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#' @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)
}
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