TEL507 — Electric Power Systems Engineering: Lecture Note

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This is the complete lecture note for TEL507 Electric Power Systems Engineering. You can read it online below, open it in the full viewer, or download the PDF for offline study. It pairs with the course's video lectures, so you can read and watch together.

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Course code: TEL 507 Course title: Electric Power Systems Engineering Course credit load: 2 Units Series 1: Modeling of Power System Components • Part 1.1: Basic Single-Phase Modeling of Power System Elements o Sub Part 1.1.1: Single-Phase Representation and the Per-Unit System o Sub Part 1.1.2: Generator and Load Modeling o Sub Part 1.1.3: The One-Line Diagram • Part 1.2: Three-Phase System Analysis o Sub Part 1.2.1: Balanced Three-Phase Systems and Symmetrical Components o Sub Part 1.2.2: Per-Phase Equivalent Circuit Analysis o Sub Part 1.2.3: Power in Three-Phase Systems • Part 1.3: Three-Phase Models of Transmission Lines and Transformers o Sub Part 1.3.1: Transmission Line Parameters and the Line Model o Sub Part 1.3.2: Three-Phase Transformer Connections and Modeling o Sub Part 1.3.3: Per-Unit Representation of Transformers • Part 1.4: Formation of the System Admittance Matrix o Sub Part 1.4.1: Building the Bus Admittance (Ybus) Matrix o Sub Part 1.4.2: Incorporating Transformers and Lines into Ybus o Sub Part 1.4.3: Properties and Applications of the Ybus Matrix Introduction Every power system, however large or complex, is ultimately built up from a small set of recurring components: generators, transformers, transmission lines, and loads. Before any meaningful analysis of a network's behaviour can begin, each of these components must first be

reduced to a workable mathematical model, and the entire network expressed on a common, consistent basis. This Series opens the course by establishing exactly that foundation, starting from the single-phase representation of a balanced system and building steadily towards the compact matrix form in which modern power system studies are actually carried out. The aim of this Series is to equip you with the ability to model individual power system components on a per-unit basis, analyse balanced three-phase networks using their single-phase equivalents, represent transmission lines and transformers in three-phase form, and assemble these individual models into the system-wide bus admittance matrix that underpins load flow and fault studies later in this course. We shall commence this Series by examining basic single-phase modeling and the per-unit system. Next, we will consider the analysis of balanced three-phase systems using per-phase equivalent circuits. Following that, we will examine the three-phase modeling of transmission lines and transformers. Finally, we will conclude this Series by showing how these individual component models are assembled into the system admittance matrix. Series Learning Outcomes Upon completing this Series, you should be able to: • SLO 1.1: describe the per-unit system and the single-phase representation of power system elements, • SLO 1.2: model generators, loads, and the one-line diagram of a power system, • SLO 1.3: analyse balanced three-phase systems using per-phase equivalent circuits, • SLO 1.4: calculate real and reactive power in a balanced three-phase system, • SLO 1.5: represent transmission lines and three-phase transformer connections, • SLO 1.6: apply per-unit representation to transformer modeling, • SLO 1.7: construct the bus admittance (Ybus) matrix of a power system, • SLO 1.8: explain the properties and applications of the Ybus matrix, 1.1 Basic Single-Phase Modeling of Power System Elements 1.1.1 Single-Phase Representation and the Per-Unit System The per-unit system expresses every quantity in a power network, voltage, current, power, and impedance alike, as a fraction of a chosen reference or base value, rather than in ordinary volts,

amperes, watts, and ohms. A base megavolt-ampere, common to the whole system, and a base kilovolt, chosen separately for each voltage level, together fix a base current and a base impedance for that level, so that any actual quantity divided by its corresponding base yields a dimensionless per-unit value that can be compared directly with quantities from an entirely different part of the network. This approach matters because a real power system links generators, transformers, and loads rated at widely different voltages and capacities, and comparing their impedances in ohms directly would be almost meaningless. Working in per-unit removes transformer turns ratios from the calculation entirely when base voltages on each side of a transformer are chosen in the same ratio as its own turns ratio, and it keeps typical per-unit impedance values clustered in a narrow, easily recognisable range regardless of the equipment's actual physical size. Worked example: A transformer rated at 20 kV with an actual reactance of 4 ohms, referred to a base impedance of 20 ohms at that voltage level, has a per-unit reactance of 4 divided by 20, or 0.20 per unit. Application: Per-unit modeling is applied to every generator, transformer, and line in this course from this Series onward, so a consistent choice of system base MVA is established before any component is modeled. Fill in the blank: A quantity's per-unit value is obtained by dividing its actual value by the corresponding ________ value. 1.1.2 Generator and Load Modeling For most steady-state power system studies, a synchronous generator is modeled as a constant internal electromotive force, commonly labelled E, in series with the machine's synchronous reactance, an approximation that holds well for balanced, steady operating conditions and greatly simplifies network calculations by replacing a physically complex rotating machine with a single voltage source and a single series reactance. A power system load may be represented in more than one way depending on the study being performed: as a constant power demand, drawing fixed real and reactive power regardless of the bus voltage, which suits load flow studies where voltage varies only modestly, or as a constant impedance, whose current and power vary directly with voltage, a representation more common in stability and fault studies where voltage can swing considerably during the disturbance. Worked example: A generator delivering rated output is represented as an internal EMF E behind its synchronous reactance Xs, feeding the system bus through that reactance alone. Application: Choosing constant-power load modeling for a routine load flow study, rather than constant-impedance modeling, is a standard simplification used throughout this course unless a study specifically requires otherwise.

Fill in the blank: For most steady-state studies, a synchronous generator is modeled as a constant ________ behind its synchronous reactance. 1.1.3 The One-Line Diagram A one-line diagram represents a complete balanced three-phase power system using a single line and a set of standard symbols, one symbol each for generators, transformers, transmission lines, circuit breakers, and loads, since all three phases of a balanced system behave identically and repeating the same information three times would add clutter without adding useful information for planning or analysis purposes. Beyond the basic connections between components, a one-line diagram typically also records each item's rating: generator MVA and voltage, transformer MVA and voltage ratio, and line length or impedance, information that is drawn directly from the diagram when the per-unit model of each component is subsequently built, making the one-line diagram the essential starting point for every power system study that follows in this course. Worked example: A simple generating plant's one-line diagram shows a generator symbol connected through a step-up transformer symbol to a transmission line symbol leading to a distant substation bus. Application: Building the per-unit model of a network always begins by reading the ratings recorded on its one-line diagram, so accurate interpretation of this diagram is a prerequisite for every later calculation in this course. Fill in the blank: A ________ diagram represents a balanced three-phase power system using a single line and standard symbols. Figure 1.1: One-line diagram of a simple generation and transmission arrangement.

Pilot questions 1.1 1. Explain the purpose of the per-unit system in power system analysis. (Linked to SLO 1.1) 2. Describe how a synchronous generator is modeled for steady-state analysis. (Linked to SLO 1.2) 3. Distinguish between constant-power and constant-impedance load modeling. (Linked to SLO 1.2) 4. Explain why a one-line diagram uses a single line to represent a three-phase system. (Linked to SLO 1.2) 5. List the component ratings typically recorded on a one-line diagram. (Linked to SLO 1.2) 1.2 Three-Phase System Analysis 1.2.1 Balanced Three-Phase Systems and Symmetrical Components A balanced three-phase system carries three voltages, or currents, of equal magnitude, each displaced from the next by exactly one hundred and twenty electrical degrees, a symmetry that arises naturally from the physical construction of a three-phase generator and that, once established, allows the whole system's behaviour to be deduced from a single representative phase rather than requiring all three to be tracked separately throughout every calculation. When a fault or an unequal loading disturbs this symmetry, the resulting unbalanced set of phasors can still be analysed by decomposing it into three balanced sets, known as symmetrical components: a positive-sequence set matching the normal balanced rotation, a negative-sequence set of opposite rotation, and a zero-sequence set in which all three phasors align, a technique introduced here in outline and developed more fully when this course later examines fault analysis. Worked example: A balanced three-phase voltage set of 11 kV line-to-line has each phase voltage displaced 120 degrees from the next, with identical magnitude across all three phases. Application: Recognising that a system is balanced is the first step in every three-phase analysis in this course, since it justifies reducing the problem

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