Enhanced Decision Support for a Changing Electricity Landscape:

Transcription

1 Enhanced Decision Support for a Changing Eectricity Landscape: The GenX Configurabe Eectricity Resource Capacity Expansion Mode An MIT Energy Initiative Working Paper Revision 1.0 November 27, 2017 Jesse D. Jenkins* Nestor A. Sepuveda* *These authors contributed equay to this work Institute for Data, Systems, and Society, Massachusetts Institute of Technoogy Department of Nucear Science and Engineering, Massachusetts Institute of Technoogy MIT Energy Initiative, 77 Massachusetts Ave., Cambridge, MA 02139, USA MITEI-WP

2 Enhanced Decision Support for a Changing Eectricity Landscape: The GenX Configurabe Eectricity Resource Capacity Expansion Mode Revision 1.0 Jesse D. Jenkins & Nestor A. Sepuveda November 27, 2017 Abstract The eectric power sector is currenty undergoing severa important transitions, which individuay and coectivey have the potentia to transform the design, operation, and characteristics of eectricity systems, incuding: decarbonization of eectricity suppies; increased adoption of variabe renewabe energy and distributed energy resources; digitization of power systems; and eectrification of greater shares of heating, transportation, and industry. In the face of these transformations, many conventiona eectricity resource capacity expansion modes are no onger adequate for rigorous decision support and poicy anaysis. This working paper describes the formuation of GenX, a highy-configurabe eectricity resource capacity expansion mode that incorporates severa state-of-the-art improvements in eectricity system modeing to offer improved decision support for a changing eectricity andscape. GenX is a constrained optimization mode that determines the mix of eectricity generation, storage, and demand-side resource investments and operationa decisions to meet eectricity demand in a future panning year at owest cost subject to a variety of power system operationa constraints and specified poicy constraints, such as CO 2 emissions imits. The appropriate eve of mode resoution with regards to chronoogica variabiity of eectricity demand and renewabe energy avaiabiity, power system operationa detai and unit commitment constraints, and transmission and distribution network representation each vary for a given panning probem or poicy question. As such, the GenX mode is designed to be highy configurabe, with severa different degrees of resoution possibe on each of these three key dimensions. The mode is capabe of representing a fu range of conventiona and nove eectricity resources, incuding therma generators, variabe renewabe resources (wind and soar), run-of-river, reservoir and pumped-storage hydroeectric generators, energy storage devices, demand-side fexibiity, and severa advanced technoogies such as high temperature nucear reactors and carbon capture and storage. Two optiona modues aso aow modeing of heat storage, industria heat demand, and co-generation of heat and power; and distributed energy resources depoyed at distribution votages. The mode has been impemented in Juia Language. These authors contributed equay to this work Institute for Data, Systems, and Society, Massachusetts Institute of Technoogy Department of Nucear Science and Engineering, Massachusetts Institute of Technoogy 1

3 Contents 1 Introduction 4 2 Mode Introduction 7 3 Notation Mode Indices and Sets Decision Variabes Parameters Mode Formuation 17 5 Description of the Mode Indices and Sets Decision Variabes Objective Function Accounting for CO 2 Emissions Limits Accounting for Renewabe Energy Requirements Accounting for Demand Baance Accounting for Transmission and Network Expansion Between Zones Accounting for Transmission Losses Accounting for Unit Commitment Non-Custered Therma Technoogies: Operationa Requirements Accounting for Renewabe Resources Accounting for Storage Technoogies Accounting for Demand Side Resources Accounting for NACC and Heat Storage

4 5.15 Accounting for Hydro Reservoir Resources Accounting for Operating Reserves Accounting for Distribution Losses and Expansion Non-Negativity and Integraity Constraints Appendix A: GenX Use Cases 61 References 66 3

5 1 Introduction The eectric power sector is currenty undergoing severa important transitions, which individuay and coectivey have the potentia to transform the design, operation, and characteristics of eectricity systems. These transitions incude the drive to decarbonize eectricity generation to hep confront cimate change, increased adoption of distributed energy resources and decentraization of eectricity service provision, digitization of power systems, eectrification of greater shares of transportation, heating and industria energy demand, and the growth of variabe renewabe energy resources such as wind and soar energy. These transitions are occurring against the backdrop of rapidy changing technoogy costs, introduction of new technoogies and resources, and significant poicy uncertainty. Decision support toos, incuding power system optimization modes, can hep expore these important transitions, iuminate key mechanisms, uncertainties and risks, and hep guide power system panners, poicy makers and businesses. In particuar, capacity expansion (or capacity panning) modeing toos have historicay been used to hep expore the east-cost mix of various avaiabe eectricity generation resources under a given scenario. Capacity expansion modes are heaviy empoyed in east-cost or integrated resource panning [1 4] for reguated or pubicy-owned utiities. In addition, whie eectricity markets in many jurisdictions are now competitive and investment decisions are made by diverse individua actors, the eectricity sector remains heaviy reguated everywhere and extensivey infuenced by market design decisions, reguated tariffs, and pubic poicy incentives (e.g., tax poicies, mandates). Capacity expansion modes can thus pay a critica roe in poicy anaysis and indicative panning [5] to inform the many processes by which reguators and states guide eectricity market actors to achieve societa objectives, incuding economic efficiency, security, and environmenta outcomes. Capacity expansion modes aso serve a usefu roe in techno-economic assessment of emerging eectricity generation, storage, and demand-side resources and their impact on eectricity systems (e.g., [6 9]). Unfortunatey, conventiona capacity expansion panning methods are no onger adequate to rigorousy evauate options in the face of the ongoing transformation of power systems. Conventiona methods, incuding the screening curves or non-sequentia oad duration curve methods [2, 10 13] at the heart of many widey used inear programming-based capacity expansion modes (e.g., [14 16]), typicay ignore severa features that are increasingy important to eectricity resource investment and panning decisions. First, conventiona modes typicay represent the operation of power systems with very imited detai, frequenty ignoring key features such as inter-tempora constraints on rates of change in power pant output (ramp rates), unit commitment decisions (start-up, shut-down) and minimum stabe output eves for therma power pants, and the various casses of frequency reguation and operating reserves required to ensure reiabiity in the face of unpanned power pant or transmission ine outages or errors in eectricity demand or renewabe energy forecasts. Abstracting these important power system operationa detais in capacity panning modes can resut in significant errors, particuary in power systems with high shares of variabe renewabe energy resources. 4

6 Second, many modes represent chronoogica variabiity of eectricity demand and renewabe energy resource quaity in a highy abstracted manner, such as a imited number of time sices, oad bocks, or simpified oad duration curves. Faiing to accuratey account for the chronoogica variabiity and correations between both renewabe energy output and eectricity demand can aso resut in significant errors in capacity expansion decisions. Third, conventiona modes typicay ignore eectricity transmission and distribution network infrastructure. This prevents accurate evauation of the potentia vaue and impact of distributed energy resources, which are depoyed at different votage eves and ocations in the distribution network, as we as renewabe energy resources, which entai tradeoffs between siting at ocations with differing resource quaity and differing impact on transmission networks or requirements for network expansion. Fourth, most power system modes represent eectricity demand as exogenous and incude itte if any integration with other adjacent sectors, such as transportation or heating energy demand. As demand-side fexibiity becomes an increasingy important component of power system panning and operations and as eectricity expands to provide a greater share of fina energy demand in transportation, heating, and industria processes, capacity panning modes wi need to be further improved to capture these important inkages. In short, new decision support toos are needed for a changing eectricity andscape, incuding improved eectricity resource capacity expansion modes. Recent research has improved capacity panning methods and begun to address many of the shortcomings described above, incuding: enhanced representation of operation and unit commitment constraints in capacity panning modes [17 23]; representation of transmission network expansion and constraints and tradeoffs in renewabe energy siting [21, 24 28]; improved representation of demand-side fexibiity and distributed energy resources [29]; and new methods for representing tempora variabiity in demand and renewabe resource quaity [20, 22, 30 33]. Despite these methodoogica deveopments and ever-improving computationa resources, eectricity resource capacity expansion modes based on inear programming (LP) or mixed integer inear programming (MILP) methods continue to be constrained by computationa compexity and the high dimensionaity of reaistic power system optimization probems. These computationa constraints ead to inevitabe tradeoffs between computationa tractabiity and the degree of mode resoution on each of three key dimensions: 1. Representation of chronoogica variabiity in demand and renewabe resources; 2. Representation of power system operationa detai and constraints; and 3. Representation of transmission and distribution networks. Figure 1 depicts severa common options for the eve of detai aong each of these three dimensions. Additiona factors adding to dimensionaity incude: the number of distinct resource types and options 5

7 considered; modeing inkages to other sectors, such as heating and transportation demand; and endogenous treatment of uncertainty via stochastic or robust optimization methods. Unfortunatey, it remains infeasibe to simutaneousy mode the highest degree of detai possibe aong a dimensions at once. Instead, power system modeers must carefuy seect the appropriate eve of detai or abstraction and adopt dimensionaity reduction techniques appropriate to the questions at hand. Figure 1: Common options for mode resoution aong three key dimensions In ight of these chaenges, this paper introduces GenX, a highy configurabe eectricity resource capacity expansion mode intended to offer improved decision support capabiities for a changing eectricity andscape. This working paper describes the current version of the mode and is intended as a iving document to be revised upon subsequent improvements and iterations of the mode. GenX is a constrained optimization mode that determines the mix of eectricity generation, storage, and demand-side resource investments and operationa decisions to meet eectricity demand in a future panning year at owest cost subject to a variety of power system operationa constraints and specified poicy constraints, such as CO 2 emissions imits. As the appropriate eve of mode resoution with regards to chronoogica variabiity of oad and renewabe energy avaiabiity, operationa detai and constraints, and transmission and distribution network representation varies for a given panning probem or poicy question, the mode is designed to be highy configurabe, with severa different degrees of resoution possibe on these three key dimensions. These different configurations incude a variety of state-of-the-art techniques for addressing each of the three dimensions described. The remainder of this document is structured as foows: Section 2 describes the genera structure of the GenX mode, incuding the various options for configuring mode resoution with regards to chronoogy, operationa detai, and networks. Section 3 ists the notation used throughout the remainder of the document. Section 4 provides the fu mathematica formuation of the mode. Section 5 provides a comprehensive description of the GenX mode incuding options for configuring the mode. Finay, Appendix A ists a set of pubications (theses, working papers, reports, and pubished journa artices) empoying GenX, to give the reader an idea of the various use cases for the mode. 6

8 2 Mode Introduction The GenX mode formuation (described in detai in subsequent sections) aows for the simutaneous co-optimization of seven interinked power system decision ayers: 1. Capacity expansion panning (e.g., investment and retirement decisions for a fu range of centraized and distributed generation, storage, and demand-side resources) 2. Houry dispatch of generation, storage, and demand-side resources, 3. Unit commitment decisions and operationa constraints for therma generators, 4. Commitment of generation, storage, and demand-side capacity to meet system operating reserves requirements, 5. Transmission network power fows (incuding osses) and network expansion decisions, 6. Distribution network power fows, osses, and network reinforcement decisions, and 7. Interactions between eectricity and heat markets. Depending on the dimensionaity of the probem, it may not be possibe to mode a seven decision ayers at the highest possibe resoution of detai, so the GenX mode is designed to be highy configurabe, aowing the user to specify the eve of detai or abstraction aong each of these seven ayers or to omit one or more ayers from consideration entirey. For exampe, whie investment and dispatch decisions (Layers 1 and 2) are a consistent feature of the mode under a configurations, the user has severa options with regards to representing the operationa constraints on various therma power pants (e.g., coa, gas, nucear, and biomass generators). Unit commitment (e.g., start-up and shut-down) decisions [34] (Layer 3) can be modeed at the individua power pant eve (as per [20]); by using an efficient custering of simiar or identica units (as per [17 19]); by using a inear reaxation (or convex hu) of the integer unit commitment constraints set; or ignoring unit commitment decisions entirey and treating generator output as fuy continuous. Furthermore, different eves of resoution can be seected for each individua resource type, as desired (e.g., arger therma units can be represented with integer unit commitment decisions whie smaer units can be treated as fuy continuous). In such a manner, the mode can be configured to represent operating constraints on therma generators at a eve of resoution that achieves a desired baance between abstraction error and computationa tractabiity and provides sufficient accuracy to generate insights for the probem at hand. The mode can aso be configured to consider commitment of capacity to suppy frequency reguation and operating reserves needed by system operators to robusty resove short-term uncertainty in oad and renewabe energy forecasts and power pant or transmission network faiures (Layer 4). Aternativey, reserve commitments can be ignored if desired. 7

9 Simiary, the mode aows for transmission networks to be represented at severa eves of detai (Layer 5) incuding: at a noda or zona eve with a inearized DC approximation of AC power fows between nodes or zones (as per [28, 29, 35]); at a zona eve with transport constraints on power fows between zones (as per [25, 26, 36]); or as a singe zone probem where transmission constraints and fows are ignored. In cases where a noda or zona transmission mode is empoyed, network capacity expansion decisions can be modeed or ignored, and transmission osses can be represented with a piecewise inear approximation of quadratic osses due to power fows between nodes or zones (as per [37, 38]), with the number of segments in the piecewise approximation specified by the user as desired. In a muti-zona or noda configuration, GenX can therefore consider siting generators in different ocations, incuding baancing tradeoffs between access to different renewabe resource quaity, siting restrictions, and impacts on network congestions, power fows and osses. If desired, GenX can aso represent distribution networks using a nove zona approximation (Layer 6, see Section 5.17), with each zone representative of a different distribution network topoogy and votage eve (see Figure 2). Eectricity demand as we as capacity investment and operationa decisions are then indexed across each zone in the system, enabing the mode to seect the optima ocation of capacity investments and operations in each ocation, incuding considering distributed energy resources (DERs, such as distributed soar PV, energy storage, fue ces, etc.) in different distribution votage zones. Power fows between votage eves can be constrained to represent transformer capacity constraints. Losses due to power fows within each distribution network zone can be represented as a piecewise inear approximation of a poynomia function of power injections and withdrawas within each zone, which can be parameterized based on detaied offine AC power fow simuations for the representative networks [39]. Distribution network reinforcement costs associated with changes in peak power injections or withdrawas within each distribution votage eve and network zone can aso be represented as piecewise inear functions parameterized based on offine modeing using a suitabe combination of network panning and optima power fow modeing [40]. Thus, the GenX mode can be configured to consider DERs, incuding baancing tradeoffs between economies of unit scae at different votage eves on the one hand, and the differentia impacts or benefits of ocating DERs at different zones or votage eves on the other hand. Figure 2: Schematic representation of muti-zona configuration with transmission and distribution network zones and siting of resources at different votage eves and zones 8

10 Finay, the mode can be configured to consider interactions between eectricity generation and the heating sector (Layer 7), incuding modeing combined heat and power generation, use of excess eectricity for eectricay-heated therma storage or suppy of industria process heat, or use of heating inputs for topping cyces in advanced generators such as a Nucear Air-Brayton Combined Cyce (NACC) concept [9, 41]. With appropriate configuration of the mode, GenX thus aows the user to tractaby consider severa interinking decision ayers in a singe, monoithic optimization probem that woud otherwise have been necessary to sove in different separated stages or modes. Figure 3 refects the range of configurations currenty possibe aong the three key dimensions of chronoogica detai, operationa detai, and network detai. Figure 3: Range of configurations currenty impemented in GenX aong three key dimensions of mode resoution The mode is usuay configured to consider a fu year of operating decisions at an houry interva to represent some future panning year. In this sense, the current formuation is static because its objective is not to determine when investments shoud take pace over time, but rather to produce a snapshot of the minimum-cost generation capacity mix under some pre-specified future conditions. However, the current impementation of the mode can be run in sequence (with outputs from one panning year used as inputs for another subsequent panning year) to represent a step-wise or myopic expansion of the network. In the future, the mode may be revised to aow simutaneous co-optimization of sequentia panning decisions. In addition, to improve computationa tractabiity, the mode can consider a reduced number of representative hours within the future panning year, seected using an appropriate time domain reduction technique [20, 22, 30 33]. From a centraized panning perspective, this formuation can hep to determine the investments needed to suppy future eectricity demand at minimum cost, as is common in east-cost utiity panning or integrated resource panning processes. In the context of iberaized markets, the mode can be used by reguators and poicy makers for indicative energy panning or poicy anaysis in order to estabish a 9

11 ong-term vision of efficient market and poicy outcomes. The mode can aso be used for techno-economic assessment of emerging eectricity generation, storage, and demand-side resources and to enumerate the effect of parametric uncertainty (e.g., technoogy costs, fue costs, demand, poicy decisions) on the system-wide vaue or roe of different resources. The high eve structure of the GenX mode is presented in Tabe 1, with reference to each equation impementing the various components of the configurabe mode. GenX is impemented using Juia Language [42]. Juia is a high-eve, high-performance dynamic programming anguage for technica computing, with syntax that is famiiar to users of other technica computing environments. Additionay, the mode is impemented using JuMP [43], a domain-specific modeing anguage for mathematica programming embedded in Juia. JuMP supports a number of open-source and commercia sovers for a variety of probem casses, incuding inear programming, mixed-integer programming, second-order conic programming, semidefinite programming, and noninear programming. The sover used in the present work was Gurobi deveoped by Gurobi Optimization [44]. Tabe 1: Mode s Genera Structure and Reference to Equations Minimize Investment costs + Operationa costs - Heat Market Saes (1) subject to: Investment decisions constraints (2 3) CO 2 emissions constraints (4 5) Minimum renewabe energy mandate constraints (6 7) Demand baance constraint (8) Transmission network reated constraints (15 29) Unit commitment constraints (30 39) Constraints for therma technoogies w/unit commitment (36 35) Constraints for other therma (40 43) Renewabe technoogies operationa constraints (44 45) Storage resources operationa constraints (46 52) Demand-side management constraints (53 55) Demand response constraint (56) NACC operationa constraints (57 60) Heat storage operationa constraints (61 69) Hydro reservoir resources operationa constraints (70 74) Operating reserves reated constraints (76 117) Distribution network reated constraints ( ) Non-negativity/integraity constraints ( ) 10

12 3 Notation 3.1 Mode Indices and Sets Notation Tabe 2: Mode Indices and Sets Description t, e T where t denotes an hour and T is the set of hours in the data series (e is an aternate index). z, d Z where z denotes a zone/node and Z is the set of zones/buses in the network (d is an L aternate index). where denotes a ine and L is the set of transmission ines in the network. y, x G where y denotes a technoogy and G is the set of avaiabe technoogies (x is an s S m M H G RE G O G DR G AN G HO G W G UC H D RE N D RE E L R Z V Z PW T PI T aternate index). where s denotes a segment and S is the set of consumers segments for price-responsive demand curtaiment. where m denotes a segment used in piecewise approximation of quadratic functions and M is the set of segments [0 : M] where H is the subset of therma resources. where RE is the subset of renewabe energy resources. where O is the subset of storage resources excuding heat storage. where DR is the subset of demand response resources. where AN is the subset of advance nucear resources (NACC). where HO is the subset of heat storage resources. where W is the subset of hydro reservoir resources. where UC is the subset of therma resources subject to unit commitment constraints. where D is the subset of dispatchabe a renewabe resources. where N D is the subset of non-dispatchabe b renewabe resources. Subset of transmission ines ines eigibe for reinforcement Subset of transmission zones Subset of distribution zones Subset of hours in which aggregate peak withdrawa may occur in distribution zones Subset of hours in which aggregate peak injection may occur in distribution zones a Generation curtaiment aowed i.e., utiity scae b Generation curtaiment not aowed i.e., residentia 11

13 3.2 Decision Variabes Tabe 3: Decision Variabes Notation Ω R + R + Θ y,t,z R + Π y,t,z R + Γ y,t,z R + Λ s,t,z R +,t R Φ,t R ϕ max Description Instaed capacity of technoogy y in zone z [MW]. Retired capacity of technoogy y from existing capacity in zone z [MW]. Energy injected into the grid by technoogy y at hour t in zone z [MWh]. Energy withdrawn from grid by technoogy y at hour t in zone z [MWh]. Stored energy eve of technoogy y at end of hour t in zone z [MWh]. Non-served energy/curtaied demand from the price-responsive demand segment s at hour t in zone z [MWh]. Losses in ine at hour t [MWh]. Power fow in ine at hour t [MWh]. R + Expansion of transmission capacity in ine [MW]. Φ +,t, Φ,t R + Power fow absoute vaue auxiiary variabes for ine [MW] at time t in positive (+) and negative (-) domains. + m,,t, m,,t R + Segment m of piecewise approximation of quadratic transmission osses ON + m,,t, ON m,,t {0, 1} ϑ z,t R function for ine at time t [MW] in positive (+) and negative (-) domains. Activation variabe for segment m of piecewise approximation of quadratic transmission osses function for ine at time t in positive (+) and negative (-) domains. Bus ange of zone/bus z at hour t [rad]. υ y,t,z Z + Commitment state of generator custer y at hour t in zone z. χ y,t,z Z + Startup events of generator custer y at hour t in zone z. ζ y,t,z Z + Shutdown events of generator custer y at hour t in zone z. ɛ y,t,z R + σ y,t,z R + ν y,t,z R + Heat from storage sod by technoogy y at hour t in zone z [MWh]. Heat from storage used for generation by technoogy y at hour t in zone z [MWh]. Heat from natura gas combustion used for generation by technoogy y at hour t in zone z [MWh]. r +,t R + Reserves contribution up [MW] from technoogy y in zone z at time t. r,t R + Reserves contribution down [MW] from technoogy y in zone z at time t. f +,t R + f,t R + r +C,t R + Frequency reguation contribution up [MW] from technoogy y in zone z at time t. Frequency reguation contribution down [MW] from technoogy y in zone z at time t. Reserves contribution up [MW] from storage technoogy y during charging process in zone z at time t. Continued on next page 12

14 Notation Tabe 3 continued from previous page Description r,t C R + Reserves contribution down [MW] from storage technoogy y during charging process in zone z at time t. f,t +C R + Frequency reguation contribution up [MW] from storage technoogy y during charging process in zone z at time t. f,t C R + Frequency reguation contribution down [MW] from storage technoogy y during charging process in zone z at time t. r,t +D R + Reserves contribution up [MW] from storage technoogy y during discharging process in zone z at time t. r,t D R + Reserves contribution down [MW] from storage technoogy y during discharging process in zone z at time t. f,t +D R + Frequency reguation contribution up [MW] from storage technoogy y during discharging process in zone z at time t. f,t D R + Frequency reguation contribution down [MW] from storage technoogy y during discharging process in zone z at time t. r +,unmet t R + Unmet reserves up [MW] in time t. r,unmet t R + Unmet reserves down [MW] in time t z,t R+ Losses within distribution zone z at hour t [MWh]. + m,z,t, m,z,t R + Segment m for piecewise approximation of quadratic term in distribution ON + m,z,t, ON m,z,t {0, 1} osses function for zone z at time t [MW] in the positive (+) and negative (-) domains. Activation variabe for segment m of piecewise approximation of quadratic term in distribution osses function for zone z at time t in positive (+) and negative (-) domains. λ W z R+ New power withdrawa network capacity added to distribution zone z λ I z R+ φ W z,t R+ φ I z,t R+ φ,w m,z,t R+ [MW]. New power injection network capacity added to distribution zone z [MW]. Power withdrawa margin gained via optima dispatch of distributed resources in distribution zone z [MW] at hour t. Power injection margin gained via optima dispatch of distributed resources in distribution zone z [MW] at hour t. Segment m for inear approximation of network withdrawa margin gained from optima dispatch of distributed resources in zone z at hour t. 13

15 3.3 Parameters Notation π D t,z n sope s n size s Ω Ω size INV EST π F OM π V OM π F UEL ST ART ɛ CO2 ρ min π η oss η up η down µ stor µ DSM τ κ up κ down τ up τ down Tabe 4: Mode Parameters Description Eectricity demand at hour t in zone z [MWh]. Cost of non-served energy/demand curtaiment for price-responsive demand segment s [$/MWh]. Size of price-responsive demand segment s as a fraction of the houry zona demand [%]. Maximum new capacity of technoogy y in zone z [MW]. Existing instaed capacity of technoogy y in zone z [MW]. Unit size of technoogy y in zone z [MW]. Investment cost (annua amortization of tota construction cost) for technoogy y in zone z [$/MW-yr]. Fixed O&M cost of technoogy y in zone z [$/MW-yr]. Variabe O&M cost of technoogy y in zone z [$/MWh]. Fue cost of technoogy y in zone z [$/MWh]. Startup cost of technoogy y in zone z [$/startup]. CO 2 emissions per unit energy produced by technoogy y in zone z [tons/mwh]. Minimum stabe power output per unit of instaed capacity for technoogy y in zone z [%]. Sef discharge rate per hour per unit of instaed capacity for storage technoogy y in zone z [%]. Singe-trip efficiency of storage charging/demand deferra for technoogy y in zone z [%]. Singe-trip efficiency of storage discharging/demand satisfaction for technoogy y in zone z [%]. Power to energy ratio of storage technoogy y in zone z [MW/MWh]. Maximum percentage of houry demand that can be shifted by technoogy y in zone z [%]. Time periods over which demand can be deferred using demand-side management technoogy y in zone z before demand must be satisfied [hours]. Maximum ramp-up rate per time step as percentage of instaed capacity of technoogy y in zone z [%/hr]. Maximum ramp-down rate per time step as percentage of instaed capacity of technoogy y in zone z [%/hr]. Minimum uptime for therma generator type y in zone z before new shutdown [hours]. Minimum downtime or therma generator type y in zone z before new restart [hours]. η heat Heat to eectricity conversion efficiency for NACC technoogy y in zone z [%]. Continued on next page 14

16 Notation µ heat Tabe 4 continued from previous page Description Peak to base generation ratio of for NACC technoogy y in zone z [%]. Maximum avaiabe generation per unit of instaed capacity during hour t for ρ max y,t,z H t,z πz HEAT w eve ϕ map,z technoogy y in zone z [%]. Heat demand at hour t in zone z [MWh]. Heat price in zone z [$/MWh]. Initia eve of hydro reservoir y in zone z [%]. Topoogy of the network, for ine : ϕ map,z destination, 0 otherwise. ϕ max ϕ vot ϕ ohm ϕ oss ϕ θ ϕ max π T CAP ɛ max z γ + γ ι + ι Transmission capacity of ine [MW]. Transmission votage of ine [kv]. Transmission resistance of ine [Ohms]. = 1 for zone z of origin, 1 for zone z of Linear transmission osses per unit of power fow across ine [p.u.]. Maximum ange difference of ine [rad]. Maximum power fow capacity reinforcement for ine [MW] Transmission power fow reinforcement cost for ine [$/MW]. CO 2 emissions constraint for zone z [tons/mwh]. Max. contribution of capacity to reserves up [p.u.] for technoogy y in zone z Max. contribution of capacity to reserves down [p.u.] for technoogy y in zone z Max. contribution to frequency reguation up [p.u.] for technoogy y in zone z Max. contribution to frequency reguation down [p.u.] for technoogy y in zone z R +D Reserves requirement up as a function of houry oad [%]. +V RE R Reserves requirement up as a function of houry variabe renewabe resource avaiabiity[%]. R D Reserves requirement down as a function of houry oad [%]. V RE R Reserves requirement down as a function of houry variabe renewabe resource avaiabiity[%]. F D Frequency reguation requirement as a function of houry oad [%]. F V RE π unmet µ RE Frequency reguation requirement as a function of houry variabe renewabe resource avaiabiity[%]. Penaty for unmet reserve requirement [$/MW]. z Minimum penetration of quaifying renewabe energy resources required in zone z [%]. Distribution network reinforcement cost for zone z [$/MW]. πz DCAP λ I z λ W z λ I z λ W z Maximum aggregate power injection possibe in distribution zone z [MW] Maximum aggregate power withdrawa possibe in distribution zone z [MW] Maximum distribution network aggregate injection capacity reinforcement for zone z [MW] Maximum distribution network aggregate withdrawa capacity reinforcement for zone z [MW] Continued on next page 15

17 Notation N W,sqrt z N W,inear z φ W z S φ,w m,z ϕ down z,d ϕ Net z ϕ W z ϕ I z ϕ Int z M Tabe 4 continued from previous page Description Coefficient for square-root term for distribution network withdrawa margin gained via dispatch of distributed resources Coefficient for inear term for distribution network withdrawa margin gained via dispatch of distributed resources Maximum possibe distribution network withdrawa margin that can be gained via dispatch of distributed resources Sope of each segment m for inear approximation of square root term in function for network withdrawa margin that can be gained via dispatch of distributed resources [MW] Set of distribution zones d downstream of each distribution zone z: ϕ down z,d = 1 for zone d if z = d or if there is a path from z to d and d is at a ower votage than z, 0 otherwise. Within zone distribution oss coefficient for quadratic term of poynomia function for osses due to net withdrawas in zone z Within zone distribution oss coefficient for inear term of poynomia function for osses due to aggregate withdrawas in zone z Within zone distribution oss coefficient for inear term of poynomia function for osses due to aggregate injections in zone z Within zone distribution oss intercept coefficient for poynomia function for osses in zone z Number of segment to use in piecewise inear approximation of quadratic terms in transmission and distribution osses functions 16

18 4 Mode Formuation This section presents the fu mathematica formuation of the different equations that comprise the optimization mode, starting with the objective function Eq. 1 and then a the different constraints Eq A textua description of each eement of the mode is provided in Section 5. min { ( z Z y G + z Z + z Z + z Z z Z + ( t T + ( L + z V y G t T t T s S y G t T y G t T INV EST (π Ω size Ω ) + (π F OM Ω size ( ( ((π V OM n sope π unmet (r +,unmet t π T CAP s Λ s,t,z ) ( ) ST ART π χ y,t ( ) πz HEAT ɛ y,t,z ϕ max ) ( + Ω )) + π F UEL ) Θ y,t,z ) + (π V OM Π y,t,z ) + (πz HEAT ν y,t,z ) ) t ) + r,unmet ) ( π DCAP z ( λ W z + λ I z)) } (1) ) subject to Ω Ω, y G, z Z (2) Ω size, y G, z Z (3) Ω size y G t T (ɛco2 (Θ y,t,z + Π y,t,z )) ɛ max z t T D t,z, z Z (4) z Z y G t T (ɛco2 (Θ y,t,z + Π y,t,z )) z Z t T (ɛmax z D t,z ), (5) y RE t T Θ y,t,z µ RE z t T D t,z, z Z (6) z Z y RE t T Θ y,t,z z Z t T (µre z D t,z ) (7) 17

19 y H Θ y,t,z + y D Θ y,t,z + y N D Θ y,t,z + y O (Θ y,t,z Π y,t,z ) + y DR ( Θ y,t,z + Π y,t,z ) y HO Π y,t,z + y W Θ y,t,z + y AN (Θ y,t,z + η heat (σ x,t,z + ν y,t,z )) + s S Λ s,t,z L (ϕmap,z Φ,t ) 1 2 L ( ϕmap,z β,t ( )) z,t = D t,z, z Z, t T (8) ϕ max Φ,t ϕ max, (L \ E), t T (9) (ϕ max + ϕ max ) Φ,t (ϕ max + ϕ max ), E, t T (10) ϕ max ϕ max, E, t T (11) Φ,t = (ϕvot ) 2 ϕ z Z ohm (ϕmap,z ϑ z,t ), L, t T (12) ϕ θ z Z (ϕmap,z ϑ z,t ) ϕ θ, L, t T (13) ϑ 1,t = 0, t T (14) 0 if osses. 0 β,t ( ) = ϕ oss Φ,t if osses. 1, L, t T (15),t if osses. 2 Φ,t = Φ +,t Φ,t, L, t T (16) Φ,t = Φ +,t + Φ,t, L, t T (17) Φ +,t ϕmax, L, t T (18) Φ,t ϕmax, L, t T (19) 18

20 (,t = ϕohm (ϕ vot ) 2 m M (S+ m, + m,,t + S m, m,,t ), ) L, t T Where: S + m, = (m 1) 1+ 2 (2 M 1) (ϕmax + ϕ max ) m [1: M], L S m, = (m 1) 1+ 2 (2 M 1) (ϕmax + ϕ max ) m [1: M], L (20) + m,,t, m,,t <= m, m [1 : M], L, t T Where:,z = (1+ 2) 1+ 2 (2 M 1) (ϕmax (2 M 1) (ϕmax + ϕ max ) if m=1 + ϕ max ) if m > 1, (21) m [1:M] ( + m,,t ) + 0,,t = Φ,t, L, t T (22) m [1:M] ( m,,t ) 0,,t = Φ,t, L, t T (23) + m,,t <= m, ON + m,,t, m [1 : M], L, t T (24) m,,t <= m, ON m,,t, m [1 : M], L, t T (25) + m,,t ON + m+1,,t m,, m [1 : M], L, t T (26) m,,t ON m+1,,t m,, m [1 : M], L, t T (27) + 0,,t ϕmax (1 ON + 1,,t ), L, t T (28) 0,,t ϕmax (1 ON 1,,t ), L, t T (29) υ y,t,z Ω + Ω size, y UC, z Z, t T (30) χ y,t,z Ω + Ω size, y UC, z Z, t T (31) ζ y,t,z Ω + Ω size, y UC, z Z, t T (32) υ y,t,z = υ y,t 1,z + χ y,t,z ζ y,t,z, y UC, z Z, t T (33) Θ y,t,z ρ min Ω size υ y,t,z, y (UC H), z Z, t T (34) 19

21 Θ y,t,z ρ max y,t,z Ω size υ y,t,z, y (UC H), z Z, t T (35) Θ y,t 1,z Θ y,t,z κ down ρ min Ω size χ y,t,z Ω size (υ y,t,z χ y,t,z ) + min(ρ max y,t,z, max(ρ min, κ down )) Ω size ζ y,t,z, y (UC H), z Z, t T (36) Θ y,t,z Θ y,t 1,z κ up Ω size (υ y,t,z χ y,t,z ) + min(ρ max y,t,z, max(ρ min, κ up )) Ω size χ y,t,z ρ min Ω size ζ y,t,z, y (UC H), z Z, t T (37) υ y,t,z ṱ t=t τ up χ y,ˆt,z, y UC, z Z, t T (38) ( Ω + Ω size ) υ y,t,z ṱ t=t τ up ζ y,ˆt,z, y UC, z Z, t T (39) Θ y,t 1,z Θ y,t,z κ down ( + Ω ), y (H \ UC), z Z, t T (40) Θ y,t,z Θ y,t 1,z κ up ( + Ω ), y (H \ UC), z Z, t T (41) Θ y,t,z ρ min ( + Ω ), y (H \ UC), t T, z Z (42) Θ y,t,z ρ max y,t,z ( + Ω ), y (H \ UC), t T, z Z (43) Θ y,t,z ρ max y,t,z ( + Ω ), y D, t T, z Z (44) Θ y,t,z = ρ max y,t,z ( + Ω ), y N D, t T, z Z (45) Γ y,t,z = Γ y,t 1,z ( ) Θy,t,z + (η up η down Π y,t,z ) (η oss Γ y,t,z ), y O, t T, z Z (46) Γ y,t,z ( +Ω ) µ, y O, t T, z Z (47) stor Π y,t,z ( +Ω ), y O, t T, z Z (48) η up Π y,t,z ( +Ω ) µ stor Γ y,t,z, y O, t T, z Z (49) Θ y,t,z η down ( + Ω ), y O, t T, z Z (50) Θ y,t,z Γ y,t,z, y O, t T, z Z (51) 20

22 ( ) Θy,t,z + (η up η down Π y,t,z ) ( + Ω ), y O, t T, z Z (52) Γ y,t,z = Γ y,t 1,z Θ y,t,z + Π y,t,z, y DR, t T, z Z (53) Π y,t,z µ DMS D t,z, y DR, t T, z Z (54) t+τ ˆt=t+1 Θ y,ˆt,z Γ y,t,z, y DR, t T, z Z (55) Λ s,t,z (n size s D t,z ), s S, t T, z Z (56) Θ y,t,z = ( + Ω ), y (AN \ UC), t T, z Z (57) σ x,t,z + ν y,t,z µ heat ( + Ω ), y (AN \ UC), x HO, t T, z Z (58) Θ y,t,z = ρ max y,t,z Ω size υ y,t,z, y (AN UC), t T, z Z (59) σ x,t,z + ν y,t,z µ heat Ω size υ y,t,z, y (AN UC), x HO, t T, z Z (60) Γ y,t,z = Γ y,t 1,z ( ) Θy,t,z + (η up η down Π y,t,z ) (η oss Γ y,t,z ), y HO, t T, z Z (61) Γ y,t,z ( +Ω ) µ, y HO, t T, z Z (62) stor Π y,t,z ( +Ω ), y HO, t T, z Z (63) η up Π y,t,z ( +Ω ) µ stor Γ y,t,z, y HO, t T, z Z (64) Θ y,t,z η down ( + Ω ), y HO, t T, z Z (65) Θ y,t,z Γ y,t,z, y HO, t T, z Z (66) ( ) Θy,t,z + (η up η down Π y,t,z ) ( + Ω ), y HO, t T, z Z (67) ɛ y,t,z + σ y,t,z = Θ y,t,z, y HO, t T, z Z (68) y HO ɛ y,t,z H t,z, t T, z Z (69) Γ y,t,z = Γ y,t 1,z ( ) ( Θy,t,z ρ + max η down y,t,z ( +Ω ) µ stor ), y W, t T, z Z (70) 21

23 Γ y,1,z = weve ( +Ω ) µ, y W, z Z (71) stor Γ y,t,z ( +Ω ) µ, y W, t T, z Z (72) stor Θ y,t,z η down ( + Ω ), y W, t T, z Z (73) Θ y,t,z Γ y,t,z, y W, t T, z Z (74) Θ y,t,z ρ min, y W, z Z (75) F D z Z D t,z + F V RE z Z y (D N D) (Ω ρ max y,t,z) y G z Z f,t, + t T (76) F D z Z D t,z + F V RE z Z y (D N D) (Ω ρ max y,t,z) y G z Z f,t, t T (77) R +D z Z D t,z +R +V RE z Z y G y (D N D) (Ω ρ max y,t,z)+α t ( ) z Z r+,t + r +,unmet t, t T (78) max(ω size ) if cont. 1 max(max(ω size ), max(ϕ max )) if cont. 2 α t ( ) = max(max(ω size ), max(ϕ max )) y Ω 0 if cont. 3, t T (79) max(max(ω size ), max(ϕ max )) y υ y,t,z 0 if cont. 4 R D z Z D t,z + R V RE z Z y G y (D N D) (Ω ρ max y,t,z) z Z r,t + r,unmet t, t T (80) f +,t ι + (Ω size υ y,t,z ), y (UC H), t T, z Z (81) f,t ι (Ω size υ y,t,z ), y (UC H), t T, z Z (82) r +,t γ + (Ω size υ y,t,z ), y (UC H), t T, z Z (83) 22

24 r,t γ (Ω size υ y,t,z ), y (UC H), t T, z Z (84) f +,t ι + ρ max y,t,z( + Ω ), y / (UC N D DR), t T, z Z (85) f,t ι ρ max y,t,z( + Ω ), y / (UC N D DR), t T, z Z (86) r +,t γ + ρ max y,t,z( + Ω ), y / (UC N D DR), t T, z Z (87) r,t γ ρ max y,t,z( + Ω ), y / (UC N D DR), t T, z Z (88) f +,t = f +D,t + f +C,t, y O, t T, z Z (89) f,t = f D,t + f C,t, y O, t T, z Z (90) r +,t = r +D,t + r +C,t, y O, t T, z Z (91) r,t = r D,t + r C,t, y O, t T, z Z (92) Θ y,t,z f,t r,t ρ min Ω size υ y,t,z, y UC, z Z, t T (93) Θ y,t,z + f +,t + r +,t ρ max y,t,z Ω size υ y,t,z, y UC, z Z, t T (94) Θ y,t,z f,t r,t ρ min ( + Ω ), y H, t T, z Z (95) Θ y,t,z + f +,t + r +,t ρ max y,t,z( + Ω ), y H, t T, z Z (96) Θ y,t,z f,t r,t 0, y D, t T, z Z (97) Θ y,t,z + f +,t + r +,t ρ max y,t,z( + Ω ), y D, t T, z Z (98) Π y,t,z + f C,t + r C,t ( +Ω ) η up, y O, t T, z Z (99) Π y,t,z + f,t C + r,t C ( +Ω ) µ Γ stor y,t,z, y O, t T, z Z (100) Π y,t,z f +C,t r +C,t 0, y O, t T, z Z (101) 23

25 Θ y,t,z + f +D,t + r +D,t η down ( + Ω ), y O, t T, z Z (102) Θ y,t,z + f +D,t + r +D,t Γ y,t,z, y O, t T, z Z (103) Θ y,t,z f,t D + r,t D 0, y O, t T, z Z (104) ( ) Θ y,t,z+f +D,t +r+d,t + η down ( η up (Π y,t,z + f C,t + r C,t) ) ( + Ω ), y O, t T, z Z (105) Θ y,t,z + f +,t + r +,t η down ( + Ω ), y W, t T, z Z (106) Θ y,t,z + f +,t + r +,t Γ y,t,z, y W, t T, z Z (107) Θ y,t,z f,t r,t 0, y W, t T, z Z (108) f +,t ι + (η heat f,t ι (η heat r +,t γ + (η heat r,t γ (η heat µ heat µ heat µ heat µ heat Ω size υ y,t,z ), y (UC AN ), t T, z Z (109) Ω size υ y,t,z ), y (UC AN ), t T, z Z (110) Ω size υ y,t,z ), y (UC AN ), t T, z Z (111) Ω size υ y,t,z ), y (UC AN ), t T, z Z (112) σ x,t,z + ν y,t,z (f,t +r,t ) η heat 0, y (UC AN ), x HO, t T, z Z (113) σ x,t,z + ν y,t,z + (f +,t +r+,t ) η heat µ heat Ω size υ y,t,z, y (UC AN ), x HO, t T, z Z (114) Π y,t,z + f,t + r,t ( +Ω ), y OH, t T, z Z (115) η up Π y,t,z + f,t + r,t ( +Ω ) µ stor Γ y,t,z, y OH, t T, z Z (116) Π y,t,z f +,t r +,t 0, y OH, t T, z Z (117) 24

26 ( ) z,t = ϕ Net M z m=1 S m,z + + m,z,t + S m,z + m,z,t +ϕ W z W z,t + ϕ I z I z,t + ϕ Int z, z V, t T Where: S + m,z = (m 1) 1+ 2 (2 M 1) (λi z + λ I z) m [1: M], z V S m,z = (m 1) 1+ 2 (2 M 1) (λw z + λ W z ) m [1: M], z V W z,t = d V ϕdown z,d ( D z,t + y O,HO (Π y,t,z) + ) y DR (Θ y,t,z), z V, t T I z,t = y / DR (Θ y,t,z) z V, t T (118) + m,z,t, + m,z, m [1: M], z V, t T Where: (1+ 2) 1+ 2 (2 M 1) (λi z + λ I z) if m=1 + m,z = (2 M 1) (λi z + λ I z) if m > 1 (119) m,z,t, m,z, m [1: M], z V, t T Where: (1+ 2) 1+ 2 (2 M 1) (λw z + λ W z ) if m=1 m,z =, (120) (2 M 1) (λw z + λ W z ) if m > 1 M m=1 M m=1 ( ) + m,z,t + 0,z,t = (W z,t I z,t ) z V, t T (121) ( ) m,z,t 0,z,t = (W z,t I z,t ) z V, t T (122) + m,z,t S + m,z,t ON + m,z,t m [1: M], z V, t T (123) m,z,t S m,z,t ON m,z,t m [1: M], z V, t T (124) + m,z,t ON + m+1,z,t + m,z m [1: (M 1)], z V, t T (125) m,z,t ON m+1,z,t m,z m [1: (M 1)], z V, t T (126) 25

27 + 0,z,t (λw z + λ W z ) (1 ON 1,z,t + ), z V, t T (127) 0,z,t (λi z + λ I z) (1 ON1,z,t ), z V, t T (128) λ W z + λ W z + φ W z,t W z,t, z V, t PW (129) λ I z + λ I z + φ I z,t I z,t, z V, t PI (130) λ W z λ W z, z V (131) λ I z λ I z, z V (132) φ W z,t = N W,sqrt z Where: ( ) M m=1 Sm,z φ,w φ,w m,z,t + Nz W,inear DERz,t W z Z, t PW DER W z,t = d V ϕdown z,d ( y N D,DR (Θ y,t,z) + y DR (Π y,t,z) + s S (Λ s,t,z)), z Z, t PW (133) M m=1 φ,w m,z = DER W z,t z Z, t PW (134) φ,w m,z φ,w m,z m [1 : M], z Z Where: φ,w 6 φ m,z = W z M (M+1) (2 M+1) m2 m [1 : M], z V (135) φ I z,t = 0, z Z, t T (136) Ω, 0, y / UC, z Z (137) Ω, 0 Z +, y UC, z Z (138),t, Φ +,t, Φ,t 0, L, t T (139) + m,,t, m,,t 0, m M, L, t T (140) Φ m,+,on,t, Φ m,,on,t {0, 1}, m M, L, t T (141) ϕ max 0, E (142) 26

28 ϕ max = 0, / E (143) Θ y,t,z 0, y G, t T, z Z (144) Π y,t,z 0, y (O HO DR), t T, z Z (145) Γ y,t,z 0, y (O HO DR W), t T, z Z (146) Π y,t,z = 0, y / (O HO DR), t T, z Z (147) Γ y,t,z = 0, y / (O HO DR W), t T, z Z (148) Λ s,t,z 0, s S, t T, z Z (149) υ y,t,z, χ y,t,z, ζ y,t,z = 0, y / UC, t T, z Z (150) υ y,t,z, χ y,t,z, ζ y,t,z 0 Z +, y UC, t T, z Z (151) ɛ y,t,z, σ y,t,z = 0, y / HO, t T, z Z (152) ɛ y,t,z, σ y,t,z 0, y HO, t T, z Z (153) ν y,t,z = 0, y / AN, t T, z Z (154) ν y,t,z 0, y AN, t T, z Z (155) r +,t, r,t, f +,t, f,t 0, y / (N D DR), t T, z Z (156) r +,t, r,t, f +,t, f,t = 0, y (N D DR), t T, z Z (157) r +C,t, r C,t, f +C,t, f C,t, r +D,t, r D,t, f +D,t, f D,t 0, y O, t T, z Z (158) r +C,t, r C,t, f +C,t, f C,t, r +D,t, r D,t, f +D,t, f D,t = 0, y / O, t T, z Z (159) r +,unmet t, r,unmet t 0, t T (160) 27

29 z,t 0 z V, t T (161) + m,z,t, m,z,t 0, m [1 : M], z V, t T (162) λ W z, λ I z 0, z V (163) φ W z,t, φ I z,t 0, z V, t T (164) φ,w m,z,t 0, m [1 : M], z zv, t T (165) 28

30 5 Description of the Mode This section describes the different indices and sets used in the formuation; and then it describes the different genera-form equations that make up the mode under various possibe configurations. 5.1 Indices and Sets Five indices are used in this mode: y, x represent technoogies G; t, e represent hours T ; z represents a zone/node Z; represents a transmission ine L; and s represents a consumers segment S. G denotes the set of resources that can be buit/depoyed, containing a the different therma technoogies (nucear, coa, combined cyce gas turbines (CCGTs), open cyce gas turbines (OCGTs)), different variabe renewabe energy technoogies (wind, soar photovotaic, soar therma), different storage technoogies (pumped hydro, batteries, compressed air (CAES), heat storage), various hydroeectric generators (run-of-river and reservoir hydro), as we as demand side mechanisms ike shiftabe demand. In addition, H G denotes the subset of therma generation resources (coa, nucear, CCGT, OCGT, etc.); D G, denotes the subset dispatchabe (e.g., curtaiabe) variabe renewabe resources (soar and wind); N D G, denotes the subset of non-dispatchabe (e.g., non-curtaiabe) renewabe capacity (such as rooftop soar PV); O G, denotes the subset of eectrochemica and mechanica storage technoogies; DR G, denotes the subset of demand response technoogies or shiftabe oad; AN G, denotes the subset of advance nucear technoogies (Nucear Air Combined Cyce (NACC)); HO G, denotes the subset of heat storage technoogies (eectricay-heated therma storage); W G, denotes the subset of hydro reservoir resources; UC G, denotes the subset of therma and advance nucear technoogies for which unit commitment constraints are considered (this set may be empty if unit commitment decisions are not considered for any resources); and RE G, denotes the subset of renewabe energy resources that quaify to fufi a minimum renewabe energy generation requirement or mandate (e.g., a renewabe portfoio standard requirement), if any is modeed. T denotes the set of hours modeed in the simuation (e.g., 8760 hours in a fu year, or some reduced set of representative hours). Z denotes the number of nodes/zones simuated in the anaysis. This number coud range from 1, when the network is represented as a singe node, to very high numbers when trying to describe the rea topoogy of the network at a noda resoution. In addition, R Z denotes the subset of nodes at the transmission eve; and V Z denotes the subset of nodes at the distribution eve. S denotes mutipe bocks or segments of curtaiabe demand, in order to represent price responsive demand curtaiment or a piecewise approximation of increasing wiingness to pay for eectricity at different price eves. L denotes the number of transmission ines simuated in the anaysis. This number coud range from 0, when the network is represented as a singe node, to very high numbers when trying to describe the rea 29

31 topoogy of the network. In addition, E L denotes the subset of transmission ines eigibe for reinforcements or construction. 5.2 Decision Variabes The GenX mode can operate in either a greenfied or brownfied mode for each technoogy independenty. That is, it can sove starting from an existing brownfied capacity mix,, whie making decisions about buiding new capacity, Ω, and retiring existing capacity,. Otherwise, GenX soves a greenfied expansion probem assuming no existing capacity, making decisions about new capacity, Ω, from scratch. Maximum instaed capacity can be specified for each resource type and each zone (see Eq. 2) to refect constraints on the siting resources. When operating in brownfied mode, constraint Eq. 3 ensures that tota retired capacity does not exceed the initia instaed capacity. Capacity additions for a units of specific technoogy y in zone z beonging to the set UC are treated as integer decisions to add a fixed and indivisibe increment of capacity Ω size (e.g., 200 MW or 600 MW). For a other technoogies UC, the investment decision variabes take continuous positive vaues i.e., the mode coud decide to insta, for exampe, 10.5 MW of capacity for soar, wind or therma generators that do not beong to the set UC. When custered unit commitment is activated for technoogy y, then the investment decision variabe can take ony positive integer variabes that represent the number of pants in custer y i.e., the mode coud decide to insta, for exampe, 5 units with a tota generation capacity equa to the number of pants times the pants size of the custer Ω size. For any given technoogy y in zone z, it is possibe to generate/inject, Θ y,t,z, of energy at each hour t. The maximum amount of generation/injection wi be imited by the net capacity instaed equa to Ω size ( + Ω ), or tota existing capacity pus instaed additions ess retirements and a set of different operationa constraints that are appied depending on the type (subset) of the specific technoogy y. At the same time, for energy storage devices beonging to O, energy can be stored/withdraw, Π y,t,z, at each hour t. The net change in energy stored, Γ y,t,z, at time t wi depend on the amount of energy discharged, Θ y,t,z, the amount of energy charged, Π y,t,z, and the storage energy eve at time t 1. For non-storage technoogies the variabes for charge and storage eve are set to zero or eiminated from the probem. For every hour, the system must resove how much energy to inject/withdraw in each zone z given the houry demand D t,z and the variabe costs of the different eectricity resource options. Consumers present different preferences about their wiingness to pay for eectricity at different prices; i.e., if the houry margina cost of eectricity suppy goes above a consumer s margina vaue of consumption, that consumer is better off not consuming and wi thus curtai demand. For this purpose, the mode can decide how much demand not to serve Λ s,t,z at time t in zone z with different costs for each segment of demand s. Each segment is represented by a per unit portion n size s of the houry demand in zone z that is wiing to pay no more to consume energy than the specified price n sope s per unit energy. When more than one zone is modeed, energy can fow, Φ,t, through the ine at time t connecting zones 30