R/pof_future_transformer_11_20kv.R

In CNAIM: Common Network Asset Indices Methodology (CNAIM)

#' @importFrom magrittr %>%
#' @title Future Probability of Failure for 6.6/11kV and 20kV Transformers
#' @description This function calculates the future
#' annual probability of failure for 6.6/11kV and 20kV transformers.
#' The function is a cubic curve that is based on
#' the first three terms of the Taylor series for an
#' exponential function. For more information about the
#' probability of failure function see section 6
#' on page 34 in CNAIM (2021).
#' @inheritParams pof_transformer_11_20kv
#' @param simulation_end_year Numeric. The last year of simulating probability
#'  of failure. Default is 100.
#' @return DataFrame. Future probability of failure
#' along with future health score
#' @source DNO Common Network Asset Indices Methodology (CNAIM),
#' Health & Criticality - Version 2.1, 2021:
#' \url{https://www.ofgem.gov.uk/sites/default/files/docs/2021/04/dno_common_network_asset_indices_methodology_v2.1_final_01-04-2021.pdf}
#' @export
#' @examples
#' # Future probability of a 6.6/11 kV transformer
#' future_pof_transformer <-
#' pof_future_transformer_11_20kv(hv_transformer_type = "6.6/11kV Transformer (GM)",
#' utilisation_pct = "Default",
#' placement = "Default",
#' altitude_m = "Default",
#' distance_from_coast_km = "Default",
#' corrosion_category_index = "Default",
#' age = 20,
#' partial_discharge = "Default",
#' temperature_reading = "Default",
#' observed_condition = "Default",
#' reliability_factor = "Default",
#' moisture = "Default",
#' oil_acidity = "Default",
#' bd_strength = "Default",
#' simulation_end_year = 100)
pof_future_transformer_11_20kv <-
  function(hv_transformer_type = "6.6/11kV Transformer (GM)",
           utilisation_pct = "Default",
           placement = "Default",
           altitude_m = "Default",
           distance_from_coast_km = "Default",
           corrosion_category_index = "Default",
           age,
           partial_discharge = "Default",
           temperature_reading = "Default",
           observed_condition = "Default",
           reliability_factor = "Default",
           moisture = "Default",
           oil_acidity = "Default",
           bd_strength = "Default",
           simulation_end_year = 100) {

    `Asset Register Category` = `Health Index Asset Category` =
      `Generic Term...1` = `Generic Term...2` = `Functional Failure Category` =
      `K-Value (%)` = `C-Value` = `Asset Register  Category` = NULL
    # due to NSE notes in R CMD check

    # Ref. table Categorisation of Assets and Generic Terms for Assets  --
    asset_type <- hv_transformer_type

    asset_category <- gb_ref$categorisation_of_assets %>%
      dplyr::filter(`Asset Register Category` == asset_type) %>%
      dplyr::select(`Health Index Asset Category`) %>% dplyr::pull()

    generic_term_1 <- gb_ref$generic_terms_for_assets %>%
      dplyr::filter(`Health Index Asset Category` == asset_category) %>%
      dplyr::select(`Generic Term...1`) %>% dplyr::pull()

    generic_term_2 <- gb_ref$generic_terms_for_assets %>%
      dplyr::filter(`Health Index Asset Category` == asset_category) %>%
      dplyr::select(`Generic Term...2`) %>% dplyr::pull()

    # Normal expected life for 6.6/11 kV transformer ------------------------------
    normal_expected_life <- gb_ref$normal_expected_life %>%
      dplyr::filter(`Asset Register  Category` == asset_type) %>%
      dplyr::pull()

    # Constants C and K for PoF function --------------------------------------
    k <- gb_ref$pof_curve_parameters %>%
      dplyr::filter(`Functional Failure Category` ==
                      asset_category) %>% dplyr::select(`K-Value (%)`) %>%
      dplyr::pull()/100

    c <- gb_ref$pof_curve_parameters %>%
      dplyr::filter(`Functional Failure Category` ==
                      asset_category) %>% dplyr::select(`C-Value`) %>%
      dplyr::pull()

    # Duty factor -------------------------------------------------------------
    duty_factor_tf_11kv <- duty_factor_transformer_11_20kv(utilisation_pct)

    # Location factor ----------------------------------------------------
    location_factor_transformer <- location_factor(placement,
                                                   altitude_m,
                                                   distance_from_coast_km,
                                                   corrosion_category_index,
                                                   asset_type)

    # Expected life for 6.6/11 kV transformer ------------------------------
    expected_life_years <- expected_life(normal_expected_life,
                                         duty_factor_tf_11kv,
                                         location_factor_transformer)

    # b1 (Initial Ageing Rate) ------------------------------------------------
    b1 <- beta_1(expected_life_years)

    # Initial health score ----------------------------------------------------
    initial_health_score <- initial_health(b1, age)

    ## NOTE
    # Typically, the Health Score Collar is 0.5 and
    # Health Score Cap is 10, implying no overriding
    # of the Health Score. However, in some instances
    # these parameters are set to other values in the
    # Health Score Modifier calibration tables.
    # These overriding values are shown in Table 35 to Table 202
    # and Table 207 in Appendix B.

    # Measured condition inputs ---------------------------------------------
    mcm_mmi_cal_df <-
      gb_ref$measured_cond_modifier_mmi_cal

    mcm_mmi_cal_df <-
      mcm_mmi_cal_df[which(mcm_mmi_cal_df$`Asset Category` == asset_category), ]

    factor_divider_1 <-
      as.numeric(mcm_mmi_cal_df$
                   `Parameters for Combination Using MMI Technique - Factor Divider 1`)

    factor_divider_2 <-
      as.numeric(mcm_mmi_cal_df$
                   `Parameters for Combination Using MMI Technique - Factor Divider 2`)

    max_no_combined_factors <-
      as.numeric(mcm_mmi_cal_df$
                   `Parameters for Combination Using MMI Technique - Max. No. of Combined Factors`
      )

    # Partial discharge -------------------------------------------------------
    mci_hv_tf_partial_discharge <-
      gb_ref$mci_hv_tf_partial_discharge

    ci_factor_partial_discharge <-
      mci_hv_tf_partial_discharge$`Condition Input Factor`[which(
        mci_hv_tf_partial_discharge$
          `Condition Criteria: Partial Discharge Test Result` ==
          partial_discharge)]

    ci_cap_partial_discharge <-
      mci_hv_tf_partial_discharge$`Condition Input Cap`[which(
        mci_hv_tf_partial_discharge$
          `Condition Criteria: Partial Discharge Test Result` ==
          partial_discharge)]

    ci_collar_partial_discharge <-
      mci_hv_tf_partial_discharge$`Condition Input Collar`[which(
        mci_hv_tf_partial_discharge$
          `Condition Criteria: Partial Discharge Test Result` ==
          partial_discharge)]

    # Oil acidity -------------------------------------------------------------
    oil_test_mod <- oil_test_modifier(moisture,
                                      oil_acidity,
                                      bd_strength)


    # Temperature readings ----------------------------------------------------
    mci_hv_tf_temp_readings <-
      gb_ref$mci_hv_tf_temp_readings

    ci_factor_temp_reading <-
      mci_hv_tf_temp_readings$`Condition Input Factor`[which(
        mci_hv_tf_temp_readings$
          `Condition Criteria: Temperature Reading` ==
          temperature_reading)]

    ci_cap_temp_reading <-
      mci_hv_tf_temp_readings$`Condition Input Cap`[which(
        mci_hv_tf_temp_readings$
          `Condition Criteria: Temperature Reading` ==
          temperature_reading)]

    ci_collar_temp_reading <-
      mci_hv_tf_temp_readings$`Condition Input Collar`[which(
        mci_hv_tf_temp_readings$
          `Condition Criteria: Temperature Reading` ==
          temperature_reading)]

    # measured condition factor -----------------------------------------------
    factors <- c(ci_factor_partial_discharge,
                 oil_test_mod$oil_condition_factor,
                 ci_factor_temp_reading)

    measured_condition_factor <- mmi(factors,
                                     factor_divider_1,
                                     factor_divider_2,
                                     max_no_combined_factors)

    # Measured condition cap --------------------------------------------------
    caps <- c(ci_cap_partial_discharge,
              oil_test_mod$oil_condition_cap,
              ci_cap_temp_reading)
    measured_condition_cap <- min(caps)

    # Measured condition collar -----------------------------------------------
    collars <- c(ci_collar_partial_discharge,
                 oil_test_mod$oil_condition_collar,
                 ci_collar_temp_reading)
    measured_condition_collar <- max(collars)

    # Measured condition modifier ---------------------------------------------
    measured_condition_modifier <- data.frame(measured_condition_factor,
                                              measured_condition_cap,
                                              measured_condition_collar)

    # Observed condition inputs ---------------------------------------------
    oci_mmi_cal_df <-
      gb_ref$observed_cond_modifier_mmi_cal

    oci_mmi_cal_df <-
      oci_mmi_cal_df[which(oci_mmi_cal_df$`Asset Category` == asset_category), ]

    factor_divider_1 <-
      as.numeric(oci_mmi_cal_df$
                   `Parameters for Combination Using MMI Technique - Factor Divider 1`)

    factor_divider_2 <-
      as.numeric(oci_mmi_cal_df$
                   `Parameters for Combination Using MMI Technique - Factor Divider 2`)

    max_no_combined_factors <-
      as.numeric(oci_mmi_cal_df$
                   `Parameters for Combination Using MMI Technique - Max. No. of Combined Factors`
      )

    oci_hv_tf_tf_ext_cond_df <-
      gb_ref$oci_hv_tf_tf_ext_cond

    ci_factor_ext_cond <-
      oci_hv_tf_tf_ext_cond_df$`Condition Input Factor`[which(
        oci_hv_tf_tf_ext_cond_df$`Condition Criteria: Observed Condition` ==
          observed_condition)]

    ci_cap_ext_cond <-
      oci_hv_tf_tf_ext_cond_df$`Condition Input Cap`[which(
        oci_hv_tf_tf_ext_cond_df$`Condition Criteria: Observed Condition` ==
          observed_condition)]

    ci_collar_ext_cond <-
      oci_hv_tf_tf_ext_cond_df$`Condition Input Collar`[which(
        oci_hv_tf_tf_ext_cond_df$`Condition Criteria: Observed Condition` ==
          observed_condition)]

    # Observed condition factor -----------------------------------------------
    observed_condition_factor <- mmi(factors = ci_factor_ext_cond,
                                     factor_divider_1,
                                     factor_divider_2,
                                     max_no_combined_factors)

    # Observed condition cap ---------------------------------------------
    observed_condition_cap <- ci_cap_ext_cond

    # Observed condition collar ---------------------------------------------
    observed_condition_collar <- ci_collar_ext_cond

    # Observed condition modifier ---------------------------------------------
    observed_condition_modifier <- data.frame(observed_condition_factor,
                                              observed_condition_cap,
                                              observed_condition_collar)

    # Health score factor ---------------------------------------------------
    health_score_factor <-
      health_score_excl_ehv_132kv_tf(observed_condition_factor,
                                     measured_condition_factor)

    # Health score cap --------------------------------------------------------
    health_score_cap <- min(observed_condition_cap, measured_condition_cap)

    # Health score collar -----------------------------------------------------
    health_score_collar <-  max(observed_condition_collar,
                                measured_condition_collar)

    # Health score modifier ---------------------------------------------------
    health_score_modifier <- data.frame(health_score_factor,
                                        health_score_cap,
                                        health_score_collar)

    # Current health score ----------------------------------------------------
    current_health_score <-
      current_health(initial_health_score,
                     health_score_modifier$health_score_factor,
                     health_score_modifier$health_score_cap,
                     health_score_modifier$health_score_collar,
                     reliability_factor = reliability_factor)

    # Probability of failure ---------------------------------------------------
    probability_of_failure <- k *
      (1 + (c * current_health_score) +
         (((c * current_health_score)^2) / factorial(2)) +
         (((c * current_health_score)^3) / factorial(3)))

    # Future probability of failure -------------------------------------------

    # the Health Score of a new asset
    H_new <- 0.5

    # the Health Score of the asset when it reaches its Expected Life
    b2 <- beta_2(current_health_score, age)
    if (b2 > 2*b1){
      b2 <- b1*2
    } else if (current_health_score == 0.5){
      b2 <- b1
    }

    if (current_health_score < 2) {
      ageing_reduction_factor <- 1
    } else if (current_health_score <= 5.5) {
      ageing_reduction_factor <- ((current_health_score - 2)/7) + 1
    } else {
      ageing_reduction_factor <- 1.5
    }

    # Dynamic part
    pof_year <- list()
    future_health_score_list <- list()
    year <- seq(from=0,to=simulation_end_year,by=1)

    for (y in 1:length(year)){
      t <- year[y]

      future_health_Score <- current_health_score*exp((b2/ageing_reduction_factor) * t)

      H <- future_health_Score

      future_health_score_limit <- 15
      if (H > future_health_score_limit){
        H <- future_health_score_limit
      } else if (H < 4) {
        H <- 4
      }

      future_health_score_list[[paste(y)]] <- future_health_Score
      pof_year[[paste(y)]] <- k * (1 + (c * H) +
                                     (((c * H)^2) / factorial(2)) +
                                     (((c * H)^3) / factorial(3)))
    }

    pof_future <- data.frame(
      year=year,
      PoF=as.numeric(unlist(pof_year)),
      future_health_score = as.numeric(unlist(future_health_score_list)))
    pof_future$age <- NA
    pof_future$age[1] <- age

    for(i in 2:nrow(pof_future)) {

      pof_future$age[i] <- age + i -1

    }

    return(pof_future)
  }