Modeling and Analysis of Wholesale Competitive Electricity Markets: A Case For Zambia

E. Moyo et al. Int. Journal of Engineering Research and Applications www.ijera.com
ISSN: 2248-9622, Vol. 5, Issue 7, (Part - 4) July 2015, pp.07-12
www.ijera.com 7|P a g e
Modeling and Analysis of Wholesale Competitive Electricity
Markets: A Case For Zambia
E. Moyo, B. R. Pokhrel and B. Adhikary
Kathmandu University, Nepal
Abstract-
Electricity markets all over the world are moving towards greater reliance on competition and this has become a
global trend as a method of best practice. However, before competition is introduced in electricity markets it is
imperative to model and assess the behavior of the market. The assessment includes calculating the market
performance indices to determine the levels of market power exploitation by the Generating Companies
(GenCos) that will participate in the market. This paper presents a study on modeling and analysis of wholesale
competitive electricity market for a developing country to help regulators assess and predict market behaviour.
It involves modeling and simulation of the Zambian power system network in Agent-Based Modeling of
Electricity Systems (AMES) using real system data to pick out critical information that enables us to assess the
status of the market. The results indicate that market power exploitation is prevalent for the two largest GenCos
assessed.
Keywords: AMES, DCOPF, Locational Marginal Prices (LMPs), Residual Supply Index (RSI), Lerner Index
(LI), Relative Market Advantage Index (RMAI), Zambian Power Network.
I. INTRODUCTION
Restructuring in developing countries is still at its
infancy stage and is mainly driven as a part of
government’s macroeconomic policy to encourage
privatization and investments mainly in the
generation sector. Furthermore, the increase in power
demand has also enhanced some private sector
interest to invest in the power sector. It has been
observed through working electricity markets and
research that workable competitive electricity market
can drive this investment and reduce prices by
introducing cheaper generation technologies in the
network. In a competitive market environment,
infrastructure additions (Generation, Transmission
and Distribution equipment etc) are a result of
investment by independent companies seeking profit
from their investments.
In developing countries however, there are no
market operators and new generation investments is
driven mainly through signed Power Purchase
Agreements (PPAs).
The electricity supply in Zambia can best be
described as an oligopoly with the presence of
Lunsemfwa Hydro Power Company (LHPC,
52.5MW) an Independent Power Producer (IPP) and
Copperbelt Energy Corporation (CEC) an
independent transmission company on the Copperbelt
province. It is dominated by the state owned utility,
Zesco with generation, transmission and distribution
business units. The grid connected generation is
hydro based which include Kafue Gorge Power
Station (KGPS, 990MW), Kariba North Bank Power
Station (KNBPS, 720MW), Victoria Falls Power
Station (VFPS, 108MW) and four small hydros in the
northern part of the country with a total capacity of
23.75MW.
II. MARKET PERFORMANCE MEASURES
According to [1] and [2] market concentration is
the extent to which a relatively large share of market
activity is carried out by a relatively small number of
participant firms. The intuitive idea is that
anticompetitive behavior by firms is to be expected in
a market that is highly concentrated. Market
concentration measures are most often applied to the
seller side of a market. These measures depend
critically on the number of firms selling into a
market; and the relative “market share” of these seller
firms as measured either by output, by sales revenues,
or by operating capacity.
All else equal, these measures indicate an increase
in concentration either when the number of firms
decreases or when the market share of the largest
firms increases. The market concentration measures
used in this study include the Lerner Index (LI),
Residual Supply Index (RSI) and the Relative Market
Advantage Index (RMAI). Detailed formulas and
description of these concentration measures can be
found in [1].
III. AMES TEST BED SOFTWARE
AMES (Agent-based Modeling of Electricity
Systems) is an open-source agent-based
computational laboratory designed for the systematic
RESEARCH ARTICLE OPEN ACCESS

study of restructured wholesale power markets
operating over AC transmission grids subject to
congestion. Hourly Locational Marginal Prices
(LMPs) for the day-ahead market are determined via
DC Optimal Power Flow (DCOPF) based on the
demand bids and supply offers of traders with
learning capabilities. AMES incorporates, in
simplified form, core features of the wholesale power
market design proposed by the U.S. FERC. A detailed
description of AMES and its features can be found in
[3] [4] [5] [6] [7] [8] and [9].
IV. MODELING AND SIMULATION OF
THE ZAMBIAN NETWORK IN AMES
In the study the objective is to minimize generator
total variable costs in (1) subject to power-flow
balance constraints, transmission branch limits, and
GenCo capacity constraints.
Min 𝑎𝑃𝐺𝑖 + 𝑏𝑃𝐺𝑖
2𝐼
𝑖=1 + 𝜋 𝛿 𝑘 − 𝛿 𝑚
2
𝑘𝑚 ∈𝐵𝑅
(1)
A 33 bus system high voltage network of the
Zambian system was modeled with grid connected
generating stations. In the study seven GenCos were
considered with VFPS modeled as three different
companies comprising VFPS A, VFPS B and VFPS
C, others include KGPS, KNBPS, LHPC and the
small hydro power stations in the northern part of the
country were grouped together to form one company
called SmallHydros. Fourteen Load Serving Entities
(LSEs) were selected as bulk supply points. The cost
functions determined in [10] are used in this study
and are given in Table 1.
Table 1: Cost Functions used in the Study
Power Station
Cost function coefficients
a($/MWh) b($/MW2
h)
KGPS 0.465240492 0.00004348
KNBPS 1.127592221 0.000579739
VFPS A = SmallHydros 1.032842787 0.085033729
VFPS B = VFPS C =
LHPC
0.756703828 0.000145758
The simulation can be controlled to run for a
specified number of days. In this case, weekly load
simulations were conducted for a 100 day period to
depict one season loads on the assumption that the
change in the load profile between weeks and/or
months during a season is minimal or negligible
The cases that were modeled include a single
buyer model (base case) and a wholesale model
(contract case). The study considered RSI, LI and
RMAI calculations to determine market power abuse
and the effects of constrained generation on profits
and LMPs for the two largest power stations for the
above mentioned cases. The study also considered the
RSI calculation for the forecasted generation and
demand for the year 2020.
V. RESULTS AND DISCUSSION
A. Base Case
The RSI results for the two largest GenCos,
KGPS and KNBPS are given in Table 2. It can be
observed that none of the GenCos has an RSI value
that is above 1. This means that the two GenCos are
exhibiting potential seller market power because total
demand cannot be met without their capacity. KGPS
exhibits the worst RSI result.
The Results of the RMAI from day 5 to day 100
on a 5 day incremental basis are shown in Fig. 1 and
Fig. 2. The RMAI values for both GenCos are greater
than 0, a necessary condition for the GenCos to
exercise market power. However, in this case KNBPS
exhibit the worst RMAI result.
The results of the LI, also calculated from day 5 to
day 100 on a 5 day incremental basis at hour 19, are
shown in Fig. 3 and Fig. 4 for KGPS and KNBPS
respectively. The LI values for both GenCos are
greater than 0, a condition necessary for the GenCos
to exercise market power during the time period. In
this case, however, the LI results agree with the RSI.
B. Contract Case
The RSI results for the two largest GenCos,
KGPS and KNBPS are given in Table 3. It can be
observed that the RSI values have improved
compared to the base case; however KGPS is still
exhibiting potential for seller market power. KNBPS
exhibits potential for seller market power during the
peak period only, however if we use the rule that RSI
should be greater than 1.1 ninety-five percent of the
time then KNBPS does not meet the criteria based on
24 hours for the entire simulated season.
The RMAI values for both GenCos are worse off
compared to the base case. In this case KNBPS
exhibit very high levels of market power. This result
does not agree with the RSI results. This is because
there is a huge variation in the GenCo profits
benchmark for the contract case and this forms the
basis for the RMAI calculation.
The LI values show fluctuations between the first
day and day 55 for both GenCos and are slightly
worse off compared to the base case. This is because
a significant amount of supply has been taken out of
the market which results in rise in prices as exhibited
by the LMPs. This result is expected since the LI is
calculated with reference to the true marginal costs
which are the same for both the contract and the base
case.
C. RSI Forecasted Generation Case
The RSI was calculated based on the lower, base
and upper forecasted peak demand for the supply that
is due to be completed by 2020. The RSI results for
the four largest GenCos, KGPS, KNBPS, KGL and
Mamba are given in Table 4. It can be observed that
the RSI values are above 1 for the lower and base
peak demand scenarios. Since these peak demand
values represent peaks in the year 2020, it can be

inferred that all GenCos except KGPS will have RSI
values greater than 1.1 for 95% of the time in 2020
for the lower and base peak demand scenarios. From
this result we can predict that the market is moving
towards a situation where abuse of market power
won’t be prevalent. However it should be noted that
RSI does not take into consideration the complexities
of physical network architecture that could possibly
give otherwise results.
Figure 1: Relative Market Advantage Index Trend for Kafue
Gorge Power Station (KGPS)
Figure 2: Relative Market Advantage Index Trend for Kariba
North Bank Power Station (KNBPS)
Figure 3: Lerner Index Trend for Kafue Gorge Power Station
(KGPS)
Figure 4: Lerner Index Trend for Kariba North Bank Power
Station (KNBPS)
D. Comparison of Profits and LMPs under
Constrained Conditions
Fig. 5 shows the effect on the profits for KGPS
under the different scenarios. It can be observed that
KGPS would earn the highest profits when KNBPS is
constrained during the base case and it would earn the
lowest profits on the average when it is unconstrained
during the contract case. When KGPS is constrained
both under the base and contract case it is
substantially earning reasonably high profits
compared to the unconstrained base and contract
cases respectively. This can give KGPS incentives to
strategically withhold output in order to raise its
profits. The market regulator, Energy Regulation
Board (ERB) of Zambia would therefore be required
to assess the true status of the GenCo under these
scenarios.
On the other hand, KNBPS would earn the highest
profits when KGPS is constrained under the contract
case and it would earn the lowest profits on the
average during the entire run when it is unconstrained
during the contract case. Fig. 6 shows the effect on
the profits for KNBPS under the different scenarios.
When KNBPS is constrained during the base case, it
also earns higher profits compared to the
unconstrained base case, which can give it incentives
to operate and offer output on the market which is
less than its maximum available capacity. The market
regulator, ERB would therefore be required, like in
the KGPS case, to assess the true status of the GenCo
under this scenario as well. It is also worth
mentioning that it would not be in the interest of any
of the GenCos to withhold capacity to facilitate
higher profits for its competitor unless the GenCos
collude. The market regulator, ERB should therefore
be wary of such issues and act accordingly to curb
them
Fig. 7 shows the LMP trend under the different
scenarios at hour 19 from day 5 to 100. It can be
observed that the market produces the highest LMPs
when KGPS is constrained during the contract case.
This observation tallies with the trend in profits for
KGPS shown in Figure 9. As expected the lowest
0
1
2
3
4
5
6
5 20 35 50 65 80 95
RelativeMarketAdvantage
Index
Day
Relative Market Advantage Index - KGPS
Base Case
RMAI
Contract RMAI
0
200
400
600
800
1000
1200
5
20
35
50
65
80
95
RelativeMarketAdvantage
Index
Day
Relative Market Advantage Index - KNBPS
Base Case
RMAI
Contract RMAI
0
0.5
1
5 20 35 50 65 80 95
LernerIndex
Day
Lerner Index - KGPS
Contract
Base
0
0.2
0.4
0.6
0.8
1
5
15
25
35
45
55
65
75
85
95
LernerIndex
Day
Lerner Index - KNBPS
Basecase
Contract Case

average LMPs are observed during the unconstrained
base case. The base case and contract case LMPs
increase by about 300% and 600% on average
respectively when compared with the benchmark
LMPs (when GenCos submit true marginal costs).
Overall, KGPS and KNBPS both tend to earn
higher profits when KGPS is constrained during the
contract case and lower profits when KNBPS is
constrained during the contract case. The two
scenarios also have the highest average LMP at 14.2
$/MWh and second lowest LMP at 7.5$/MWh
respectively.
Table 2: Residual Supply Index (RSI) Values – Base Case
BASE CASE
Hour
Total
System
Load
RSI
(KGPS)
RSI
(KNBPS)
Station
Capacity MW
0:00 1537.43 0.58815 0.76377 KGPS 990
1:00 1515.28 0.59675 0.77493 KNBPS 720
2:00 1491.19 0.60639 0.78745 VFPS A 8
3:00 1474.21 0.61337 0.79652 VFPS B 60
4:00 1514.43 0.59708 0.77537 VFPS C 40
5:00 1558.31 0.58027 0.75353 LHPC 52.5
6:00 1588.48 0.56925 0.73922 SmallHydros 23.75
7:00 1592.87 0.56768 0.73718 Total supply 1894.25
8:00 1642.64 0.55048 0.71485
9:00 1616.04 0.55954 0.72661
10:00 1561.14 0.57922 0.75217
11:00 1593.05 0.56762 0.73710
12:00 1566.578 0.57721 0.74956
13:00 1536.18 0.58863 0.76439
14:00 1481.48 0.61036 0.79261
15:00 1453.24 0.62222 0.80801
16:00 1509.93 0.59886 0.77768
17:00 1543.08 0.58600 0.76097
18:00 1578.53 0.57284 0.74388
19:00 1666.05 0.54274 0.70480
20:00 1620.27 0.55808 0.72472
21:00 1555.62 0.581275 0.75483
22:00 1534.96 0.589101 0.76500
23:00 1516.04 0.596452 0.77454
VI. CONCLUSIONS
The study has shown that GenCos bid in the
market with profit maximization as their objective
function. It has shown that GenCos subsequently
changed their bids in the day-ahead market following
the profit results of their earlier bids. The study has
also shown that it is possible for KGPS & KNBPS to
withhold capacity in order to raise their profits.
Regulatory mechanisms need to be in place to ensure
that producers do not bid excessively beyond their
operating costs.
The Zambian network considered in the study
indicates that the market is highly concentrated. The
market performance measures calculated, i.e. RSI,
RMAI and LI, indicate seller market power by the
two largest GenCos, KGPS and KNBPS. The RSI is
not greater than 1.1 for 95% of the time for the base
case and contract case. The RSI value for the
projected generation and forecasted demand case
greatly improves and all GenCos except one meet the
CAISO threshold indicating that the market is
heading towards low concentration.
Despite the prevalence of market exploitation by
the two largest GenCos assessed, electricity markets
can work in Zambia with strict market rules until such
a time the market matures.
The wholesale model (contract case) is
recommended for the Zambian market as it will
provide the much needed future revenue streams
security needed by investors rather than using PPAs.
This is coupled with the fact that in hydro systems
prices vary seasonally making contracts easier to
implement.
REFERENCES
[1] A. Somani and L. Tesfatsion, "An Agent Based Test Bed
Study of Wholesale Power Market Performance Measures,"
IEEE Computational Intelligence Magazine (, Vols. 3, No. 4,,
pp. 56-72, November, 2008.
[2] P. Vassilopoulos, "Models for the Identification of Market
Power in Wholesale Electricity Markets," 2003.
[3] D. Koesrindartoto, J. Sun and L. Tesfatsion, "An Agent-Based
Computational Laboratory for Testing the Economic
Reliability of Wholesale Power Market Designs," in IEEE
Power Engineering Society Conference Proceedings,
California, June, 2005.
[4] H. Li, J. Sun and L. Tesfatsion, "Separation and Volatility of
Locational Marginal Prices in Restructured Wholesale Power
Markets," March, 2010.
[5] L. Tesfatsion, "The AMES Wholesale Power Market Test Bed
as a Stochastic Dynamic State-Space Game," August, 2008.
[6] L. Tesfatsion and H. Li, "Capacity Withholding in
Restructured Wholesale Power Markets: An Agent-Based Test
Bed Study," Seattle, 2009.
[7] L. Tesfatsion and J. Sun, "Dynamic Testing of Wholesale
Power Market Designs: An Open-Source Agent-Based
Framework," Computational Economics, July, 2007.
[8] L. Tesfatsion and J. Sun, "DC-OPF Formulation with Price-
Sensitive Demand Bids," 2008.
[9] L. Tesfatsion and H. Li, "The AMES Wholesale Power
Market Test Bed: A Computational Laboratory for Research,
Teaching, and Training," in IEEE Power and Energy Society
General Meeting, 2009.
[10] J. Mwanza, "Economic Modeling of Hydro Power System
Operations," Kathmandu University, Kathmandu, 2010.
[11] R. Bo, "Congestion and Price Prediction in Locational
Marginal Pricing Markets Considering Load Variation and
Uncertainty," University of Tennessee, Knoxville, 2009.
[12] E. Moyo and F. S. Chanda, "Zambia and Its Small
Hydropower Potential," Hangzhou Regional Centre,
Hangzhou, China, 2009.
[13] A. Sheffrin, J. Chen and B. Hobbs, "Watching Watts to
Prevent Abuse of Power," IEEE Power and Energy Magazine,
p. 58–65, July/August 2004.
[14] L. Tesfatsion, "DC Optimal Power Flow Formulation in
AMES," 2010.
[15] I. Wangensteen, Power System Economics - the Nordic
Electricity Market, Trondheim: Tapir Academic Press,
December, 2011.
[16] P. Yangdon, "Modeling and Analysis of a Competitive
Electricity Market in Bhutan," Chalmers University,
Göteborg, 2009.

[17] T. J. Overbye and J. D. Weber, "An Individual Welfare
Maximization Algorithm for Electricity Markets," in IEEE
Transactions on Power Systems, August 2002.
[18] L. Tesfatsion and J. Sun, "Open-source software for power
industry research, teaching, and training: A DC-OPF
illustration," in IEEE Proceedings PES GM, Tampa, Florida,.,
June, 2007.
Table 3: Residual Supply Index (RSI) Values – Contract Case
CONTRACT CASE
Hour Total System Load RSI (KGPS) RSI (KNBPS) Station Capacity MW Contract
Market
Supply
0:00 1537.436549 0.848328 1.023945 KGPS 990 400 590
1:00 1515.288127 0.860727 1.038911 KNBPS 720 400 320
2:00 1491.195524 0.874634 1.055697 VFPS A 8
3:00 1474.210043 0.884711 1.06786 VFPS B 60
4:00 1514.433683 0.861213 1.039497 VFPS C 40
5:00 1558.317209 0.836961 1.010224 LHPC 52.5
6:00 1588.488337 0.821064 0.991037 SmallHydros 23.75
7:00 1592.87508 0.818802 0.988307 Total supply 1894.25
8:00 1642.649548 0.793992 0.95836
9:00 1616.045956 0.807062 0.974137
10:00 1561.142071 0.835446 1.008396
11:00 1593.051021 0.818712 0.988198
12:00 1566.578541 0.832547 1.004897
13:00 1536.184049 0.849019 1.02478
14:00 1481.487333 0.880365 1.062615
15:00 1453.248698 0.897472 1.083263
16:00 1509.939443 0.863776 1.042591
17:00 1543.086595 0.845222 1.020196
18:00 1578.535119 0.826241 0.997285
19:00 1666.0562 0.782837 0.944896
20:00 1620.276843 0.804955 0.971593
21:00 1555.62978 0.838406 1.01197
22:00 1534.963772 0.849694 1.025594
23:00 1516.046398 0.860297 1.038392
Table 4: Residual Supply Index (RSI) Values – Forecast Case
2020 RSI CALCULATION BASED ON CURRENT PROJECTS
Projected Peak
Load (MW) RSI (KGPS)
RSI
(KNBPS) RSI (KGL) RSI (MAMBA) Station Capacity MW
Lower Case 2583 1.058556 1.163086 1.15147116 1.20954317 KGPS 990
Base Case 2732 1.000824 1.099652 1.0886713 1.14357613 KNBPS 720
Upper Case 3243 0.843124 0.92638 0.9171292 0.96338267 VFPS A 8
VFPS B 60
VFPS C 40
LHPC 52.5
SmallHydros 23.75
Proj. Gen* ITT 120
Proj. Gen* KGL 750
Proj. Gen* MAMBA 600
Proj. Gen* KNBE 360
Total supply 3724.25
*Projected Generation

Figure 5: Kafue Gorge Power Station (KGPS) Profit Trends
Figure 6: Kariba North Bank Power Station (KNBPS) Profit Trends
Figure 7: Locational Marginal Prices (LMPs) Trends
0
50,000
100,000
150,000
200,000
250,000
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Profits($/D)
Day
KGPS Profits Under Different Case Scenarios
Base
Constrained KGPS-Base
Constrained KNBPS - Base
Contract
Constrained KGPS -Contract
Constrained KNBPS - Contract
0
20,000
40,000
60,000
80,000
100,000
120,000
140,000
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Profits($/D)
Day
KNBPS Profits Under Different Case Scenarios
Base
Contract
0
2
4
6
8
10
12
14
16
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
LocationalMarginalPrices($/MWh)
Day
Various Case Scenarios LMPs from Day 5 to 100 at hr 19
Base
Contract

Modeling and Analysis of Wholesale Competitive Electricity Markets: A Case For Zambia

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