In scenarios involving parallel transformers with disparate ratings, developing per-unit models requires accommodating off-nominal turns ratios. This situation arises when the selected base voltages are not proportional to the transformer’s voltage ratings. Consider a transformer where the rated voltages are related by the term a. If the chosen voltage bases satisfy a relationship involving term b, term c is defined as the ratio of these bases. This ratio is then substituted into the...

An RC circuit consists of resistance and capacitance, while in an RL circuit, capacitance is replaced by an inductor. RL and RC circuits are first-order differential circuits that store energy. An RC circuit stores energy in the electric field, while an RL circuit stores energy in the magnetic field. When connected to a battery, an RC circuit charges the capacitor, causing the current to decrease from maximum to zero upon being fully charged. This increases the voltage across the capacitor from...

In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.
With a step-up transformer at the source, the voltage is increased, thereby reducing the current in the transmission lines since power loss in...

A clipper circuit is a fundamental wave-shaping device that harnesses the unique properties of diodes to alter and control waveform characteristics. This technology is widely used in electronic devices, especially in television and radar communication systems, where it enhances waveform modulation in both transmitters and receivers.
The operation of a clipper circuit can be exemplified by analyzing a dual-clipper configuration setup that integrates two ideal diodes, each paired with a biasing...

In an ideal transformer, it is assumed that there are no energy losses, and, hence, all the power at the primary winding is transferred to the secondary winding. However, in reality,  the transformers always have some energy losses, and, hence, the output power obtained at the secondary winding is less than the input power at the primary winding due to energy losses.
There are four main reasons for energy losses in transformers.
The first cause can be  the high resistance of the...

Radial systems employ time-delay overcurrent relays to reduce load interruptions. When a fault occurs, the nearest breaker opens first, while upstream breakers remain closed due to longer delay settings. This approach ensures minimal disruption to the rest of the system.
In a radial system with a fault downstream of the third breaker, ideally, only the third breaker will open, isolating the fault and interrupting the load connected beyond it. The second breaker has a longer delay setting,...