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International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 10 No: 06
24
Meeting Load Demand at Least Cost in
De-centralised Electricity Environment
Hafiz T. Hassan, Kashif Imran, Muhammad F. Aslam and Intesar Ahmad
Abstract— This paper presents a least cost method of
operating a power plant in view of variable spot price of
electricity and load demand greater than plant capacity.
Manager of an industrial power plant has to operate its
generators at appropriate operating levels. Furthermore,
manager has to put up a demand bid to a power exchange in
order to cover the remaining load demand such that overall cost
remains minimal. Fuel consumption data of three generators has
been used in this paper to determine generators operating levels
and a demand bid over a range of spot prices. Our results
demonstrate that electricity trading through a power exchange
leads to considerable savings when spot price drops below fixed
price.
Index Terms— De-centralised Electricity
Demand Bid, Least Cost Operation, Spot Price.
Environment,
I. INTRODUCTION
I
F cheap electricity is available in a de-centralised electricity
environment (DEE) then industry may shut down or run its
generators at their lower limits and buy bulk of its power
from market. With increasing spot price it becomes profitable
to meet more and more of load demand by own power
generation. If load demand is less than installed capacity then
surplus power can be sold in case electricity fetches a high
spot price. Industrial setups can maximize their profits by
ensuring maximum saving in their electricity utilization. It is
possible to meet electricity requirements in a most cost
efficient manner by determining own production level and
amount of power bought and / or sold in view of variable spot
price.
The rest of this paper is organized as follows: In Section II,
several topics relevant to DEE are discussed. These include
Unit Commitment, Spot Price, Price Forecasting and Plant
Information Systems. Mathematical model is outlined in detail
in Section III. It includes the function to be minimized as well
as constraints and bounds. Solution Methodology is presented
in Section IV and it involves determination of generator
coefficients and transmission pricing. Section V displays
results of simulations carried out. Section VI concludes this
paper.
II.
DE-CENTRALIZED ELECTRICITY ENVIRONMENT
A. Unit Commitment
Unit Commitment Problem (UCP) is solved to determine
which generating units must be on and which should be off
before optimization problem determines the level of
generation by each unit. This problem takes a new twist when
electricity is traded at power exchange and a possible solution
is suggested in [1]. If a generating unit is committed to run in
a certain interval of time as a solution of UCP then it can not
be shut down. In such a case, the generator must operate at or
above its minimum capacity even if its operation is
uneconomical. Such decisions are due to a variety of
constraints imposed on generators and power system as a
whole. There is a minimum spinning reserve that has to be
maintained in view of system stability and reliability [2].
Moreover, thermal unit constraints limit minimum up and
down times to allow gradual temperature changes in
generators [3].
B. Spot Price
Some industrial customers, for example metal industry, can
bear with a reduction in their power supply [4]. This may give
rise to numerous interruptible contracts individually
negotiated with various industrial customers [5]. Power
Exchange (PX) develops a demand curve from aggregated
demand bids for each hour, on a day-ahead basis, starting with
the highest priced bids and ending at the lowest ones. This
gives rise to a set of hourly demand curves for next day each
resembling a descending staircase - see Fig. 1. Demand curve
starts with highest price for un-interruptible power supply. It
is followed by different reduced prices for different levels of
acceptable interruptions.
Manuscript received October 23, 2010.
H. T. Hassan is with University of Engineering and Technology, Lahore,
Pakistan (e-mail: tehzibulhasan@gmail.com).
K. Imran is with the COMSATS Institute of Information Technology,
Lahore, Pakistan (phone: +92-322-4570244; fax: +92-5321045; e-mail:
kashifimran@ciitlahore.edu.pk).
M. F. Aslam is with Superior University, Lahore, Pakistan (e-mail:
mfaslam@gmail.com).
I. Ahmad is with the COMSATS Institute of Information Technology,
Lahore, Pakistan (e-mail: drintesarahmad@ciitlahore.edu.pk).
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Interruptible
Contracts
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International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 10 No: 06
Fig. 1. A typical demand curve showing interruptible contracts
25
Fig. 3. Determination of Spot Price and required Power Production
approach has been shown to be highly effective when
compared to existing methods [14].
Fig. 2. A supply curve showing change in price due to production
method
Similarly a supply curve is established for each hour of the
next day by aggregating supply bids in opposite order to the
demand bids i.e. starting with the lowest priced bids from
plants such as hydro or nuclear and ending at the highest ones
from plants operating on gas and oil [6]. It leads to a supply
curve, for every hour of the next day, as an ascending
staircase pattern - see Fig. 2. Hourly spot price of electricity
is determined on a day-ahead basis by intersection of the
respective demand and supply curves as shown in Fig. 3. The
point of intersection determines the hourly spot price and
required power generation.
C. Price Forecasting
Forecasting electricity prices on a day-ahead basis is a
crucial activity that enables decision making on part of market
participants including managers of industrial power plants.
Various price forecasting methods have proved useful
including non-linear heuristic, linear regression and datamining based techniques.
Non linear heuristic methods can be further classified into
fuzzy models, artificial neural networks (ANN), chaotic
models and evolutionary computation. Heuristic methods have
been extensively applied to price forecasting [7]-[10]. Linear
regression techniques include auto-regressive moving average
(ARMA) and generalized autoregressive conditional
heteroskedasticity (GARCH). Regression techniques are used
for modelling the changing price and its volatility. [11]-[12].
Data mining techniques have been utilized for price
forecasting in recent years [13] and a latest data mining-based
D. Plant Information Systems
Due to the deregulation of the electricity market, power
systems have become more dynamic and offer better
opportunities for all market participants. Role of plant
information systems in DEE has increased manifolds and
internet has found a variety of applications in power system
monitoring and electricity trading [15]. Intelligent Agents can
share information through intranet for economical operation
of thermal power plants in a distributed DEE [16-17].
In order to perform as a dominant market participant, it is
crucial to have greater understanding regarding the real time
plant operation and constantly changing spot price of
electricity. Since corporate offices and plants are usually
resided at geographically distant locations, it has become very
important to access process data for e-monitoring from a
central expertise centre [18]. A web-based real time power
system dynamic performance monitoring system is highly
suitable for today’s increasingly dynamic power systems [19].
More importantly, access to power plant data enables trading
activities such as bidding for supply and demand of electricity
and hence ensures operational optimisation of an industrial
power plant.
III.MATHEMATICAL MODEL
A. Minimization Function
A mathematical function incorporating hourly spot price
and cost of generation and transmission can be developed for
a power plant operating in a DEE [20]. Cost function in (1)
must be minimised in order to maximize profits of an industry.
Cost = CP ( Pp ) + CTb ( Pb ) + CTs ( Ps ) + CB ( Pb ) − I S ( Ps )
(1)
where
CP ( Pp ) = ∑ i =1 CPi ( Ppi ) = ∑ i =1α i *Ppi2 + βi * Ppi + γ i
n
n
(2)
and
Cp : Hourly cost of total production of the power plant, Pp.
Cpi : Hourly cost of production of the i-th generator, Ppi.
CTb : Hourly cost of transmission of the power bought, Pb.
CTs : Hourly cost of transmission of the power sold, Ps.
CB : Hourly cost of Pb.
IS : Hourly income from Ps.
ρ : Hourly spot price of electricity.
α, β, γ : Generator coefficients.
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International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 10 No: 06
B. Connstraints and Bounds
Operation of industrial power plant is subject to certain
non-linear, linear, equality and inequality constraints and
bounds as outlined below in (3), (4), (5), (6) and (7).
Pp + Pb – Ps = Pd
Pb * P s = 0
Ppi ≤ Pmax
Ppi ≥ Pmin
Ppi ≥ 0
(3)
(4)
(5)
(6)
(7)
Last two constraints put a limit on minimum level of
generator operation. If power plant generators can not be shut
down and must operate at or above its minimum capacity then
only first of the two equations is considered. However, it is
crucial to check both equations one at a time and choose
optimum result in case generators can be shut down.
IV. METHODOLOGY
A. Generator Data
Generator coefficients (α, β and γ) are used to model the
hourly cost function of operating a generator in terms of its
power production [3]. We took real Heavy Fuel Oil
consumption data of three diesel generators in a power plant –
see Table I. Cost of Heavy Fuel Oil was taken as 50 Rs./ltr
and a density of 930 gms./ltr was assumed [21]. Generator
coefficients presented in Table II were calculated and used in
our simulation.
TABLE I
FUEL CONSUMPTION DATA FOR GENERATORS
Gen
No.
Max
Capacity
(MW)
Min
Operation
(MW)
1
18.4
6.44
2
23.4
8.19
3
17.1
5.99
Power
(MW)
18.4
16.56
6.44
23.4
18.72
8.19
17.1
15.39
5.99
Fuel Usage
(gms/kWh
)
192
189
197
198
196
202
183
180
181
TABLE II
GENERATOR COEFFICIENTS
Coefficients
α (Rs/MW2h)
β Rs/MWh
γ Rs/h
Generator 1
170
5,956
22,804
Generator 2
48
9,009
11,933
Generator 3
58
8,343
6,886
26
TABLE III
COST OF TRANSMISSION
Cost of Transmission for
Bought Power, CTb
400 Rs/MW
Cost of Transmission for
Sold Power, CTs
200 Rs/MW
B. Transmission Pricing
Two philosophies are commonly used for transmission
pricing in the de-centralized markets: Point-to-point tariff and
the point-of-connection (POC) tariff [22]. The point-to-point
tariff is also called transaction based tariff because it is
specific to a particular sale of power from a designated seller
to a designated buyer. The basic principle of POC tariff is that
payment at the point of connection gives access to the whole
transmission network, and thus the whole electricity market.
POC tariff is universal as it is applicable to both PX trades and
bilateral transactions.
One of the desired features of a pricing scheme is that it
should provide appropriate price signals [23]. This means that
the generators and the loads should pay different rates
depending upon the surplus or deficit status of a Distribution
Company (DISCO). Locational Transmission Price (LTP) for
each node is decided by the results of real power tracing. LTP
of a node reflects usage of various transmission lines and
elements by load or generator on that node. LTP can be
calculated by equations given in [24] and results can directly
be used as POC tariffs for all nodes in the system. However,
for practical implementation the LTP in a DISCO must be
aggregated to get a single price for that DISCO.
In our case, generators are located in the region of Lahore
Electricity Supply Company (LESCO) where power is deficit.
Hence, POC tariff for generators should be less than that for
loads. POC tariff for generators and loads in four western
states of India has been determined and it is in the range of
few hundred rupees per megawatt of power transmitted. POC
tariffs assumed for our simulation are given in Table III [25].
V. RESULTS
The optimization problem has been solved for both cases of
load demand being more and less than plant capacity. Both
scenarios in which generators can and can not be shut down
are simulated in Matlab. Furthermore, results for the scenario
of load demand smaller than plant capacity whether generators
have to be kept on or can be shut down are presented in [25]
for two generators. That work has now been extended to three
generators and results are presented here for the case of load
demand larger than plant capacity whether generators can be
shut down or have to be kept on. A program was developed
that used Matlab’s inbuilt fmincon function to find values of
power produced and bought for minimal cost. Underlying
technique of fmincon is Sequential Quadratic Programming
and this function is used for constrained nonlinear problems.
The program stored results of fmincon and plotted the results
presented below by using standard Matlab functions.
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A. Generators can be shut down
Power production graphs of generators vary between upper
limit and zero level showing generators shut down status.
There is no supply bid in this case because total plant capacity
of 58.9 MW is smaller than 80 MW load demand. Below a
spot price of Rs 8,100 per MWh it becomes economical to
shut down all three generators as shown in Fig. 4. As soon as
Rs 8,100 per MWh limit is exceeded, all three generators
come on and generation level of generator 1 starts increasing
simultaneously. Between the range of Rs 8,100 and Rs 8,600
per MWh generators 2 and 3 are run at their lower limits of
operation. At a spot price of Rs 8,600 per MWh generator 3
starts taking increasing load but generator 2 keeps operating at
its lower limit. When spot price rises to Rs 9,400 per MWh
then generator 2 also starts to take more load than its lower
limit – see Fig. 4. Generator 3 reaches its upper limit before
the other two generators at a spot price of Rs 10,000 per
MWh. Generators 1 and 2 continue to take increasing load
between spot price range of Rs 10,000 per MWh and Rs
10,700 per MWh. Then at a spot price of Rs 10,700 per MWh,
generators 1 and 2 simultaneously reach their upper limits.
Maximum power demanded from PX is total 80 MW load
demand and minimum power demanded is 26.72 MW – see
Fig. 5. Between spot price range of Rs 8000 per MWh and Rs
8100 per MWh power demand drops from 80 MW to 58.9
MW as all three generators turn on. Then power demand
gradually drops to 26.72 MW as all three generators reach
their upper limits as shown in Fig. 5.
25
Power (MW)
20
Generator 1
Generator 2
Generator 3
15
10
5
0
0
2
4
6
8
10
12
14
Spot Price (1000 Rs/MWh)
16
18
20
Fig. 4. Power production of generators when these can be shut down
80
70
Power (MW)
There is a great uncertainty in hourly spot prices which are
highly volatile and as a result sudden spikes and dips occur in
these prices. Historical and real time data of the Australian
National Electricity Market (ANEM) is publicly made
available by National Electricity Market Management
Company (NEMMCO) through its website. It shows that
electricity price experiences changes in the approximate range
of half to double of the normal price. In our case, normal price
is taken as Rs 11,000 per MWh so our range of interest is
approximately Rs 5,000 per MWh to Rs 20,000 per MWh
[25].
27
60
50
40
30
20
0
2
4
6
8
10
12
14
Spot Price (1000 Rs/MWh)
16
18
20
Fig. 5. Demand Bid when generators can be shut down
Cost of electricity per hour increases as hourly spot price
rises. Over a spot price range of Rs 5,000 per MWh to Rs
20,000 per MWh cost changes from Rs. 573,600 to Rs.
1,086,000 – see Fig. 6.
Savings in cost of electricity are calculated with reference
to the power purchased at a fixed rate of Rs. 11,000 per MWh
in a regulated environment in addition to own power
production. However, as spot price keeps on rising power
purchase becomes overly expensive. When compared to a
fixed cost scenario of regulated environment, there is an
additional cost (leading to negative portions in graph of
saving). Reference cost of operation is calculated to be Rs
837,587. At a spot price of Rs. 5,000 per MWh there is a
considerable saving of as much as nearly Rs. 364,000 per
hour.to a negative portion in graph of saving) of about Rs.
246,000 per hour at a spot rate of Rs. 20,000 per MWh – see
Fig. 7. It is interesting to compare the results with those in
[25] which show that electricity trading in a power exchange
always leads to savings if load demand is less than plant
capacity because in that case a power plant starts saving as
soon as spot price varies from fixed price.
B. Generators have to be kept on
Power production graphs of generators vary between upper
and lower permissible limits of generators. There is no supply
bid in this case as well because total plant capacity of 58.9
MW is smaller than 80 MW load demand. Below a spot price
of Rs 7700 per MWh it only remains economical to run all
three generators at their lower limits as shown in Fig. 8. As
soon as Rs 7700 per MWh limit is exceeded, generation level
of genereator 1 starts increasing. Between the range of Rs
7700 and Rs 8600 per MWh generators 2 and 3 are run at
their lower limits of operation. After that power production
graph exactly resembles that case in which generators can be
shut down– see Fig. 8.
Between spot price range of Rs 7700 per MWh and Rs
8600 per MWh power demand drops from 58.90 MW to 56.87
MW as generator 1 starts taking more load than its lower limit
and generators 2 and 3 are run at their lower limits. Then
power demand gradually drops to 26.72 MW as all three
generators reach their upper limits as shown in Fig. 9.
Cost of electricity per hour increases as hourly spot price
rises. Over a spot price range of Rs 5,000 per MWh to Rs
20,000 per MWh cost changes from Rs. 536,700 to Rs.
1,086,000 as shown in Fig. 10. It is important to note that at a
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International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 10 No: 06
spot price of Rs 20,000 per MWh cost remains the same
whether generators can be shut down or have to be kept on.
At a spot price of Rs. 5,000 per MWh there is a
considerable saving of as much as nearly Rs. 300,800 per
hour. However, as spot price keeps on rising power purchase
becomes overly expensive. When compared to a fixed cost
scenario of regulated environment, there is an additional cost
(leading to a negative portion in graph of saving) of about Rs.
248,700 per hour at a spot rate of Rs. 20,000 per MWh – see
Fig. 11.
28
Cost (Million Rs/h)
1.0
0.8
0.6
0.4
0.2
0
2
4
6
8
10
12
14
Spot Price (1000 Rs/MWh)
16
18
20
Fig. 10. Cost when generators have to be kept on
0.2
1.2
0
-0.2
Saving (Million Rs/h)
Cost (Million Rs/h)
1.0
0.8
0.6
0.4
-0.4
0.6
0.4
0.2
0
0.2
-0.2
0
0
2
4
6
8
10
12
14
Spot Price (1000 Rs/MWh)
16
18
-0.4
0
20
4
6
8
10
12
14
Spot Price (1000 Rs/MWh)
16
18
20
Fig. 11. Saving when generators have to be kept on
Fig. 6. Cost when generators can be shut down
It is possible to save Rs. 67,000 per hour at a spot price of
Rs. 5,000 per MWh and saving increases to Rs. 102,000 per
hour at a spot rate of Rs. 20,000 per MWh – see Fig. 12.
0.7
Saving (Million Rs/h)
2
0.5
0.3
VI. CONCLUSION
0.1
-0.1
-0.3
0
2
4
6
8
10
12
14
Spot Price (1000 Rs/MWh)
16
18
20
Fig. 7. Saving when generators can be shut down
22
20
Power (MW)
18
Generator 1
Generator 2
Generator 3
16
14
12
10
8
6
4
0
2
4
6
8
10
12
14
Spot Price (1000 Rs/MWh)
16
18
20
Fig. 8. Power production of generators when these have to be kept on
60
Our results show that profits of industrial plants are
maximized by participation in a de-centralised electricity
market through a power exchange. At high spot price savings
become negative meaning that additional cost is incurred.
However, at low spot price savings take place that increase
with a fall in spot price because it becomes economical to
reduce own production and buy cheaper electricity from
power exchange. When spot price drops to Rs 5,000 per MWh
and generators have to be kept on then savings of Rs. 300,800
per hour are ensured with reference to a total operational cost
of Rs 837,587 that means a saving of 35.91%. Furthermore, if
generators can be shut down then at the spot price of Rs 5,000
per MWh savings increase to Rs. 364,000 per hour that
corresponds to a saving of as much as 43.46%.
Decentralization ensures that not only industry can maximize
its profit but surplus power of industrial setups can be fed to
national grid thus having potential of alleviating acute power
shortage in Pakistan today.
55
ACKNOWLEDGMENT
Power (MW)
50
Authors would like to acknowledge the support provided by
their respective universities to conduct this research work.
45
40
35
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Spot Price (1000 Rs/MWh)
16
18
20
Fig. 9. Demand Bid when generators have to be kept on
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Kashif Imran received his elementary education from England where he
obtained GCSEs and GCEs. He did B.Sc. and M.Sc. in Electrical Engineering
from University of Engineering and Technology (UET), Lahore, Pakistan. His
area of specialization during both degrees was electrical power.
He started his career as a Lecturer at UET Lahore. Then he moved to
SIEMENS where he worked as Engineer on project coordination of 132kV
grid stations. Later he joined NESPAK, leading engineering consultancy firm
of Pakistan, as a Design Engineer in Power Distribution Section. In NESPAK,
his professional experience includes design of overhead and underground
power distribution systems for a variety of buildings and installations.
Currently, he is Lecturer at COMSATS Institute of IT, Lahore, Pakistan where
he teaches Electric Machines. He is an accomplished researcher with a high
Impact Factor research paper titled “Simulation Analysis of Emissions
Trading Impact on a Non-Utility Power Plant” that was published in Elsevier
International Journal of Energy Policy in 2009. His book titled “Power
Exchange as a Deregulated Electricity Market” is in press to be published by
Lambert Academic Publishing, Germany. His research interests include Power
System Economics, Restructured Power Systems Simulation, Energy
Management Systems and Power System Protection.
Mr. Imran is a member of Pakistan Engineering Council.
Hafiz Tehzeebul Hassan did B.Sc. and M.Sc. in Electrical Engineering from
UET, Lahore.
He later joined UET as a faculty member. His professional experience
involves supervision of HV equipment tests as In-Charge of HV Lab in UET.
He is an Associate Professor and a PhD student at UET Lahore. His research
interests include Power System Analysis, Restructured Power Systems and
Multi-Agent Systems.
Mr. Hassan is a member of Pakistan Engineering Council.
Muhammad Farooq Aslam obtained PhD in Electrical Engineering from
UET, Lahore.
He has served UET Lahore as a faculty member for over thirty years. He is
a Professor and Chairman of the Department of Electrical Engineering at
UMT Lahore. His research interests include Deregulated Electricity Markets,
Artificial Intelligence and Multi-Agent Systems.
Mr. Aslam is a member of Pakistan Engineering Council.
Intesar Ahmad did B.Sc. and M.Sc. in Electrical Engineering from UET,
Lahore and University of New South Wales, Australia respectively. In 2008,
he obtained PhD in Electrical Engineering from University of Adelaide,
Australia.
He has served as a faculty member in NUST Pakistan. Currently, he is
Assistant Professor at COMSATS Institute of IT, Lahore, Pakistan. His
research interests include Online Condition Monitoring of Electric Machines
and Power Market Reforms.
Dr. Ahmad is a member of Pakistan Engineering Council.
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