Environmental Engineering Reference
In-Depth Information
i
AB
v
AB
A
B
Figure A.1
Circuit element
i
AB
R
v
AB
A
B
+-
v
Figure A.2
DC circuit example
equipment found in a power systems network. In the analysis that follows, whenever lower
case letters are used for circuit variables such as voltage, current and power, it will be taken
that these refer to instantaneous values. The voltage
v
AB
describes the potential difference of
terminal A with respect to terminal B at one instant. If the potential of A is higher than that
of B then
v
AB
is positive. It follows that
v
BA
=
v
AB
. Now
i
AB
will be defi ned as the current
that fl ows from A to B
through
the element. If the current transfers positive charge from A
to B then
i
AB
is said to be positive. Again it follows that
i
BA
=
−
i
AB
.
Power in electricity is given by the product of voltage and current. For the element in
Figure A.1 the instantaneous power
p
is given by
−
pvi
=
AB AB
(A.1)
Figure A.1 encapsulates the convention for the reference voltage and current directions in
this simple circuit confi guration which, for obvious reasons, is known as a
one - port
. When
setting up the reference directions in a one-port it is said that one looks into the terminals
AB towards the circuit in question.
If
v
AB
and
i
AB
are both positive then
p
is also positive and the element is a
consumer
or
sink
of electrical power. The truth of this simple convention can be tested by examining the
simple DC circuit of Figure A.2. Here the circuit element is a plain resistor and terminals
AB are connected to a battery of the polarity shown. With this DC
excitation
the instantaneous
quantities are of course the same as the steady state values;
v
AB
and
i
AB
are both positive in
this case and the power
p
associated with the resistor is consumed and irreversibly converted
into heat. Figure A.3 is identical to Figure A.2 but now the battery can be considered as being
the element in the box of Figure A.1. Therefore the terminals AB are looked into downwards
rather than upwards, with the result that current
i
AB
has reversed direction.
