International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.5, pp. 1913-1916
ISSN 2078-2365
http://www.ieejournal.com/
Unit Commitment with Economic Dispatch
M.S.Krishnarayalu
Department of Electrical and Electronics Engineering,
V.R Siddhartha Engineering College, Vijayawada, AP, 520007, India.
mskr@vrsiddhartha.ac.in
Abstract — Economic Dispatch (ED) in power systems
is very important as it saves lot of money. There are two
basic methods available. One is classical method where
all units are committed and consumption of fuel is
optimized by an optimization method. Second one is
Unit Commitment (UC) method. In UC, units are
committed based on their efficiency order and on load
demand with most efficient unit committed first. Now a
method called Unit Commitment with Economic
Dispatch (UCED) is proposed combining these two
methods. The efficacy of this new method is illustrated
via a three unit thermal plant system.
Index Terms — Fuel cost, Optimization, Economic
Dispatch, Unit Commitment
Terminology:
H– Heat input, MBtu/h
h – Hour
F– Fuel cost, `/h
` – Indian Rupees
I.
II.
TFC – Total fuel cost, `/h
IFC– Incremental fuel cost, `/MWh
– IFC of power system, `/MWh
dFj/dPj– IFC of unit j, `/MWh
Lj – Penalty factor of unit j
UC – Unit Commitment
ED – Economic Dispatch
INTRODUCTION
Economic Dispatch of power is one of the most
important problems of power systems [1-9]. It is
mainly tackled by two methods. Method one gives
optimal power generation required to meet the load
demand PD, with minimum total fuel cost, through a
coordination equation. This is known as classical ED.
In this method all units are turned on to meet the PD.
The second method is Unit Commitment (UC). Here
the most efficient unit is committed first followed by
next efficient unit and so on. Here all units need not
be committed. All units may be demanded
(committed) only for large peak loads. There are
many methods of UC are available in literature.
However no UC solution is perfect. They have
certain strengths and some weaknesses [5]. In this
paper a new approach is presented mixing the ED and
UC methods.
BASIC METHODS
Here we discuss the two basic methods of economic
dispatch namely Classical Economic Dispatch and
Unit Commitment.
Classical Economic Dispatch: This method
minimizes total fuel cost (TFC) using Lagrange
method resulting in a coordination equation that gives
rise to optimum generations that minimize TFC. The
objective is scheduling the output of each plant/unit
such that the total fuel cost of all the plants/units is
minimum for a given load demand PD.
N = number of plants/units
1913
Krishnarayalu
Unit Commitment with Economic Dispatch
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.5, pp. 1913-1916
ISSN 2078-2365
http://www.ieejournal.com/
TFC = F1+ F2+…+ FN=∑𝑁
(1)
𝑗=1 𝐹𝑗
F1, F2,…,FN - fuel cost of individual plants/units
PT = total power input to the network from all
plants/units
= P1+ P2+…+ PN=∑𝑁
(2)
𝑗=1 𝑃𝑗
P1, P2,…,PN - power outputs of individual
plants/units
PD = total power demanded by the loads of the entire
system
PL = total transmission loss
Hence
Ф = PD + PL- ∑𝑁
(3)
𝑗=1 𝑃𝑗 = 0
is the equality constraint for optimization.
L = FT +  Ф = Lagrange function
= augmented cost function
(4)
 - a constant called Lagrangian multiplier
For minimum FT, L/Pj = 0, j
This results in  = (dFj/dPj) / [1- (PL /Pj)],
= Lj (dFj/dPj), `/MWh
j = 1, … N.
(5)
(5) is the coordination equation for finding optimum
generation schedules that minimize TFC.
Lj= 1/[1- (PL /Pj)]
= penalty factor for plant j
= 1 if transmission losses were neglected (zero).
If transmission losses are included Lj will be more
(penalty) and IFC of the power system will be high.
If maximum and minimum generations are specified
for each unit, some units will be unable to operate at
the same IFC as others. Then
dFj/dPj≥ ,
Pj = Pjmin
dFj/dPj=,
Pjmin<Pj<Pjmax
dFj/dPj≤ ,
Pj = Pjmax
(6)
Unit Commitment:
To commit a generating unit is to turn it on. That is
to bring the unit up to rated speed, synchronize it to
the system so that it can deliver power to the
network. A great deal of money (fuel) can be saved
by turning the units off (decommitting) when they
are not needed. The salient points of UC are
 It is not economical to run all the units
available all the time.


Determination of units of a plant that should
operate for a particular load
UC is important for thermal power plants
than other types of plants such as hydro (the
operating cost and start-up times for hydro
plants are negligible).
Constraints in UC: Many constraints like online and
offline reserves, minimum up time, minimum down
time, crew constraints, maintenance constraints are
to be considered in UC for committing and
decommitting of units.
The UC problem can be very difficult. Let us
consider the following situation.
1) It is required to establish a loading pattern
for M intervals per day. Then M will be 24
for one hour interval.
2) There are N units to commit and dispatch.
3) Any one unit can supply the total load
demand PD. Also any combination of units
can also supply the PD.
For the total period of M intervals, the maximum no.
of possible combinations is (2N-1)M which can be a
very large number. For N=20, (2 N-1)24 =3.12 x10144,
indicates the difficulty of UC.
Some approaches of UC
 Priority List method: A simple approach to
the problem is to apply priority ordering
(most efficient plant/unit is loaded first and
so on). Efficiency of units may be
determined from full load average
production costs of units.
 Optimal approach
using
Dynamic
programming
 Lagrange Relaxation method
 Mixed Integer Programming
III.
UNIT COMMITMENT WITH
ECONOMIC DISPATCH (UCED)
Here a method named Unit Commitment with
Economic Dispatch (UCED) is proposed combining
the basic principles of Economic Dispatch and Unit
Commitment methods. Firstly list out the units
according to their efficiency. Initially the most
1914
Krishnarayalu
Unit Commitment with Economic Dispatch
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.5, pp. 1913-1916
ISSN 2078-2365
http://www.ieejournal.com/
efficient unit is committed as in UC. Continue
loading this unit till maximum generation according
to PD. If PD is more than maximum generation limit
of this unit, commit the next most efficient unit. Now
using the coordination equation (5) determine the
optimum generations of these two units for the P D.
Continue this process by committing next efficient
unit as PD increases further. Also continue to find
optimum generations using the coordination equation
(5). Here computations are unique. Firstly the most
efficient unit is committed. Accordingly P D is
supplied by this unit till its maximum generation
limit is reached. When next unit is committed optimal
power generation is computed using coordination
equation (5). Hence computations are unique.
IV.
Table 3 : Unit Efficiency Order
Unit
1
2
3
IFC = dF/dP
`/MWh
IFC at Full
Load
Efficiency
Order
`/MWh
97.94
94.02
118.78
2
1
3
79.2+0.03124P1
78.5+0.0194P2
95.64+0.11568P3
Load demand PD varies from 300 MW to 1200 MW.
Optimum power generations and total fuel cost (TFC)
for classical ED, UC and UCED methods are
computed and shown in Tables 4, 5 and 6
respectively. From these tables it can be observed
UCED method is the most economical compared to
classical ED and Unit Commitment methods.
CASE STUDY
Consider a three unit thermal plant with the following
data. Here transmission losses are neglected.
Table 1: Data of three unit thermal plant
Unit
1
2
3
H, MBtu/h
Cost of
510+7.2P1+0.00142P1^2
310+7.85P2+0.00194P2^2
78+7.97P3+0.00482P3^2
MBtu, `
11
10
12
Pmin,
MW
Pmax,
MW
150
100
50
600
400
200
Table 4: ED – Classical
The resulting fuel cost and unit efficiency order are
given in Tables 2 and 3 respectively.
Table 2: Fuel Cost
Unit
1
2
3
F, `/h
5610+79.2P1+0.01562P1^2
3100+78.5P2+0.0194P2^2
936+95.64P3+0.05784P3^2
PD, MW
P1, MW
P2, MW
300
400
500
600
700
800
900
1000
1100
1200
150
183.9
239.29
294.69
350.09
405.48
460.88
477.185
600
600
100
166.1
210.71
255.31
299.91
344.52
389.12
400
400
400
ED
P3, MW
50
50
50
50
50
50
50
122.815
100
200
TFC, `/h
34848
43240
51821
60575
69502
78602
87876
98118
10744
11873
1915
Krishnarayalu
Unit Commitment with Economic Dispatch
International Electrical Engineering Journal (IEEJ)
Vol. 6 (2015) No.5, pp. 1913-1916
ISSN 2078-2365
http://www.ieejournal.com/
Table 5: UC – Priority List Method
PD, MW
P1, MW
P2, MW
300
400
500
600
700
800
900
1000
1100
1200
0
0
100
200
300
400
500
600
600
600
300
400
400
400
400
400
400
400
400
400
UC
P3, MW
TFC,
0
0
0
0
0
0
0
0
100
200
`/h
28396
37604
51290
59679
68380
77393
86719
96357
10744
11873
committed for a given PD. In UCED only required
number of units is committed according to PD as in
UC. In UCED computations are unique not trial and
error values. A three unit thermal power system is
taken as a case study. From Tables 4 and 5 UC is
economical than classical ED. Comparing Tables 4,5
and 6 UCED is the most economical for different P D.
Here what is presented is the basic idea of UCED
only, viz commit the units based on their efficiency
and share the load according to coordination equation
(5) if number of units is two or more. Further
research on this method may leads to its commercial
use.
ACKNOWLEDGEMENTS
The author greatly acknowledges Siddhartha
Academy of General and Technical Education,
Vijayawada for providing the facilities to carry out
this research.
Table 6: UCED
PD, MW
P1, MW
UCED
P2, MW
P3, MW
TFC,
300
400
500
600
700
800
900
1000
1100
1200
0
0
266.99
322.39
377.78
433.18
500
600
600
600
300
400
233.01
277.61
322.22
366.82
400
400
400
400
`/h
28396
37604
50314
59154
68168
77355
86719
96357
10744
11873
0
0
0
0
0
0
0
0
100
200
REFERENCES
1.
2.
3.
4.
5.
6.
7.
V.
CONCLUSIONS
A new unit commitment method named UCED is
proposed by committing the units based on their
efficiency as in UC and computing the optimum
generation using the coordination equation (5) of
classical ED method when more than one unit are
committed. In classical ED method all units are
8.
9.
Allen J. Wood and Bruce F. Wollenberg “Power Generation,
Operation & Control” 2/e, Wiley India, New Delhi, 2010.
J.J.Grainger and W.D.Stevenson Jr, Power system analysis, Tata
McGraw Hill, New Delhi, 2012.
HadiSaadat, “Power System Analysis” ,Tata McGraw Hill, New
Delhi, 2007.
IJ Nagrath and DP Kothari Modern power system analysis 4/e,
TMH, New Delhi, 2014
Sayeed Salam, “Unit Commitment Solution Methods”, World
Academy of Science, Engineering and Technology 11 2007, pp
320-325.
Juan Pablo Fossati, Memoria de Trabajos de DifusiónCientífica
y Técnica, núm. 10 (2012) 83, ISSN 1510-7450 • ISSN (enlínea)
1688-9584
Brittany Wright, A Review of Unit Commitment, ELENE4511,
May 28, 2013
Surekha P. et. al. , Unit Commitment and Economic Load
Dispatch using Self Adaptive Differential Evolution, WSEAS
Transactionson Power Systems, E-ISSN: 2224-350X, 159-171
Issue 4, Volume 7, October 2012
Mohammad Reza Salimian and Mohammad Taghi Ameli,
HGAPSO based method for solving Unit Commitment Problem,
IEEJ Vol. 6 (2015) No. 3, pp 1834-1840. ISSN 2078-2365
1916
Krishnarayalu
Unit Commitment with Economic Dispatch