Abstract
This chapter presents a generic mixed integer linear programming (MILP) model that integrates the unit commitment problem (UCP), i.e., daily energy planning with the long-term generation expansion planning (GEP) framework. Typical daily constraints at an hourly level such as start-up and shut-down related decisions (start-up type, minimum up and down time, synchronization, soak and desynchronization time constraints), ramping limits, system reserve requirements are combined with representative yearly constraints such as power capacity additions, power generation bounds of each unit, peak reserve requirements, and energy policy issues (renewables penetration limits, CO2 emissions cap and pricing). For modelling purposes, a representative day (24 h) of each month over a number of years has been employed in order to determine the optimal capacity additions, electricity market clearing prices, and daily operational planning of the studied power system. The model has been tested on an illustrative case study of the Greek power system. Our approach aims to provide useful insight into strategic and challenging decisions to be determined by investors and/or policy makers at a national and/or regional level by providing the optimal energy roadmap under real operating and design constraints.
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Abbreviations
- EU:
-
European Union
- GEP:
-
Generation Expansion Planning
- MILP:
-
Mixed Integer Linear Programming
- NGCC:
-
Natural Gas Combined Cycle
- NGGT:
-
Natural Gas Turbine (or Natural Gas Open Cycle)
- O&M:
-
Operational and Maintenance
- RET:
-
Renewable Energy Technologies
- SMP:
-
System Marginal Price
- UCP:
-
Unit Commitment Problem
- \(a \in A\) :
-
Set of start-up types {hot, warm, cold}
- \(bl \in BL\) :
-
Set of blocks of the energy offer function of each hydrothermal unit (or energy bids for load representatives)
- \(i \in I^{EX}\) :
-
Set of existing units
- \(i \in I^{HT}\) :
-
Set of hydrothermal units
- \(i \in I^{NEW}\) :
-
Set of new candidate units
- \(i \in I^{RES}\) :
-
Set of renewable units (including hydro units)
- \(i \in I^{RES - }\) :
-
Set of renewable units (not including hydro units)
- \(i \in I^{S}\) :
-
Set of units \(i \in I\) that are (or can be) installed in sector \(s \in S\)
- \(i \in I^{TH}\) :
-
Set of thermal units
- \(i \in I^{z}\) :
-
Set of units \(i \in I\) that are (or can be) installed in zone \(z \in Z\)
- \(i \in I\) :
-
Set of all units
- \(m \in M\) :
-
Set of months
- \(nc \in NC^{s}\) :
-
Set of neighbouring countries \(nc \in NC\) interconnected with sector \(s \in S\)
- \(nc \in NC^{z}\) :
-
Set of neighbouring countries \(nc \in NC\) interconnected with zone \(z \in Z\)
- \(nc \in NC\) :
-
Set of interconnections (neighbouring countries)
- \(s \in S^{{s^{'} }}\) :
-
Set of sectors \(s \in S\) interconnected with sector \(s^{'} \ne s \in S\)
- \((s, s^{{\prime }} ) \in S\) :
-
Set of sectors
- \((t,t^{{\prime }} ) \in T\) :
-
Set of hours
- \((y,y^{'} ) \in Y\) :
-
Set of years
- \(z \in Z\) :
-
Set of zones
- \(AV_{i,z,m,t}\) :
-
Availability factor of each unit \(i \in I^{RES}\) in zone \(z \in Z\), month \(m \in M\), and hour \(t \in T\) (p.u.)
- \(CEXPB_{nc,bl,y,m,t}\) :
-
Export (load) revenues of block \(bl \in BL\) of interconnection \(nc \in NC\), in year \(y \in Y\), month \(m \in M,\) and hour \(t \in T\) (€/MW)
- \(CFL_{{s,s^{'} ,y}}\) :
-
Maximum corridor flow from sector \(s \in S\) to sector \(s^{'} \ne s \in S\) in year \(y \in Y\) (MW)
- \(CIMPB_{nc,bl,y,m,t}\) :
-
Marginal cost of block \(bl \in BL\) of the imported energy offer function from interconnection \(nc \in NC\), in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (€/MW)
- \(CIM_{nc,y}\) :
-
Power capacity of interconnection \(nc \in NC\) in each year \(y \in Y\) (MW)
- \(CO_{2} \_CAP_{y}\) :
-
Maximum allowable CO2 emissions produced in year \(y \in Y\) (t CO2)
- \(CO_{2} \_EF_{i,bl}\) :
-
CO2 emission factor of each unit \(i \in I^{TH}\), in power capacity block \(bl \in BL\) (tCO2/MWh)
- \(CPB_{i,bl,y,m,t}\) :
-
Marginal cost of block \(bl \in BL\) of the energy offer function of each unit \(i \in I^{HT}\), in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (€/MW)
- \(CR1_{i,y,m,t}\) :
-
Price of the primary energy offer of each unit \(i \in I^{HT}\), in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (€/MW)
- \(CR2_{i,y,m,t}\) :
-
Price of the secondary range energy offer of each unit \(i \in I^{HT}\), in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (€/MW)
- \(CRF_{i}\) :
-
Capital recovery factor of each unit \(i \in I^{NEW}\) (p.u.)
- \(CSD_{i}\) :
-
Shut-down cost of each thermal unit \(i \in I^{TH}\) (€)
- \(DUR_{m}\) :
-
Duration of each month (in days)
- \(Dem_{s,y,m,t}\) :
-
Power load of sector \(s \in S\), in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(EFORIM_{nc,y}\) :
-
Unavailability factor of each interconnection \(nc \in NC\) in each year \(y \in Y\) (p.u.)
- \(EFOR_{i,y}\) :
-
Unavailability factor of each unit \(i \in I^{TH}\) in each year \(y \in Y\) (p.u.)
- \(Exblock_{nc,bl,y,m,t}\) :
-
Quantity of each power capacity block \(bl \in BL\) of each interconnection \(nc \in NC\) (exports), in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(FOM_{i}\) :
-
Fixed operational and maintenance cost of each unit \(i \in I^{RES - }\) (€/MW)
- \(FastR2Req_{y,m,t}^{down}\) :
-
System requirements in fast secondary-down reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(FastR2Req_{y,m,t}^{up}\) :
-
System requirements in fast secondary-up reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(IC_{i,y}\) :
-
Installed capacity of unit \(i \in I^{EX}\) in year \(y \in Y\) (MW)
- \(INL_{z,y,m,t}\) :
-
Injection losses coefficient in zone \(z \in Z\), year \(y \in Y\) month \(m \in M\), and hour \(t \in T\) (p.u.)
- \(INVC_{i,y}\) :
-
Investment cost of unit \(i \in I^{NEW}\) in year \(y \in Y\) (€/MW)
- \(Imblock_{nc,bl,y,m,t}\) :
-
Quantity of each power capacity block \(bl \in BL\) of each interconnection \(nc \in NC\) (imports), in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(MRES_{y}\) :
-
Maximum RES penetration in year \(y \in Y\) (p.u.)
- \(PBL_{i,bl,y,m,t}\) :
-
Quantity of each power capacity block \(bl \in BL\) of the energy offer function of unit \(i \in I^{HT}\) in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(PFX_{i,y,m,t}\) :
-
Fixed (non-priced) component of the energy offer function of each unit \(i \in I\) in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(PMAX_{i}^{dp}\) :
-
Maximum power output (dispatchable phase) of each unit \(i \in I^{HT}\) (MW)
- \(PMAX_{i}^{sc}\) :
-
Maximum power output (when providing secondary reserve) of each unit \(i \in I^{HT}\) (MW)
- \(PMIN_{i}^{dp}\) :
-
Minimum power output (dispatchable phase) of each unit \(i \in I^{HT}\)(MW)
- \(PMIN_{i}^{sc}\) :
-
Minimum power output (when providing secondary reserve) of each unit \(i \in I^{HT}\)(MW)
- \(PSK_{i}\) :
-
Power output of each thermal unit \(i \in I^{TH}\) when operating in soak phase (MW)
- \(R1Req_{y,m,t}\) :
-
System requirements in primary-up reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(R1_{i}\) :
-
Maximum contribution of unit \(i \in I^{HT}\) in primary reserve (MW)
- \(R2Req_{y,m,t}^{down}\) :
-
System requirements in secondary-down reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(R2Req_{y,m,t}^{up}\) :
-
System requirements in secondary-up reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(R2_{i}\) :
-
Maximum contribution of unit \(i \in I^{HT}\) in secondary reserve (MW)
- \(R3Req_{y,m,t}\) :
-
System requirements in tertiary reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(R3_{i}^{nsp}\) :
-
Maximum contribution of unit \(i \in I^{HT}\) in non-spinning tertiary reserve (MW)
- \(R3_{i}^{sp}\) :
-
Maximum contribution of unit \(i \in I^{HT}\) in spinning tertiary reserve (MW)
- \(REN_{y}\) :
-
RES penetration target in the power mix in year \(y \in Y\) (p.u.)
- \(RES\_CAP_{i,z,y}\) :
-
Maximum allowable capacity of each unit \(i \in I^{RES - }\) in zone \(z \in Z\), year \(y \in Y\) (p.u.)
- \(RR\_down_{i}\) :
-
Ramp-down rate of unit \(i \in I^{HT}\) (MW)
- \(RR\_sec_{i}\) :
-
Ramp rate of unit \(i \in I^{HT}\) when providing secondary reserve (MW)
- \(RR\_up_{i}\) :
-
Ramp-up rate of unit \(i \in I^{HT}\) (MW)
- \(T\_con_{i}\) :
-
Construction time of unit \(i \in I^{NEW}\) (y)
- \(T\_dn_{i}\) :
-
Desynchronization time of thermal unit \(i \in I^{TH}\) (h)
- \(T\_down_{i}\) :
-
Minimum down time of thermal unit \(i \in I^{TH}\) (h)
- \(T\_sd_{i}\) :
-
Non-operational time (after being shut-down) of thermal unit \(i \in I^{TH}\) (h)
- \(T\_sd_{i}^{cold}\) :
-
Non-operational time of thermal unit \(i \in I^{TH}\) before going from warm to cold standby condition (h)
- \(T\_sd^{prior}\) :
-
Extended time period in the past (greater than the higher cold reservation time of all thermal units) (h)
- \(T\_sd_{i}^{warm}\) :
-
Non-operational time of thermal unit \(i \in I^{TH}\) before going from hot to warm standby condition (h)
- \(T\_sk_{i}^{a}\) :
-
Type-\(a\) soak time of thermal unit \(i \in I^{TH}\) (h)
- \(T\_sn_{i}^{a}\) :
-
Type-\(a\) synchronization time of thermal unit \(i \in I^{TH}\) (h)
- \(T\_sd_{i}^{1,2}\) :
-
Non-operational time of thermal unit \(i \in I^{TH}\) before changing standby condition (h) (1: from hot to warm condition, 2: from warm to cold condition)
- \(T\_up_{i}\) :
-
Minimum up time of thermal unit \(i \in I^{TH}\) (h)
- \(RSV\) :
-
Minimum peak reserve requirements (p.u.)
- \(cf_{{s,s^{'} ,y,m,t}}\) :
-
Corridor power flow from sector \(s \in S\) to \(s \ne s^{'} \in S\) in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(c_{i,y}\) :
-
Power capacity of unit \(i \in I\) in year \(y \in Y\) (MW)
- \(expb_{nc,bl,y,m,t}\) :
-
Quantity of power capacity block \(bl \in BL\) exported to neighbouring country \(nc \in NC\), in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(exp_{nc,y,m,t}\) :
-
Total energy withdrawal (exports) to neighbouring country \(nc \in NC\), in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(fastr2_{i,y,m,t}^{down}\) :
-
Contribution of unit \(i \in I^{HT}\) in fast secondary-down reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(fastr2_{i,y,m,t}^{up}\) :
-
Contribution of unit \(i \in I^{HT}\) in fast secondary-up reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(im\_inj_{nc,y,m,t}\) :
-
Net (taking into account energy losses) energy injection (imports) to neighbouring country \(nc \in NC\), in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(impb_{nc,bl,y,m,t}\) :
-
Quantity of power capacity block \(bl \in BL\) imported from neighbouring country \(nc \in NC\), in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(imp_{nc,y,m,t}\) :
-
Energy injection (imports) from neighbouring country \(nc \in NC\), in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(nc_{i,y}\) :
-
Newly-built capacity of unit \(i \in I^{NEW}\) available for the first time in year \(y \in Y\) (MW)
- \(p\_dn_{i,y,m,t}\) :
-
Power output of thermal unit \(i \in I^{TH}\) when operating in the desynchronization phase in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(p\_inj_{i,y,m,t}\) :
-
Net (taking into account energy losses) energy injection (generation) from unit \(i \in I^{HT}\), in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(p\_sk_{i,y,m,t}\) :
-
Power output of thermal unit \(i \in I^{TH}\) when operating in the soak phase in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(pb_{i,bl,y,m,t}\) :
-
Quantity of power capacity block \(bl \in BL\) of unit \(i \in I^{HT}\), dispatched in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(p_{i,y,m,t}\) :
-
Energy injection (generation) from unit \(i \in I^{HT}\), in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(r1_{i,y,m,t}^{up}\) :
-
Contribution of unit \(i \in I^{HT}\) in primary-up reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(r2_{i,y,m,t}^{down}\) :
-
Contribution of unit \(i \in I^{HT}\) in secondary-down reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(r2_{i,y,m,t}^{up}\) :
-
Contribution of unit \(i \in I^{HT}\) in secondary-up reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(r3_{i,y,m,t}\) :
-
Total contribution of unit \(i \in I^{HT}\) in tertiary reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(r3_{i,y,m,t}^{nsp}\) :
-
Contribution of unit \(i \in I^{HT}\) in non-spinning tertiary reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(r3_{i,y,m,t}^{sp}\) :
-
Contribution of unit \(i \in I^{HT}\) in spinning tertiary reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\) (MW)
- \(cn_{i,y}\) :
-
Equals 1 if the decision for the construction of unit \(i \in I^{NEW}\) is to be taken in year \(y \in Y\)
- \(w_{i,y,m,t}\) :
-
Equals 1 if unit \(i \in I^{HT}\) is shut-down in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\)
- \(x\_3ns_{i,y,m,t}\) :
-
Equals 1 if unit \(i \in I^{HT}\) contributes to non-spinning tertiary reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\)
- \(x\_dn_{i,y,m,t}\) :
-
Equals 1 if thermal unit \(i \in I^{TH}\) operates in the desynchronization phase in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\)
- \(x\_dp_{i,y,m,t}\) :
-
Equals 1 if unit \(i \in I^{HT}\) operates in the dispatchable phase in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\)
- \(x\_sc_{i,y,m,t}\) :
-
Equals 1 if unit \(i \in I^{HT}\) contributes to secondary reserve in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\)
- \(x\_sk_{i,y,m,t}\) :
-
Equals 1 if thermal unit \(i \in I^{TH}\) operates in the soak phase in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\)
- \(x\_sk_{i,y,m,t}^{a}\) :
-
Equals 1 if thermal unit \(i \in I^{TH}\) operates in the type-\(a\) soak phase in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\)
- \(x\_sn_{i,y,m,t}\) :
-
Equals 1 if thermal unit \(i \in I^{TH}\) operates in the synchronization phase in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\)
- \(x\_sn_{i,y,m,t}^{a}\) :
-
Equals 1 if thermal unit \(i \in I^{TH}\) operates in the type-\(a\) synchronization phase in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\)
- \(x\_st_{i,y,m,t}\) :
-
Equals 1 if unit \(i \in I^{HT}\) starts-up in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\)
- \(x\_st_{i,y,m,t}^{a}\) :
-
Equals 1 if a type-\(a\) start-up decision is taken for thermal unit \(i \in I^{TH}\) in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\)
- \(x_{i,y,m,t}\) :
-
Equals 1 if unit \(i \in I^{HT}\) is committed (operational) in year \(y \in Y\), month \(m \in M\), and hour \(t \in T\)
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Financial support from the European Commission’s Marie Curie IRSES project (Contract No: PIRSES-GA-2011-294987) “Energy Systems Engineering” (ESE) is gratefully acknowledged.
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Koltsaklis, N.E., Kopanos, G.M., Georgiadis, M.C. (2017). An Optimization Framework for Power Systems Planning Considering Unit Commitment Constraints. In: Kopanos, G., Liu, P., Georgiadis, M. (eds) Advances in Energy Systems Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-42803-1_15
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