5  Regions and trade

Everything so far lived in one region. Real systems are several places at once, each with its own resources, its own demand, and links that let power flow between them. This chapter adds space: a three-region electricity system, a transmission link and a rest-of-world import, then two questions that only space can pose — where a new electricity load wants to be, and what storage and transmission are worth in a fully renewable system.

source("R/workshop-model.R")
library(dplyr)

Outputs below are illustrative — with eval: false nothing runs at render.

5.1 Three regions, three endowments

The trick to a multi-region model is that every data frame carries a region column, so one object can describe all regions at once with different numbers. Here the endowments are deliberately asymmetric: R1 sits on cheap coal, R2 on gas, R3 has the best wind and sun and no domestic fossil fuel.

Regions here are flat labels R1–R3. The geoscales package generalises this to nested spatial hierarchies (zones within regions within a system), just as timescales does for time — the space and time “bricks” of the optimal2050 ecosystem.

REG <- c("R1", "R2", "R3")

# per-region VRE capacity-factor profiles (deterministic, shipped with energyRt)
prof3 <- utopia_profiles(REG, calendar = "utopia_s4h24")

weather_WSOL <- prof3$weather |>
  filter(resource == "WSOL") |>
  select(region, timeslice, wval)

weather_WWIN <- prof3$weather |>
  filter(resource == "WWIN") |>
  select(region, timeslice, wval)
ELC <- newCommodity("ELC", unit = "PJ", timeframe = "HOUR")
COA <- newCommodity(
  name      = "COA",
  unit      = "PJ",
  timeframe = "ANNUAL",
  emis      = data.frame(comm = "CO2", unit = "kt/PJ", emis = 95)
)
GAS <- newCommodity(
  name      = "GAS",
  unit      = "PJ",
  timeframe = "ANNUAL",
  emis      = data.frame(comm = "CO2", unit = "kt/PJ", emis = 56)
)
CO2 <- newCommodity("CO2", unit = "kt", timeframe = "ANNUAL")
SOL <- newCommodity("SOL", unit = "PJ", timeframe = "HOUR")
WIN <- newCommodity("WIN", unit = "PJ", timeframe = "HOUR")

# domestic fossil supply exists only where the endowment is (R1 coal, R2 gas)
SUP_COA <- newSupply(
  name      = "SUP_COA",
  commodity = "COA",
  unit      = "PJ",
  supply    = data.frame(region = "R1", cost = 2.5)
)
SUP_GAS <- newSupply(
  name      = "SUP_GAS",
  commodity = "GAS",
  unit      = "PJ",
  supply    = data.frame(region = "R2", cost = 6.0)
)

# free renewable resources everywhere
SUP_SOL <- newSupply(
  name      = "SUP_SOL",
  commodity = "SOL",
  unit      = "PJ",
  supply    = data.frame(region = REG, cost = 0)
)
SUP_WIN <- newSupply(
  name      = "SUP_WIN",
  commodity = "WIN",
  unit      = "PJ",
  supply    = data.frame(region = REG, cost = 0)
)

# demand, larger in R1/R2 than in R3
DEM_ELC <- newDemand(
  name      = "DEM_ELC",
  commodity = "ELC",
  unit      = "PJ",
  demand    = data.frame(region = REG, year = 2050, demand = c(80, 70, 40))
)

WSOL <- newWeather(name = "WSOL", timeframe = "HOUR", weather = weather_WSOL)
WWIN <- newWeather(name = "WWIN", timeframe = "HOUR", weather = weather_WWIN)
ECOA <- newTechnology(
  name    = "ECOA",
  input   = list(comm = "COA", unit = "PJ", combustion = 1),
  output  = list(comm = "ELC", unit = "PJ"),
  ceff    = data.frame(comm = "COA", cinp2use = 0.40),
  invcost = list(invcost = 2000),
  fixom   = 55,
  cap2act = 31.536,
  olife   = 30L,
  region  = REG
)
EGAS <- newTechnology(
  name    = "EGAS",
  input   = list(comm = "GAS", unit = "PJ", combustion = 1),
  output  = list(comm = "ELC", unit = "PJ"),
  ceff    = data.frame(comm = "GAS", cinp2use = 0.58),
  invcost = list(invcost = 900),
  fixom   = 25,
  cap2act = 31.536,
  olife   = 25L,
  region  = REG
)
ESOL <- newTechnology(
  name    = "ESOL",
  input   = list(comm = "SOL", unit = "PJ"),
  output  = list(comm = "ELC", unit = "PJ"),
  ceff    = data.frame(comm = "SOL", cinp2use = 1),
  weather = list(weather = "WSOL", comm = "SOL", waf.fx = 1),
  invcost = list(invcost = meur_gw(650)),
  fixom   = 12,
  cap2act = 31.536,
  olife   = 25L,
  region  = REG
)
EWIN <- update(
  ESOL,
  name    = "EWIN",
  input   = list(comm = "WIN", unit = "PJ"),
  ceff    = data.frame(comm = "WIN", cinp2use = 1),
  weather = list(weather = "WWIN", comm = "WIN", waf.fx = 1),
  invcost = list(invcost = meur_gw(1300)),
  fixom   = 35
)
STG_ELC <- newStorage(
  name      = "STG_ELC",
  commodity = "ELC",
  invcost   = list(invcost = meur_pj_kwh(200)),
  cap2stg   = 4,
  seff      = data.frame(inpeff = 0.95, outeff = 0.95),
  olife     = 20L,
  region    = REG
)

draw(ECOA) # coal in, electricity out -- the same diagram in every region
draw(ESOL)

hor <- newHorizon(2025:2055, c(1, 10, 10, 10))

3.1 — Regions in isolation. Assemble the six-technology system across REG with no link between regions, solve, and read the generation mix per region. Determine where each region lands, and explain what isolation costs the renewables-rich R3.

repo_iso <- newRepository(
  "repo_iso",
  ELC, COA, GAS, CO2, SOL, WIN,
  SUP_COA, SUP_GAS, SUP_SOL, SUP_WIN, DEM_ELC,
  ECOA, EGAS, ESOL, EWIN, WSOL, WWIN, STG_ELC
)

mod_iso <- newModel(
  name     = "ISO",
  data     = repo_iso,
  region   = REG,
  discount = WS_DISCOUNT,
  calendar = WS_CAL,
  horizon  = hor
)

scen_iso <- solve_model(mod_iso)

getData(scen_iso, "vTechCap", merge = TRUE)               # capacity by region and tech
autoplot(scen_iso) + theme_ws()                           # generation mix per region

Each region solves its own least-cost problem: R1 leans on its cheap coal, R2 on gas, and R3 on wind and solar backed by whatever firm capacity it can afford locally. Isolated, R3 cannot sell its cheap renewable surplus to anyone, so it over-builds firm capacity (or spills) — the first hint that a wire would pay.

5.2 A transmission link

newTrade() connects regions. We give it a fixed existing capacity — a wire that already exists — rather than letting the model build one, so the value we measure later is clean. teff is the throughput efficiency (losses).

TBD_R1_R2 <- newTrade(
  name      = "TBD_R1_R2",
  commodity = "ELC",
  routes    = data.frame(src = c("R1", "R2"), dst = c("R2", "R1")),
  trade     = data.frame(src = c("R1", "R2"), dst = c("R2", "R1"), teff = 0.95),
  capacity  = data.frame(stock = 5),
  olife     = 50L
)
TBD_R2_R3 <- newTrade(
  name      = "TBD_R2_R3",
  commodity = "ELC",
  routes    = data.frame(src = c("R2", "R3"), dst = c("R3", "R2")),
  trade     = data.frame(src = c("R2", "R3"), dst = c("R3", "R2"), teff = 0.95),
  capacity  = data.frame(stock = 5),
  olife     = 50L
)

3.2 — The value of the wire. Add both links, solve, and compare total cost and the generation mix with the isolated case from 3.1. Determine the direction of flow and whether R3 now exports its renewables. Draw the network with plot_trade_map().

repo_TR <- newRepository(
  "repo_TR",
  ELC, COA, GAS, CO2, SOL, WIN,
  SUP_COA, SUP_GAS, SUP_SOL, SUP_WIN, DEM_ELC,
  ECOA, EGAS, ESOL, EWIN, WSOL, WWIN, STG_ELC,
  TBD_R1_R2, TBD_R2_R3
)

mod_TR  <- newModel(
  name     = "TR",
  data     = repo_TR,
  region   = REG,
  discount = WS_DISCOUNT,
  calendar = WS_CAL,
  horizon  = hor
)

scen_TR <- solve_model(mod_TR)

getData(scen_TR, "vObjective", merge = TRUE)                   # vs scen_iso
getData(scen_TR, "vTradeIr", merge = TRUE, timeframe = "highest") # flows by slice

# the corridor network on a stylised map (needs the sf package)
plot_trade_map(repo_TR, map = utopia_modules$maps$honeycomb)

Total cost falls: cheap renewable energy in R3 now displaces dearer generation next door, so the system builds less firm plant overall. The flows run from wherever power is momentarily cheapest toward wherever it is dearest — often out of R3 at midday. A wire is a substitute for both generation and storage.

5.3 Rest-of-world import

An import brings a commodity in from outside the modelled regions at a price — not a region, just a border. Here, imported gas is available everywhere as a backstop fuel.

IMP_GAS <- newImport(
  name      = "IMP_GAS",
  commodity = "GAS",
  unit      = "PJ",
  import    = data.frame(region = REG, price = 8.0) # dearer than R2's domestic gas
)

3.3 — The marginal fuel. Add IMP_GAS and solve. Determine where the model chooses to import rather than build, and identify what sets the electricity price at the margin in regions with no domestic fuel.

repo_M <- newRepository(
  "repo_M",
  ELC, COA, GAS, CO2, SOL, WIN,
  SUP_COA, SUP_GAS, SUP_SOL, SUP_WIN, IMP_GAS, DEM_ELC,
  ECOA, EGAS, ESOL, EWIN, WSOL, WWIN, STG_ELC,
  TBD_R1_R2, TBD_R2_R3
)

mod_M  <- newModel(
  name     = "M",
  data     = repo_M,
  region   = REG,
  discount = WS_DISCOUNT,
  calendar = WS_CAL,
  horizon  = hor
)

scen_M <- solve_model(mod_M)

getData(scen_M, "vImportRow", merge = TRUE) # imported gas, by region

mod_M is the model we carry into the policy scenarios of ?sec-policy. Imports fill the gap where building is not worth it — a region short of both fuel and wire capacity leans on the border, and the import price becomes the ceiling that domestic options must beat.

5.4 Where does a new load want to be?

Now the spatial question in its sharpest form. Suppose policy commits to deploying a fixed amount of a new electricity-consuming technology — an electrolyser, a fleet of data centres — and lets the model choose which regions host it. The load consumes electricity to make a product PRD with an annual demand; a system-wide capacity target (summed over regions, by year) fixes how much is built; the optimiser places it.

PRD     <- newCommodity("PRD", unit = "PJ", timeframe = "ANNUAL") # e.g. hydrogen
DEM_PRD <- newDemand(
  name      = "DEM_PRD",
  commodity = "PRD",
  unit      = "PJ",
  demand    = data.frame(year = 2050, demand = 30)                # met from any region
)

# a new load: consumes ELC (hourly), makes PRD; buildable in every region
LOAD_base <- newTechnology(
  name    = "LOAD",
  desc    = "New base load",
  input   = list(comm = "ELC", unit = "PJ"),
  output  = list(comm = "PRD", unit = "PJ"),
  ceff    = data.frame(comm = "ELC", cinp2use = 1.4), # 1 / efficiency
  af      = data.frame(af.lo = 0.9),                  # must run flat, every hour
  invcost = list(invcost = meur_gw(500)),
  fixom   = 10,
  cap2act = 31.536,
  olife   = 20L,
  region  = REG
)

# system-wide deployment target: total installed capacity over all regions
TARGET <- newConstraint(
  name     = "TARGET",
  eq       = ">=",
  for.each = data.frame(year = 2050),
  term1    = list(variable = "vTechCap", for.sum = list(region = REG, tech = "LOAD")),
  rhs      = data.frame(year = 2050, rhs = 1.2),
  defVal   = 0
)

draw(LOAD_base) # electricity in, product (PRD) out

3.4 — Siting a base load. Add PRD, DEM_PRD, LOAD_base and TARGET to the model, solve, and read vTechNewCap for LOAD by region. A base load runs flat around the clock — determine which region the model selects, and explain why.

repo_base <- newRepository(
  "repo_base",
  ELC, COA, GAS, CO2, SOL, WIN, PRD,
  SUP_COA, SUP_GAS, SUP_SOL, SUP_WIN, IMP_GAS, DEM_ELC, DEM_PRD,
  ECOA, EGAS, ESOL, EWIN, WSOL, WWIN, STG_ELC,
  TBD_R1_R2, TBD_R2_R3, LOAD_base, TARGET
)

mod_base  <- newModel(
  name     = "SITE_BASE",
  data     = repo_base,
  region   = REG,
  discount = WS_DISCOUNT,
  calendar = WS_CAL,
  horizon  = hor
)

scen_base <- solve_model(mod_base)

getData(scen_base, "vTechNewCap", tech = "LOAD", merge = TRUE) # region allocation

A must-run load needs firm, cheap power every hour, so it gravitates to the region that can supply that most cheaply around the clock — the coal/gas regions rather than renewables-rich R3, whose cheap energy comes and goes with the weather. Flat demand wants flat supply.

3.5 — Siting a flexible load. Now make the same load flexible: it may consume whenever power is cheap, provided it makes its annual PRD in total. Set af.lo = 0, af.up = 1 and re-solve. Determine whether the model moves it to a different region.

LOAD_flex <- update(
  LOAD_base,
  desc = "New flexible load",
  af   = data.frame(af.lo = 0, af.up = 1) # run any hour, idle any hour
)

repo_flex <- newRepository(
  "repo_flex",
  ELC, COA, GAS, CO2, SOL, WIN, PRD,
  SUP_COA, SUP_GAS, SUP_SOL, SUP_WIN, IMP_GAS, DEM_ELC, DEM_PRD,
  ECOA, EGAS, ESOL, EWIN, WSOL, WWIN, STG_ELC,
  TBD_R1_R2, TBD_R2_R3, LOAD_flex, TARGET
)

mod_flex  <- newModel(
  name     = "SITE_FLEX",
  data     = repo_flex,
  region   = REG,
  discount = WS_DISCOUNT,
  calendar = WS_CAL,
  horizon  = hor
)

scen_flex <- solve_model(mod_flex)

getData(scen_flex, "vTechNewCap", tech = "LOAD", merge = TRUE)

Because it can wait for cheap hours, the flexible load is drawn toward R3: it absorbs wind and solar that would otherwise be curtailed (the surplus of Section 4.6), turning it into product instead of waste. Same target, opposite siting — flexibility, not the average price, decides where it belongs. This flexible load is exactly an electrolyser; Chapter 6 builds one properly.

5.5 The value of storage and transmission

The renewables-rich cases hint at it; now measure it. Take a fully renewable system — drop the thermal plants so only wind, solar, storage and wires remain — and price storage and transmission by removing them and reading how much total cost rises.

# renewable-only repository: no ECOA/EGAS, no fossil supply/import
repo_re <- newRepository(
  "repo_re",
  ELC, SOL, WIN, PRD,
  SUP_SOL, SUP_WIN, DEM_ELC, DEM_PRD,
  ESOL, EWIN, WSOL, WWIN, STG_ELC,
  TBD_R1_R2, TBD_R2_R3, LOAD_flex, TARGET
)

# the same system with storage removed, and with transmission removed
repo_re_noSTG <- newRepository(
  "repo_re_noSTG",
  ELC, SOL, WIN, PRD,
  SUP_SOL, SUP_WIN, DEM_ELC, DEM_PRD,
  ESOL, EWIN, WSOL, WWIN,
  TBD_R1_R2, TBD_R2_R3, LOAD_flex, TARGET
)
repo_re_noTR <- newRepository(
  "repo_re_noTR",
  ELC, SOL, WIN, PRD,
  SUP_SOL, SUP_WIN, DEM_ELC, DEM_PRD,
  ESOL, EWIN, WSOL, WWIN, STG_ELC,
  LOAD_flex, TARGET
)

3.6 — What are storage and transmission worth? Solve the renewable system in full, then again with storage removed, and again with transmission removed. The cost increase on removal is the value. Inspect vDummyImport each time — if it is non-zero the model is meeting demand with expensive penalty slack, and the measured “value” is partly that penalty.

mod_re     <- newModel("RE_full",  data = repo_re,       region = REG,
                       discount = WS_DISCOUNT, calendar = WS_CAL, horizon = hor)
mod_re_noS <- newModel("RE_noSTG", data = repo_re_noSTG, region = REG,
                       discount = WS_DISCOUNT, calendar = WS_CAL, horizon = hor)
mod_re_noT <- newModel("RE_noTR",  data = repo_re_noTR,  region = REG,
                       discount = WS_DISCOUNT, calendar = WS_CAL, horizon = hor)

scen_re     <- solve_model(mod_re)
scen_re_noS <- solve_model(mod_re_noS)
scen_re_noT <- solve_model(mod_re_noT)

obj_full <- getData(scen_re,     "vObjective", merge = TRUE)$value
obj_noS  <- getData(scen_re_noS, "vObjective", merge = TRUE)$value
obj_noT  <- getData(scen_re_noT, "vObjective", merge = TRUE)$value

obj_noS - obj_full # value of storage: cost increase when removed
obj_noT - obj_full # value of transmission

# is the model quietly buying unmet demand as penalty slack?
getData(scen_re_noS, "vDummyImport", merge = TRUE)
getData(scen_re_noT, "vDummyImport", merge = TRUE)

Remove storage and the system must either over-build renewables to cover the evening or lean on the wire; remove the wire and every region must self-balance its own weather — either way total cost rises, and that rise is what the missing asset was worth. Watch vDummyImport: if removing an asset leaves demand unservable, the model quietly buys the shortfall as penalty slack rather than reporting infeasible, and the cost balloons — a valid ranking of value, but read knowing part of it is the penalty, not real dispatch. Storage and transmission are partial substitutes: each buys back the curtailment the other would leave on the table.

5.6 What you built

Space added the questions a single region cannot ask. You assembled a multi-region system from region-keyed data, connected it with a fixed transmission link and a rest-of-world import, mapped the network with plot_trade_map(), and used it to site a new load — discovering that a flexible consumer wants to live where the renewables are while a firm one does not — and to value storage and transmission by removing them from a fully renewable system. Chapter 6 turns to the inside of the box: how to model processes like the electrolyser, a blast furnace, or a vehicle fleet. ?sec-policy takes mod_M and puts policy on it.