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Power Tracing in a Deregulated Power System : IEEE 14-Bus Case
Satyavir Singh
Indian Institute of Technology, Rookee,India
E-mail: satyavir.sv@gmail.com
Abstract
In this present era , a fair transmission pricing scheme is
an important issue due to incresed deregulation and
restructuring of power sector. In this view, issue of
tracing the flow of electricity has been gain importance
as its solution helps in evaluating a fair and transparent
tariff.An electricity tracing method would make it
possible to charge the generators and/or consumers on
the basis of actual transmission facility used. This paper
focuses on tracing of electricity using Bialek’s tracing
algorithm .Case study is carried out using an IEEE 14-
bus system with three simultaneous bilateral transactions
simulated in Power world simulator.
1. Introduction
Power system operation in many electricity supply
systems worldwide, has been experiencing dramatic
changes due to the on going restructuring of the industry.
The vertically integrated structure of power industry is
being replaced by market structure which led to a
significant increase in power wheeling transactions. In
such a structure a transmission system is being used by
multiple generation and load entities that do not own the
transmission system. In view of market operation it
becomes more important to know the role of individual
generators and loads to transmission lines and power
transfer between individual generators to loads. Basically
there are three methods for power tracing which are
described below [1]:
1.1. Node method
In a meshed transmission network there are number of
possible routes by which electrical power can flow from
sources to sinks. It is possible to determine relation
between the generators/loads and the flows in
transmission lines by means of sensitivity analysis, that is
by determining how a change in nodal
generation/demand influences the flow in a particular line
[2, 3]. Although this method based on dc load flow and
sensitivity analysis cannot consider accurately, the
reactive power transfer allocation and system non
linearity. A novel electricity tracing method has been
proposed [4] which, under the assumption that nodal
inflows are shared proportionally between the nodal
outflows, allows one to trace the flow of electricity in a
meshed network. This method was proposed by J.Bialek
[5] .The complete description of this method for the
tracing of real power is given in section 2.
The characteristics of nodal method are given below:
(i) The transmission losses must be removed from the
lines before the application of the method.
(ii) Matrix calculation is more complex and the speed is a
problem for a big network.
(iii) The method can handle cyclic flows in the system, so
the method is suitable for systems with loop flows.
(iv) If MVAR tracing is required, the method becomes
messy with the introduction of artificial nodes.
In [6] a new method for determining the generator’s
contribution to a particular load is presented. The method
uses the nodal generation distribution factors (NGDF-s).
It features a search algorithm, capable of handling the
active and reactive powers. Paper [7] provides new
insights into the electricity tracing methodology, by
representing the inverted tracing upstream and
downstream distribution matrices in the form of matrix
power series and by applying linear algebra analysis. A
rigorous mathematical proof of the invertibility of the
tracing distribution matrices is given, along with a proof
of convergence for the matrix power series
1.2. Graph method
This method assumes that a generator has the priority to
provide power to the load on the same bus and is based
on the following lemmas of graph theory [8].
Lemma 1: A lossless, finite-nodes power system without
loop flow has at least one pure source, i.e. a generator bus
with all incident lines carrying outflows.
Lemma 2: A lossless, finite-nodes power system without
Satyavir Singh et al ,Int.J.Computer Technology & Applications,Vol 3 (3), 887-894
IJCTA | MAY-JUNE 2012 Available online@www.ijcta.com
887
ISSSN:2229-6093
loop flow has at least one pure sink, i.e. a load bus with
all incident lines carrying inflows. The characteristics of
the graph method are:
(i) The transmission losses must be removed from the
lines before the application of the method.
(ii) Extraction factor, Contribution factor matrices are
sparse and easy to calculate.
(iii) The method cannot handle loop flows, but is able to
detect loop flows.
(iv) A generator has the priority to provide power to the
load on the same bus
1.3. Method of commons
This method was proposed by Kirschen and additional
details of the method can be found in [8, 9]. The
technique can be applied to both active and reactive
power. The principal ideas of the method are presented
below.
(i) The transmission losses can be directly accounted for
and the contributions to them calculated.
(ii) The contribution factors to all the loads inside a
Common as well as the outflows are constant.
(iii) More simple and intuitive for large systems.
(iv) The size and shape of a Common is subjected to
change radically even with a small change in the
direction of line flows.
2. Proportional sharing principle
The proportional sharing principle is based on kirchhoff’s
current law and is topological in nature. It deals with a
general transportation problem and assumes that the
network node is a perfect mixer of incoming flows.
Practically the only requirement for the input data is that
Kirchhoff’s current law must be satisfied for all the nodes
in the network.In this respect the method is equally
applicable to ac as well as dc power flow. Figure1
illustrates the basic principal to trace the flow of
electricity where four lines are connected to bus i two
with inflows and two with out flows.The nodal sum i.e.
total incoming or total outgoing power at node i is equal
to 100 MW. According to proportional sharing principle
The 40MW out flowing in line i-m consists of 40𝑀𝑊
100𝑀𝑊× 10𝑀𝑊 = 4𝑀𝑊
Supplied by line j-i, and
40𝑀𝑊
100𝑀𝑊× 90𝑀𝑊 = 36𝑀𝑊
Supplied by line k-i. In the same way , the 60MW out
flowing in line i-n consists of
Figure 1. proportinal sharing principle
60𝑀𝑊
100𝑀𝑊× 10𝑀𝑊 = 6𝑀𝑊
Supplied by j-i, and
60𝑀𝑊
100𝑀𝑊× 90𝑀𝑊 = 54𝑀𝑊
Supplied by line k-i.
Bialek’s tracing algo is based on the proportional sharing
principle with two tracing algorithms viz upstream and
downstream looking algorithm the description of these
methods are given in section 2.1 and 2.2 respectively.
2.1. Tracing Electricity using upstream looking
algo
The total flow 𝑃𝑖 , the inflow to the 𝑖𝑡ℎbus, is the sum of
all the inflows through the lines connected to the bus and
the local bus injection.
𝑃𝑖 = 𝑃𝑖−𝑗 𝑗ɛℜ + 𝑃𝐺𝑖 𝑓𝑜𝑟 𝑖 = 1,2, … … … . 𝑛 ...(1)
where ℜ is the set of nodes directly supplying node i,
implying power flow towards 𝑖𝑡ℎnode. If the line losses
are neglected, then 𝑃𝑗−𝑖 = 𝑃𝑖−𝑗 . Equation (1) can be
further expanded to become:
𝑃𝑖 = 𝑃𝑗−𝑖
𝑃𝑗𝑃𝑗 𝑗ɛℜ + 𝑃𝐺𝑖 𝑓𝑜𝑟 𝑖 = 1,2, … … … . 𝑛 ...(2)
By defining 𝑐𝑗𝑖 = 𝑃𝑗−𝑖
𝑗 to express relationship between
line flow and the nodal flow at the 𝑗𝑡ℎnode, using
proportional sharing principle 𝑃𝑗−𝑖 = 𝑐𝑗𝑖 𝑃𝑗 , substituting
this in (2) yields:
𝑃𝑖 − 𝐶𝑗𝑖 𝑃𝑗𝑗ɛℜ = 𝑃𝐺𝑖 𝑜𝑟 𝐴𝑢𝑃 = 𝑃𝐺 ...(3)
P is the vector of gross nodal flows; 𝑃𝐺 is the vector of
nodal generations, while 𝐴𝑢 is called the Upstream matrix,
which elements can be generalized as follow:
10MW
90MW
40MW
60MW
i j
k
m
n
Satyavir Singh et al ,Int.J.Computer Technology & Applications,Vol 3 (3), 887-894
IJCTA | MAY-JUNE 2012 Available online@www.ijcta.com
888
ISSSN:2229-6093
𝐴𝑢 𝑖𝑗 =
1 𝑓𝑜𝑟 𝑖 = 𝑗
−𝐶𝑗𝑖 = − 𝑃𝑗−𝑖
𝑃𝑗 𝑓𝑜𝑟 𝑗ɛℜ
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
...(4)
The 𝑖𝑡ℎelement of 𝑃 = 𝐴𝑢−1𝑃𝐺 shows the participation
of the 𝑘𝑡ℎgeneration to the 𝑖𝑡ℎnodal flow and determines
the relative participation of the nodal generations in
meeting a retailer’s demand, given as:
𝑃𝑖 = 𝐴𝑢−1
𝑖𝑘𝑛𝑘=1 𝑃𝐺𝑘 𝑓𝑜𝑟 𝑖 = 1,2, … …… . 𝑛 ...(5)
A line out flow in line j-i from node i can be therefore
calculated using proportional sharing principle ,as
𝑃𝑗−𝑖 =𝑃𝑗−𝑖
𝑃𝑖 𝐴𝑢
−1 𝑖𝑘
𝑛𝑘=1 𝑃𝐺𝑘 𝑓𝑜𝑟 𝑖 = 1,2, … . 𝑛 ...(6)
Finally, load demand at the 𝑖𝑡ℎ bus, applying the
proportional methodology is given by:
𝑃𝐿𝑖 =𝑃𝐿𝑖
𝑃𝑖𝑃𝑖
𝑃𝐿𝑖 =𝑃𝐿𝑖
𝑃𝑖 𝐴𝑢
−1 𝑖𝑘
𝑛𝑘=1 𝑃𝐺𝑘 𝑓𝑜𝑟 𝑖 = 1,2, … … . 𝑛 ...(7)
This equation shows the contribution of the 𝑖𝑡ℎsystem
generator to the 𝑘𝑡ℎ load demand and can be used to trace
where the power of a particular load comes from.
2.2. Tracing Electricity using downstream
looking algo
The total flow 𝑃𝑖 , the outflow to the 𝑖𝑡ℎbus, is the sum of
all the outflows through the lines connected to the bus
and the local bus load
𝑃𝑖 = 𝑃𝑖−𝑙 𝑙ɛ𝜇 + 𝑃𝐿𝑖 𝑓𝑜𝑟 𝑖 = 1,2, … … … . 𝑛 ...(8)
where μ is the set of nodes directly supplied from node i,
implying power flowing from the 𝑖𝑡ℎnode. If the line
losses are neglected, then 𝑃𝑙−𝑖 = 𝑃𝑖−𝑙 .Equation (8) can
be further expanded into:
𝑃𝑖 = 𝑃𝑙−𝑖
𝑃𝑙𝑃𝑙 𝐿ɛ𝜇 + 𝑃𝐿𝑖 𝑓𝑜𝑟 𝑖 = 1,2, … … … . 𝑛 ...(9)
Defining 𝑐𝑙𝑖 = 𝑃𝑙−𝑖
𝑃𝑙 expressing relationship between line
flow and the nodal flow at the 𝑙𝑡ℎ node and using
proportional sharing principle, 𝑃𝑙−𝑖 = 𝑐𝑙𝑖𝑃𝑙 . Substituting
this in (9) yields
𝑃𝑖 − 𝐶𝑙𝑖𝑃𝑙𝑙ɛ𝜇 = 𝑃𝐿𝑖 𝑜𝑟 𝐴𝑑𝑃 = 𝑃𝐿 ...(10)
𝑃 is the vector of net nodal powers; 𝑃𝐿is the vector of
nodal load demands, while 𝐴𝑑 is called the Downstream
matrix, which elements can be generalized as follow:
𝐴𝑑 𝑖𝑙 =
1 𝑓𝑜𝑟 𝑖 = 𝑙
−𝐶𝑙𝑖 = − 𝑃𝑙−𝑖
𝑃𝑙 𝑓𝑜𝑟 𝑙ɛ𝜇
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
...(11)
The 𝑖𝑡ℎelement of 𝑃 = 𝐴𝑑−1𝑃𝐿 shows the distribution of
the 𝑖𝑡ℎnodal power between all the loads in the system.
In summation form,
𝑃𝑖 = 𝐴𝑑−1
𝑖𝑘𝑛𝑘=1 𝑃𝐿𝑘 𝑓𝑜𝑟 𝑖 = 1,2, … … … . 𝑛 ...(12)
The inflow to node i from line i-l can be calculated using
the proportional sharing principle as
𝑃𝑖−𝑙 =𝑃𝑖−𝑙
𝑃𝑖 𝐴𝐷
−1 𝑖𝑘
𝑛𝑘=1 𝑃𝐿𝑘 𝑓𝑜𝑟 𝑖 = 1,2, … . 𝑛 ...(13)
this equation allows to determine how the line flows
supply individual loads.
The generation at a node is also an inflow and can be
calculated using the proportional sharing principle as
𝑃𝐺𝑖 =𝑃𝐺𝑖
𝑃𝑖𝑃𝑖
𝑃𝐺𝑖 =𝑃𝐺𝑖
𝑃𝑖 𝐴𝑑
−1 𝑖𝑘
𝑛𝑘=1 𝑃𝐿𝑘 𝑓𝑜𝑟 𝑖 = 1,2, … … . 𝑛 ...(14)
This equation again shows that the share of the output of
the 𝑖𝑡ℎ generator used to supply the 𝑘𝑡ℎ load demand. The
results obtained in case of equation (7) and equation (14)
are same i.e in case of equation (14) a transpose of table 2
results.
3. Results and discussion
IEEE 14-bus system is simulated in power world
simulator with additional three bilateral transactions
which involve different transaction locations. The detail
of the transactions are as follows:
T1: Injection of 20 MW at bus1 and removal at bus 5;
T2: Injection of 20 MW at bus2 and removal at bus 14;
T3: Injection of 20 MW at bus3 and removal at bus 1;
The transmission network data and load flow results are
given in table 4-7. The proportional sharing
Satyavir Singh et al ,Int.J.Computer Technology & Applications,Vol 3 (3), 887-894
IJCTA | MAY-JUNE 2012 Available online@www.ijcta.com
889
ISSSN:2229-6093
Figure 2. IEEE 14-bus system simulated in power
world simulator
approach has been tested on IEEE 14-bus system using
Matlab simulation program.
Table 1 depicts the contribution of generators to line
flows , 𝑃𝑖𝑗 ,𝑡𝑟𝑎𝑛𝑠 is the power flow in line i-j , 𝑃𝐺𝑖 ,𝐿𝐼𝑁𝐸 is
the contribution of generator Gi(connected to bus i) to the
line flows. The graphical reprentation of table 1 is shown
in figure 3. It can be seen that generator G3 contribute
zero power to the transmission system . The reason
behind it is that the total power of generator G3 is goes to
local load i.e. L3 which can be seen in table 2 and figure
4.Table 3 depicts the contribution of line flows to loads.
Again it can be seen that load L1 is free from
transmission system use. This is due to fact that power is
available locally for this load by generator G1 which can
be seen in figure 4. Results are also verified in table 1,2
and 3 and a slight mismatch is there because of losses in
the system. Proportional sharing of losses can also be
done for more accurate results. .
3.1 Contribution of generators to line flow
Table 1. Contribution of generators to line flows
BUS(i-j) 𝑷𝒊𝒋,𝒕𝒓𝒂𝒏𝒔
𝑷𝑮𝟏,𝑳𝑰𝑵𝑬
𝑷𝑮𝟐,𝑳𝑰𝑵𝑬
𝑷𝑮𝟑,𝑳𝑰𝑵𝑬
1-2 151.0 151.0 0 0
1-5 82.9 82.9 0 0
2-3 67.4 48.2341 19.1659 0
2-4 64.9 46.4450 18.4550 0
2-5 53.0 37.9289 15.0711 0
3-4 -8.7 6.8857 1.8143 0
4-5 -50.4 44.8107 5.5893 0
4-7 35.9 28.4135 7.4865 0
4-9 20.5 16.2250 4.2750 0
5-6 52.7 46.8557 5.8442 0
6-11 7.8 6.9350 0.8650 0
6-12 9.5 8.4465 1.0535 0
6-13 24.3 21.6052 2.6948 0
7-8 0 0 0 0
7-9 35.9 28.4135 7.4865 0
9-10 4.8 3.7990 1.0010 0
9-14 22.2 17.5705 4.6295 0
10-11 -4.2 3.7342 0.4658 0
12-13 3.3 2.9340 0.3660 0
13-14 13.6 12.0918 1.5082 0
Satyavir Singh et al ,Int.J.Computer Technology & Applications,Vol 3 (3), 887-894
IJCTA | MAY-JUNE 2012 Available online@www.ijcta.com
890
ISSSN:2229-6093
Figure 3. Contribution of generators to line flows
3.2 Contribution of generators to load:
Table 2. Contribution of generators to loads
BUS LOAD(MW) 𝑷𝑮𝟏,𝑳𝑶𝑨𝑫(MW)
𝑷𝑮𝟐,𝑳𝑶𝑨𝑫(MW)
𝑷𝑮𝟑,𝑳𝑶𝑨𝑫(MW)
1 20 20 0 0
2 21.7 15.5294 6.1706 0
3 94.2 54.0301 20.5653 19.6046
4 47.8 37.8320 9.9680 0
5 27.6 24.5392 3.0608 0
6 11.2 9.9579 1.2421 0
7 0 0 0 0
8 0 0 0 0
9 29.5 23.3482 6.1518 0
10 9 7.5333 1.4667 0
11 3.5 3.1119 0.3881 0
12 6.1 5.4235 0.6765 0
13 13.5 12.0029 1.4971 0
14 34.9 28.9166 5.9834 0
TOTAL 319 242.2250 57.1704 19.6046
0
20
40
60
80
100
120
140
160
Lin
e 1-
2
Lin
e 1-
5
Lin
e 2-
3
Lin
e 2-
4
Lin
e 2-
5
Lin
e 3-
4
Lin
e 4-
7
Lin
e 4-
9
Lin
e 4-
5
Lin
e 5-
6
Lin
e 6-
11
Lin
e 6-
12
Lin
e 6-
13
Lin
e 7-
8
Lin
e 7-
9
Lin
e 9-
10
Lin
e 9-
14
Lin
e 1
0-1
1
Lin
e 1
2-1
3
Lin
e 1
3-1
4
Lin
e fl
ow
(MW
)
G3
G2
G1
Satyavir Singh et al ,Int.J.Computer Technology & Applications,Vol 3 (3), 887-894
IJCTA | MAY-JUNE 2012 Available online@www.ijcta.com
891
ISSSN:2229-6093
Figure 4. Contribution of generators to loads
3.3. Contribution of line flows to loads
Table 3. Contribution of line flows to loads
LOAD
LINE
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 TOTAL
1-2 0 15.9032 52.9128 25.5469 7.8533 3.1869 0 0 15.7664 3.8696 0.9959 1.7357 3.8413 15.3660 146.978
1-5 0 0 2.5670 13.3996 17.4823 7.0943 0 0 8.2697 3.8517 2.2170 3.8638 8.5511 14.4267 81.7237
2-3 0 0 67.1300 0 0 0 0 0 0 0 0 0 0 0 67.1300
2-4 0 0 5.1730 27.0028 0 0 0 0 16.6649 2.9583 0 0 0 12.2866 64.0856
2-5 0 0 1.6292 8.5045 11.0957 4.5026 0 0 5.2486 2.4446 1.4071 2.4523 5.4272 9.1564 51.8682
3-4 0 0 9.3820 0 0 0 0 0 0 0 0 0 0 0 9.3820
4-7 0 0 0 0 0 0 0 0 18.8677 3.3493 0 0 0 13.9106 36.1276
4-9 0 0 0 0 0 0 0 0 10.6320 1.8874 0 0 0 7.8387 20.3581
4-5 0 0 4.1070 21.0028 0 0 0 0 13.2307 2.3487 0 0 0 9.7547 50.4439
5-6 0 0 0 0 0 11.2000 0 0 0 3.7632 3.5000 6.1000 13.5000 13.1504 51.2136
6-11 0 0 0 0 0 0 0 0 0 3.8212 3.5539 0 0 0 7.3751
6-12 0 0 0 0 0 0 0 0 0 0 0 6.1753 1.6400 1.5976 9.4129
6-13 0 0 0 0 0 0 0 0 0 0 0 0 12.0800 11.7672 23.8472
7-8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7-9 0 0 0 0 0 0 0 0 18.8685 3.3495 0 0 0 13.9112 36.1292
9-10 0 0 0 0 0 0 0 0 0 5.2420 0 0 0 0 5.2420
9-14 0 0 0 0 0 0 0 0 0 0 0 0 0 22.3740 22.3740
10-11 0 0 0 0 0 0 0 0 0 3.7670 0 0 0 0 3.7670
12-13 0 0 0 0 0 0 0 0 0 0 0 0 1.6473 1.6046 3.2519
13-14 0 0 0 0 0 0 0 0 0 0 0 0 0 13.5280 13.5280
0
10
20
30
40
50
60
70
80
90
100
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14Gen
erat
or
con
trib
uti
on
to
load
(MW
)
G3
G2
G1
Satyavir Singh et al ,Int.J.Computer Technology & Applications,Vol 3 (3), 887-894
IJCTA | MAY-JUNE 2012 Available online@www.ijcta.com
892
ISSSN:2229-6093
Figure 5. Contribution of line flows to loads
4. Bus data and load flow results:
Table 4. Line data for the test system
Table5. Load flow result
0
10
20
30
40
50
60
70
80
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14
Line 1-2Line 1-5Line 2-3Line 2-4Line 2-5Line 3-4Line 4-7Line 4-9Line 4-5Line 5-6Line 6-11Line 6-12Line 6-13Line 7-8Line 7-9Line 9-10Line 9-14Line 10-11Line 12-13Line 13-14
Satyavir Singh et al ,Int.J.Computer Technology & Applications,Vol 3 (3), 887-894
IJCTA | MAY-JUNE 2012 Available online@www.ijcta.com
893
ISSSN:2229-6093
Table 6: Transformer data record
Table 7: Power flow results with generator and load data record
Conclusion
In a deregulated environment, generation, transmission
and distribution are independent activities. This
unbundling of the transmission services has resulted in
need to trace the flow of power i.e. to assess the impact of
a particular generator or the load on the power system.
This paper is based on Bialek’s tracing method which
may be applied to both real and reactive power flows.
The results corresponding to the upstream looking
algorithm tabulated in table 1 and 2 allows one to assess:
What amount of power from a generator goes to
a particular transmission line (Table 1).
What amount of power from a generator goes to
a particular load (Table 2).
The results corresponding to the downstream looking
algo tabulated in table 2 and 3 allows one to assess:
What amount of power from a generator goes to
a particular load (Table 2).
The contribution of a particular transmission line
flow to a particular load (Table 3).
References
[1] M. W. Mustafa and H. Shareef, “A Comparison of Electric
Power Tracing Methods Used in Deregulated Power Systems” First International Power and Energy Conference PECon 2006, Putrajaya, Malaysia, November 28-29, 2006, pp. 156-160
[2] Rudnick. H., Palma. R. and Fernandez. J. E., "Marginal
pricing and supplement cost allocation in transmission open
access', IEEE Trans., PWRS-10, (2), 1995, pp. 1125-1142.
[3] NG. W.Y., "Generalized generation distribution factors for
power system security evaluations", IEEE Trans., PAS-100, (3),
1981, pp.1001-1005.
[4] Bialek, J., “Identification of source-sink connections in
transmission networks”. Proceedings of fourth IEE conference
on Power system control and management, London, April 1996,
pp. 200-204.
[5] J. Bialek, "Tracing the flow of electricity," IEE Proc. Gener.
Transm. Distrib. vol. 143. no. 4. Jul 1996, pp. 313- 320.
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ISSSN:2229-6093
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