Random furrowing for a stochastic unit commitment solution
P C THOMAS
1*
, SHINOSH MATHEW
2
, BOBIN K MATHEW
3
1,2,3
Dept. of Electrical and Electronics Engg.,
Amal Jyothi College of Engineering, Kanjirapally.
INDIA
Abstract: - The Unit Commitment Problem involves the inherent difficulty of obtaining optimal
combinatorial power generation schedules over a future short term period. The formulation of the
generalized Unit Commitment Schedule formulation involves the specific combination of
generation units at several de-rated capacities during each hour of the planning horizon, the load
demand profile, load indeterminateness and several other operating constraints. This largely
deterministic schedule continues to find favor with several plant operators, keeping in mind the
close operating time-periods involved. However, the deterministic nature of the load profile is
sought to be phased out by a stochastic pattern that is realistic and mirrors real-life situations,
owing to modern trends in Demand side management. This shift is in tune with the ongoing
power restructuring activities of electricity power reforms. The stochastic profile is obtained by a
suitably tuned 2-parameter Weibull distribution that uses appropriate shape and scale parameters.
The resulting band of generated load profiles are used to evaluate net power and penal costs
associated with a set of pervasive randomized probability indices. The exact UCS comprises of a
specific unit absolute state corresponding to a certain time period within the planning horizon.
Subsequently, regression analysis is applied to establish the correlation between the absolute
states and the cumulative randomized load demand against the intervals within the planning
horizon. This method is analogous to random furrowing of probabilistic demand profile.
Key-Words:
Heuristic, stochastic load pattern, Polynomial regression, Power restructuring,
Probabilistic demand profile, Statistical quotients, Random furrowing, Unit Commitment
schedule, Weibull distribution
Received: June 14, 2022. Revised: August 16, 2023. Accepted: September 28, 2023. Published: November 6, 2023.
1. Introduction
The Unit Commitment Problem (UCP) in a
micro-level power system involves the
determination of start-up and shut-down
schedule of units within a generating block, to
meet the forecasted demand over a future
short term period. The unit commitment
decision involves the specific combination of
units at corresponding de-rated capacities
during each hour of the planning horizon,
considering system capacity requirements,
load demand indeterminateness and several
other constraints. The constraints that are
inherent to a micro power system include
probabilistic fluctuations and random nature
of load profiles within each cycle. This is due
to the fact that randomness, inaccurate load
forecasts and probabilistic distribution
function assignations suffer from the inherent
volatile nature of demand and.
The related Unit Commitment Schedules
(UCS) involves the allocation of system
demand and spinning reserve capacity among
the operating units for each specific hour of
operation. The minimization objective is to
obtain an overall least cost solution for
operating the power system over the
scheduling horizon. The UCP belongs to the
class of complex combinatorial optimization
problems, involving both integer and
continuous variables. Solutions for realistic
situations have generally defied application of
rigorous techniques [1,2].
Over the years, there has been
considerable shift from a deterministic hourly
load formulation towards a stochastic one [1].
A case in point is the adoption of hourly
demand by a multi-variate normal distribution
approximation. Caprices of nature, power
swings and local switching contribute to the
aggravation of the problem. The said factors
cause chaos in the ordering of the demand.
Hence it is pertinent to extract a semblance of
order from the very random nature of the
demand. The proposed method uses the
concept of absolute states and cumulative
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random demand to determine efficient
UCS[3].
2. Problem Statement
The overall objective function of the UCPs of
N generating units for a scheduling time
horizon T is given by [3].
Where, i = Unit i, t = time period,
U
it
= Unit status (1 or 0)
P
it
= Output power of unit i at time t.
= Operation cost of committed unit i,
= Start-up/shut-down variable
= Start-up/shutdown variable (fn. of
the down time of unit i)
= System peak demand (MW) at t
subject to constraints.
(a) Load demand constraints:
(b) Spinning reserve:
Spinning reserve, R
t
is the total amount of
generation capacity specified by the system
operator from all synchronized units to meet
any variation in operating conditions.
R
t
is obtained by an initial
deterministic percentage of PD
t
at the t
th
hour,
followed up with random values
subsequently.
(c) Generation limits
where
and
are the extreme
generation limits of unit i. Besides, there are
secondary constraints relating to minimum
up/down time, unit initial status, crew
constraints, maintenance issues, etc.
3. Proposed method – Random
furrowing
The Unit Commitment Problem (UCP)
has thrown up several solution methods [4,5].
The authors have developed a random
furrowing technique to generate a generic
solution. This method attempts to graft
random variables into the generating block
and the demand data, and thus obtain an
acceptable UCS.
The modified representation of a
generation block is represented in Table-1.
Normally, each unit is characterized by a
nominal power rating which has a 2-state
operation (Up and Down). In such a case, the
maximum and minimum power ratings
merely serve as limit constraints. By
themselves, they do not form power states.
This shortcoming is addressed while
considering a micro-level power system,
which consists of a fewer number of units;
each, assuming a relatively larger number of
de-rated states [4].
Table 1: Generic data for generation
Using an appropriate interval value k
i
(Column5), P
it
is made to swing between P
min i
and P
max i
for the i
th
unit in the t
th
interval.
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Hence, P
it
assumes all states between P
min i
and P
max i
, thereby overlapping its nominal
rating. The corresponding large number of de-
rated power states in such a power system are
often much more that in a middle-order power
system with a larger number of generating
units [7].
The power states are termed as i) Absolute
states and ii) Period states. The number of
period states is determined by the
combinatorial function
For instance (k
1
+2)C
1
represents an
n
C
r
function. The number of absolute states is
defined by
where k
1,
k
2,
k
3, ……….
k
n
are listed earlier
t=time period in the planning horizon. (Here,
24 Hours)
The introduction of the interval factor k
serves 2 main objectives.
a)
The ramping constraint is obviated.
b)
A multiplicity of de-rated power states
is created for each unit, thereby
introducing a localized multi-state
operation.
c)
Recognizing that the hourly demands
are stochastic quantities, the absolute
states conform to a random set of
variables with a high degree of
probability.
The demand is qualified with the aid of
suitable random parameters introduced in
Table-2.
Table 2: Demand profiles
Columns 1 and 2 are standard entries obtained
by regression or experience.
Column 3 is a measure of the spinning
reserve, as a % of Column-2. In this case, it
creates an escalation factor.
Column-4 is obtained from a random
generator.
Columns 5 to 8 are subsequently determined
to enhance the variables.
The earlier tables along with Equations(1-8)
are used to generate the trial solution using a
MATLAB script file. A Unit commitment
schedule has been prepared for the Case
study. It includes a specific condition
(Column 11). When the generation is short of
the demand, condition-1 is in place. In the
reverse case, penal power and penal costs are
calculated, giving rise to Condition-2. The
detailed method is amplified in Fig.1.
Fig.1: Proposed algorithm
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The crux of the method is dependent on the
following plots
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Volume 5, 2023
a)
Hourly interval Vs. Absolute state (t
Vs. Sa
i
)
b)
Hourly interval Vs. Cumulative
random demand (t Vs. cr
i
)
4. Case study
Consider a generating block, which is
representative of an Independent power
producer whose base details are specified in
Table 3.
Table 3: Typical generating block data
Column-3 represents the % fluctuation in load
demand, which is designed to escalate the.
demand. The swing on the lower side is not
considered.
To illustrate, the 7 stages for Unit-1stretch
from 5 to 10 MW.
Column 5 represents the number of intervals
k
i
between P
min
and P
max
. These determine the
de-rated power states as indicated in Table 4.
Columns 6, 7 & 8 correspond to the terms in
Equation (2).
The load demand is projected on a 24 hour
basis in Table 5.
For instance, at the 20
th
hour, the demand is
likely to be (44×1.05= 46.2 MW). Column-4
represents a series of random numbers
generated from either MATLAB or Excel.
Table-5 is enhanced to create a modified
demand as detailed in Table 6.
Table-4. De-rated power states (MW)
Unit-1
0
5.00
5.71
6.43
7.14
7.86
8.57
9.29
10.00
Unit-2
0
6.00
7.75
9.50
11.25
13.00
14.75
16.50
18.25
20.00
Unit-3
0
10.00
12.78
15.56
18.33
21.11
23.89
26.67
29.44
32.22
35.00
Table 5. Load demand data
To
illust
rate, the 7 stages for Unit-1 stretch from 5 to
10 MW.
The load demand is projected on a 24 hour
basis in Table 5.
Colu
mn-3 represents the % fluctuation in load
demand, which is designed to escalate the
demand. The swing on the lower side is not
considered. For instance, at the 20th hour, the
demand is likely to be (44×1.05= 46.2 MW).
Column-4 represents a series of random
1
2
3
4
1
2
3
4
Hour
Demand
(MW)
Fluct.
(%)
Rand
Hour
Demand
(MW)
Feluct.
(%)
Rand
1
10
2
0.7119
13
30
4
0.2139
2
10
3
0.9450
14
28
4
0.4182
3
10
3
0.2922
15
35
3
0.0711
4
11
3
0.6137
16
55
4
0.1209
5
15
4
0.0003
17
35
3
0.6105
6
20
5
0.1567
18
36
3
0.6858
7
26
5
0.4863
19
40
4
0.2576
8
27
4
0.0980
20
44
5
0.5343
9
50
3
0.2860
21
43
7
0.4205
10
31
6
0.0413
22
20
6
0.2588
11
32
6
0.1775
23
13
3
0.5793
12
32
5
0.6418
24
9
2
0.7996
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numbers generated from either MATLAB or
Excel. Table-5 is enhanced to create a
modified demand as detailed in Table 6. [5]
Table-6.: Modified Demand data
1
2
3
4
5
6
7
8
9
Hr.
Dem
Fluct.
Rand.
Cum.
Rand
Dem
with
fluc.
Cum.dem
with fluc.
Fluc.
dem
with
rand.
Cum.fluc
dem with
rand.
MW
%
MW
1
10
2
0.711
0.7119
10.20
10.20
7.26
7.26
2
10
3
0.945
1.6569
10.30
20.50
9.73
17.00
3
10
3
0.292
1.9491
10.30
30.80
3.01
20.01
4
11
3
0.613
2.5629
11.33
42.13
6.95
26.96
5
15
4
0.000
2.5632
15.60
57.73
0.00
26.96
6
20
5
0.156
2.7199
21.00
78.73
3.29
30.26
7
26
5
0.486
3.2063
27.30
106.03
13.28
43.53
8
27
4
0.098
3.3043
28.08
134.11
2.75
46.29
9
50
3
0.286
3.5904
51.50
185.61
14.73
61.02
10
31
6
0.041
3.6317
32.86
218.47
1.36
62.38
11
32
6
0.177
3.8092
33.92
252.39
6.02
68.40
12
32
5
0.641
4.4511
33.60
285.99
21.57
89.96
13
30
4
0.213
4.6650
31.20
317.19
6.67
96.64
14
28
4
0.418
5.0833
29.12
346.31
12.18
108.82
15
35
3
0.071
5.1545
36.05
382.36
2.57
111.38
16
55
4
0.120
5.2754
57.20
439.56
6.92
118.30
17
35
3
0.610
5.8859
36.05
475.61
22.01
140.31
18
36
3
0.685
6.5718
37.08
512.69
25.43
165.74
19
40
4
0.257
6.8294
41.60
554.29
10.72
176.46
20
44
5
0.534
7.3637
46.20
600.49
24.68
201.14
21
43
7
0.420
7.7843
46.01
646.50
19.35
220.49
22
20
6
0.258
8.0431
21.20
667.70
5.49
225.98
23
13
3
0.579
8.6225
13.39
681.09
7.76
233.74
24
9
2
0.799
9.4221
9.18
690.27
7.34
241.08
ū
0.392
4.7858
10.04
105.84
σ n-1
0.264
2.3647
7.57
77.31
The mechanism for generating Table 6
follows the pattern elucidated earlier. Based
on the cost coefficients, the generating costs
of the 3 units have been calculated and
summarized in Table-7.
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Table 7: Costs (INR) at de-rated power states
Unit\State
1
2
3
4
5
6
7
8
9
10
11
1
100
125
131
139
147
156
165
176
187
2
123
172
203
242
288
342
404
473
550
635
3
204
299
357
430
516
616
730
857
999
1155
1324
To cite an example, considering Unit-
1,the operational cost of running Unit-2 at 6
MW is INR.172. State generation was
achieved by a program coded in MATLAB.
The complete enumeration gives rise
to 23736 states. For brevity, a certain part of
the state listing is reproduced in Table 8.
Table 8: State enumeration
1
2
3
4
5
6
7
8
Period
Abs
State
Period
state
Unit state
U-1
U-2
U-3
Net
cost
Cond
INR
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1
988
988
9
10
10
460.89
1
1
989
989
9
10
11
491.68
1
2
990
1
1
1
2
522.00
2
2
991
2
1
1
3
146.57
1
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
24
23735
988
9
10
10
418.46
1
24
23736
989
9
10
11
446.23
1
Since this table is vital for further progress, a
summary is in order.
Col.1 ~ Time period T (Hourly basis 1, 2,
…… , 24)
Col.2 Absolute state number (Across all time
periods)
Col.3 ~ Unit wise state number (Across a
particular time-period
The number of states within a
particular time-period, as represented inCol.2
should have been different, owing to the
generally differing values of intervals k.
However, these have been made equal (In this
specific case ~ 989), by considering null
entities.
Col.4,5& 6 ~ Specific de-rated power states
of Unit Nos. 1,2 & 3.For instance, absolute
state number 23735 denotes Unit State-988at
the 24
rd
hour, wherein State-9 of Unit-1 (10
MW), State-10 of Unit-2 (20 MW) and State-
10of Unit-3 (32.22 MW) are considered.
Col.7 ~ This forms the net cost, taking into
account the operational and penal cost. Penal
power is presumptive of the generated power
that is not utilized.
Col.8 ~ Indicates a specific condition.
1~Spinning reserve 2~None
5. Results
The Unit Commitment schedule
(UCS) is prepared by indexing the unabridged
Table-8 at 2 levels. The first level is on the
basis of the time period. The second level
indexes the net operational cost (Col.7). The
complete UCS is listed in Table 9.
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Table 9: Unit Commitment Schedule (UCS)
1
2
3
4
5
6
7
8
Hour
Abs.
state
Period
state
State
Gen.
Op. Cost
U-1
U-2
U-3
(Hr.)
(MW)
(INR)
1
121
121
2
2
1
11
72.31
2
1110
121
2
2
1
11
72.48
3
2099
121
2
2
1
11
72.48
4
3198
231
3
2
1
11.71
79.53
5
4177
221
3
1
2
15.71
126.25
6
5177
232
3
2
2
21.71
174.27
7
6837
903
9
3
2
27.75
261.31
8
7816
893
9
2
3
28.78
288.24
9
8886
974
9
9
7
52.14
1039.26
10
9806
905
9
3
4
33.31
391.89
11
10816
926
9
5
3
34.03
405.2
12
11805
926
9
5
3
34.03
404.91
13
12793
925
9
5
2
31.25
346.91
14
13771
914
9
4
2
29.5
300.17
15
14663
817
8
5
4
36.09
466.29
16
15811
976
9
9
9
57.69
1308.86
17
16641
817
8
5
4
36.09
466.29
18
17620
807
8
4
5
37.12
505.96
19
18621
819
8
5
6
41.65
652.4
20
19763
972
9
9
5
46.58
825.63
21
20611
831
8
6
7
46.17
820.3
22
21001
232
3
2
2
21.71
174.49
23
22319
561
6
2
1
13.86
103.79
24
22868
121
2
2
1
11
70.02
This particular UCS is sought to be
characterized by the average operational cost
over 24 hours.. The next step is to modify the
UCS to make it more amenable to
generalization. The algorithm specified in
Fig.1 is used to generate trial solutions. The
pessimistic (highest load profile) has been
selected as the base profile.10 trials were
considered, the last being the most optimistic
load profile. [6]
Table. 10. Load demand statistics
1
2
3
4
5
6
7
Case
Rand
Cum
Rand
Rand
Dem
Cum
Rand
Dem
Multiplier (ū/ σ n-1)
Base
ū
0.393
4.786
10.045
105.837
1.369
Col.6
σ n-1
0.265
2.365
7.574
77.311
2.024
Col.4
Trial-1
ū
0.483
6.526
14.623
169.807
1.445
-do-
σ n-1
0.327
3.270
12.536
117.507
1.996
Trial-2
ū
0.547
6.506
19.378
206.702
1.303
-do-
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σ n-1
0.276
4.000
14.267
158.650
1.627
Trial-3
ū
0.557
6.881
20.560
236.961
1.362
-do-
σ n-1
0.263
4.195
14.649
174.029
1.640
Trial-4
ū
0.515
6.830
20.162
238.579
1.454
-do-
σ n-1
0.265
3.792
14.826
164.085
1.801
Trial-5
ū
0.522
6.837
21.186
261.693
1.465
-do-
σ n-1
0.275
3.966
14.919
178.627
1.724
Trial-6
ū
0.618
7.772
26.281
302.907
1.426
-do-
σ n-1
0.337
4.449
18.145
212.439
1.747
Trial-7
ū
0.568
6.483
25.362
268.186
1.346
-do-
σ n-1
0.272
4.066
16.120
199.263
1.594
Trial-8
ū
0.451
5.489
20.240
231.694
1.442
-do-
σ n-1
0.343
3.187
17.003
160.725
1.723
Trial-9
ū
0.375
3.989
19.183
190.930
1.232
-do-
σ n-1
0.266
2.880
15.866
154.955
1.385
Trial-10
ū
0.399
5.309
18.630
229.644
1.705
-do-
σ n-1
0.305
2.631
13.674
134.689
2.018
Table 11. Load trials
1
2
3
4
5
6
7
8
Case
Multip.
Coefficients
Remarks
(ū/ σ n-1)
p1
p2
p3
p4
p5
Base
1.369
0.01
-0.65
7.05
1066.0
-1064.5
Abs State
2.024
0.00
0.12
-1.42
11.61
-3.91
Cum Ran Dem
0.02
-1.13
12.52
1435.8
-1449.3
Final fit
Trial-1
1.445
-0.02
0.92
-15.28
1149.6
-894.8
-do-
1.996
0.00
0.09
-0.63
10.50
-0.6
-0.03
1.15
-20.82
1640.3
-1291.9
Trial-2
1.303
0.02
-1.16
21.96
877.2
-272.5
-do-
1.627
0.00
0.11
-0.71
13.1
-14.9
0.03
-1.68
29.77
1121.6
-330.8
Trial-3
1.362
-0.03
1.57
-27.78
1226.7
-965.0
-do-
1.64
0.00
-0.08
3.08
-8.90
16.7
-0.05
2.28
-42.88
1684.8
-1341.3
Trial-4
1.454
0.00
-0.18
4.91
991.07
-414.2
-do-
1.801
0.00
-0.12
3.10
-5.89
19.4
0.00
-0.05
1.54
1451.6
-637.3
Trial-5
1.465
-0.04
1.99
-38.12
1342.6
-1399.7
-do-
1.724
0.00
-0.18
4.38
-11.15
19.2
-0.06
3.23
-63.39
1986.1
-2083.8
Trial-6
1.426
-0.04
2.14
-37.72
1280.2
-945.1
-do-
1.747
0.00
0.12
0.02
10.2
10.9
-0.06
2.86
-53.83
1807.5
-1366.7
Trial-7
1.346
-0.03
1.32
-23.14
1157.1
-480.2
-do-
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1.594
0.00
0.21
-2.40
26.38
-23.9
-0.03
1.45
-27.31
1515.2
-608.2
Trial-8
1.442
-0.01
0.37
-7.47
1059.0
-304.0
-do-
1.723
0.00
0.04
1.00
0.67
23.7
-0.01
0.46
-12.50
1525.4
-479.1
Trial-9
1.232
0.00
0.02
-1.54
1025.4
-263.7
-do-
1.385
0.00
0.06
-0.13
8.17
-8.03
0.00
-0.06
-1.72
1252.1
-313.9
Trial-10
1.705
-0.02
1.12
-19.22
1121.4
-344.1
-do-
2.018
0.00
-0.08
1.03
15.15
-7.2
-0.04
2.06
-34.84
1881.4
-572.1
For the base profile
Q
1
= Col.6 ratio = (105.837/77.311) = 1.369
and
Q
2
= Col.4 ratio = (4.786/2.365) = 2.024 and
so on for all 10 trials.
Characteristic regression factors A, B are
determined from Table 11.
Considering the base case, Q
1 ≡
1.369, Q
2
≡
2.024
The absolute space regression polynomial is
given by
The cumulative random demand variable is
extrapolated to
The effective fit is determined by the heuristic
Such characteristic equations are developed
for 10 trials, the results of which are
enumerated in Table 2. This is plotted for the
base profile in Fig.2
.
Fig.2: Plot of heuristic
0 5 10 15 20 25
0
0.5
1
1.5
2
2.5
x 104
Time period (t)
Abs. state/Cum Random demand/Heuristic (y)
y=0.01*t4-0.65*t3+7.05*t2+1066*t+1064.5
y=0.12*t3-1.42*t2+11.61*t-3.91
y=0.02*t4-1.13*t3+12.52*t2+1435.84*t-1449.38
Abs. state
Cum Rand demand
Heuristic
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Table 12, being calculated for 11 trials, has
been pruned to display the first 3 trials only.
The underlined entries indicate that the
calculated absolute space identifier have
exceeded the upper ceiling (23736 for the
specified Case study). In addition, some
negative values have been generated.These
are potential errors which need to be
addressed at alater stage. Space contraints
dictate the non-inclusion of individual cost
figures in Table 12. However, the total
operating costs for each trial have been
indicated.
Table 12 has been summarized in
Table 13, indicating the excess bound cases
and the operating cost error. The error is the
maximum for the base profile, tailing off to
acceptable values for optimistic load profiles,
indicating the efficacy of the proposed
method.
Table 12:Application of heuristic to determine absolute states
Hour
Base
Trial-1
Trial-2
Trial-3
Actual
Calc
Actual
Calc
Actual
Calc
Actual
Calc
1
121
-2
341
329
671
819
331
303
2
1110
1464
1330
1914
1660
2019
1430
1874
3
2099
2942
2319
3470
2649
3259
2419
3385
4
3198
4427
3528
5002
3188
4532
3518
4846
5
4177
5914
4507
6514
4078
5829
4298
6267
6
5177
7398
5397
8011
5727
7143
5848
7657
7
6837
8875
6848
9494
6739
8469
6860
9022
8
7816
10340
7827
10967
7838
9800
7729
10370
9
8886
11792
8897
12431
8877
11131
8888
11706
10
9806
13226
9817
13888
9708
12457
9829
13034
11
10816
14640
10707
15337
10828
13776
10839
14357
12
11805
16033
11816
16778
11796
15083
11828
15677
13
12793
17403
12773
18211
12575
16376
12785
16995
14
13771
18749
13782
19633
13762
17654
13564
18310
15
14663
20070
14784
21043
14795
18915
14775
19621
16
15811
21367
15822
22437
15713
20159
15604
20926
17
16641
22639
16762
23810
16773
21386
16753
22220
18
17620
23887
17741
25160
17752
22596
17643
23499
19
18621
25113
18742
26481
18753
23792
18644
24757
20
19763
26318
19743
27766
19634
24975
19755
25988
21
20611
27504
20732
29009
20743
26149
20634
27182
22
21001
28675
21331
30204
21661
27316
21672
28331
23
22319
29833
21979
31342
22309
28482
21880
29424
24
22868
30981
22978
32415
23308
29650
22968
30450
Cost
19686
24592
20726
27284
22025
24048
23458
23681
% Error
25
32
10
1
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Table 13. Summary of heuristic application
Trials
Base
1
2
3
4
5
6
7
8
9
10
States in excess of
bounds (Max-24)
7
8
6
6
8
8
7
6
7
5
10
% Error
25
32
10
1
3
3
9
11
20
21
8
6. Conclusion
The paper proposes a new method to
generate generalized sub-optimal Unit
Commitment schedules. This is effective in
micro-level power systems which are
characterized by a few units possessing
relatively large number of de-rated states. In
such situations, the method tackles
probabilistic demand by introducing a
measure of randomness in the load profile.
The load profile is categorized into a
spectrum varying from the pessimistic to the
optimistic. For each profile, a set of random
numbers are generated, from which the
cumulative randomized demand values are
obtained. The pessimistic profile is chosen as
the base, for which a pair of statistical
quotients are determined. Further,
enumeration is carried out to determine a base
Unit Commitment schedule, which generates
a set of absolute state identifiers. The
identifiers and cumulative randomized
demand values are plotted against the periods
in the planning horizon, yielding 4
th
degree
polynomial regression characteristics. These
characteristics are fused with the statistical
quotients to yield a trial heuristic. When
expanded over the planning horizon, the
heuristic calculates a new set of Unit
Commitment schedules. This is tested over
the entire load spectrum.
A case study for a 3-unit system with
multiple de-rated states has been used to
simulate the proposed method. It has also
been tested on a spectrum of 10 load profiles
with a fair degree of success. The 2 main
drawbacks pertain to the solution state
identifiers overstepping the state limits, and
the error quantum. These are proposed to be
tackled in future work. Nevertheless, at this
stage, the proposed method shows a lot of
promise in achieving a robust, sub-optimal
Unit Commitment schedule. [7]
References
[1]
J.Endrenyi, Reliability Modeling in
Electric Power Systems, New York, USA,
John Wiley and Sons, 1978.
[2]
Alberto Leon Garcia, Probability and
Random Processes for Electrical
Engineering, 2nd ed. New York, USA:
Pearson Education, 1994.
[3]
Ce Shang, Teng Lin, A linear reliability
evaluated unit-commitment,IEEE
Transactions on Power Systems, Vol. 37,
No. 5, Sept. 2022.
[4]
Yiping Yuan, Yao Zhang, Jianxue Wang,
Zhou Liu, Zhe Chen, Enhancement in
reliability-constrained unit commitment
considering state-transition-process and
uncertain resources, IET Generation,
Transmission & Distribution, Vol.15,
Issue 24, pp. 3488-3501.
[5]
P.C.Thomas, Balakrishnan.P.A,
Reliability analysis of smart-grid
generation pools, IEEE 2011 PES
Innovative Smart Grid Technologies
Conference; Dec. 2011, Kollam, India.
[6]
Menghan Zhang, Zhifang Yang, Wei Lin,
Juan Yu, Wenyan Li, Internalization of
Reliability Unit Commitment in day-ahead
market: Analysis and Interpretation,
Applied Energy, Vol. 326. Nov. 2022.
[7]
Yong Liang, Long He, Xinyu Cao, Zuo-
Jun Shen, Stochastic control for smart grid
users with flexible demand, IEEE Trans on
Smart Grids, Vol.4, 2013;pp. 2296-2308.
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DOI:10.37394/232025.2023.5.14
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Volume 5, 2023
Contribution of Individual Authors to the
Creation of the Scientific Article
P.C.Thomas established the linkage of the
phantom unit commitment to the stochastic
process. He further set out the algorithm in
Fig.1.
Shinosh Mathew was instrumental in
developing the MATLAB code necessary for
the different load trials.
Bobin K Mathew executed the necessary
statistics.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
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