Transcript optimal generator redispatching for congestion management using
Panida Boonyaritdachochai
Power Quality and Energy Efficiency Engineer 28 th 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.
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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 ij g
P ij
V i 2 G ij
V i V j G ij
cos
(θ i
θ j )
V i V j B ij
sin
(θ i
θ j )
Let;
n
1
H
n
n n
1
1
(1) (2)
7
II.
Objective Function for Congestion Management
Minimize
Ng
g
C
g
g
ΔP
g
Subjected to
ΔP
g min
ΔP
g
ΔP
g max
;g
1,2,
,N
g
ΔP
g min
P
g
P
g min g Ng
1 ΔP g
0
and
ΔP
g max
P
g max
- P
g Ng g
1
GS ij g ΔP g
F l 0
F l max ;l
1,2,
,n l
8
III. Particle Swarm Optimization (PSO) Schemes
Figure 1: bird flocking and Fish schooling The position and velocity of the
X p
p
1
p
2
,
,x p pd
particle in
d
dimensions can be expressed as
V p
p
1
p
2
,
,v pd
The best previous position of a particle is recorded and represented as
pbest
p
p1
,p
p2
,
,p
pd
If the
g
particle is the best among all particles in the group, it is presented as
gbest g
g g1 ,g g2 ,
,g gd
9
A.
Classical Particle Swarm Optimization (CPSO)
v
k pd
1
w
v
k pd
c
1
rand
1
pbest
pd
x
pd
c
2
rand
2
gbest
gd
x
pd
B.
Particle Swarm Optimization with Time-Varying Inertia Weight (PSO-TVIW)
v k pd
1
C
w
v k pd
c 1
rand 1
pbest pd
x pd
c 2
rand 2
gbest gd
x pd
2
2
2
4
, where 4.1
4.2
w max
w min
k max
k max k
w min
C.
Particle Swarm Optimization with Time-Varying Acceleration Coefficients (PSO-TVAC)
c 1
c 1f
c 1i
k k max
c 1i
c 2
c 2f
c 2i
k k max
c 2i
10
11
Figure 2: Flowchart of congestion management by PSO-TVAC. 12
Congested Line
1 to 2 Figure 3: IEEE 30-bus system.
Table 2: Congested line in IEEE 30-bus system.
Real Power Flow (MW)
170
Line Limit (MVA)
130
Over the Limit (MW)
40 13
Table 3: Solutions by PSO schemes in IEEE 30-bus system.
GS ΔP 1 (MW) ΔP 2 (MW) ΔP 5 (MW) ΔP 8 (MW) ΔP 11 (MW) ΔP 13 (MW) Total power redispatch (MW) Cost ($/hr)
0.0000
-0.8908
-0.8527
-0.7394
-0.7258
-0.6869
CPSO
-55.9
22.6
16.2
10.5
5.6
2.6
113.2
287.1
PSO TVIW
-50.13
18.88
13.21
9.15
5.87
4.14
101.4
253.1
PSO TVAC
-49.25
17.51
14.02
9.88
6.8
3.01
100.5
247.5
Figure 4: GS values in IEEE 30-bus system.
Figure 5: GS values to power redispatching in IEEE 30-bus system.
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Figure 6: IEEE 118-bus system.
Table 4: Congested line in IEEE 118-bus system.
Congested Line
89 to 90
Active Power Flow (MW)
260
Line Limit (MVA)
200
Over the Limit (MW)
60 15
Gen no.
1 4 6 8 10 12 15 18 19 24 25 26 27 31 32 34 36 40 Table 5: GS values of 54 generators in IEEE 118-bus system.
GS (10 -3 )
0 -0.0005
-0.0001
-0.0014
-0.0014
0.0004
0.0021
0.0051
0.0046
0.1350
0.0484
0.0337
0.0451
0.0339
0.0477
-0.0323
-0.0329
-0.0343
Gen no.
42 46 49 54 55 56 59 61 62 65 66 69 70 72 73 74 76 77
GS (10 -3 )
-0.0375
-0.0242
-0.0460
-0.0838
-0.0871
-0.0854
-0.1100
-0.1160
-0.1130
-0.1350
-0.0983
0.2120
0.3690
0.2326
0.3400
0.5410
0.8650
0.0012
Gen no.
80 85 87
89 90
91 92 99 100 103 104 105 107 110 111 112 113 116
GS (10 -3 )
-0.9250
50.068
50.654
74.455
-701.15
-427.90
-28.411
-9.391
-12.915
-12.737
-12.854
-12.772
-12.202
-12.274
-12.07
-11.747
0.0110
-0.1750
Figure 7: The GS values of 54 generators in IEEE 118-bus system.
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Table 6: Solutions by PSO schemes in IEEE 118-bus system.
ΔP 1 (MW) ΔP 85 (MW) ΔP 87 (MW) ΔP 89 (MW) ΔP 90 (MW) ΔP 91 (MW) Total power redispatch (MW) Cost ($/hr) GS
0 0.05007
0.05065
0.07446
-0.70150
-0.42790
CPSO
-5.9
-12.1
-31.5
-62.0
65.1
26.8
226.6
1183.8
PSO TVIW
-5.5
-12.1
-28.2
-59.8
76.4
29.8
211.7
1108.4
PSO TVAC
-4.4
-10.3
-22.0
-58.5
69.4
24.7
189.3
907.7
Figure 8: GS values to real power re-dispatching in IEEE 118-bus system.
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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.
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2.
3.
4.
5.
6.
7.
8.
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