Electrical Engineering

I don't know what kind of transformer you are talking about, but most utility distribution transformers are star connected on the primary side.

It might be different in some other countries, but in the UK, three-phase distribution transformers are always connected in delta on their primary (high voltage) side, and in star (wye) on the secondary (low voltage) side. The primary line voltage is 11 kV, while the secondary line/phase voltages are 400 V and 230 V.

In the United States and Canada, the primary winding is also connected in delta -however, the secondary side is also connected in delta, with one phase centre- tapped to provide the split-phase 240/120 V arrangement.

The reason for using a delta connection is because three-phase high-voltage lines are supplied as three line conductors -there is no provision for a neutral- so there is no practical advantage in having a star-connected primary.

If an AC current is sinusoidal, then the peak value of a current with an RMS value of 2A is 2.8A, or 2A times the square root of 2.

However, very few current waveforms are sinusoidal. In fact, they are often far from sinusoidal - they are more often pulsating - because most power supplies, even switching power supplies, only draw current when the rectifier diodes conduct to recharge the primary filter capacitor. That only occurs once (half wave rectifier) or twice (full wave rectifier) each line cycle.

The square root of 2 rule does apply if the load is purely resistive and the voltage is also sinusoidal. Most voltages are also not sinudoidal, because of the pulsating current issue, and because conductors are not perfect zero impedance conductors. Voltage waveforms, however, are more closely sinudoidal than current waveforms.

The most accurate way to measure the peak current value is to observe it with an oscilloscope. If you want the analytic approach, you need to back calculate from peak value to RMS value, knowing that RMS value is the square root of the sum of the squares of the observations divided by N, as delta T approaches zero, and N approaches infinity. (Best to just use the oscilloscope.)

The power factor of an AC electric power system is defined as the ratio of the real power flowing to the load to the apparent power,[1][2] and is a number between 0 and 1 (frequently expressed as a percentage, e.g. 0.5 pf = 50% pf). Real power is the capacity of the circuit for performing work in a particular time. Apparent power is the product of the current and voltage of the circuit. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power can be greater than the real power.

In an electric power system, a load with low power factor draws more current than a load with a high power factor for the same amount of useful power transferred. The higher currents increase the energy lost in the distribution system, and require larger wires and other equipment. Because of the costs of larger equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial customers where there is a low power factor.

Linear loads with low power factor (such as induction motors) can be corrected with a passive network of capacitors or inductors. Non-linear loads, such as rectifiers, distort the current drawn from the system. In such cases, active or passive power factor correction may be used to counteract the distortion and raise power factor. The devices for correction of power factor may be at a central substation, or spread out over a distribution system, or built into power-consuming equipment.