The basic equations describing the voltage and current in a single phase are

e(t) = 2E(t) cos[ωt +δ (t)] and

i(t) = 2I (t) cos([ωt +δ (t) +ϕ (t)],

where 2E and 2I represent the peak values of voltage and current, ω is frequency in radians per second, δ (t) is the reference angle in radians, and ϕ (t) is the power factor angle.

The instantaneous power is defined as

P(t) = e(t)i(t) = E(t)I (t) cosϕ (t){1+ cos 2[ωt +δ (t)]}+ E(t)I (t)sinϕ (t){1+ 2[ωt +δ (t)]}

A small change in the value of ω will impact the voltage of the generation and thus the power negatively. A typical voltage and frequency variation during a day is shown in figure.

A slight change in Grid frequency can play havoc in a isolated grid system. Broadly, Off-nominal frequency can impact reliability and markets efficiency in four ways.

1. It could damage equipment (generation, transmission, or load).

2. It could degrade the quality of the product being delivered to end users (too low and lights would flicker unacceptably, for example).

3. It could result in the collapse of the power system itself (by triggering protective system actions, for example).

4. It could result in overloading transmission lines as various generators try to restore system frequency impacting markets efficiency.

A slight change in Grid frequency can play havoc in a isolated grid system. Broadly, Off-nominal frequency can impact reliability and markets efficiency in four ways.

1. It could damage equipment (generation, transmission, or load).

2. It could degrade the quality of the product being delivered to end users (too low and lights would flicker unacceptably, for example).

3. It could result in the collapse of the power system itself (by triggering protective system actions, for example).

4. It could result in overloading transmission lines as various generators try to restore system frequency impacting markets efficiency.

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