Notes in Power System Analysis

Power System Analysis

Notes in Power System Analysis consists in three main topics, power flow analysis, fault current calculations, and power systems dynamics and stability. Part I of these notes addresses the initial two items, whilst Part II provides an introduction to dynamics and stability in power systems. The appendices include concise overviews of phase-shifting transformers and power system protections.

The notes begin with a derivation and examination of the models for the most prevalent power system components utilized in power flow analysis. A derivation of the power flow equations built in physical principles is thereafter presented. The resultant non-linear equations pertain to actual power systems of considerable dimension and must be solved numerically.

A summary of the most frequently employed approaches for solving these equations is presented. The significance of power flow analysis in the planning, operation, and evaluation of power systems is examined.

Figure 1 – Five-bus system

The next subject addressed in these lecture notes involves fault current calculations in power systems. A methodical procedure for calculating fault currents in extensive meshed power systems will be developed.

The required models will be given and the underlying assumptions of their derivation will be analyzed. The required models will be provided, and the assumptions behind their formulation will be examined.

In Part II the dynamic behaviour of the power system during and after disturbances (faults) will be studied. The concept of power system stability is defined, and different types of power system instabilities are discussed.

Figure 2 – Schematic description of powers and torques in synchronous machines

While the phenomena in Part I could be studied by algebraic equations, the description of the power system dynamics requires models based on differential equations. These lecture notes provide only a basic introduction to the topics above.

To facilitate for readers who want to get a deeper knowledge of and insight into these problems, bibliographies are given in the text.

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