PhD Thesis - Cranfield University

Chapter 5
To enforce and guarantee that the power balance policy (equation 5-8) is always met, an
addition to the policy definition is required. Since the reference power of the ultracapacitors
is determined after the battery reference power, there is a possibility that insufficient
ultracapacitor power levels may causes the power balance equation not to be satisfied. This
occurs at a condition when,
Puc Load
batt
max ( k ) < P ( k ) − P ( k )
(5-24)
Under this condition, the battery power is increased to compensate for the unavailable
ultracapacitor power by altering the predetermined reference battery power such that,
P batt
Load
uc
' ( k ) = P ( k ) − P max ( k )
(5-25)
From a power management point of view, this condition results in a non-ideal situation,
which causes the maximum battery power limit to be exceeded in order to satisfy the power
balance policy. For the purpose of policy evaluation over a period of time, it is possible to
capture this condition and encode it as a penalty tracking function as follows,
Pf PMS = i{
k , P 'batt
, Puc
, PLoad
}
(5-26)
where i is an incremental index with initial value zero and advances by a unit step each time
(5-25) is invoked such that,
⎧i
( k − 1)
+ 1 if Puc
max ( k ) < PLoad
( k ) − Pbatt
( k )
i(
k ) = ⎨
(5-27)
⎩i
( k − 1)
otherwise
Therefore a high value of i results in a high PMS policy penalty count. The invocation of
each penalty point as well as the respective power values is then traceable with reference to
time step k.
147