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Introduction to flextools

Source: vignettes/flextools.Rmd
flextools.Rmd

Functions optimize_demand(), smart_charging() and add_battery_optimization() provide a framework to optimize time-series demand profiles according to different parameters, such as:

  • Contextual variables for the optimization problem (local energy generation, static load, grid capacity, etc.). These values must be collected in a data frame through the opt_data parameter.
  • Optimization objective, whether to minimize the net power, the energy cost or both.
  • Direction to shift energy (forwards or backwards)
  • Time horizon of the energy shift, being the maximum number of time-slots to shift demand from
  • Optimization window characteristics, such as the length (in days), the starting hour or the hours where energy shifting is allowed.
  • Penalty on change for the flexible load (parameter lambda). The higher lambda, the lower flexibility potential.

Moreover, package flextools provides an example data set of time-series energy and prices profiles to test its functions, called energy_profiles. We will filter the whole data set for just a single week, and rename the variables with custom names to fit the column names required in the flextools functions:

opt_data <- energy_profiles %>% 
  filter(isoweek(datetime) == 18) %>% 
  rename(
    production = solar
  )

head(opt_data)
## # A tibble: 6 × 7
##   datetime            production building price_imported price_exported
##   <dttm>                   <dbl>    <dbl>          <dbl>          <dbl>
## 1 2023-05-01 00:00:00          0     1.53         0.0999          0.025
## 2 2023-05-01 00:15:00          0     1.49         0.0999          0.025
## 3 2023-05-01 00:30:00          0     1.45         0.0999          0.025
## 4 2023-05-01 00:45:00          0     1.41         0.0999          0.025
## 5 2023-05-01 01:00:00          0     1.37         0.0955          0.025
## 6 2023-05-01 01:15:00          0     1.32         0.0955          0.025
## # ℹ 2 more variables: price_turn_up <dbl>, price_turn_down <dbl>

For that week, we have a building energy consumption profile and a solar PV production profile, together with prices for imported and exported energy and for the imbalance market:

Net power minimization

To minimize the energy exchanged with the distribution grid while maximizing the use of local generation, using the flexibility from a power demand profile (e.g. heatpumps, electric vehicles, etc.) or from a battery, we make use of Quadratic programming to obtain the optimal setpoints for the flexible assets. See the article Net power optimization to learn more about the problem formulation for both demand flexbility and battery flexibility. Below, you can find examples of both applications.

Demand flexibility

Let’s consider that the building demand profile is flexible and can be optimized. For than, we create a new column flexible in the opt_data tibble in order to tell the optimization function which is the flexible load. Since we want to perform net power minimization, then we set opt_objective = "grid" and for this example we will shift energy forward:

opt_building <- opt_data %>% 
  mutate(
    flexible = building
  ) %>% 
  optimize_demand(
    opt_objective = "grid",
    direction = "forward"
  )

We see that the power demand during peak hours (18:00 - 22:00) is still high since we can’t postpone energy after midnight (optimization window is from 00:00 to 00:00 by default). Then we can try setting the optimization window from 5:00AM to 5:00AM:

opt_building <- opt_data %>% 
  mutate(
    flexible = building
  ) %>% 
  optimize_demand(
    opt_objective = "grid",
    direction = "forward",
    window_start_hour = 5
  )

The power peak reduction during evening peak hours is much more relevant now.

Battery flexibility

Instead of using a building we can use a battery, considering a capacity of 50kWh and a charge/discharge power of 4kW. See that now we use the building column as static to avoid optimizing the building profile:

opt_battery <- opt_data %>% 
  mutate(
    static = building
  ) %>%
  add_battery_optimization(
    opt_objective = "grid",
    Bcap = 50, Bc = 10, Bd = 4,
    window_start_hour = 5
  )

Cost minimization

To minimize the energy cost while maximizing the income from imbalance markets, using the flexibility from a power demand profile (e.g. heatpumps, electric vehicles, etc.) or from a battery, we make use of Quadratic programming to obtain the optimal setpoints for the flexible assets. See the article Energy cost optimization to learn more about the problem formulation for both demand flexbility and battery flexibility. Below, you can find examples of both applications.

Demand flexibility

Imagine that the source of flexibility in the building is a heat-pump with a water tank storage. Therefore, in this case we shift energy backward to store hot water in the tank. To perform cost optimization, now we set opt_objective = "cost":

opt_building <- opt_data %>% 
  select(datetime, production, building, price_imported, price_exported) %>% 
  mutate(
    flexible = building
  ) %>% 
  optimize_demand(
    opt_objective = "cost",
    direction = "backward"
  )

We see that a lot of power demand is concentrated when the price has lower values to obtain the minimum energy cost. This behavior can be constrained by multiple ways:

  • Define a maximum load power: this can be done by adding the variable load_capacity in the opt_data parameter in the optimization function
  • Define a maximum grid (net) power: this can be done by adding the variable grid_capacity in the opt_data parameterin the optimization function
  • Use a penalty on change: this can be done by using the lambda parameter in the optimization function

For example, let’s consider a maximum power demand of 5kW with a lambda = 0.005:

opt_building <- opt_data %>% 
  select(datetime, production, building, price_imported, price_exported) %>% 
  mutate(
    flexible = building,
    load_capacity = 5
  ) %>% 
  optimize_demand(
    opt_objective = "cost",
    direction = "backward",
    lambda = 0.005
  )

Battery flexibility

The same example can be done with a battery, considering a capacity of 50kWh and a charge/discharge power of 4kW. See that now we use the building column as static to avoid optimizing the building profile:

opt_battery <- opt_data %>% 
  select(datetime, production, building, price_imported, price_exported) %>% 
  mutate(
    static = building
  ) %>%
  add_battery_optimization(
    opt_objective = "cost",
    Bcap = 50, Bc = 4, Bd = 4,
    window_start_hour = 5
  )

Since this example considers constant exported energy price, we can appreciate that battery discharges when the imported price goes up, and charges when the imported prices goes down. Moreover, we can see that the charging hours are mainly during solar production times, to minimize imported/exported energy.

However, we see that the price fluctuation makes to increase the variability of the battery profile. To avoid switching from charging to discharging in small periods of time, the lambda parameter has been introduced to the problem formulation. Thus when lambda > 0, there is a penalty on changes of the battery power between consecutive time-slots. In this case, a value of lambda = 0.1 gives reasonable results:

opt_battery <- opt_data %>% 
  select(datetime, production, building, price_imported, price_exported) %>% 
  mutate(
    static = building
  ) %>%
  add_battery_optimization(
    opt_objective = "cost",
    Bcap = 50, Bc = 4, Bd = 4,
    window_start_hour = 5,
    lambda = 0.1
  )

To find the optimal lambda, we can apply an iteration over multiple values and calculate two significant indicators: the energy cost (the lower the better) and the crossover times, so the times that the battery shifted from charging to discharging (the lower the better).

The following plot shows the normalized values (between 0 and 1) from these two indicators according to the lambda value:

We could consider the optimal lambda the “knee” of the curves, so approximately lamda=0.1 as we have used before.

Now let’s consider the prices for the imbalance market, assuming more income thanks to providing flexibility to the power system. We can appreciate how the battery is charging and discharging following the imbalance prices, specially for the “turn-up price” which has high values during certain periods:

opt_battery <- opt_data %>% 
  select(datetime, production, building, price_imported, price_exported, price_turn_up, price_turn_down) %>% 
  mutate(
    static = building
  ) %>%
  add_battery_optimization(
    opt_objective = "cost",
    Bcap = 50, Bc = 4, Bd = 4,
    window_start_hour = 5,
    lambda = 0.1
  )

Combined objectives

To minimize the energy cost and the impact in the distribution grid, using the flexibility from a power demand profile (e.g. heatpumps, electric vehicles, etc.) or from a battery, we make use of Quadratic programming to obtain the optimal setpoints for the flexible assets. See the article Combined optimization to learn more about the problem formulation for both demand flexbility and battery flexibility. Below, you can find examples of both applications.

Demand flexibility

The parameter opt_objective can be "grid", "cost" or a number between 0 and 1, being 0 the equivalent to “cost” and 1 the equivalent to “grid”. Thus, when opt_objective is a number, the optimization problem combines both objectives.

To show the effect of this term, we can calculate the demand profiles corresponding to three different values of opt_objective:

opt_building <- purrr::map(
  list(objective_0.25 = 0.25, objective_0.5 = 0.5, objective_0.75 = 0.75),
  ~ opt_data %>% 
    select(datetime, production, building, price_imported, price_exported) %>% 
    mutate(
      flexible = building
    ) %>% 
    optimize_demand(
      opt_objective = .x,
      direction = "forward"
    )
) %>% 
  as_tibble()

We see that during production hours all three profiles follow the PV production as much as possible, but they differ in the periods where the prices fluctuates the most. This is also caused by the difference between a constant and low export price and a high and variable import price.

Battery flexibility

The same example can be done with a battery, considering a capacity of 50kWh and a charge/discharge power of 4kW. See that now we use the building column as static to avoid optimizing the building profile:

opt_battery <- purrr::map(
  list(objective_0.25 = 0.25, objective_0.5 = 0.5, objective_0.75 = 0.75),
  ~ opt_data %>% 
    select(datetime, production, building, price_imported, price_exported) %>% 
    mutate(
      static = building
    ) %>%
    add_battery_optimization(
      opt_objective = .x,
      Bcap = 50, Bc = 4, Bd = 4,
      window_start_hour = 5
    )
) %>% 
  as_tibble()

An interesting outcome of this simulation is that combining both objectives also smoothes out the effect of the price fluctuation in the battery profile. Since now it is also important to reduce the impact on the distribution network, now the lambda is not so required.