Page 48 - Energize May 2022

TECHNICAL

of the reactive power on voltage magnitude in terms of dQ/dV , as
13
it possesses a good linearity in an acceptable range, deriving from
the natural property of the overhead transmission line that the
inductance is far greater than resistance.
By contrast, active power has a negligible impact on the voltage
magnitude, which is the reason that various types of reactive
power suppliers, so-called reactive power compensators (such as
SVC, STATCOM, synchronous condenser and so on), are installed
in the transmission system to supply and stabilise the system
voltage. However, in the distribution system, the relationship
between voltage magnitude and active/reactive power is not as
straightforward as that in the transmission system, because the
cable selected for low and medium voltage systems has a significant
resistance component. Therefore, it is necessary to have not
only a reactive power supplier but also an active power supplier
(distributed energy storage devices) installed in the system properly.
A voltage sensitivity analysis for a distribution system,
particularly for a microgrid, becomes challenging because of the
coupled impact of active and reactive power on bus voltages. In
this paper, four indexes derived from Newton-Raphson power flow
calculation are proposed and used for evaluating the sensitivity of
PQ nodes in the power network.

11
The active and reactive power equations for bus i are computed as :

U 1, U 2, U 3, and U 4 naturally represent the voltage change (both
angle and magnitude) per increment of power (both active
and reactive) not only on the same bus, but also represent
the impacts on other buses. They contain all the information
about system line structure and configuration. However, they
In this equation, P i and Q i are injection active and reactive power are hardly analysed and criticised when the system is large and
of bus i, respectively. V i and V j are the voltage amplitude of bus i complex.
and j, respectively. Y ij represents mutual admittance. G ii and B ii are Therefore, to meet the objective of voltage assessment while
conductance and susceptance components of self-admittance at simplifying the analysis, four voltage sensitivity indexes are defined
bus i. O ij represents the polar angle of self-admittance at branch i to in equations (9 to 12). These indexes are the summation of the
j. δi and δj are the voltage angles at bus i and bus j, respectively. By columns of the inverted Jacobian matrix divided by the number of
differentiating equations (1) and (2) with respect to voltage angles
and magnitudes, the famous Newton-Raphson power flow equation
is obtained in equation (3), where [J] is Jacobian matrix containing
partial derivatives of active power and reactive power with respect
to voltage angles and magnitudes:

Equation (3) is used to solve the power flow in a power system,
while also looking to solve voltage sensitivity analysis increments of
voltage angles and magnitudes. Therefore, a reversed calculation is
proposed in this paper.
The equation is shown in (4), where [U] is defined as inverse
Jacobian matrix. It also has four components, shown in equations
(5 to 8):

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