Calculate inter- and intra-industry balances for PSUT (RUVY) matrices2

Balances are an important aspect of analyzing material and energy conversion chains in the PSUT framework with the RUVY matrices. Often, balances are calculated on energy or exergy flows. Balances can be calculated for mass flows or monetary flows, too.

Usage

calc_inter_industry_balance(
  .sutmats = NULL,
  R = Recca::psut_cols$R,
  U = Recca::psut_cols$U,
  V = Recca::psut_cols$V,
  Y = Recca::psut_cols$Y,
  balance = Recca::balance_cols$inter_industry_balance_colname
)

calc_intra_industry_balance(
  .sutmats = NULL,
  U = Recca::psut_cols$U,
  V = Recca::psut_cols$V,
  balance = Recca::balance_cols$intra_industry_balance_colname
)

Arguments

.sutmats: A named list of matrices or an SUT-style, wide-by-matrices data frame with columns of matrices, including R, U, V, and Y.
R: Resources (R) matrix or name of the column in .sutmats that contains same. Default is "R".
U: Use (U) matrix or name of the column in .sutmats that contains same. Default is "U".
V: Make (V) matrix or name of the column in .sutmats that contains same. Default is "V".
Y: Final demand (Y) matrix or name of the column in .sutmats that contains same. Default is "Y".
balance: The name of the column containing energy balance vectors. Defaults are balance_cols$inter_industry_balance_colname or "SUTInterIndustryBalance" for calc_inter_industry_balances() and balance_cols$intra_industry_balance_colname or "SUTIntraIndustryBalance" for calc_intra_industry_balances().

Value

A list or data frame containing balances.

Details

Inter-industry (between-industry) balances

In a PSUT description of a material or energy conversion chain, all of every product leaving one industry must arrive at another industry. calc_inter_industry_balances() calculates these between-industry balances via ((R + V)^T^ - (U + Y))i. Inter-industry balances are calculated for products (not industries).

Intra-industry (across-industry) balances

calc_intra_industry_balances() calculates across-industry balances via (U^T^ - V)i (i.e., inputs - outputs). Inter-industry balances are calculated for industries (not products), and the result is a column vector of industry balances.

Outputs

The argument balance specifies the name of the result. By default, the output of calc_inter_industry_balances() is balance_cols$inter_industry_balance_colname or "SUTInterIndustryBalance". By default, the output of calc_intra_industry_balances() is balance_cols$intra_industry_balance_colname or "SUTIntraIndustryBalance".

For inter-industry (between-industry) balances, the result is a column vector of product balances. The result should always be the 0 vector, regardless of the quantity represented by the matrices.

In a PSUT description of a mass or energy conversion chain, the meaning of intra-industry (across-industry) balances depends on the construction of the matrices and the quantity represented by the matrices. When all losses are accounted in the matrices themselves, the calculation of intra-industry balances for conversion chains of conserved quantities (e.g., mass, energy, money) should give the 0 vector with industries in rows. When losses are not accounted in the matrices, the calculation of intra-industry balances gives losses.

For conversion chains of unconserved quantities (e.g., entropy and exergy), when losses are accounted in the matrices, the intra-industry balance gives generation or destruction. When losses are not accounted in the matrices, the intra-industry balance gives the sum of generation, destruction and losses.

Examples

# Inter-industry balances
inter <- UKEnergy2000mats |>
  dplyr::filter(LastStage %in% c("Final", "Useful")) |>
  tidyr::pivot_wider(names_from = matrix.name, values_from = matrix) |>
  calc_inter_industry_balance()
inter[[Recca::balance_cols$inter_industry_balance_colname]][[1]]
#>                     Industry
#> Crude                      0
#> Crude [from Dist.]         0
#> Crude [from Fields]        0
#> Diesel                     0
#> Diesel [from Dist.]        0
#> Elect                      0
#> Elect [from Grid]          0
#> NG                         0
#> NG [from Dist.]            0
#> NG [from Wells]            0
#> Petrol                     0
#> Petrol [from Dist.]        0
#> attr(,"rowtype")
#> [1] "Product"
#> attr(,"coltype")
#> [1] "Industry"
inter[[Recca::balance_cols$inter_industry_balance_colname]][[2]]
#>                             Industry
#> Crude                   0.000000e+00
#> Crude [from Dist.]      0.000000e+00
#> Crude [from Fields]     0.000000e+00
#> Diesel                  0.000000e+00
#> Diesel [from Dist.]     0.000000e+00
#> Elect                   0.000000e+00
#> Elect [from Grid]       0.000000e+00
#> LTH                     0.000000e+00
#> Light                   0.000000e+00
#> MD [from Car engines]   0.000000e+00
#> MD [from Truck engines] 2.273737e-13
#> NG                      0.000000e+00
#> NG [from Dist.]         0.000000e+00
#> NG [from Wells]         0.000000e+00
#> Petrol                  0.000000e+00
#> Petrol [from Dist.]     0.000000e+00
#> attr(,"rowtype")
#> [1] "Product"
#> attr(,"coltype")
#> [1] "Industry"
# Intra-industry balances
intra <- UKEnergy2000mats |>
  dplyr::filter(LastStage %in% c("Final", "Useful")) |>
  tidyr::pivot_wider(names_from = matrix.name, values_from = matrix) |>
  calc_intra_industry_balance()
intra[[Recca::balance_cols$intra_industry_balance_colname]][[1]]
#>                   Product
#> Crude dist.           550
#> Diesel dist.          350
#> Elect. grid           125
#> Gas wells & proc.    2075
#> NG dist.               50
#> Oil fields           2575
#> Oil refineries       5075
#> Petrol dist.          750
#> Power plants         9700
#> attr(,"rowtype")
#> [1] "Industry"
#> attr(,"coltype")
#> [1] "Product"
intra[[Recca::balance_cols$intra_industry_balance_colname]][[2]]
#>                      Product
#> Car engines       22999.6000
#> Crude dist.         545.0000
#> Diesel dist.        367.9998
#> Elect. grid         125.0000
#> Furnaces           5000.0000
#> Gas wells & proc.  2075.0000
#> Light fixtures     4800.0000
#> NG dist.             45.0000
#> Oil fields         2575.0000
#> Oil refineries     5075.0000
#> Petrol dist.        526.9997
#> Power plants       9700.0000
#> Truck engines     13250.0200
#> attr(,"rowtype")
#> [1] "Industry"
#> attr(,"coltype")
#> [1] "Product"