Lecture 5- Effective Load Carrying Capability of a Resource

We use the assumed form of H x given in (†):
H x ce pKe Ke
x c ce
1 p Ke
x ce
x ce
c pe 1 p
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1
BASIC IDEA
The shape of the LOLP curve as a function of the total system load indicates that its tail portion may be effectively approximated by an exponential Such an approximation is used to evaluate the effective load carrying capability of an added resource
system load MW
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specified LOLP level
ANNUAL LOLP AS A FUNCTION OF SYSTEM LOAD
R
A L
where A is the total available capacity of the supply resources
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dH x d x K H 0 and H x
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x0
Ke
x
Ke x
x0
8
© 2002 - 2010 George Gross, University of Illinois at Urbana-Champaign, All Rights Reserved.
, i.e., we define
p
with
p
ce
H ce H 0 LOLP base
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LOLP IN TERMS OF RESERVES
We are interested to study H x for an isolated
system up to the limiting value, where
p
c
i
i

p
,
is the peak load
For the annual peak load, we compute the LOLP
which is given by LOLP H 0 Note that as x increases, H x also increases
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H x
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P R A x
9
and express it in terms of H values as
© 2002 - 2010 George Gross, University of Illinois at Urbana-Champaign, All Rights Reserved.
Ke e
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Baidu Nhomakorabea
x
ce
© 2002 - 2010 George Gross, University of Illinois at Urbana-Champaign, All Rights Reserved.
LOLP
base
ce
H x
H x
x
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ADDITION OF A RESOURCE
LOLP IN TERMS OF RESERVES
A loss of load event occurs whenever R 0 and
the LOLP is given by P{ R 0 } The definition of LOLP in terms of the reserves r.v. is given by
We construct the LOLP curve by scaling the
annual peak load and daily peaks by 1 for a
range of values of
In an analogous scaling operation, we construct a
ADDITION OF A RESOURCE
The relationship () holds for all x and in particular, for the value x ce :
H x ce pH x c ce 1 p H x ce
LOLP
base
P R 0
We define the general distribution function
H x P R x ,
where, the dummy variable x describes the
system reserves
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probability existing system base case existing system + resource mix change load increment that the system may carry at the specified reliability level
H x pH x c 1 p H x
We interpret H x as the LOLP curve for the
()
modified base case system with the addition of a
resource with capacity c and F.O.R. 1 p
We denote the base case LOLP by LOLP base We define the term ce to be the amount of load increment above
p
for which the modified sys–
base
tem has the value LOLP
Reference: L.L. Garver, “Effective Load Carrying
Capability of Generating Units”, IEEE Transactions
on Power Apparatus and Systems, vol. PAS–85, No. 8,
August 1966, pp. 910–919
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ANNUAL LOLP AS A FUNCTION OF SYSTEM LOAD
LOLP IN TERMS OF RESERVES
We can approximate H x in the neighborhood of x 0 by an exponential
H x Ke x
K , 0
(†)
From curve fitting at 0 , H 0 , we determine
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ADDITION OF A RESOURCE
probability corresponds to peak load p corresponds to peak load p ce
ADDITION OF A RESOURCE
H x P R A x A c P A c A 0 P A 0
P R x


H x P R x c p P R x 1 p Therefore,
second LOLP curve for the base case system
augmented by the change in the resource mix
For the specified LOLP level, we determine the load increment that corresponds to the effective load carrying capability of the resource mix change
ECE 588 – Electricity Resource Planning
5. Effective Load Carrying Capability of a Resource
George Gross
Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign
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RESERVES
Power systems require reserves to provide a cushion for changes in unit availability – forced outages – and to cover errors in the forecasts of the load Planning reserves are defined as the r.v.
ADDITION OF A RESOURCE
Consider the base case system plus a resource
with capacity c whose available capacity r.v. is
c A 0
We define
with probability p with probability 1 p