Panida Boonyaritdachochai
Power Quality and Energy Efficiency Engineer
28th September 2010
Power Quality (Thailand) Ltd., Co.
52/44 Moo. 1, Ramkhamhaeng Rd., Soi 90, Sapansoong,
Bangkok 10240, Thailand
1

Introduction

Objectives

Methodology


Generator Indicator for Congestion Management

Objective Function

PSO Schemes (CPSO, PSO-TVIW and PSO-TVAC)
Numerical Results
2
Introduction
 Congestion is the overloading in transmission lines. It could be caused
by
 unexpected outages of generation
 sudden increase of load
 tripping of transmission lines
 failure of other equipment
 The SO is responsible for determining the necessary actions to ensure
that no violations of the grid constraints occur.
 Transmission congestion can cause additional outages, increase the
electricity prices in some regions and can threaten system security and
reliability.
 The cost to relieve congestion can increase to a level that could present
a barrier in electricity trading
3
Introduction (Cont.)
 Network overloading can be relieved by different control:
 power generation rescheduling
 operation of FACTS controllers
 line switching
 load shedding
The power transferring should satisfy customer requirement with lowest
cost while solve the congestion problems.
 The installation of equipment should not be first choice for the SO to
deal with congestion problems.
 Therefore the power redispatching approach is significant as the prior
approach for congestion management.
4
Introduction (Cont.)
Indicator techniques of the sensitivity factor are discussed
 Generator sensitivity (GS) technique proposes in [1] for optimum
selection of participating generators.
 [2], [3] and [4] introduce transmission congestion distribution factors
(TCDFs).
 In [5] presents technique based on sensitivity of current flow to
congested line.
[6] and [7] have proved that PSO is the best optimizer among GA, NN and EP.
PSO is appropriate for complex problems as defined in [8] which is due to:
 discontinuities
 higher order nonlinearities
 prohibit operating zone
 ramprate limits of generators
 PSO is increasingly gaining acceptance for solving a variety of power
system problems as in [9] due to simplicity, superior convergence, high
solution quality.
5
 To propose active power redispatching to alleviate the overload in
transmission system by optimal generators.
 The optimal generators are indicated by generator sensitivity (GS)
technique. Its aim is to find the most effective participating generators in
congestion management.
 The minimum adjustment cost and real power redispatching are
considered in the problem formulation.
 To explore the ability of PSO-TVAC compared with PSO-TVIW and
CPSO
6
I.
Generator Sensitivity (GS)
GS gij

ΔPij
ΔPGg
Pij θi
Pji θ j


θi PGg
θ j PGg
Pij   Vi 2Gij  ViV j Gij cos(θi  θ j )  ViV j Bij sin (θi  θ j )
Δθ   H 1 ΔP 
n1
Let;
M H1
M 
n n
=
0


0



0


n n
0
θ 2
P2

θ n
P2



(2)
(3)
n1

(1)



θ 2 
Pn 
 
θ n 

Pn 

0
(4)
n n
7
II.
Objective Function for Congestion Management
Minim ize C g ΔPg ΔPg
Ng
(5)
g
Subjected to
ΔPg
min
ΔPg
 ΔPg  ΔPg
min
Ng
 ΔP
g 1
Ng

g 1
g
max
 Pg  Pgmin
;g  1,2,,Ng
(6)
and ΔPg max  Pgmax - Pg
0



  GS ij  ΔPg   Fl0  Flmax
g 


(7)
;l  1,2, ,nl
(8)
8
III. Particle Swarm Optimization (PSO) Schemes
Figure 1: bird flocking and Fish schooling
The position and velocity of the p particle in d dimensions can be expressed as
X p  x p1,xp 2 ,,xpd 
and

V p  v p1,v p 2 , ,v pd

 The best previous position of a particle is recorded and represented as
pbestp   p p1 ,pp2 ,,ppd 
If the g particle is the best among all particles in the group, it is presented as
gbestg  g g1,gg2 ,,ggd 
9
A.
Classical Particle Swarm Optimization (CPSO)
vkpd1  w vkpd  c1  rand1   pbestpd  x pd  c2  rand2  gbestgd  x pd  (9)
B.
Particle Swarm Optimization with Time-Varying Inertia Weight (PSO-TVIW)


vkpd1  C w vkpd  c1  rand1   pbestpd  x pd  c2  rand2  gbestgd  x pd  (10)
Where;
C.
C
2
2      4
2
, where 4.1    4.2
and
w  wmax  wmin 
kmax
 k
k max
 wmin
Particle Swarm Optimization with Time-Varying Acceleration Coefficients
(PSO-TVAC)
c1  c1f  c1i 
k
k max
 c1i
and
c2  c2f  c2i 
k
k max
 c2i
10
x kpd1  x pd  v kpd1
(11)
Table 1: Parameters of PSO.
11
Figure 2: Flowchart of congestion management by PSO-TVAC.
12
Figure 3: IEEE 30-bus system.
Table 2: Congested line in IEEE 30-bus system.
Congested Line
Real Power Flow (MW)
Line Limit (MVA)
Over the Limit (MW)
1 to 2
170
130
40
13
Table 3: Solutions by PSO schemes
in IEEE 30-bus system.
GS
CPSO
PSOTVIW
PSOTVAC
ΔP1 (MW)
0.0000
-55.9
-50.13
-49.25
ΔP2 (MW)
-0.8908
22.6
18.88
17.51
ΔP5 (MW)
-0.8527
16.2
13.21
14.02
ΔP8 (MW)
-0.7394
10.5
9.15
9.88
ΔP11 (MW)
-0.7258
5.6
5.87
6.8
ΔP13 (MW)
-0.6869
2.6
4.14
3.01
Total power
redispatch (MW)
113.2
101.4
100.5
Cost ($/hr)
287.1
253.1
247.5
Figure 4: GS values in IEEE 30-bus system.
Figure 5: GS values to power redispatching
in IEEE 30-bus system.
14
Figure 6: IEEE 118-bus system.
Table 4: Congested line in IEEE 118-bus system.
Congested Line
Active Power Flow (MW)
Line Limit (MVA)
Over the Limit (MW)
89 to 90
260
200
60
15
Table 5: GS values of 54 generators
in IEEE 118-bus system.
Gen
no.
1
4
6
8
10
12
15
18
19
24
25
26
27
31
32
34
36
40
GS (10-3)
0
-0.0005
-0.0001
-0.0014
-0.0014
0.0004
0.0021
0.0051
0.0046
0.1350
0.0484
0.0337
0.0451
0.0339
0.0477
-0.0323
-0.0329
-0.0343
Gen
no.
42
46
49
54
55
56
59
61
62
65
66
69
70
72
73
74
76
77
GS (10-3)
-0.0375
-0.0242
-0.0460
-0.0838
-0.0871
-0.0854
-0.1100
-0.1160
-0.1130
-0.1350
-0.0983
0.2120
0.3690
0.2326
0.3400
0.5410
0.8650
0.0012
Gen
no.
80
85
87
89
90
91
92
99
100
103
104
105
107
110
111
112
113
116
GS (10-3)
-0.9250
50.068
50.654
74.455
-701.15
-427.90
-28.411
-9.391
-12.915
-12.737
-12.854
-12.772
-12.202
-12.274
-12.07
-11.747
0.0110
-0.1750
Figure 7: The GS values of 54 generators
in IEEE 118-bus system.
16
Table 6: Solutions by PSO schemes
in IEEE 118-bus system.
GS
CPSO
PSOTVIW
PSOTVAC
ΔP1 (MW)
0
-5.9
-5.5
-4.4
ΔP85 (MW)
0.05007
-12.1
-12.1
-10.3
ΔP87 (MW)
0.05065
-31.5
-28.2
-22.0
ΔP89 (MW)
0.07446
-62.0
-59.8
-58.5
ΔP90 (MW)
-0.70150
65.1
76.4
69.4
ΔP91 (MW)
-0.42790
26.8
29.8
24.7
Total power
redispatch (MW)
226.6
211.7
189.3
Cost ($/hr)
1183.8
1108.4
907.7
Figure 8: GS values to real power re-dispatching
in IEEE 118-bus system.
17
The optimal power redispatching approach based on PSO-TVAC is superior to
CPSO and PSO-TVIW in providing the better congestion management for both
IEEE 30 and 118 bus systems.
 GS technique uses to select participating generators for real power adjustment. It
could reduce computational effort.
The proposed approach is useful for the SO to manage the congestion in
electricity market environment.
18
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