Name some applications of power flow calculations in the planning and operation of electrical power systems. Which variables are specified as inputs, and which variables are obtained as results?
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How can other important network quantities be calculated from the nodal voltages (nodal currents, nodal powers, branch voltages, branch currents, branch power flows)?
How does the sign of the power depend on the reference system used?
Describe the most important node types used in power flow calculations.
Explain the network equations in admittance form as the starting point of the nodal method for power flow calculation. How is the nodal admittance matrix constructed?
Which conditions must be fulfilled for the system of nodal voltage equations to yield a unique solution for the nodal voltages?
Why is the system of equations for power flow calculations non-linear?
How is the slack node incorporated into the solution of the nodal voltage equations? How can the problem be treated if more than one slack node is present?
Describe the principle of solving a linear system of equations by reformulating it as a fixed-point problem, and illustrate the procedure specifically for the network equations in admittance form using Jacobi method.
Explain the idea of the Gauss–Seidel method for the iterative solution of the network equations. What advantages does it have over the Jacobi method, and how can its convergence be further accelerated?
Do iterative methods always converge? On which factors does convergence depend on?
State the advantages and disadvantages of the nodal method for solving the power flow problem.
Explain the concept of the NR method for power flow calculation and illustrate the power flow using a Π element.
Outline the main steps in the derivation of the Jacobian for power flow calculation. How is the starting value for the next iteration step obtained?
Specify explicitly the Jacobian of a function f in two variables, f(x,y).
What are the convergence properties of the NR method?
How does the NR method differ from the simplified NR method? What are the advantages and disadvantages?
What is the idea of adaptive step-size control in the NR method? Which advantages can result from its use?
Explain the principle of LU decomposition for solving linear systems of equations.
Compare the nodal method and the NR method for solving the power flow equations.
What important conclusions regarding active and reactive power flow in high-voltage networks can be drawn from the power flow equations? Which simplifications are involved?
Describe the method of decoupled power flow calculation. Which simplifications are made, and what are the advantages and disadvantages?
Which additional simplifications lead to the fast decoupled power flow method? What is the main advantage of these simplifications for the iterative calculation of nodal voltages?
What are the assumptions underlying the DC power flow calculation, and in which applications is it used?
Derive the equation system of the DC power flow calculation and name the variables involved.
How is the power transmitted through the branches of the network determined from the solution of the DC power flow?
State possible reasons that can lead to divergence of power flow calculations.
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