which applications do they arise in the planning and operation of electrical power systems?

How is the power transfer distribution factor (PTDF) defined, and how can it be physically interpreted?

Why is the PTDF derived from a DC power flow calculation not exact, and which simplifying assumptions lead to this approximation?

How is the line outage distribution factor (LODF) defined, and how can it be obtained from the PTDF?

What is the purpose of grid reduction in power system analysis? Explain the basic principle using the Ward equivalent.

To what extent does the extended Ward equivalent improve the representation provided by a reduced grid, and why is this extension necessary?

Explain the principle of the REI equivalent and the construction of equivalent networks for short-circuit current calculations.

What role does state estimation play in grid operation? Why is it necessary?

What is the state estimation problem in electrical power systems? How are measurement errors typically modelled?

What are the normal equations, and what is the underlying principle behind their derivation? How are non-linear relationships between nodal voltages and measured variables taken into account?

Give a non-trivial example of a relationship between nodal voltages and measured variables.

What are pseudo-measurements, and what purpose do they serve in state estimation?

How can incorrect measurements be identified in state estimation?

What is meant by an optimised power flow calculation? Give practical examples of the characteristics of the associated mathematical optimisation problem (objective function, decision variables, equality and inequality constraints).

In principle, how can the optimised power flow problem be solved, and what difficulties may arise?

Formulate the problem of economic dispatch as an optimisation problem.

Sketch and interpret the cost function, the incremental cost function, and the unit heat rate of a thermal power plant.

Sketch and interpret the input/output curve, the incremental input/output curve, and the plant efficiency of a hydroelectric power plant.

Explain the solution method for economic dispatch, and in particular discuss the Lagrangian and the equal incremental cost criterion.

How is the solution of the economic dispatch characterised when transmission losses are neglected? How does the solution change when a unit reaches its power limits?

How can transmission losses be taken into account when determining the economic dispatch? What is the significance of the penalty factor?

Describe the unit commitment problem. What is the main difference between this and economic dispatch? Which aspects make it difficult to determine a solution?

Formulate the unit commitment problem as a mathematical optimisation problem and provide examples of objective functions, decision variables, and constraints.

How can transmission power limits be formulated as additional constraints in the unit commitment problem?

What approaches do you know for incorporating uncertainties into unit commitment? Describe the basic ideas underlying common methods.

How can unit commitment be carried out using a priority list? What information is required for this approach?

Explain the idea of dynamic programming for solving the unit commitment optimisation problem. What types of problems can be addressed using this method, and which principle underlies the solution methodology?

Explain the idea of Lagrangian relaxation for solving the unit commitment optimisation problem. What role does the dual problem play in comparison with the primal problem?

How can unit commitment problems be formulated as mixed-integer optimisation problems?

Describe the idea of the branch-and-bound method for solving mixed-integer optimisation problems.

Describe the idea of Benders decomposition for solving linear optimisation problems.