Power System congestion Management
Using Probabilistic Load Flow
G. Vuc1, C. Barbulescu1, S. Kilyeni1
1Electrical
and Power Engineering Faculty, “Politehnica” University of Timisoara,
Timisoara, Romania, E-mail: gheorghe.vuc@et.upt.ro
In an open access environment, the generation pattern are not certain, the paths of supply
are more diverse, load characteristic become more unpredictable and so congestion
situations tend to be unpredictable with deterministic load flow. A consequence is that in
actual competitive power market the probabilistic load flow analysis can provide better
tools and information for a more efficient congestion management. In this work we use
the probabilistic load flow to investigate by sensitivity of branches power flow – demand
the best congestion management scenario. By this way we can simultaneously exhibit
possible congestions not screened in classical deterministic power load flow (resulting
from demand uncertainty and volatility) and the most appropriate power plants that can
be utilized to solve these congestions. We consider the Monte Carlo simulation generated
in Matlab and interfaced with Powerworld software to solve each deterministic case
corresponding to an individual Monte Carlo set of demand values. Statistical analyses of
obtained results are made with statistical package R. The numerical simulations are made
for the fifty buses TEST50 Power department power system test. Conclusions are
encouraging for extended studies in this direction viewing current trends caused by
increased risks derived from much more uncertainty and volatility on the competitive
market compared with old monopolist market.
1. Introduction
Power system engineers are increasingly concerned with the current state of the global
electricity enterprise and the infrastructure for which it is responsible. Today’s electricity
supply system is aging, under stress, often not well maintained, and being physically used in
ways for which it was not designed. It is no longer sufficient for the engineer to try to
influence the state of the industry by presenting good technical arguments to regulators,
policy-makers and other stakeholders. Engineers must communicate the vision that they
have for an electricity infrastructure which would meet society’s needs for a reliable, secure,
clean and environmentally friendly supply of electric energy.
This stress and overall vulnerability of the electrical infrastructure appears to be growing
due to liberalization of national markets, growing demand and the transactions among the
local and regional systems, resulting in an infrastructure that is more complex and difficult
to manage:
 demand is always growing and although, this growth may be forecast, it cannot be
anytime easily faced (also because the public often contrasts construction of power plants
and transmission lines). Power systems have been developed in the past 50 years so as to
ensure mutual assistance between national subsystems: today’s market development with
its high level of cross-border exchange was out of the scope of the original system design.
 market liberalization involves that multiple operators exchange critical information so as
to jointly operate the system, hence a number of key control systems need drastic reviews
in order to fit to operation in a market context. As the system substantially depends on its
supporting information and communication infrastructure because almost all system vital
functions are remotely controlled, an increased control systems complexity, as in turn
raise system vulnerability, due both to accidental faults and malicious attacks.
The general industry practice for security assessment has been to use a deterministic
approach: the power system is designed and operated to withstand a set of contingencies
referred to as “normal contingencies” selected on the basis that they have a significant
likelihood of occurrence. This is usually referred to as the N-1 criterion because it examines
the behaviour an N-component grid following the loss of any one of its major components.
Load flow analysis is then applied to evaluate the resulting grid conditions.
Power engineers need new instruments developed according to the situations created ready
to analyze the power systems operating conditions. Such an instrument or method is called
probabilistic load flow (PLF), which we are trying to present it in this paper. This new method
of optimal power flow (OPF) can be successfully applied in the case of stochastic power
systems, which are represented by the cases analyzed above and is specially designed for risk
management.
This succinct and partial overview clearly shows that electricity is indeed a very special
case. The new breeze of competition which has blown such high hopes will gradually give
way to the icy winds of reality.
2. Mathematical model
For actual restructured power markets the locational marginal pricing appears as the best
method to deal with the mixture of engineering and financial problems of optimal dispatch
and open access to transmission network. This is done by solving an optimal problem, with
marginal prices as part of solution.
The objective function for such a problem is defined [2] as
(1)
OF   CGi ( PGi )   CCi ( PCi )  CSB ( PSB )   PT  (Sl  Slmax )
in \ SB
in \ SB
ij
i , jn
ij
where, CGi ( PGi ) is the generation hourly cost for bus i, CC ( PC ) is the cost of reducing electric
i
i
power demand for bus i, CSB ( PSB ) is the generation cost for slack bus, and PT (Sl  Slmax ) is
ij
ij
the penalty cost of exceeding the MVA maxim limit of a branch.
The constraints for active and reactive power are

in \ NE
PGi  PNE 

in \ NE
PCi  P
PGimin  PGi  PGimax ;
(1a)
i n
PGi  PCi  U i  Yij  U j  cos( i   i   ij ); i  n
(1b)
(1c)
(1d)
(1e)
(1f)
(1g)
QGi  QCi  U i  Yij  U j  sin( i   i   ij );
(1h)
min
Gi
 QGi  Q
;
i n
min
Ci
 PCi  P
;
i n
min
Ci
 QCi  Q
;
i n
min
i
 Ui  U
;
i n
max
Gi
Q
P
Q
U
max
Ci
max
Ci
max
i
in
in
in
Pl ij  Pl max
ij ;
Pl ij  U i2  YLij  cos Lij  U i  YLij  U j  cos( i   j   Lij )
tlmin  tl  tlmax
(1i)
(1j)
when the load Pci is considered as probabilistic value, the problem become a probabilistic load
flow problem more complex and more difficult to solve. In our work we considered the Monte
Carlo simulation and an interface to Powerworld software to solve each deterministic case
corresponding to Monte Carlo set of demand values.
3. Probabilistic power flow (PPF) study
The load was considered as a probabilistic value with a normal Gauss distribution function:
N ( , )
(2)
with average value μ and standard deviation σ, as aleatory uncertainties, for which is
possible to determine by observations the distribution function type and the characteristic
parameters.
Sources were accepted as non-aleatory uncertainties type and the network structure with
simple contingencies. Our simulation was made with TEST50 buses test power system
having the scheme presented in Fig. 1 [9].
Simulations were made in Powerworld 8, by changing in this view the actual load from
external generated sets of load values. In order to get a much real significance for each
simulation were used 1000 values sets externally generated.
3 2 3 .1 3 7 M VR6 .0 0 0 M W
1 8 4 .0 0 0 M W
9 6 .0 0 0 M VR
S15
2 0 .6 7 4
O2 2 0
2 7 7 .1 7 7
S220
3 0 4 .9 5 4
O4 0 0
4 9 6 .9 6 1
6 8 0 .0 0 0 0 0 0 M W
5 0 0 .2 9 5 8 3 7 M VR
C4 0 0
C1 5
3
3 9 9 .0 5 2
1 5 .6 4 0 8 2 4 kV
8 0 .0 0 0 M W
6 0 .0 0 0 M VR
2 3 1 .1 5 0 1 9 2 kV
G2 2 0
2 2 2 .9 3 3 5 9 4 kV
7 1 .4 8 M W
5 2 .1 8 M VR
14
11
C2 2 0
1 3 5 .4 0 M W
3 0 0 .0 0 0 M W
1 8 5 .0 0 0 M VR
2 3 7 .0 0 0 M W
3 5 .0 0 0 M VR
1 .5 1 M W
2 7 .3 8 M VR
2 2 2 .1 7 5 2 4 7 kV
C1 1 0
2 6 .3 9 M VR
17
1 1 5 .8 8 0 2 1 9 kV
T2 2 0
F2 2 0
13
2 0 5 .2 8 8
J1 1 0
1 1 3 .8 0 1 3 8 4 kV
19
1 7 0 .0 0 0 M W
9 0 .0 0 0 M VR
F1 0
3 2 .0 0 0 M W
1 0 .0 0 0 M VR
4 8 .4 8 M W
3 .3 9 M VR
7 5 .6 M VR
1 1 4 .2 3 1 9 9 5 kV
K1 1 0
20
H2 2 0
2 2 1 .6 6 0 8 4 3 kV
I2 2 0
2 2 0 .8 6 5 7 6 8 kV
15
16
2 2 .0 0 0 M W
4 .0 0 0 M VR
5 0 .0 0 0 0 0 0 M W
1 8 .9 4 1 0 0 0 M VR
M110
24
H1 1 0
23
1 1 4 .1 4 5 6 6 8 kV
I1 1 0
22
5 8 .0 0 0 M W
D1 0
3 3 .0 0 0 M VR
1 0 .3 2 7 kV
4
3 5 .0 0 0 M W
8 .0 0 0 M VR
1 2 .0 0 0 M W
5 .0 0 0 M VR
1 1 5 .7 1 3 8 0 6 kV
D1 1 0
1 1 5 .2 0 3 8 6 5 kV
18
L1 1 0
N1 1 0
1 1 3 .6 2 2 7 3 4 kV
8 3 5 .4 7 9
1 1 3 .9 6 7 2 7 0 kV
21
25
1 2 0 .0 0 0 M W
R4 0 0
3 0 .0 0 0 M VR
2 2 .0 0 0 M VR
1 7 5 .0 0 0 M W
2 0 .0 0 0 M W
1 2 .0 0 0 M VR
E1 1 0
2 4 .0 0 0 M W
1 0 .0 0 0 M VR
1 1 4 .8 4 4 4 6 0 kV
5 3 0 .8 9 M W
4 3 0 .0 0 0 M W
8 0 .0 0 0 M VR
D2 2 0
12
5
2 2 6 .8 0 5 3 8 9 kV
1 0 6 .4 3 M VR
B2 2 0
2 3 7 .4 9 9 4 3 5 kV
10
8
B1 5
1 5 .9 3 7 7 2 0 kV
2 0 .0 0 0 0 0 0 M W
1 0 .6 5 0 0 0 0 M VR
5 3 0 .0 0 0 M W
1 4 0 .0 0 0 M VR
8 .0 0 0 M W
6 .0 0 0 M VR
1 6 9 .0 7 3 3 1 8 M W
-1 8 .2 5 8 0 0 5 M VR
A4 0 0
B4 0 0
3 9 8 .8 4 0 3 6 3 kV
4 0 0 .1 8 5 1 2 0 kV
8 0 .0 0 0 M W
6 0 .0 0 0 M VR
2
1 0 0 .0 0 0 M VR
5 4 0 .0 0 0 M W
9 6 8 .0 0 0 0 0 0 M W
2 4 .7 5 0 0 0 0 kV
3 6 5 .1 4 7 7 3 6 M VR
7 5 .0 0 0 M W
6 0 .0 0 0 M VR
P400
P220
2 3 1 .2 7 0
9
A2 2 0
2 3 1 .8 0 9 2 5 0 kV
1
2 4 .7 5 0 0 kV
Q4 0 0
4 1 3 .7 1 0
7
A2 4
2 4 .0 2 4
P24
8 0 .0 0 0 M W
6 0 .0 0 0 M VR
8 2 5 .0 0 0 M W
4 2 0 .6 1 7 M VR
P15
1 1 1 0 .4 4 3 3 5 9 M W 1 5 6 .0 0 0 M W
4 2 0 .0 2 3 2 8 5 M VR 5 0 .0 0 0 M VR
6 1 1 .2 6 0
V2 2 0
3 3 2 .9 3 0
3 1 1 .5 0 9
Q2 2 0
U2 2 0
2 1 6 .9 5 9
1 3 6 .8 5 9
Y1 1 0
Q1 1 0
1 6 1 .5 2 0
1 5 .6 6 8
1 4 8 .1 4 8
2 5 0 .0 0 0 M W
2 0 0 .6 6 8 M VR
X1 1 0
1 1 4 .2 4 1
V1 1 0
Y1 0
3 1 6 .6 1 9
1 2 .5 9 2
W2 2 0
4 7 .6 M VR
W2 4
3 2 .6 4 1
W1 1 0
1 6 2 .1 2 7
4 0 0 .0 0 0 M W
5 0 .0 0 0 M W
3 0 .0 0 0 M VR
2 3 3 .9 5 6 M VR
1 0 .1 6 0
V1 0
5 .0 0 0 M W
7 0 .0 0 0 M W 3 .0 0 0 M VR
4 4 .5 0 0 M VR
W1 0
1 4 .7 8 2
2 0 .0 0 0 M W
2 1 0 .0 0 0 M W
1 5 .0 0 0 M VR
3 2 4 .7 7 6 M VR
Figure 1: TEST 50 buses test power system.
The results are to be interpreted for each element of test system (branch, generator or
consumer) to establish the behaviour in real market context.
Generators were considered with quadratic cost curves, rel. (3):
C  Pg   A  B  Pg  C  Pg2
(3)
with each curve coefficients presented in Table 1.
Generator
P 7-1 (G1)
P 11-3 (G3)
P 26-27 (G27)
AGC
YES
YES
YES
A
200
300
100
B
20
40
10
C
0.02
0.025
0.01
Table 1: Generators with AGC cost curves coefficients
Only the generators G1, G3 and G27 have the AGC on, so only these generators can be used
to manage the congestion situations.
In our work we considered that during the probabilistic load flow a possible congestion
situation can be identified by the greater average generation cost, which can be also compare
with the deterministic average MW cost, presented in Table 1.
P 7-1 P 11-3 P 26-27 Total gen. Total gen. Average gen.
(G1) (G3) (G27) cost [$/hour] P [MW] cost [$/MW]
-1046.35 -680.0 -825.00
98,093
4,335
22.63
Table 2: Deterministic operating parameters
Among all 1000 simulation cases it were identified as congestion situation 22, other 467
being only suspected of congestion and need further analysis. Some of congestion situations
are showed in Table 3.
P 7-1
P 11-3
P 26-27
Total gen. Total gen. Average gen. Results
(G1) [MW] (G3) [MW] (G27) [MW] cost [$/hour] P [MW] cost [$/MW] analysis
-769.94
-620.15
-892.40
98,103
4,325
22.7
Congestion
-778.78
-628.63
-899.76
99,305
4,346
22.8
Congestion
-756.64
-626.33
-901.80
98,220
4,332
22.7
Congestion
-762.81
-629.52
-894.43
98,522
4,332
22.7
Congestion
-815.47
-605.41
-896.78
99,456
4,355
22.8
Congestion
-765.08
-620.24
-909.24
98,248
4,332
22.7
Congestion
-780.66
-612.42
-900.24
98,262
4,332
22.7
Congestion
-758.39
-622.95
-903.43
97,778
4,312
22.7
Congestion
-841.02
-572.52
-906.20
98,751
4,354
22.7
Congestion
-1068.92 -707.76
-898.14
121,749
4,723
25.8
Analysis
-771.48
-644.56
-902.27
100,204
4,362
23.0
Congestion
-751.16
-635.61
-911.11
98,796
4,342
22.8
Congestion
-787.68
-627.23
-906.30
99,863
4,361
22.9
Congestion
-798.95
-610.03
-908.23
99,317
4,359
22.8
Congestion
Table 3: Possible congestion situations
For the main parameters characterising the probabilistic load flow presented in Table 4, we
identified 22 congestion cases, all being positive solved by redispachting generation in OPF,
and other 467 cases to be futher analysed.
Average:
Standard deviation:
Max:
98,578
7,209
121,749
4,363 22.56
120 1.04
4,723 25.78
Cases:
Congestion
22 2.20%
Need analysis 467 46.70%
OK
511 51.10%
Table 4: Probabilistic load flow characteristics
The above figures show that a large number of cases tend to be out of the 95% confidence
zone. This can be explained by different optimal dispatching for different load demand
combinations. However, for the largest hourly generation cost this is caused by the positive
congestion management (see Table 5).
P 7-1
P 11-3
P 26-27
Total gen. Total gen. Average gen. Results
(G1) [MW] (G3) [MW] (G27) [MW] cost [$/hour] P [MW] cost [$/MW] analysis
-911.13
-486.55
-918.96
97,425
4,362
22.3
-771.48
-644.56
-902.27
100,204
4,362
23.0
Congestion
-973.91
-432.33
-921.36
97,534
4,362
22.4
-938.07
-465.12
-905.89
97,328
4,361
22.3
-787.68
-627.23
-906.30
99,863
4,361
22.9
Congestion
Table 5: Congestion positive management
It can be view that despite of an initial 10% standard deviation rate to mean value proposed
for individual load demand, the total load demand results in only about 3% standard
deviation. However, the hourly generation cost shows a much greater standard deviation.
The conclusion in such cases is that this greater deviation is generated by deviation from
optimal generation cost imposed from congestion management corresponding to individual
cases. This can be view in Table 4 that for almost equal total load demand the hourly
generation cost gets significant different values as consequence of positive management of
congestion situations.
Figure 2: Relation between 15 -10 branch power flow and the adiacent active demand
The most likely congestion situation is for the 15 – 10 branch. In competitive market it is
possible to solve a congestion situation also by consumer contribution. A solution is need only
when the positive management by generators redispatching is not possible. In our simulation we
found that all congestion situations could be solve only by generators contribution. Anyway the
Figure 2 shows that only a diminish of demand in bus 14 and / or an increase of bus 13 demand
can contribute to solve a congestion situation on 15 – 10 branch.
Figure 3: Mean / Error evolution for generator G1 versus branch 15 – 10 power flow
For the most likely congestion situation on the 15 – 10 branch we see that a positive
management by redispatching generators it is not possible without generator G1
contribution. It can be seen in Figure 3 a relation between 15 – 10 branch power flow and
generator G1 active power. It can be see that a major influence of G1 active power appears
in vicinity of extremes and have a variable influence depending on the demand change
distribution on the network reflected by Monte Carlo simulation. Further investigation is
needed to catch this in an algorithm for intelligent scenario of congestion management.
4. Conclusion
Our work shows that are possible for really possible deviation from deterministic
representation of load demand to get unexpected congestion situations that are not showed
by a classical power flow analysis.
The relations established by numerous (1000 to 5000) cases considered for the Monte Carlos
simulation can show much more information for an intelligent management scenario in
congestion situations.
For the numeric simulations realised we can conclude that the TEST50 system test can
manage positive all the congestions that appears in our simulation, the penalty term of
objective function (1) being 0 in all cases, in presence of significant values of dispatching
term of objective function.
This work shows that probabilistic power flow can be a more useful tool in congestion
management for actual competitive power market environment. In addition, we can
conclude that more investigation in this direction is needed.
The competitive market, with much more uncertainties than the monopolistic market,
imposes a more elaborated analysis for power flow studies and the most important factor
must be the more volatile characteristic of demand. In an open access environment, the
generation pattern are not certain, the paths of supply are more diverse and future load
characteristic become more unpredictable and congestion situations tend to be unpredictable
with deterministic load flow.
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