This document summarizes a student's research project investigating the influence of emissions trading schemes on electricity markets and prices using Benders decomposition. The student aimed to modify existing models to allow calculation of shadow prices for constraints in order to determine electricity prices. Due to time constraints, the student was unable to create a working program but provided code in an appendix that could be built upon. The document includes sections on problem formulation, generation scheduling, Benders decomposition, the software used, and conclusions.

1. 1
Influence of Emissions Trading Scheme on
Electricity Markets and Prices
Nicola Pellow
MEng Electrical and Mechanical Engineering
Supervised by Dr Ivana Kockar
Friday 24th
September 2010

2. 2
Contents
Contents .......................................................................................................................................... 2
Reflective Statement....................................................................................................................... 2
Introduction .................................................................................................................................... 3
Background.................................................................................................................................. 3
Aim .............................................................................................................................................. 3
Problem Formulation...................................................................................................................... 4
Generation Scheduling ................................................................................................................ 4
Benders Decomposition............................................................................................................... 5
Program Creation ........................................................................................................................ 6
Conclusion....................................................................................................................................... 6
Bibliography .................................................................................................................................... 7
Appendix A – Code.......................................................................................................................... 9
Appendix B – Notation.................................................................................................................. 10
Reflective Statement
I have reallyenjoyedthissummerinternship and am very grateful for the opportunity. Previous to this
internshipI had very little idea what a research post in a University would involve. The induction days
were bothhelpful,particularlythe first one which introduced the whole aim of the scheme and gave a
chance to see the posters of other researchers.
Throughthe course of thissummerI have metnumerous PhD students and lecturers who were all very
helpful.Ialsohada chance to get to know other research interns, who have become good friends, and
heard about their various projects from completely different departments. My supervisor was very
helpful,thoughoftenawayatconferences,whichmeantthatnotas much progresswasmade as I would
have hoped. Hopefully though it is work that will be able to be continued by my supervisor, possibly
with my help during the year.
I have thoroughly enjoyed the summer and the project I was involved in. My research was in an area
which I have not had much opportunity to study within the context of my course but may link in with
some of my final year classes and is possibly an area I would be interested in further pursuing.
I definitely have a much better picture of what a researchers’ job involves now. It is a very different
experience toundergraduate studyor the industry placements I have had. I am still not sure whether I
would consider doing a PhD but feel more able to make an informed decision.

3. 3
Introduction
Background
One of the strategic aims of the UK government is to ensure sustainable and secure energy supply.
Within the electricity sector this implies using different sources of generation, and especially the
building and integration of renewable resources. It also means setting limitations on greenhouse gas
emissionsproducedbythermal generation.The laterismanagedthroughthe EuropeanUnionEmissions
Trading Scheme (ETS), which is a “cap and trade” mechanism that restricts the total quantity of
emissions to the targeted level. This is then distributed among industrial installations, including
electricitygenerators.Inordertoproduce electricity,generatorswilluse these allowances. If they wish
to generate more than the allocated allowance permit, generating companies will need to purchase
additional allocations from installations that have not fully utilized their allocations, or pay high
penalties.
The ETS will influence the electricity generation sector in a few ways. First, amounts and prices of
allowancesmaydetermine availabilityof thermal generators[1].Second,pricesof allocationsmayaffect
energyprices,butwill alsohave effectonprofitabilityof differentgenerationtechnologies. This further
means that a generation mix will be affected by the price (and future forecasted prices) of carbon
emissions. Finally, integration of renewable generation will also depend on the availability of the
electricity network infrastructure, and the lack of transmission capacity can significantly undermine
planned emissions reductions [2].
Aim
The aim of this research is to study the influence of the ETS and network capacity on generation
availability and prices in electricity markets. This will build on work presented in [1] and [2], which
modelled generation scheduling with ETS and very simplified transmission constraints in electricity
markets.Inthispreviouswork,amethod that yielded only decisions variables was used, while (due to
the MIP nature of the problem) shadow prices associated with the constraints were not considered.
However,incentralizedelectricity markets these shadow prices are often used as electricity prices. To
allow for a calculation of these prices, problem formulations from [1] and [2] will be modified for the
applicationof decomposition techniques. In particular, this summer project will investigate the use of
Benders decomposition to solve for this type of the problem.

4. 4
Problem Formulation
Generation Scheduling
The problemthatneedstobe solvedisknownasSecurityConstrainedUnitCommitment (SUCU). Figure
1 showsthe hierarchyforcalculatingSUCU, whichis basedon the existing set up in restructured power
systems. This investigation looked into solving this problem using Benders Decomposition which is
describedbelow. The solutionrequired isthe on/off state of generation unitswhich satisfy the network
constraints.
Figure 1: ISO and Market Participants [3]
The objective is to minimise:
𝑍 = ∑∑ 𝑐𝑖 𝑝𝑖𝑡 + 𝑠𝑡𝑖 𝛼𝑖𝑡 + 𝑠𝑑 𝑖 𝛽𝑖𝑡
𝑁𝐺
𝑖=1
𝑇
𝑡=1
Thisfunctionrepresentsthe start-up,shutdownandproduction costs(notationisexplainedinAppendix
B). This must be solved subject to the following constraints:
Logically, a unit that is online cannot be started up and a unit that is offline cannot be shutdown:
𝛼𝑖𝑡 − 𝛽𝑖𝑡 = 𝐼𝑖𝑡 − 𝐼𝑖(𝑡−1)
Minimum up and down times of units:
∑ 𝐼𝑖𝑡
𝑡+𝑇𝑖,𝑚𝑖𝑛
𝑜𝑛
−1
𝑡
≥ 𝛼𝑖𝑡 𝑇𝑖,𝑚𝑖𝑛
𝑜𝑛
∑ 𝐼𝑖𝑡 ≥
𝑁𝑇
𝑡
𝛼𝑖𝑡(𝑁𝑇− 𝑡 + 1)
∑ [1 − 𝐼𝑖𝑡]
𝑡+𝑇𝑖,𝑚𝑖𝑛
𝑜𝑓𝑓
−1
𝑡
≥ 𝛽𝑖𝑡 𝑇𝑖,𝑚𝑖𝑛
𝑜𝑓𝑓
∑[1 −
𝑁𝑇
𝑁
𝐼𝑖𝑡] ≥ 𝛽𝑖𝑡(𝑁𝑇 − 𝑡 + 1)
GENCOs TRANSCOs DISCOs
Master Problem
(Optimal Generation)
Subproblem
(NetworkSecurityCheck)
Schedules
UCCuts

5. 5
Systemreserve requirements:
∑ 𝑝𝑖,𝑚𝑎𝑥 𝐼𝑖𝑡 ≥ 𝐷𝑡 + 𝑅 𝑡
𝑁𝐺
𝑖=1
Hourlypowerdemand:
∑𝑝𝑖𝑡 = 𝐷𝑡
𝑁𝐺
𝑖=1
Thermal unitcapacityconstraint:
𝑃𝑖,𝑚𝑖𝑛 𝐼𝑖𝑡 ≤ 𝑝𝑖𝑡 ≤ 𝑃𝑖,𝑚𝑎𝑥 𝐼𝑖𝑡
Hourlynetworkconstraint:
−𝑃𝐿 𝑘𝑚,𝑚𝑎𝑥 ≤ 𝑓𝑘𝑚𝑡(𝐼̅, 𝑝̅) ≤ 𝑃𝐿 𝑘𝑚,𝑚𝑎𝑥
Benders Decomposition
Figure 2: Benders Decomposition Solution Framework [3]
The Benders decomposition was investigated, in which the problem is decomposed into a master
problem and two sub-problems representing feasibility and optimal operation sub-problems. The
master problem is a mixed integer program (MIP).
Once a potential solution is identified by the master problem, the feasibility sub-problem will check
whether this solution can meet the constraints. From this a corresponding Benders cut is obtained,
which is added to the master problem for solving the next iteration. Once a solution to the optimal
operation sub-problem is found this will form one or more constraints for the next iteration of the
optimal operation sub-problem by using dual multipliers. The iterative process continues until a
converged optimal solution is found [3].
Master Problem
Feasibility Check
Subproblem
Feasibility Check
Subproblem
Optimal Operation Subproblem
Infeasibility CutInfeasibility Cut
Feasibility Cut
Plan
Plan Plan

6. 6
Program Creation
The software usedtobuilda program was XpressIVE. This uses similar structures to C++ but is specially
designed for the solving of Mixed Integer Problems (MIP). A model already existed that was used to
solve BendersDecompositionproblemsandsothe aimwasto adapt thisto solve the problemexplained
above.
However,itwasa complicatedlanguage tolearn and a lack of organisation meant that this was left too
late and so it was not possible to produce a working code that met the objectives. But hopefully the
code producedcan be carried onby othersto produce a useful programinthe future (the code that was
produced is attached in Appendix A).
Conclusion
In the future there will be a need for a huge increase in the amount of electricity that comes from
renewable sources, which brings with it additional complexities for the scheduling of generation to
ensure that demand and supply are always matched. It is important that further research is done into
the effects of the ETS on pricing and availability.
Bendersdecompositioncouldprovideauseful methodforsolvingthe more complex problems that will
arise. It was not possible in the course of this project to produce a working program that showed this
but hopefully the work done will provide a first step which can be built upon further.

7. 7
Bibliography
[1] I. Kockar, A. J. Conejo and J. R. McDonald “Influence of the Emission Trading Scheme on Market
Clearing”. (Invited Paper). International Journal of Electrical Power and Energy Systems, Vol. 31, No. 9
(Special Issue withselected papers from the 17th Power System Computation Conference (PSCC)), pp.
465-473.
[2] I.Kockar “GenerationSchedulingwithETSandTransmissionCapacity”,submittedtothe Special Issue
on Impacts of Emission Trading on Power Industry and Electricity Markets, International Journal of
Energy Sector Management
[3] Shahidepour S. M. and Fu Y., “Benders decomposition in restructured power systems”, Electric
Power and Power Electronics Center, Illinois Institute of Technology
[4] Glover and Sarma, “Power System Analysis and Design”, 2008
[5] Wood and Wollenberg, “Power Generation, Operation and Control”, 1984
[6] MacKay D.J.C., “Sustainable Energy – Without the hot air”, 2008
[7] Castillo E., Conejo A., Pedregal P., Garcia R. and Alguacil N., “Building and Solving Mathematical
Programming Models in Engineering and Science”, John Wiley & Sons, 2002
[8] Kockar, “EU Perspective on the Kyoto Protocol”, 2006
[9] DTI, UK, “Energy White Paper: Our Energy Future – creating a low carbon economy”, 2003
[10] DTI, UK, “Energy White Paper: Meeting the Energy Challenge”, 2007
[11] ILEX Consulting, Report for DTI, UK, “Impact of the EU ETS on European Electricity Prices”, 2004
[12] IPA EnergyConsulting,ReportforDTI,UK, “Implicationsof the EU ETS for the UK Power Generation
sector”, 2005
[13] SijmJ.P.M,BakkerS.J.A.,ChenY.,HarmsenH.W. and Lise W., ECN report, “CO2 Price Dynamics: The
implications of EU emissions trading for the price of electricity”, 2005
[14] Kockar I., Conedjo A.J. and McDonald J.R., “Influence of the Emission Trading Scheme on Market
Clearing”, Invited Journal of Electrical Power and Energy Systems, Vol. 31, No. 9 pp465-473, 2009
[15] Kockar I., “Generation Scheduling with ETS and Transmission Capacity”, submitted to the Special
Issue onImpacts of EmissionTradingonPowerIndustryandElectricityMarkets,International journal of
Energy Sector Management, 2009
[16] Betz R., Sato M, “Emissions Trading: Lessons learnt from the 1st
phase of the EU ETS and prospects
for the 2nd
phase”, Clim. Policy 2006
[17] Benders, “Partitioning procedures for solving mixed-variable programming problems”, 1962

8. 8
[18] Cordeau, “The Benders Decomposition Method”, 2007
[19] Shahidehpour S. M. and Fu Y., “Applying Benders Decomposition to Power Systems”, IEEE Power
and Energy Magazine, 2005.
[20] Shahidepour S. M., Yamin H. Y. and Al-Tallaq K., “New approach for dynamic optimal power flow
using Benders decomposition in a deregulated power market”, 2002
[21] Shahidepour S. M. and Ma H., “Transmission-constrained unit commitment based on Benders
decomposition”, Illinois Institute of Technology, Chicago, 1998
[22] Alguacil N.andConejoA.J.,“MultiperiodOptimal PowerFlow UsingBenders Decomposition”, IEEE
TRANSACTIONS ON POWER SYSTEMS. Vol.. IS, NO. I, FEBRUARY 2000
[23] “Multiple models and parallel solving with Mosel”, Dash Optimization Whitepaper, October 2006
[24] “Xpress-Mosel Reference manual”, FICO, March 2009

9. 9
Appendix A – Code
model Project01
uses "mmxprs";
parameters
N_gen=2 !# of generators
T_horizon=2 !# of periods in a time horizon
N_bus=3 !# of buses
end-parameters
declarations
unit_number: array(1..N_gen) of real !unit number
Pg: array(1..T_horizon,1..N_bus) of real !generation output at bus
Pd: array(1..T_horizon,1..N_bus) of real !generation demand at bus
Pg_min: array(1..N_gen) of real !min generation output
Pg_max: array(1..N_gen) of real !max generation output
P: array(1..T_horizon,1..N_gen) of real !generation output
STC: array(1..N_gen) of real !start up cost
SDC: array(1..N_gen) of real !shut down cost
feas: array(1..T_horizon) of integer
r: array(1..T_horizon) of real !curtailment
D: array(1..T_horizon) of real !demand
UNITS: range
HOURS: range
BUSES: range
ust: array(1..T_horizon,1..N_gen) of mpvar
usd: array(1..T_horizon,1..N_gen) of mpvar
u: array(1..T_horizon,1..N_gen) of mpvar
infeas_flag:integer
t: integer
i: integer
zlow: real
zup: real
end-declarations
!Get input data
!Start programme
writeln("Begin running model")
HOURS:=1..T_horizon
UNITS:=1..N_gen
BUSES:=1..N_bus
while(infeas_flag>=1)do
!Solve MP1 - get zlow, ust, usd and u
!Objective : maximise total value
zlow:=sum(t in HOURS,i in UNITS) ust(t,i)*STC(i)+usd(t,i)*SDC(i)
!Restrictions
sum(t in HOURS,i in UNITS) u(t,i)*Pg_max(i)>=sum(t in HOURS) D(t)
forall(t in HOURS,i in UNITS)ust(t,i)-usd(t,i)==u(t,i)-u(t-1,i)
!All variables are 0/1
forall(t in HOURS,i in UNITS) u(t,i) is_binary
forall(t in HOURS,i in UNITS) ust(t,i) is_binary
forall(t in HOURS,i in UNITS) usd(t,i) is_binary

10. 10
minimize(zlow) !Solves the MIP problem
infeas_flag:=0
!Feasibility Check
while(t<=T_horizon)do
!feasibility check - get r(t), p(i,t), f(j,t)
!Constraints
[sum(i in UNITS)P(t,i)]-r(t) = sum(b in BUSES)[Pg(b,t)-Pd(b,t)]
Pg(t,b)<=u(t,i)*Pg_max(i) !lambdau(i)
-Pg(t,b)<=u(t,i)*Pg_min(i) !lambdal(i)
minimize(r(t))
if r(t)<>0
then feas(t):=1
!get dual multipliers lambdau(i) and lambdal(i)
!get infeasibility cut and add to MP1
else
feas(t):=0
end-if
infeas_flag:=infeas_flag+feas(t)
t+=1
end-do
end-do
Page 2 of 2
!solve optimal subproblem
while(zlow<>zup)do
get feasibility cut and add to MP1
get zlow and zup
end-do
!Print results
writeln("End running model")
end-model
Appendix B – Notation
i The number of generation unit
sti The startup cost of unit i
αi A binary variable which equals 1 if unit i is started up at hour t, and 0 otherwise
sdi The shutdown cost of uni i
βi A binary variable which equals 1 if unit i is shut down at hour t, and 0 otherwise
ci The cost coefficient of unit i
pit The power generated by unit i at hour t
Iit A binary variable that is equal to 1 if unit i is online during hour t, and 0 otherwise
Ton
i,min The minimum up time of unit i
Toff
i,min The minimum down time of unit i
NG The number of units
Dt The demand at hour t
Rt The system reserve at hour t
fkm The power flow on the line extending from bus k to bus m
PLkm,max The line capacity