ERCOT Hourly Load Data

Description

Hourly load data of different operational areas of Electric Reliability Council of Texas (ERCOT) for year 2019 - 2021. The extra day (2/29/2020) from 2020 was intentionally omitted to have 8760 data for each year.

Usage

ercot

Format

A data frame with 26280 rows and 15 variables.

Source

https://www.ercot.com/gridinfo/load/load_hist/

Examples

loads <- ercot[ercot$Year == 2019, ]$COAST
plot(loads, type = "l")
linear_loadshape <- lslin(loads, target_lf = 0.50)
summary(linear_loadshape)
#-------------------------------------
loads2 <- ercot[ercot$Year == 2020, ]$ERCOT
plot(loads2, type = "l")
linear_loadshape2 <- lslin(loads2, target_lf = 0.7)
summary(linear_loadshape2)

Load Shape Score

Description

lscore provides a diagnostic score for evaluating the derived load shape in retaining time series properties.

Usage

lscore(ls, type = "acf", output = 2, lag = NULL)

Arguments

Details

The diagnostic measure is calculated as a weighted mean absolute percent error (MAPE) of auto correlation or partial auto correlation values of the derived series with respect to the original. The values are calculated for given lag. Lag = 0 is omitted from calculation for auto correlation as it would be always 1. If o_i and d_i are the correlation values of original and derived load shape at lag i, then weighted MAPE is calculated as

wmape = \sum _{i=1}^{lag} { w_i * |(o_i - d_i) / o_i|}

where w_i = \frac{|o_i|}{\sum _{i=1}^{lag}|o_i|}

Since wmape is a measure of error, lower value indicates better preservation of time series property.

Value

A list of the followings:

• wmape: Weighted MAPE.

• lag: Lags at which ACF or PACF values were evaluated and used in calculating wmape.

• type: Type of Correlation (ACF or PACF)

• cor_x: ACF/PACF values of the original load.

• cor_y: ACF/PACF values of the derived load.

• weight: Weights at different lags used to calculate wmape.

Examples

loads <- ercot[ercot$Year == 2019, ]$COAST
linear_loadshape <- lslin(loads, target_lf = 0.4)
# --------------
scores_1 <- lscore(linear_loadshape, type = "acf", lag = 20)
print(scores_1)
# --------------
scores_2 <- lscore(linear_loadshape, type = "pacf")
print(scores_2)

Linear Method for Matching Peak and Load Factor

Description

lslin applies linear method to a reference load shape to match the peak and load factor to target values. See "Details" for the algorithm.

Usage

lslin(x, target_max = 10000, target_lf = 0.7)

Arguments

Details

The algorithm first evaluates the load factor of the reference load shape x, which is defined by the ratio of average to peak value. If the target load factor is greater than reference level, then all base values are multiplied by a number > 1. If the target load factor is less than reference level, then all base values are multiplied by a number < 1. The multipliers increase/decrease linearly and are applied to the based values after ordered.

If x' is the ordered version of x, then x'_{i} will be multiplied by 1-(i-1)*\beta, where \beta is a constant calculated as:

\beta = \frac{\sum_{i=1}^n x'_{i} - target\ load\ factor } {\sum_{i=1}^n x'_{i}(i-1)}

The load factor of the derived series matches the target. For target < base, \beta is positive and vice-versa.

The algorithm attempts hard to match the load factor of the derived load shape to the base load factor. \beta becomes large in magnitude for large difference of base and target load factor. In case \beta > 1, it is possible to get negative multipliers which force the values to be negative. This particular situation can occur when target load factor is significantly smaller than the base load factor.

If the target load factor is much bigger than the base load factor, one/both of the followings can occur:

• As a linearly increasing function is multiplied by a decreasing function (x'), it is possible that the maximum of the product can exceed the maximum value of the base (x'), resulting in a different load factor.

• As a linearly increasing function is multiplied by a decreasing function (x'), it is possible that the product is not strictly decreasing. The product array is re-ordered to produce the final values.

The return object contains a data frame df, having the following columns:

• x_index: An index given to the original load shape x, starting from 1 to length(x).

• x: The original array x, unaltered.

• x_rank: The rank of the data points of the given array x, from 1 for the peak to length(x) for the lowest value.

• x_ordered: Sorted x (largest to smallest).

• x_pu: Per unit x, derived by diving x by max(x).

• x_ordered_pu: Per unit x, sorted from largest to smallest.

• mult: Derived multipliers, would be applied to sorted per unit x.

• y_ordered_pu: Product of per unit sorted x and mult.

• y_ordered_pu2: y_ordered_pu, sorted again, in case y_ordered_pu does not become decreasing.

• y_pu: Resultant load shape in per unit. This is derived by re-ordering y_ordered_pu2 with respect to their original rank.

• y: Resultant load shape. This is derived by multiplying y_pu by taget_max / base_max

Value

A list of class "lslin", having following elements:

• df: A data frame. See "Details".

• beta: Slope of the linearly increasing/decreasing multipliers. See "Details".

• max_mult: Maximum of the multipliers.

• min_mult: Minimum of the multipliers.

• base_load_factor: Load factor of the reference load shape x.

• target_load_factor: Target load factor.

• derived_load_factor: Load factor of the derived load shape (object$df$y).

• base_max: Peak value of the base load shape, x

• target_max: Target peak value of the new load shape.

• derived_max: Peak value of the derived load shape (object$df$y)

• base_min: Minimum value of the base load shape, x

• derived_min: Minimum value of the derived load shape (object$df$y)

• dec_flag: A logical flag stating whether the multipliers resulted in strictly decreasing values. TRUE indicates the order was not preserved. Only applicable for target_max > base_max. See "Details".

• lf_flag: A logical flag indicating if the load factor of the derived shape differs from the target by more than 1%.

• min_pu_flag: A logical flag indicating existence of negative values in the derived load shape. TRUE indicates the existence of negative values. Only applicable for target_max < base_max. See "Details".

See Also

lslog, print.lslin, summary.lslin, plot.lslin, lscore

Examples

loads <- ercot[ercot$Year == 2019, ]$COAST
plot(loads, type = "l")
linear_loadshape <- lslin(loads, target_lf = 0.50)
summary(linear_loadshape)
#-------------------------------------
loads2 <- ercot[ercot$Year == 2020, ]$ERCOT
plot(loads2, type = "l")
linear_loadshape2 <- lslin(loads2, target_lf = 0.7)
summary(linear_loadshape2)#'
#-------------------------------------
loads3 <- ercot[ercot$Year == 2020, ]$ERCOT
plot(loads3, type = "l")
linear_loadshape3 <- lslin(loads3, target_lf = 0.95)
summary(linear_loadshape3)
#-------------------------------------
loads4 <- ercot[ercot$Year == 2020, ]$SCENT
plot(loads3, type = "l")
linear_loadshape4 <- lslin(loads4, target_lf = 0.3)
summary(linear_loadshape4)

Logistic Method for Matching Peak and Load Factor

Description

Logistic Method for Matching Peak and Load Factor

Usage

lslog(
  x,
  target_max = 10000,
  target_lf = 0.7,
  k = 1,
  inf_pos = 0.5,
  iter = 500,
  def_l = 1
)

Arguments

Details

The algorithm first evaluates the load factor of the reference load shape x, which is defined by the ratio of average to peak value. If the target load factor is greater than reference level, then all base values are multiplied by a number > 1. If the target load factor is less than reference level, then all base values are multiplied by a number < 1. The multipliers increase or decrease with a sigmoid pattern.

The sigmoid function is a transformed version of

f(x)=\frac{L}{1 - exp(-k(x-x_0))}

Parameter k is shape parameter, shaping the "sigmoidness" of the function. Larger value of k indicates more steepness in the function and lower value results in changes in multipliers in more linear fashion.

Location parameter x_0 controls the inflection point of the function and derived from inf_pos. inf_pos = 0.5 indicates the inflection point of the sigmoid multipliers is halfway.

The L parameter in the sigmoid is numerically solved. The number of iterations is equal to the iter argument, optimized based on the minimum difference between the derived and target load factor.

The return object contains a data frame df, having the following columns:

• x_index: An index given to the original load shape x, starting from 1 to length(x).

• x: The original array x, unaltered.

• x_rank: The rank of the data points of the given array x, from 1 for the peak to length(x) for the lowest value.

• x_ordered: Sorted x (largest to smallest).

• x_pu: Per unit x, derived by diving x by max(x).

• x_ordered_pu: Per unit x, sorted from largest to smallest.

• mult: Derived multipliers, would be applied to sorted per unit x.

• y_ordered_pu: Product of per unit sorted x and mult.

• y_ordered_pu2: y_ordered_pu, sorted again, in case y_ordered_pu does not become decreasing.

• y_pu: Resultant load shape in per unit. This is derived by re-ordering y_ordered_pu2 with respect to their original rank.

• y: Resultant load shape. This is derived by multiplying y_pu by taget_max / base_max

Value

A list of class "lslog", having following elements:

• df: A data frame. See "Details".

• k: Steepness parameter. See "Details".

• inf_pos: Inflection point parameter. See "Details".

• L: Numerically solved optimized L parameter. See "Details".

• max_mult: Maximum of the multipliers.

• min_mult: Minimum of the multipliers.

• base_load_factor: Load factor of the reference load shape x.

• target_load_factor: Target load factor.

• derived_load_factor: Load factor of the derived load shape (object$df$y).

• base_max: Peak value of the base load shape, x

• target_max: Target peak value of the new load shape.

• derived_max: Peak value of the derived load shape (object$df$y)

• base_min: Minimum value of the base load shape, x

• derived_min: Minimum value of the derived load shape (object$df$y)

• dec_flag: A logical flag stating whether the multipliers resulted in strictly decreasing values. TRUE indicates the order was not preserved. Only applicable for target_max > base_max. See "Details".

• lf_flag: A logical flag indicating if the load factor of the derived shape differs from the target by more than 1%.

• min_pu_flag: A logical flag indicating existence of negative values in the derived load shape. TRUE indicates the existence of negative values. Only applicable for target_max < base_max. See "Details".

See Also

lslin, print.lslog, summary.lslog, plot.lslog, lscore

Examples

loads <- ercot[ercot$Year == 2019, ]$COAST
plot(loads, type = "l")
logistic_loadshape <- lslog(loads, target_lf = 0.50, k = 0.5)
summary(logistic_loadshape)
#---------------------------------------------------
loads2 <- ercot[ercot$Year == 2020, ]$ERCOT
plot(loads2, type = "l")
logistic_loadshape2 <- lslog(loads2, target_lf = 0.6,
                            k = 0.5, inf_pos = 0.4)
summary(logistic_loadshape2)
#---------------------------------------------------
loads3 <- ercot[ercot$Year == 2020, ]$ERCOT
plot(loads3, type = "l")
logistic_loadshape3 <- lslog(loads3, target_lf = 0.9)
summary(logistic_loadshape3)

Plot Linear Load Shape

Description

Plot method of lslin object

Usage

## S3 method for class 'lslin'
plot(
  x,
  case = 1,
  col = c(1, 2),
  scatter = FALSE,
  legend = TRUE,
  leg_pos = "topright",
  ... = NULL
)

Arguments

Details

If scatter = FALSE then per unit load duration curve for case = 1, per unit load for case = 2, actual load (in original unit) for case = 3. If scatter = TRUE then per unit scatter plot for case = 1 or 2, actual load scatter plot for case = 3.

Value

NULL.

Examples

loads <- ercot[ercot$Year == 2019, ]$COAST
linear_loadshape <- lslin(loads, target_lf = 0.5)
# --------------
plot(linear_loadshape, col = c(2, 4))
plot(linear_loadshape, case = 2, col = c(2, 4))
plot(linear_loadshape, case = 3,
     col = c("salmon", "deepskyblue"),
     leg_pos = "topleft")

Plot Logistic Load Shape

Description

Plot method of lslog object

Usage

## S3 method for class 'lslog'
plot(
  x,
  case = 1,
  col = c(1, 2),
  scatter = FALSE,
  legend = TRUE,
  leg_pos = "topright",
  ... = NULL
)

Arguments

Details

If scatter = FALSE then per unit load duration curve for case = 1, per unit load for case = 2, actual load (in original unit) for case = 3. If scatter = TRUE then per unit scatter plot for case = 1 or 2, actual load scatter plot for case = 3.

Value

NULL.

Examples

loads <- ercot[ercot$Year == 2019, ]$COAST
loads <- ercot[ercot$Year == 2019, ]$COAST
log_loadshape <- lslog(loads, target_lf = 0.5,
                       inf_pos = 0.3, k = 0.8)
# --------------
plot(log_loadshape, col = c(2, 4))
plot(log_loadshape, case = 2, col = c(2, 4))
plot(log_loadshape, case = 3,
     col = c("salmon", "deepskyblue"),
     leg_pos = "topleft")

Print Summary of Load Shape Score

Description

Print Summary of Load Shape Score

Usage

## S3 method for class 'lscore'
print(x, ... = NULL)

Arguments

Value

NULL. Prints the summary of the load shape score.

Note

Same as summary.lscore

See Also

lslin, lscore, lscore

Examples

loads <- ercot[ercot$Year == 2019, ]$SOUTH
# --------------
log_loadshape <- lslog(loads, target_lf = 0.5)
print(lscore(log_loadshape, type = "acf"))
print(lscore(log_loadshape, type = "pacf"))
# --------------
lin_loadshape <- lslin(loads, target_lf = 0.5)
print(lscore(lin_loadshape, type = "acf"))
print(lscore(lin_loadshape, type = "pacf"))

Print Linear Load Shape

Description

Print method for summarizing lslin object

Usage

## S3 method for class 'lslin'
print(x, ... = NULL)

Arguments

Value

NULL. Prints the summary of the derived load shape using linear method.

Note

Same as summary.lslin

See Also

lslin

Examples

# ---------------------
loads <- ercot[ercot$Year == 2019, ]$COAST
linear_loadshape <- lslog(loads, target_lf = 0.5, k = 0.5)
print(linear_loadshape)
# ---------------------
loads2 <- ercot[ercot$Year == 2019, ]$ERCOT
linear_loadshape2 <- lslog(loads2, target_lf = 0.75, k = 1)
print(linear_loadshape2)

Print Logistic Load Shape

Description

Print method of lslog object

Usage

## S3 method for class 'lslog'
print(x, ... = NULL)

Arguments

Value

NULL. Prints the summary of the derived load shape using linear method.

Note

Same as summary.lslog

See Also

lslog

Examples

# ---------------------
loads <- ercot[ercot$Year == 2019, ]$COAST
logistic_loadshape <- lslog(loads, target_lf = 0.5, k = 0.5)
print(logistic_loadshape)
# ---------------------
loads2 <- ercot[ercot$Year == 2019, ]$ERCOT
logistic_loadshape2 <- lslog(loads2, target_lf = 0.75, k = 1)
print(logistic_loadshape2)

Summary of Load Shape Score

Description

Summary method of lscore object

Usage

## S3 method for class 'lscore'
summary(object, ... = NULL)

Arguments

Value

NULL. Prints the summary of the load shape score.

Note

Same as print.lscore

See Also

lslin, lslog, lscore

Examples

loads <- ercot[ercot$Year == 2019, ]$SOUTH
# --------------
log_loadshape <- lslog(loads, target_lf = 0.5)
summary(lscore(log_loadshape, type = "acf"))
summary(lscore(log_loadshape, type = "pacf"))
# --------------
lin_loadshape <- lslin(loads, target_lf = 0.5)
summary(lscore(lin_loadshape, type = "acf"))
summary(lscore(lin_loadshape, type = "pacf"))

Summary of Linear Load Shape

Description

Summary method of lslin object

Usage

## S3 method for class 'lslin'
summary(object, ... = NULL)

Arguments

Value

NULL. Prints the summary of the derived load shape using linear method.

Note

Same as print.lslin

See Also

lslin

Examples

# ---------------------
loads <- ercot[ercot$Year == 2019, ]$COAST
linear_loadshape <- lslog(loads, target_lf = 0.5, k = 0.5)
summary(linear_loadshape)
# ---------------------
loads2 <- ercot[ercot$Year == 2019, ]$ERCOT
linear_loadshape2 <- lslog(loads2, target_lf = 0.75, k = 1)
summary(linear_loadshape2)

Summary of Logistic Load Shape

Description

Print method for summarizing lslog object

Usage

## S3 method for class 'lslog'
summary(object, ... = NULL)

Arguments

Value

NULL. Prints the summary of the derived load shape using linear method.

Note

Same as print.lslog

See Also

lslog

Examples

# ---------------------
loads <- ercot[ercot$Year == 2019, ]$COAST
logistic_loadshape <- lslog(loads, target_lf = 0.5, k = 0.5)
summary(logistic_loadshape)
# ---------------------
loads2 <- ercot[ercot$Year == 2019, ]$ERCOT
logistic_loadshape2 <- lslog(loads2, target_lf = 0.75, k = 1)
summary(logistic_loadshape2)