Introduction to Power System Analysis

Explore phasors by transforming a unit phasor into a 3 V voltage and a 2 A current with a 45-degree lag, then plot time-domain waveforms and express in angle notation.

Investigate rotating phasors of voltage and current, convert unit phasors to arbitrary phasors, apply angle notation, and examine leading and lagging relationships in the time domain.

Explore how instantaneous voltage and current define power, distinguish real from reactive power, and use impedance and phasors to model energy transfer and complex power in resistive, capacitive, inductive systems.

Define real power as the average power dissipated as heat, with voltage and current in phase per the Drude model; compute it with i^2 r and RMS values.

Calculate real power in a purely resistive 200-volt circuit with 3 ohms using phasor analysis. Plot voltage, current, and the instantaneous power waveform, and verify P with I squared r.

Demonstrate real power calculation for a 150 V rms, 2 A purely resistive circuit, yielding 300 W via I squared R with R = 75 Ω, and introduce phasor plots.

Explain capacitance between conductors and how it sets charge per unit voltage, causing current to lead voltage in ac power systems, and define capacitive reactance as 1/(ωC).

Explore inductance and inductive reactance in power systems, showing how changing magnetic flux yields voltage and causes current to lag, with j omega l defining reactance for phasor analysis.

Explore total capacitance to capacitive reactance and calculate the line current for a 100 km overhead line with 7 μf/km, 200 V, 50 Hz.

Define reactive power and show how inductive or capacitive elements cause a 90 degree phase shift; use I squared x for reactive power and I squared R for real power.

Compute reactive power in a purely inductive circuit with 150 V and 2 A, using Q = I^2 X with X = 75 Ω, where current lags by 90 degrees.

Explore how resistance and reactance merge into impedance to define the voltage–current relationship, and how the R–X balance governs phase angle, power factor, and real versus reactive power.

Explore a practical mixed RLC system by converting inductance and capacitance to reactances, computing impedance, and determining the current in polar form using the impedance triangle.

Explain series and shunt configurations in power systems, showing current behavior and formulas P = I^2R, Q = I^2X for series and P = V^2/R, Q = V^2/X for parallel.

Explore how real power and reactive power coexist in mixed power systems by separating resistance and reactance, calculating P and Q, and using the power triangle with apparent power S.

Explore concept of power factor and how real, reactive, and apparent power relate through impedance. Learn how power factor near one minimizes losses and voltage drops in a power system.

Consolidate the source, line, and load impedances into a single impedance, compute the current from Ohm's law, and derive each component's real and reactive power to assess the power factor.

Examine how voltage regulation affects delivery within UK distribution limits, using a phasor diagram to show how resistive, inductive, and capacitive loads change sending and receiving end voltages.

Explore real and reactive power, inductive and capacitive effects, and the lumped element impedance model, linking apparent power and power factor to system losses in mixed power systems.

Explore the economic rationale for three-phase power over single-phase, and learn how three-phase systems use complex impedance, phasors, and Ohm's law to analyze voltage, current, and power.