Preamble

We define in this section all the critical parameters used by the notebook and source the associated scripts. We use scripts to make the notebook more natural to read in RMarkdown.

## The script sourced here creates the following objects
##   - df_all: All actual/historical data in one dataframe
##   - df_carbon: Historical daily spot carbon prices
##   - df_gas: Historical daily spot gas prices
##   - df_gen: Actual hourly generation
##   - df_power: Historical hourly day ahead power price
##   - df_tgu: Gas-fired generating unit's attributes
##   - df_util_daily: Daily periods
##   - df_util_hourly: Hourly periods
##   - plt_single_ts: Plot one time series
##   - Pyxidr color palettes

# Database used by this report
database <- "../../data/processed/tutorial1.db"

# Gas-fired generating unit's name used for the analysis
gen_unit_name <- c("PP")

source("./analyses.R")

Clean spark spread

The objective is to identify dispatch opportunities, i.e., determine when the plant should have been producing or not. The spark spread is the gross margin of a gas-fired power plant from selling a unit of electricity, having bought the natural gas required to produce this unit of electricity. A clean spark spread (“CSS”) is when we take into account the cost associated with emitting CO2 — not all markets charge yet for CO2 emissions.

CSS is defined as follows: \[ p^P - \left(p^G + tc + p^C \times \frac{cf}{2204.62}\right) \times \frac{hr}{10^3} - om \] where

• \(cf\): Carbon factor (lb/mmbtu)
• \(hr\): Heat rate (btu/kWh)
• \(om\): Variable O&M ($/MWh)
• \(p^C\): Carbon price in $/tonne
• \(p^G\): Gas price in $/mmbtu
• \(p^P\): Power price in $/MWh
• \(tc\): Natural gas transportation cost ($/mmbtu)

This is how it is implemented:

css <- function(gu, type, pp, gp, cp){
    # gu  : Gas-fired generating unit (dataframe)
    # type: pmin, pmax or duct
    # pp  : power price in $/MWh
    # gp  : gas price in $/mmbtu
    # cp  : carbon price in $/tonne

    # heat rate in btu/kWh
    hr <- switch(type, "pmin" = gu$heatrate_pmin, 
                       "pmax" = gu$heatrate, 
                       "duct" = gu$heatrate_duct)
    # variable cost in $/MWh
    vc <- switch(type, "pmin" = gu$om_pmin, 
                       "pmax" = gu$om, 
                       "duct" = gu$om_duct)

    pp - (gp + gu$tc + cp * gu$emission /  2204.62) * hr / 1e3 - vc
}

We have included variable O&M costs in our definition of CSS to represent the opportunities better.

An efficient gas-fired plant takes time to start (e.g., 1 hour in a cold start) and has minimum uptime (e.g., 6 hours) and downtime to reduce the stress on the equipment. Therefore, we are going to group all the hours into on-peak and off-peak hours to take into account the lack of flexibility. Depending on the markets, on-peak hours are usually weekdays between 6 am and 10 pm. The rest of the hours are off-peak. We expect power prices to be higher during on-peak hours than off-peak ones.

The following graphic shows the distribution of CSS (on-peak/off-peak) where 71.8% of the on-peak periods have a positive CSS while 48.4% of the off-peak periods have a positive CSS.

We expect the plant not to produce when CSS is negative and produce at nominal capacity when CSS is large (e.g., higher than $5/MWh). However, the plant had produced above minimum load respectively 94.3% and 91.8% of the on-peak and off-peak periods when CSS was negative. Therefore, there are some opportunities for better dispatching the plant.

This X-Y plot shows, among others, how often the plant was producing when CSS was negative. The plant should have produced when the CSS was positive, but it could have been in maintenance.

Assessing the dispatch opportunity

As we have seen, the plant could have made more profits if it had been better dispatched (or dispatched against market prices). We roughly compute the opportunity as follows: \[ \sum_{t} \left(\max\{css_t(pmax)\times pmax, css_t(duct)\times duct, 0\} - css_t(gen_t)\times gen_t \right) \] where

• \(css_t()\): Gross margin as a function of the energy produced in MW associated with period \(t\) ($/MWh)
• \(duct\): Generating capcity including duct fired capacity (MW)
• \(gen_t\): Actual generation for period \(t\) (MWh/h)
• \(pmax\): Nominal generating capacity (MW)
• \(t\): Period

We do this calculation over all on-peak and off-peak periods. As the following graphics show, the dispatch opportunities are fairly significant. It is important to note that a more granular shaping (e.g., by the hour) will lead to more significant opportunities.

Vizualizing client’s data

It is always a good practice to visualize the raw data for spotting any discrepancies. Script analyses.R creates a data frame df_all that includes all the client’s data. We can dump this data frame in a CSV file that we can visualize in Tableau Public (or the paid version of Tableau).