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www.elspec-ltd.com | December 2014 | SMX-0609-0101
User Manual | EQ-ST | V15
Appendix D: Basic Theory
P
REFACE
In a circuit composed of an alternating power source and a linear load, current and voltage are sinusoidal and the
load is purely resistive (ideal mode only). Pure resistivity means that both waveforms reverse their polarity at the
same time
. The product of voltage and current is positive at every
instant, indicating that the direction of energy flow does not reverse. In this case, only real power is transferred
from the power source to the load.
If loads are purely reactive (ideal mode only), the voltage and current are 90 degrees out of phase. For half of each
network cycle, the product of voltage and current is positive, while for the other half the product is negative. This
indicates that on average exactly the same amount of energy flows toward the load as flows backwards to the
source. Therefore
s no net energy flow over each single cycle and only reactive energy flows meaning there
is no net transfer of energy (to perform work) to the load.
Practical loads are composed of a combination of resistance, inductance, and capacitance, so both real and
reactive power flow to real loads. Power engineers measure apparent power as the magnitude of the vector sum
of real and reactive power. Apparent power is the product of the root-mean-square of voltage and current.
Engineers care about apparent power, because even though the current associated with reactive power does no
work at the load, it heats the wires and by doing so wastes energy. Conductors, transformers and generators
must be sized to carry the total current, not just the current that performs work.
Conventionally, capacitors are considered to generate reactive power and inductors to consume it. If a capacitor
and an inductor are placed in parallel, then the currents flowing through the inductor and the capacitor tend to
cancel rather than add. This is the fundamental mechanism for controlling the power factor in electric power
transmission; capacitors (or inductors) are inserted in a circuit to partially cancel reactive power 'consumed' by
the load.
Engineers use the following terms to describe energy flow in a system (and assign each of them a different unit to
differentiate between them):

Real power (P) or active power: units - Watt [W];

Reactive power (Q): units - Volt Ampere reactive[VAr];

Apparent Power (|S|), that is, the absolute value of complex power S: units - Volts Ampere [VA];

Phase of Voltage waveform Relative to Current
current; Current lagging Voltage (Quadrant I Vector), Current leading voltage (Quadrant IV Vector);
In the diagram below, P is the real power, Q is the reactive power (in this case positive), S is the complex power
and the length of S is the apparent power.
The Active and Reactive power composes the Apparent power in the following form:
S = √P
2
+ Q
2
,
or using complex numbers
S = P + jQ
This form of equation is based on the Pythagorean Theorem and can be illustrated as a Right triangle: