Calculate final-to-useful efficiencies for final demand and EIOU when last stage is final

Final-to-useful efficiencies for energy carriers and sectors in final demand and energy industry own use can be calculated from allocations (C_Y and C_eiou), machine efficiencies (eta_i), and (for exergetic efficiencies) exergy-to-energy ratios (phi). This function performs those calculations. By default, the output contains matrices in the same structure as Y and U_EIOU when last stage is final.

Usage

calc_eta_fu_Y_eiou(
  .c_mats_eta_phi_vecs = NULL,
  C_Y = Recca::alloc_cols$C_Y,
  C_eiou = Recca::alloc_cols$C_eiou,
  eta_i = Recca::efficiency_cols$eta_i,
  phi = Recca::psut_cols$phi,
  matricize = TRUE,
  energy_type = Recca::energy_types$energy_type,
  eta_fu = Recca::efficiency_cols$eta_fu,
  energy = Recca::energy_types$e,
  exergy = Recca::energy_types$x,
  eta_fu_Y_e = paste0(eta_fu, "_Y_", energy),
  eta_fu_Y_x = paste0(eta_fu, "_Y_", exergy),
  eta_fu_eiou_e = paste0(eta_fu, "_EIOU_", energy),
  eta_fu_eiou_x = paste0(eta_fu, "_EIOU_", exergy),
  notation = RCLabels::arrow_notation
)

Arguments

.c_mats_eta_phi_vecs: A data frame containing allocation matrices (C_Y and C_eiou), vectors of machine efficiencies (eta_i), and exergy-to-energy ratio vectors (phi). Default is NULL, in which case individual matrices or vectors can be passed to C_Y, C_eiou, eta_i, and phi.
C_Y: The name of the column in .c_mats_eta_phi_vecs containing allocation matrices for final demand (the Y in C_Y). Or a single C_Y matrix. Or a list of C_Y matrices. Default is Recca::alloc_cols$C_Y.
C_eiou: The name of the column in .c_mats_eta_phi_vecs containing allocation matrices for energy industry own use (the eiou in C_eiou). Or a single C_EIOU matrix. Or a list of C_EIOU matrices. Default is Recca::alloc_cols$C_eiou.
eta_i: The name of the column in .c_mats_eta_phi_vecs containing machine efficiencies. Or a single eta_i vector. Or a list of eta_i vectors. Default is Recca::efficiency_cols$eta_i.
phi: The name of the column in .c_mats_eta_phi_vecs containing exergy-to-energy ratios. Or a single phi vector. Default is Recca::psut_cols$phi.
matricize: A boolean that tells whether to return matrices of the same structure as Y and U_EIOU when last stage is final. Default is TRUE. FALSE returns a column vector with rows same as C_Y and C_EIOU.
energy_type, energy, exergy: See Recca::energy_types.
eta_fu: The base name of the output columns. Default is Recca::efficiency_cols$eta_fu.
eta_fu_Y_e: The name of the energy efficiency output column for energy flowing into final demand (Y). Default is paste0(eta_fu, "_Y_", energy).
eta_fu_Y_x: The name of the exergy efficiency output column for energy flowing into final demand (Y). Default is paste0(eta_fu, "_Y_", exergy).
eta_fu_eiou_e: The name of the energy efficiency output column for energy flowing into the energy industry (U_EIOU). Default is paste0(eta_fu, "_EIOU_", energy).
eta_fu_eiou_x: The name of the exergy efficiency output column for energy flowing into the energy industry (U_EIOU). Default is paste0(eta_fu, "_EIOU_", energy).
notation: The notation for the row and column labels of the matrices and vectors. Default is RCLabels::arrow_notation.

Value

A data frame or list containing final-to-useful efficiencies.

Details

The matrix formula for calculating energy efficiencies is eta_fu_E = C * eta_i, where C is one of C_Y or C_EIOU. The matrix formula for calculating exergy efficiencies from allocations and machine energy efficiencies is eta_fu_X = (phi_u_hat_inv * (C * eta_fu_hat)) * phi_u.

The C_Y matrix is assumed to have rows named with prefixes of final energy carriers and suffixes of the final demand sector into which the final energy carrier flows. The C_EIOU matrix is similar, except that its rows are named with suffixes of the energy industry sector into which the final energy carrier flows. The columns of the C_Y and C_EIOU matrices are named with prefixes of machine names and suffixes of useful energy product made by the machine. See examples.

The eta_i vector of machine efficiencies has rows named with prefixes same as C_Y and C_EIOU columns. The name of the eta_i column is not used. See examples.

The phi vector of exergy-to-energy ratios has rows named with energy carriers that correspond to the prefixes of C_Y and C_EIOU rows and the suffixes of C_Y and C_EIOU columns. See examples.

This function uses matsbyname::vec_from_store_byname() to construct the eta_i and phi vectors before multiplying, thereby eliminating unnecessary growth of the output matrices.

Examples

C_Y <- matrix(c(0.7, 0.3, 0,   0,   0,
                0,   0,   0.2, 0.5, 0.3), byrow = TRUE, nrow = 2, ncol = 5,
              dimnames = list(c("Electricity -> Non-ferrous metals",
                                "PSB -> Residential"),
                              c("Electric arc furnaces -> HTH.600.C",
                                "Electric lights -> L",
                                "Wood stoves -> LTH.20.C",
                                "Wood stoves -> LTH.50.C",
                                "Wood stoves -> MTH.100.C")))
C_Y
#>                                   Electric arc furnaces -> HTH.600.C
#> Electricity -> Non-ferrous metals                                0.7
#> PSB -> Residential                                               0.0
#>                                   Electric lights -> L Wood stoves -> LTH.20.C
#> Electricity -> Non-ferrous metals                  0.3                     0.0
#> PSB -> Residential                                 0.0                     0.2
#>                                   Wood stoves -> LTH.50.C
#> Electricity -> Non-ferrous metals                     0.0
#> PSB -> Residential                                    0.5
#>                                   Wood stoves -> MTH.100.C
#> Electricity -> Non-ferrous metals                      0.0
#> PSB -> Residential                                     0.3
eta_i <- matrix(c(0.9, 0.2, 0.4, 0.4, 0.3), nrow = 5, ncol = 1,
                  dimnames = list(c("Electric arc furnaces -> HTH.600.C",
                                    "Electric lights -> L",
                                    "Wood stoves -> LTH.20.C",
                                    "Wood stoves -> LTH.50.C",
                                    "Wood stoves -> MTH.100.C"),
                                  "eta_i"))
eta_i
#>                                    eta_i
#> Electric arc furnaces -> HTH.600.C   0.9
#> Electric lights -> L                 0.2
#> Wood stoves -> LTH.20.C              0.4
#> Wood stoves -> LTH.50.C              0.4
#> Wood stoves -> MTH.100.C             0.3
phi <- matrix(c(1, 1.1, 1 - 298.15/(600+273.15), 0.95,
                1 - (20 + 273.15)/298.15,
                1 - 298.15/(50+273.15),
                1 - 298.15/(100+273.15)),
              nrow = 7, ncol = 1,
              dimnames = list(c("Electricity", "PSB", "HTH.600.C", "L",
                                "LTH.20.C", "LTH.50.C", "MTH.100.C"),
                              "phi"))
phi
#>                    phi
#> Electricity 1.00000000
#> PSB         1.10000000
#> HTH.600.C   0.65853519
#> L           0.95000000
#> LTH.20.C    0.01677008
#> LTH.50.C    0.07736345
#> MTH.100.C   0.20099156
res <- calc_eta_fu_Y_eiou(C_Y = C_Y, C_eiou = C_Y, eta_i = eta_i, phi = phi)
res$eta_fu_Y_E
#>             Non-ferrous metals Residential
#> Electricity               0.69        0.00
#> PSB                       0.00        0.37
res$eta_fu_EIOU_E # Same because C_Y and C_EIOU are same
#>             Non-ferrous metals Residential
#> Electricity               0.69        0.00
#> PSB                       0.00        0.37
res$eta_fu_Y_X
#>             Non-ferrous metals Residential
#> Electricity          0.4718772  0.00000000
#> PSB                  0.0000000  0.03173049
res$eta_fu_EIOU_X # Same because C_Y and C_EIOU are same
#>             Non-ferrous metals Residential
#> Electricity          0.4718772  0.00000000
#> PSB                  0.0000000  0.03173049
res2 <- calc_eta_fu_Y_eiou(C_Y = C_Y, C_eiou = C_Y, eta_i = eta_i, phi = phi,
                           matricize = FALSE)
res2$eta_fu_Y_E
#>                                   eta_fu_Y_E
#> Electricity -> Non-ferrous metals       0.69
#> PSB -> Residential                      0.37
#> attr(,"coltype")
#> [1] "eta_fu_Y_E"
res2$eta_fu_Y_X
#>                                   eta_fu_Y_X
#> Electricity -> Non-ferrous metals 0.47187717
#> PSB -> Residential                0.03173049
#> attr(,"coltype")
#> [1] "eta_fu_Y_X"