Sets

Acronyms

Acronym	Description
aFRR	Automatic Frequency Restoration Reserve
BESS	Battery Energy Storage System
DA	Day-Ahead
ESS	Energy Storage System (includes BESS and HESS)
EV	Electric Vehicle
FCR-D	Frequency Containment Reserve – Disturbance
FCR-N	Frequency Containment Reserve – Normal
H-VPP	Hydrogen-based Virtual Power Plant
HESS	Hydrogen Energy Storage System
IB	Imbalance
ID	Intraday
mFRR	Manual Frequency Restoration Reserve
SoC	State of Charge
VRE	Variable Renewable Energy

The optimization model is built upon a series of indexed sets that define its dimensions, including time, space, and technology. These sets are used by Pyomo to create variables and constraints efficiently. Understanding these sets is crucial for interpreting the model’s structure and preparing input data.

The core sets are defined in the model object and are accessible throughout the formulation scripts (e.g., in oM_ModelFormulation.py).

Temporal Hierarchy

The model uses a nested temporal structure to represent time, from long-term planning periods down to hourly operational timesteps.

Sets

Symbol	Description	Pyomo Component
\(\nP\)	All periods (e.g., years in a planning horizon)	model.pp
\(\nS\)	All scenarios, representing different operational conditions within a period	model.scc
\(\nT\)	All time steps (e.g., hours or sub-hourly intervals)	model.nn

Indices

Symbol	Description	Pyomo Component
\(\periodindex\)	Period (e.g., year.)	model.p
\(\scenarioindex\)	All scenarios, representing different operational conditions within a period	model.sc
\(\timeindex\)	Time step (e.g., hours or sub-hourly intervals)	model.n
\(ps\)	Combination of period and scenario	model.ps
\(psn\)	Combination of period, scenario, and time step	model.psn

Spatial Representation

The spatial dimension defines the physical layout and regional aggregation of the energy system.

Sets

Symbol	Description	Pyomo Component
\(\nB\)	Node or bus bar in the network	model.nd
\(\nC\)	Electricity connection (from node, to node, circuit)	model.cc
\(\nLE\)	Electricity arc (transmission line)	model.eln
\(\nLH\)	Hydrogen arc (pipeline)	model.hpn
\(\nZ\)	Zone or region in the network	model.zn

Indices

Symbol	Description	Pyomo Component
\(\busindex\)	Node or bus bar in the network	nd
\(\busindexa\)	From node of a connection or arc	i
\(\busindexb\)	To node of a connection or arc	j
\(\lineindexa\)	From node of a transmission line	ijc
\(\lineindexb\)	To node of a transmission line	jic
\(\zoneindex\)	Zone or region in the network	zn

Technology and Asset Sets

The model uses a rich set of indices to differentiate between various types of technologies and assets. There is a clear separation between the electricity and hydrogen systems.

General Technology Subsets

Symbol	Description	Pyomo Component
\(\nGE\)	All electricity generation units	model.eg
\(\nGENR\)	Non-renewable electricity generators (subset of \(\nGE\))	model.egnr
\(\nGVRE\)	Variable Renewable Energy (VRE) generators (subset of \(\nGE\))	model.egvre
\(\nEE\)	Electricity energy storage systems (subset of \(\nGE\))	model.egs
\(\nGH\)	All hydrogen production units	model.hg
\(\nGHE\)	Units converting electricity to hydrogen (e.g., electrolyzers)	model.e2h
\(\nGEH\)	Units converting hydrogen to electricity (e.g., fuel cells)	model.h2e
\(\nEH\)	Hydrogen energy storage systems (subset of \(\nGH\))	model.hgs

Indices

Symbol	Description	Pyomo Component
\(\genindex\)	Generation units	g
\(\storageindex\)	Energy storage systems	e
\(\traderindex\)	Retailers	r

Demand and Retail

Symbol	Description	Pyomo Component
\(\nDE\)	All electricity demands	model.ed
\(\nDH\)	All hydrogen demands	model.hd
\(\nRE\)	All electricity retailers	model.er
\(\nRH\)	All hydrogen retailers	model.hr
\(\nKE\)	Set of peak indices for demand charge calculation	model.Peaks

Indices

Symbol	Description	Pyomo Component
\(\demandindex\)	Consumer	d
\(\traderindex\)	Retailer	r

Node-to-Technology Mappings

The model uses mapping sets to link specific assets to their locations in the network. For example:

• model.n2eg: Maps which electricity generators exist at which nodes.

• model.n2hg: Maps which hydrogen producers exist at which nodes.

• model.n2ed: Maps electricity demands to nodes.

These sets are fundamental for building the energy balance constraints at each node. By combining temporal, spatial, and technological sets, the model can create highly specific variables, such as vEleTotalOutput[p,sc,n,eg], which represents the electricity output of generator eg at a specific time (p,sc,n).