IEEE Power & Energy Magazine - January/February 2014 - 38

figure 1. A hydroelectric generator. (Image used with
permission from Holyoke Gas and Electric.)

figure 2. A diesel generator set. (Courtesy of Caterpillar.)

figure 3. A single-shaft gas turbine generator set.
(Courtesy of Solar Turbines Incorporated.)

taps on generator step-up transformers and station auxiliary
transformers cannot be changed under load, the selection of
transformer taps must be a balance between the needs of the
black-start period and normal operation, when the power
system is supplying a significant amount of load.
load flow simulations can be used to calculate the
receiving end bus voltage of the transmission lines when the
black-starting unit energizes the unloaded generator step-up
transformer and transmission lines. the charging current
generated by an unloaded transmission line will result in a
rise in voltage along the line. this is particularly true when
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ieee power & energy magazine

underground cables are used as they have significantly more
charging capacitance. the charging requirements can be
large enough to result in the bsUs absorbing reactive power.
there could be, under extreme conditions, the potential for
self-excitation, which is discussed later.
the steady-state analysis of a black-start plan should
include a step-by-step simulation of the plan to verify its
compliance with required operational limits for voltage control and power flows. the robustness of the plan for the loss
of a system component is also valuable knowledge because
the events leading to the blackout could result in some equipment unavailability during the restoration period. generally,
thermal overloads are not a restoration issue because the system is lightly loaded. this may become a concern, however,
as restoration progresses and load is picked up.

Dynamic Studies
once the steady-state analysis has been completed, a dynamic
analysis of the restoration plan is conducted. the dynamic
analysis starts from an initial steady-state operating point
representing a step in the plan. this initial system operating
condition is usually obtained from the system steady-state
analysis. one key simulation initially represents the isolated
power system and then simulates the start-up of the largest
induction motor load at the next-start generating unit. this
verifies that the voltage supply is strong enough to start the
motor and also that the voltage dip will not stall or cause the
motor contactors of running motors to drop out.
the importance of accuracy in equipment modeling must
be emphasized. the effect of the controls of an individual
unit is generally not very significant under normal operation
because a large number of units are sharing the control of
system voltage and frequency. both of these quantities are
controlled solely by the bsU during the initial restoration
period, however. the modeling of the generator, excitation
system, and speed governor is therefore very important. the
modeling of equipment that does not generally operate under
normal conditions, such as over- and under excitation limiters, can also be important. governor modeling must take into
account whether the machine is operated in an isochronous or
droop control mode, as will be discussed later. the accuracy
of the dynamic modeling parameters of any large motors to
be started are also important to motor-starting simulations.
the dynamic analysis of a black-start plan includes some
or all of the following functions:
✔ load frequency control
✔ voltage control
✔ large induction motor starting
✔ motor-starting sequence assessment
✔ self-excitation assessment
✔ system stability
✔ transient overvoltages.
because frequency may deviate significantly from its
nominal value, the effect of frequency variation on system
impedances must be modeled.
january/february 2014

Table of Contents for the Digital Edition of IEEE Power & Energy Magazine - January/February 2014