2004 IEEE International Conference on Electric Utility Deregulation, Restructuring and Power Technologies (DWT2004) April 2004 Hong

Kong

A new method for Real and Reactive power

Loss Allocation in Bilateral Markets
K. L. Lo, Fellow, IEE, and Y . A. Al-Turki, Student Member, IEEE

Abstract-- In electricity markets, every user must be Loss allocation methods that have been proposed so far
responsible for the system losses he causes. Developing a fair fall into five categories: pro rata, marginal loss,
loss allocation scheme for real and reactive power is proportional sharing circuit- based, and different
significant to avoid cross subsidies and to give correct approaches for bilateral contracts [l], [2] and [3]. A short
economic signals to market participants. This paper
introduces a new method for determining real and reactive description of the first four categories is next.
power loss allocations in bilateral contracts. The basic idea of Pro rata method is one of the most common techniques.
the method assumes that each transaction has its own effect It is based on generators injections or load real power
on the system plus its interactive effect with other level rather than on their relative locations in the network.
transactions. Each transaction share of losses is based on its In other words, loads close to the “centre of gravity” of the
contribution on the system currents flows. A method is generation subsidies remote loads and generators close to
proposed to determine these currents contributions which
need to be adjusted, due to the nonlinearity of the system, “centre of gravity” of the loads subsidies remote
using the introduced Current Adjustment Factors (CAFs). generators.
Unlike other approaches, our method can be applied Marginal loss method is based on incremental
effectively to allocate both real and reactive power losses transmission loss (ITL) coefficients. This method depends
simultaneously, which saves time and effort. It is extremely on the location of the slack bus, so, different slack bus will
easy to understand and to be implemented. Furthermore, it give different ITL’s. This method needs normalization
can determine each transaction contribution to every branch
on the system, which is helpful in congestion management. since it results in over recovery. The ITL coefficients can
Results illustrate the consistency of the method with expected be positive or negative. The negative ones can be
results. Reliability and quality of supply are out of the scope interpreted as cross subsidies [4]. Unsubsidized ITL (U-
of this paper. ITL) approach modifies the ITL method in such a way that
avoids negative losses [l]. Distributed slack bus is
Index Terms- ancillary services, loss allocation, power proposed in [3].
markets, reactive power pricing.
Proportional sharing technique [ 5 ] , [6], [7] provides
efficient computational method for loss allocation starting
I. INTRODUCTION
from the output of a converged power flow calculations.
In a Pool-based electricity market, the system operator However, it only uses first Kirrchoffs law and it is based
determines the marginal price based on bids submitted by on the proportionality sharing assumption which is neither
generators and customers while in a bilateral contract the provable nor disprovable. Further more, neither loads nor
participants negotiate the price of traded energy and then generators have control on the price they would be
inform the system operator with final commitment. This charged since they do not have any control on how their
process does not take into account the network losses [ 11. power reaches its destination and what that destination is.
Since the power network is not lossless, entities providing Circuit-based loss allocation is proposed in [ 2 ] . The
the network with the required loss must be compensated authors use the network Z-bus matrix without any
for their contribution, normally at the pool marginal price simplifying assumptions. This method is based on a
[2]. The purpose of loss allocation is to assign each user solved power flow and all its computations are based on
of the network its part of the cost of transmission loss the admittance matrix. Z-bus technique can yield negative
based on how much losses the user causes. allocation to reward those participants who contribute to
Network losses cost millions of dollars every year as reduce network losses due to their strategically well
they can count five to ten percent of the total generation in positioned location in the system, which again can be
the system [2]. So, fair allocation of the network loss has interpreted as cross subsidies.
very important impact on all users since its absence causes Unfortunately, transmission losses are nonlinear
cross subsidies and gives wrong indicative signals to function of line flows. This nonlinearity characteristic
network operator and users. A user who causes more makes it impossible to divide system losses to unique
network losses must be charged more while a user who separate parts; each part is uniquely assigned to a
helps to reduce the losses, due to counter flow, must be generator or a load. So, any loss allocation approach has a
rewarded. degree of arbitrariness. Nonetheless, there are
characteristics that a loss allocation scheme must have to
be considered as fair allocation among all participants.

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2004 IEEE International Conference on Electric Utility Deregulation, Restructuring and Power Technologies (DlZPT2004)April 2004 Hong Kong

Any Loss allocation scheme should have most of the

following characteristics:
1 ) Reflects the traded energy amount of each transaction.
2) Takes into consideration the relative location of
participants within a transaction and that for the
transaction as a whole within the network.
3) The sum of all loss allocated terms is equal to the
actual system losses. Then it is fair enough to assign each contributor its
4) Avoids volatility and cross subsidies. share of the losses as follows
5) Easy to understand and implement.
1IAvI-
6) Provides correct economic marginal signals. Rorr,A = I
1
+ /iv
fir
,
+ ? x I& x ISr x
V.4X)2
+ ? x I A ~ x I S ~ x IxR
1 , 7 ,
1IAr)- + l I B r l - IIA\,l- f l l 8 v l ~

11. PROPOSED METHOD MA

In a deregulated system, every user must be responsible (7)

llSK 12 (IBvI'
for the system losses he causes. System losses are due to = I I &+ + 2 x IAT x /ST x + 2 x I AY x I h x IXR
PhTT,
individual users and their interaction with each other llAr12 r ( l 8 r i ' ~ I A V +) I ~I h I ?

which makes loss allocation more difficult. To illustrate

this problem, assume the following branch that carries two
traded transactions; PA and pH In contrast to other methods, this proposed scheme can
be applied effectively to reactive power loss allocation.

Fig. 1. A branch that carries two traded real power flows PA and PB

Real power losses can be easily calculated as follows

More generally, for any system, real and reactive power

loss allocation can be determined through the following
procedure:
where i = current vector From a solved power flow calculations where all
transactions deliver their shares of the market, each
171 = magnetude of generator injects its actual real power share of the
market and each load consumes its whole demand
(base case), calculate all currents in all branches of
But if we try to calculate the power losses due to both the network
of the transactions individually, then
-
Ik=/kx+jIky, k = 1 , 2 ,..., NB (12)
where
(3)
NB = total number of branches
The problem comes from I k X = real part of the complex current

- * PA " E
'Loss (4) I ~ =, imaginary part of the complex current
If we keep tracing 1's of A transaction and those of B With the transaction of interest T~ inactivated, run
transaction. Then power flow program again and calculate resulted
currents in all branches

-Ti Ti Ti
l k = I k x + j Ik,, , k = 1 , 2 ,..., NB, i= 1,2,...,NT
- - ( 1 3)
where I A X , are the real parts of / A and / H where
respectively NT = total number of transactions
- -
/Ay, are the imaginary parts of / A and / E

respectively

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2004 IEEE International Conference on Electric Utility Deregulation, Restructuring and Power Technologies (DRPT2004) April 2004 Hong Kong

4. The contribution of each transaction T I ’ in a branch

is equal to the corresponding current flow difference
between the base case and when T I is inactive;
Rk = the resistance of branch b
-Ti - -Ti
Ik,cont=Ik-lk , k = 1 , 2 ,..., NB , x = the reactance of branch b
1 = 1.2. ..., NT (14) I[: =the real part of I F
5. The nonlinearity of the network due to the interaction
between loads and generators when they are run at the I$ = the imaginary part of I F
same time makes the sum of currents obtained in step
iii does not match those in step ii, i.e. It is worth it to notice here that all loss allocations are
greater than or equal to zero which ensure eliminating any
- NT-Ti
cross subsidies while at the same time the proposed
Ik # 1 Ik,cont , k = 1, 2 ,..., NB ,
i=l scheme does consider counter flow on branches which
1 = I,?, ..., NT (15) can be looked at as how much a transaction utilizes a
branch.
So, the currents in step iii need to be adjusted If a transaction (Ti) wants to increase its traded energy
according to Current Adjustment Factors (CAF’s) as while others are fixed, the marginal allocated loss of each
follows transaction with respect to T, adds up to the whole system
- NT-TI‘ marginal loss;
I k = C A & x , ~ I k , c o n t ,k = l , 2 ,..., N B , i = 1 , 2,..., NT
1=1

(16)
where CAF = Current Adjustment Factors matrix

We notice here two things; the dominant term is that

o f T i , and other transactions allocated losses are affected
too even though they have not been changed. This is due
to interactive effects with each other. For large systems,
one can divide it to smaller zones where all transactions in
CAF is generally a complex matrix which is a zone have negligible effect on other zones.
expected since the nonlinearity of the system is due to
real and imaginary factors interactions. 111. CASE STUDY
6. calculate the new adjusted currents The proposed scheme is applied on a four bus system
for illustration purposes (Fig. 2 ) . There are three
-Ti -Ti transactions on the system; T1 (between generator 1 and
I k . A d j = CAR( ~ l k . c o n t, k = 1, 2 ,..., NB,
load I), T2 (between generator 2 and load 4a) and T3
1 = 12, ..., NT (17) (between generator 3 and load 4b.) T1 and T2 have
7. Calculate the real and reactive power losses allocation fixed traded energy equal to 150 MW and T3
Ti Ti
for each transaction, qossesand Qlosses respectively participation on the market changed from 1 MW to 500
as follows MW. Generators have no restrictions on reactive power
‘ production or consumption.

hag,sum - NT
Ik - I~~,adjusted

Real = NT Ti Tj o a o m 0.OoMM
‘k Ikr,adjusted Ikr, adjusted
i = l i = l Fig. 2 . One-line diagram of the 4- bus system. Transmission
j # i
impedances are equal and given in pu.
2004 IEEE Intemational Conference on Electric Utility Deregulation, Restructuringand Power Technologies (DRPT2004) April 2004 Hong Kong

111. CONCLUSION
Results are plotted over a range of traded energy A new transmission loss allocation method has been
quantities from which we notice the following important proposed and tested. This method has the following
remarks: characteristics:
All loss allocations are greater than or equal to zero It is based on current vectors flowing in branches
which means that no cross subsidies on the system. rather than power injections.
As we see from the plots, no volatility on the scheme. It emphasizes the independent responsibility of each
The loss allocations change smoothly according to the user of the network while preserving the interaction
change of the system conditions based on transactions between all of them.
updates. To overcome the nonlinearity of the system, current
Even though T3 is the one who increases its traded adjustment factors (CAFs) have been proposed.
energy, T I and T2 are affected too. This is due to the It allocates both real and reactive power losses
interaction between the transactions on the network, simultaneously, which is time saving. It also has the
i.e. the charge for using the network. But we should ability to determine loss allocation in each branch to
emphasize that the effect on T1 and T2 is very small each user of the network.
compared to that of T3 (loss allocated to T1 and T2 It does not create cross subsidies within the network,
are almost fixed as shown in fig. 3.) yet it rewards those who contribute to loss reduction
by allocating them smaller losses compared to those
T I has negligible loss allocation compared to the
who contribute to increase losses on a certain branch.
other transactions since the load and the generator are
It is extremely simple and easy to implement.
at the same node which means that our scheme takes
into consideration the relative location of participants. Case study shows that the proposed method is
Since the calculations are based on current flows, consistent with expected results taking into considerations
reactive power loss allocations are similar to those of that every user has its own interaction with all other users
real power except the difference according to the through the cross term. However, we emphasize that
value of transmission lines reactance, which saves every loss allocation scheme is not exact but rather is
time and effort. judged on the basis of reasonable criteria such as those
If we go more deeply, Fig. 4 shows loss allocations of mentioned earlier in section I. Future work will be to
each transaction on each branch. These allocations improve the method to include reliability and quality of
are based on the degree a transaction utilizes the line. supply conditions.
For example, branch 1 is mostly utilized by T2 at low
values of T3 (high current flows from bus 2 to bus 1 Allocated P losses to the transactions
serving T2 while the opposite one helps T3.) Then,
transaction 1
as T3 goes up, it starts to participate on the branch transaction 2
(counter flow resulting in less current flowing on the transaction 3
branch.) That is why T2 loss allocation at this branch
falls meaning that the other transaction should 310
participate. When the transactions utilize the branch
equally, i.e. current from bus 2 to 1 equals that from ,
bus 1 to 2 (zero flow), both loss allocations should be _ _ _ *<a--
r _ _ - - - - - - -

-'-,
equal to zero and this happens when T3 output is 0
0 100 200 300 400 500
about 508 MW, as we can see from fig.2. If T3 T3 Traded energy (MW)
continues to increase, then it will be assigned more Allocated Q losses to the transactions
losses than T2.
Fig. 4 shows the marginal loss allocations to each
transaction as T3 increases. We notice that the
m
marginal loss allocation of T3 is the dominant which 0
reflects the fact that it is the one who increases its
output and, hence, should be allocated losses more
than others.
The scheme allocates T2 its share of the losses even
though generator 2 is the slack generator.
"0 100 200 300 400 500
T3 Traded energy (MW)
Fig. 3. Real and reactive power loss allocation to each transaction (TI
and T2 are fixed.)

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2004 IEEE International Conference on Electric Utility Deregulation, Restructuring and Power Technologies (DRPT2004) April 2004 Hong Kong

Allocated P losses of each transaction on branch 1 Allocated P losses of each transaction on branch 3

transaction 1 transaction 1
g0.3 transaction 2 transaction 2
transaction 3
E 0
- . .
g 0.2 -
v)
\
v)
0
-I \
,0.1 . ’ ,

‘. a
--- --
1
.
- - _- - _ _ :
- - - -_ . _ - _ - - - _ _ _ _

Allocated P losses of each transaction on branch 2

.-0 transaction 2
transaction 3
‘1
,
,
;
’

1
m

_ c , - -,, /’‘ ,
/

0 .- .- _.-
- 0
_-- - - . - C r

0 100 200 300 400 500 0 100 200 300 400 500
T3 Traded energy (MW) T3 Traded energy (MW)

marginal P losses of each transaction w.r.t. T3

- transaction 1 I transaction 1
transaction 2 transaction 2
transaction 3
lot 0.06
,5 - m

1
8
/ % 0.05
1
8
6- i 0.04 /

i ,
h
0.03 /
a 4-
0
/

2- ,

0 --
_ -’ __
0 100 200 300 400 500 0 100 200 300 400 IO
Traded energy (MW)
T3 T3 Traded energy (MW)
Fig. 4. Real power loss allocations on each branch of the system
(branches I,2, 3, 4, and 5.) and the marginal real power losses of each
transaction with respect to the change of T3.

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