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Documentation for the MARKAL Family of Models

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Documentation for the MARKAL Family of Models Energy Technology Systems Analysis Programme http://www.etsap.org/tools.htm Documentation for the MARKAL Family of Models October 2004 Authors: Richard Loulou Gary Goldstein Ken Noble General Map of the documentation INTRODUCTION PART I: STANDARD MARKAL Chapter 1: Concepts and Theory Chapter 2: Reference Manual PART II: MARKAL-MACRO Chapter 3: Concepts and Theory Chapter 4: Reference Manual PART II: SAGE Chapter 5: Concepts and Theory Chapter 6: Reference Manual INTRODUCTION This documentation replaces the documentation of the early version of the MARKAL model (Fishbone et al, 1983) and the many notes and partial documents which have been written since then. It is divided in three parts, each related to a different type of modeling paradigm. Part I deals with the Standard MARKAL model, an intertemporal partial equilibrium model based on competitive, far sighted energy markets. Part II discusses MARKAL-MACRO, a General Equilibrium model obtained by merging MARKAL with a set of macroeconomic equations. Part III describes the SAGE model, a time-stepped version of MARKAL where a static partial equilibrium is computed for each time period separately. Each Part is further divided in two main chapters, the first describing the properties of the model, its mathematical properties, and its economic rationale, and the second constituting a reference guide containing a full description of the parameters, variables, and equations of the model. Note that section 2.11 in Part I deals with the GAMS environment and control sequences for running the models. It appplies to all three parts of the documentation. Although the three parts are presented as separate files with their own tables of contents, the numbering of chapters, sections, and pages is continuous across all thtree parts. PART I: The Standard MARKAL Model 1. Standard MARKAL: Concepts and Theory ...............................................9 1.1 Model Summary.................................................................................................................9 1.2 The basic structure of the MARKAL model generator ...............................................10 1.2.1 Summary of the key elements of MARKAL.....................................................................11 1.2.2 Time horizon......................................................................................................................11 1.2.3 The RES concept ...............................................................................................................12 1.2.4 The MARKAL RES: Overview of MARKAL set definitions ..........................................14 1.2.4.1 SRCENCP: the set of sources and sinks.................................................................14 1.2.4.2 PRC: the set of Process technologies......................................................................15 1.2.4.3 CON: the set of conversion technologies................................................................15 1.2.4.4 DMD: the set of end-use technologies....................................................................15 1.2.4.5 DM: the set of demands for energy services...........................................................16 1.2.4.6 ENC: the set of energy carriers...............................................................................17 1.2.4.7 MAT: the set of materials .......................................................................................18 1.2.4.8 ENV: the set of environmental emissions...............................................................19 1.2.4.9 System-Wide attributes...........................................................................................19 1.2.5 Some details on the MARKAL Electricity Sector.............................................................19 1.2.5.1 Load pattern -- Demand..........................................................................................19 1.2.5.2 Load Management – Supply ...................................................................................20 1.2.5.3 Baseload Plants .......................................................................................................21 1.2.5.4 Peak requirements...................................................................................................21 1.2.5.5 Transmission and Distribution – Losses and Costs ................................................22 1.3 Economic rationale of the MARKAL model.................................................................23 1.3.1 A brief discussion of energy models..................................................................................24 1.3.1.1 Top-Down Models..................................................................................................24 1.3.1.2 Bottom-Up Models .................................................................................................25 1.3.1.3 Recent Modeling Advances ....................................................................................25 1.3.2 The MARKAL paradigm...................................................................................................27 1.3.2.1 A technology explicit model...................................................................................27 1.3.2.2 Multi-regional feature .............................................................................................27 1.3.2.3 Partial equilibrium properties .................................................................................28 1.3.2.4 Linearity..................................................................................................................28 1.3.2.5 Maximization of total surplus: Price equals Marginal value ..................................29 1.3.2.6 Competitive energy markets with perfect foresight................................................33 1.3.2.7 Marginal value pricing............................................................................................34 1.3.2.8 Profit maximization: the Invisible Hand.................................................................35 1.4 A simplified description of the MARKAL Optimization Program.............................36 1.4.1 MARKAL objective function: total system cost ...............................................................36 1.4.2 Constraints .........................................................................................................................37 1.4.2.1 Satisfaction of Energy Service Demands:...............................................................37 1.4.2.2 Capacity Transfer (conservation of investments): ..................................................37 1.4.2.3 Use of capacity:.......................................................................................................38 1.4.2.4 Balance for Commodities (except electricity and low temperature heat):..............38 1.4.2.5 Electricity & Heat Balance: ....................................................................................38 1.4.2.6 Peaking Reserve Constraint (electricity and heat sectors only):.............................38 1.4.2.7 Base Load (electricity generation only):.................................................................39 1.4.2.8 Seasonal availability factors (electricity and heat sectors only):............................39 1.4.2.9 Emission constraint(s):............................................................................................39 1.5 A simplified Mathematical Formulation of the MARKAL Linear Program.............39 1.5.1 Decision Variables.............................................................................................................40 1.5.2 Objective function..............................................................................................................41 1.5.3 Constraints (equations) ......................................................................................................43 1.5.3.1 EQ_DEM(r,t,d) - Satisfaction of Demands.............................................................43 1.5.3.2 EQ_CPT(r,t,k) - Capacity transfer..........................................................................44 1.5.3.3 EQ_UTL(r,t,k,s) - Use of capacity..........................................................................44 1.5.3.4 EQ_BAL(r,t,c,s) - Energy Balance.........................................................................44 1.5.3.5 EQ_EPK/HPK(r,t,c,s) - Electricity and heat Peak Reserve Constraint ..................45 1.5.3.6 EQ_ENV(r,t,p) - Emission constraint or tax (optional)..........................................46 1.5.3.7 EQ_BAS(r,t,c) - Electricity Baseload constraint ....................................................47 1.5.3.8 EQ_UDC(r,t,u) - User-defined constraints .............................................................47 1.5.4 Representation of oil refining in MARKAL......................................................................47 1.5.4.1 New sets and parameters.........................................................................................48 1.5.4.2 New variables..........................................................................................................48 1.5.4.3 New blending constraints........................................................................................48 1.6 Elastic demands and the computation of the supply-demand equilibrium................49 1.6.1 Theoretical considerations: the Equivalence Theorem......................................................50 1.6.2 Mathematics of the MARKAL
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