Bids using Consumer Unit Commitment (Workaround)

In this tutorial we will learn how to create bids using consumer unit commitment. Bids are not explicitly supported in Tulipa (yet), but they can be modeled with a few workarounds.

This is an advanced tutorial. It assumes some basic knowledge of Tulipa, so going through some of the earlier tutorials might be beneficial.

Introduction

In our context, a bid is a proposal to buy energy at a given price at one or more time steps. If the proposal is for a single time step, then we are going to call it a "simple bid", as opposed to a "profile bid", when it involves more than one time step. The price is constant in both cases, which allow us to always use vectors to represent the required quantities. In a "simple bid", the vectors of time steps and quantities both have 1 element.

Furthermore, the bid can be part of an "exclusive group". Inside each exclusive group, a single bid is accepted. Finally, some bids also have a curtailment possibility, i.e., they can be supplied with less energy than the maximum desired, but no less than a given percentage of the maximum (given by curtailment_minimum).

Here are some example bids:

bid_blocks = [
    (
        customer = "A",
        exclusive_group = 1,
        profile_block = 1,
        timestep = 4:4,
        quantity = [10],
        price = 5.0,
        curtailment_minimum = 1.0,
    ),
    (
        customer = "A",
        exclusive_group = 2,
        profile_block = 1,
        timestep = 2:3,
        quantity = [40, 30],
        price = 2.5,
        curtailment_minimum = 1.0,
    ),
    (
        customer = "A",
        exclusive_group = 2,
        profile_block = 2,
        timestep = 2:3,
        quantity = [20, 20],
        price = 1.5,
        curtailment_minimum = 0.8,
    ),
    (
        customer = "B",
        exclusive_group = 1,
        profile_block = 1,
        timestep = 1:6,
        quantity = [5, 10, 15, 25, 30, 15],
        price = 0.8,
        curtailment_minimum = 1.0,
    ),
]

4-element Vector{@NamedTuple{customer::String, exclusive_group::Int64, profile_block::Int64, timestep::UnitRange{Int64}, quantity::Vector{Int64}, price::Float64, curtailment_minimum::Float64}}:
 (customer = "A", exclusive_group = 1, profile_block = 1, timestep = 4:4, quantity = [10], price = 5.0, curtailment_minimum = 1.0)
 (customer = "A", exclusive_group = 2, profile_block = 1, timestep = 2:3, quantity = [40, 30], price = 2.5, curtailment_minimum = 1.0)
 (customer = "A", exclusive_group = 2, profile_block = 2, timestep = 2:3, quantity = [20, 20], price = 1.5, curtailment_minimum = 0.8)
 (customer = "B", exclusive_group = 1, profile_block = 1, timestep = 1:6, quantity = [5, 10, 15, 25, 30, 15], price = 0.8, curtailment_minimum = 1.0)

Each bid has the following data:

• customer, identifying who is the asking party;
• exclusive_group, identifying each group of exclusive bids;
• profile_block, identifying each block of bids;
• timestep, indicating the time steps of a bid;
• quantity, indicating the vector of requested quantities;
• price, indicating the price;
• curtailment_minimum, indicating the minimum percentage of energy that can be delivered under curtailment.

Notice that (customer, exclusive_group, profile_block) form a unique identifier for this bid.

In words, we can say:

• The first bid, (A, 1, 1), requests 10 KW at time step 4 and is willing to pay $5.0 per KW. No curtailment allowed.
• The second bid, (A, 2, 1), requests 40 KW at time step 2 and 30 KW at time step 3 and is willing to pay $2.5 per KW. No curtailment allowed.
• The third bid, (A, 2, 2), requests 20 KW at time step 2 and 20 KW at time step 3 and is willing to pay $1.5 per KW. At least 80% of the requested quantity per day must be satisfied.
• The fourth bid, (B, 1, 1), requests 5 KW, 10 KW, 15 KW, 25 KW, 30 KW, and 15 KW from time steps 1 to 6, in order. It is willing to pay $0.8 per KW, and no curtailment is allowed.

Finally, notice that the second and third bids share the same exclusive_group, so at most one of them can be accepted.

Modeling

We don't have an underlying energy system to make these bids, so let's create a fake scenario with

• One generator, with 1 initial unit, where the capacity is given by us;
• One consumer, with no demand (because we don't care for this problem);
• A flow between the generator and the consumer, with an operational cost given by us;

Creating initial problem with TulipaBuilder

We will use TulipaBuilder.jl to create the Tulipa problem for this problem:

using TulipaBuilder

year = 2030 # We don't need the year for anything, but we need to set it
num_timesteps = 6

function create_new_problem(;capacity = 60.0, operational_cost = 0.5)
    tulipa = TulipaData()

    add_asset!(tulipa, "Generator", :producer; capacity, operational_cost, initial_units = 1.0)
    add_asset!(tulipa, "Consumer", :consumer; peak_demand = 0.0)
    add_flow!(tulipa, "Generator", "Consumer"; operational_cost)
    # Because we need at least one profile, we explicitly set demand to 0
    attach_profile!(tulipa, "Consumer", :demand, year, zeros(num_timesteps))
end

create_new_problem (generic function with 1 method)

Notice that this is already a valid Tulipa problem, but the solution is to have no flow.

using TulipaClustering: TulipaClustering as TC
using TulipaEnergyModel: TulipaEnergyModel as TEM

tulipa = create_new_problem()

# Convert TulipaBuilder's data to TulipaEnergyModel format in the connection
connection = create_connection(tulipa, TEM.schema)

# (Fake) cluster the profiles to generate representative periods
TC.dummy_cluster!(connection; layout = TC.ProfilesTableLayout(year = :milestone_year))

# Solve the scenario
TEM.populate_with_defaults!(connection)
energy_problem = TEM.run_scenario(connection, show_log=false)

energy_problem

EnergyProblem:
  - Model created!
    - Number of variables: 6
    - Number of constraints for variable bounds: 6
    - Number of structural constraints: 12
  - Model solved!
    - Termination status: OPTIMAL
    - Objective value: 0.0
    - Objective breakdown:
      - assets_fixed_cost_aggregated_vintage_method: 0.0
      - assets_fixed_cost_compact_vintage_method: 0.0
      - assets_investment_cost: 0.0
      - flows_fixed_cost: 0.0
      - flows_investment_cost: 0.0
      - flows_operational_cost: 0.0
      - storage_assets_energy_fixed_cost: 0.0
      - storage_assets_energy_investment_cost: 0.0
      - units_on_operational_cost: 0.0
      - vintage_flows_operational_cost: 0.0

Input modification for bids

The trick to have bids is to create a new asset for each of the bids. Each of these bid assets is a consumer asset requesting the profile bid as a "demand" bid. In Tulipa, the :consumer assets can also serve as balance nodes, i.e., they are allowed to provide energy to other assets connected via outgoing flows. So, to satisfy the "demand" of the bid assets, we create a flow from the "Consumer" asset to these bid assets. To simulate the price willing to be paid by a bid, we use the operational_cost between the "Consumer" and the bid asset. In summary:

• For each (consumer, exclusive_group, profile_block) bid, create a new ':consumer' asset.
• Attach a profile with the quantities per time steps of the bid to this asset.
  • The profiles in Tulipa have to be complete, so the remaining hours are simply completed with 0.
• Create a flow between an existing :consumer and this bid asset and set operational_cost = -price.

However, this by itself is not sufficient, because there is nothing yet forcing this bid to accepted or not.

If the bid is accepted, the requested quantity is treated as a demand to be satisfied for every time step. If the bid is not accepted, there should be no flow to this asset for every time step.

The missing link is to have some kind of variable that indicates whether the bid is accepted or not. For that, we will use an existing feature of TulipaEnergyModel, Unit Commitment, but we will apply it to consumers.

By itself, however, this is not enough, because the consumer balance constraint still forces the requested bid to be satisfied, and there is nothing tying that to the unit commitment variables. Therefore, we use a special condition inside the consumer balance constraint created specifically for this case, which is to create a loop flow in the bid asset. This existence of a loop flow changes the balance constraint tying the incoming flow to the loop flow, and the loop flow is tied to the unit commitment variables by the minimum and maximum output flow ramping constraints.

These are the modifications:

• For each bid, create a new asset. We'll name it "Bid". Set
  • capacity = 1.0
  • consumer_balance_sense = "==" (which is the default)
  • initial_units = 1.0
  • peak_demand as anything positive (1.0 makes it easier to understand the results, maximum(bid_block.profile) is the common normalized way)
  • type = :consumer
  • unit_commitment = "basic"
  • unit_commitment_integer = true
• Set the time resolution of the asset to the full length of the profile (assets_rep_periods_partitions.partition = rep_periods_data.num_timesteps)
• Find an existing consumer, we'll name it "Bid Manager".
• Connect a flow from the "Bid Manager" to "Bid", with flow_milestone.operational_cost = -price.
• Create a loop flow, connecting the asset "Bid" to itself.
• Create a profile in profiles_rep_periods or profiles, depending on whether you still have to cluster or not.
  • Use the bid's quantities, normalized by peak_demand, as value, for the corresponding time steps as timestep.
  • Use 0 as value for the missing timestep.
  • Choose a profile_name
• Relate the profile above to the asset "Bid" in assets_profiles, with profile_type = 'demand'.

We can create a function to help us create a bid with the above characteristics based on a given bid_block:

function add_new_bid!(tulipa, bid_id, bid_block)
    bid_name = "bid$bid_id"
    bid_manager = "Consumer"
    peak_demand = 1.0
    add_asset!(
        tulipa,
        bid_name,
        :consumer,
        capacity = 1.0,
        consumer_balance_sense = "==",
        initial_units = 1.0,
        min_operating_point = bid_block.curtailment_minimum,
        peak_demand = peak_demand,
        unit_commitment = "basic",
        unit_commitment_integer = true,
    )
    set_partition!(tulipa, bid_name, year, 1, num_timesteps) # 1 = rep_period, there is only one
    add_flow!(tulipa, bid_manager, bid_name, operational_cost = -bid_block.price)
    add_flow!(tulipa, bid_name, bid_name)
    profile = zeros(num_timesteps)
    profile[bid_block.timestep] = bid_block.quantity / peak_demand
    attach_profile!(tulipa, bid_name, :demand, year, profile)

    return tulipa
end

add_new_bid! (generic function with 1 method)

With this function, we can go back to our initial problem and add the bid blocks from the beginning:

tulipa = create_new_problem(capacity = 60, operational_cost = 0.5)
for (bid_id, bid_block) in enumerate(bid_blocks)
    add_new_bid!(tulipa, bid_id, bid_block)
end

# Convert TulipaBuilder's data to TulipaEnergyModel format in the connection
connection = create_connection(tulipa, TEM.schema)

# (Fake) cluster the profiles to generate representative periods
TC.dummy_cluster!(connection; layout = TC.ProfilesTableLayout(year = :milestone_year))

# Solve the scenario
TEM.populate_with_defaults!(connection)
energy_problem = TEM.run_scenario(connection, show_log=false)

energy_problem

EnergyProblem:
  - Model created!
    - Number of variables: 58
    - Number of constraints for variable bounds: 58
    - Number of structural constraints: 88
  - Model solved!
    - Termination status: OPTIMAL
    - Objective value: -225.0
    - Objective breakdown:
      - assets_fixed_cost_aggregated_vintage_method: 0.0
      - assets_fixed_cost_compact_vintage_method: 0.0
      - assets_investment_cost: 0.0
      - flows_fixed_cost: 0.0
      - flows_investment_cost: 0.0
      - flows_operational_cost: -225.0
      - storage_assets_energy_fixed_cost: 0.0
      - storage_assets_energy_investment_cost: 0.0
      - units_on_operational_cost: 0.0
      - vintage_flows_operational_cost: 0.0

We can see that the objective value is different, but let's investigate the solution in more details. First, we can check which flows are not 0:

using DuckDB, DataFrames

# Helper function
df_sql(con, s) = DataFrame(DuckDB.query(con, s))

df_sql(
    connection,
    """
    SELECT from_asset, to_asset, time_block_start AS timestep, solution,
    FROM var_flow
    WHERE solution != 0
    """,
)

Second, we can also check the unit commitment variables:

df_sql(
    connection,
    """
    SELECT asset, solution,
    FROM var_units_on
    WHERE solution != 0
    """,
)

We can see from these two tables that bids 1, 2, and 3 were accepted. This mostly makes sense, except that bids 2 and 3 should not be accepted at the same time, since they are in the same exclusivity group (same exclusive_group for a given customer). This means that we have one least modification to make.

Model modification for exclusivity of the bids

This modification has to be done directly in the underlying JuMP model. The required change is to add a constraint $\displaystyle \sum_{i: i \in G_k} u_i \leq 1$, where $u_i$ are the unit commitment variables (i.e., the bid-acceptance variables), and $G_k$ are the exclusive groups.

The function below modifies a model with this constraint:

using JuMP

function add_exclusive_groups!(energy_problem, bid_blocks)
    exclusive_groups = Dict{Tuple{String,Int},Vector{Int}}() # (customer, exclusive_group) -> [bid_ids...]
    for (bid_id, bid) in enumerate(bid_blocks)
        key = (bid.customer, bid.exclusive_group)
        if !haskey(exclusive_groups, key)
            exclusive_groups[key] = Int[]
        end
        push!(exclusive_groups[key], bid_id)
    end

    for ((customer, exclusive_group), bid_ids) in exclusive_groups
        if length(bid_ids) == 1 # There is only one bid in this group, there is no need to further constrain
            continue
        end
        var = energy_problem.variables[:units_on].container
        JuMP.@constraint(
            energy_problem.model,
            sum(var[id] for id in bid_ids) <= 1,
            base_name = "exclusive_bid_group[$(customer),$(exclusive_group)]",
        )
    end
end

add_exclusive_groups! (generic function with 1 method)

We now modify our little script with this additional step:

tulipa = create_new_problem(capacity = 60, operational_cost = 0.5)
for (bid_id, bid_block) in enumerate(bid_blocks)
    add_new_bid!(tulipa, bid_id, bid_block)
end

# Convert TulipaBuilder's data to TulipaEnergyModel format in the connection
connection = create_connection(tulipa, TEM.schema)

# (Fake) cluster the profiles to generate representative periods
TC.dummy_cluster!(connection; layout = TC.ProfilesTableLayout(year = :milestone_year))

# Create the mode
TEM.populate_with_defaults!(connection)
energy_problem = TEM.EnergyProblem(connection)
TEM.create_model!(energy_problem)

# Modify the model
add_exclusive_groups!(energy_problem, bid_blocks)

# Solve the model
TEM.solve_model!(energy_problem)
TEM.save_solution!(energy_problem; compute_duals = true)

energy_problem

EnergyProblem:
  - Model created!
    - Number of variables: 58
    - Number of constraints for variable bounds: 58
    - Number of structural constraints: 89
  - Model solved!
    - Termination status: OPTIMAL
    - Objective value: -215.0
    - Objective breakdown:
      - assets_fixed_cost_aggregated_vintage_method: 0.0
      - assets_fixed_cost_compact_vintage_method: 0.0
      - assets_investment_cost: 0.0
      - flows_fixed_cost: 0.0
      - flows_investment_cost: 0.0
      - flows_operational_cost: -215.0
      - storage_assets_energy_fixed_cost: 0.0
      - storage_assets_energy_investment_cost: 0.0
      - units_on_operational_cost: 0.0
      - vintage_flows_operational_cost: 0.0

Once again, we investigate the flow and unit commitment solution:

using DuckDB, DataFrames

# Helper function
df_sql(con, s) = DataFrame(DuckDB.query(con, s))

df_sql(
    connection,
    """
    SELECT from_asset, to_asset, time_block_start AS timestep, solution,
    FROM var_flow
    WHERE solution != 0
    """,
)

and

df_sql(
    connection,
    """
    SELECT asset, solution,
    FROM var_units_on
    WHERE solution != 0
    """,
)

Now, we can see that bids 1, 2, and 4 are accepted.

Testing more cases

To play around a little more, we can wrap this is a function and try a few cases:

function full_bid_run(bid_blocks; capacity, operational_cost)
    tulipa = create_new_problem(; capacity, operational_cost)
    for (bid_id, bid_block) in enumerate(bid_blocks)
        add_new_bid!(tulipa, bid_id, bid_block)
    end

    # Convert TulipaBuilder's data to TulipaEnergyModel format in the connection
    connection = create_connection(tulipa, TEM.schema)

    # (Fake) cluster the profiles to generate representative periods
    TC.dummy_cluster!(connection; layout = TC.ProfilesTableLayout(year = :milestone_year))

    # Create the mode
    TEM.populate_with_defaults!(connection)
    energy_problem = TEM.EnergyProblem(connection)
    TEM.create_model!(energy_problem)

    # Modify the model
    add_exclusive_groups!(energy_problem, bid_blocks)

    # Solve the model
    TEM.solve_model!(energy_problem)
    TEM.save_solution!(energy_problem; compute_duals = true)

    flow_solution = Dict(
        (row.from_asset, row.to_asset, row.timestep) => row.solution
        for row in DuckDB.query(
            connection,
            """
            SELECT from_asset, to_asset, time_block_start AS timestep, solution,
            FROM var_flow
            WHERE solution != 0
            """,
        )
    )

    bid_id_lookup = Dict("bid$bid_id" => bid_id for bid_id = 1:length(bid_blocks))

    accepted_bids = [
        round(Int, bid_id_lookup[row.asset]) # The solution is returned as float
        for row in DuckDB.query(
            connection,
            """
            SELECT asset, solution,
            FROM var_units_on
            WHERE solution != 0
            """,
        )
    ]

    return energy_problem.objective_value, flow_solution, accepted_bids
end

energy_problem

EnergyProblem:
  - Model created!
    - Number of variables: 58
    - Number of constraints for variable bounds: 58
    - Number of structural constraints: 89
  - Model solved!
    - Termination status: OPTIMAL
    - Objective value: -215.0
    - Objective breakdown:
      - assets_fixed_cost_aggregated_vintage_method: 0.0
      - assets_fixed_cost_compact_vintage_method: 0.0
      - assets_investment_cost: 0.0
      - flows_fixed_cost: 0.0
      - flows_investment_cost: 0.0
      - flows_operational_cost: -215.0
      - storage_assets_energy_fixed_cost: 0.0
      - storage_assets_energy_investment_cost: 0.0
      - units_on_operational_cost: 0.0
      - vintage_flows_operational_cost: 0.0

Now that we have a function that runs the whole process based on the given bid blocks, the generator capacity, and the operational cost to deliver the generated energy, we can verify these cases:

• There is enough capacity to accept all bids and there is no generation cost, so we expect the all bids to be accepted. Notice that bids 2 and 3 are exclusive, so only bids 1, 2, and 4 are accepted.

_, _, accepted_bids = full_bid_run(bid_blocks; capacity = 999.9, operational_cost = 0.0)
@assert accepted_bids == [1, 2, 4]

[ Info: [2026-11-04T07:48:06.502 UTC] Creating EnergyProblem internal tables
[ Info: [2026-11-04T07:48:06.801 UTC] Computing variable indices
[ Info: [2026-11-04T07:48:06.828 UTC] Computing constraint indices
[ Info: [2026-11-04T07:48:06.892 UTC] Preparing profiles
[ Info: [2026-11-04T07:48:06.897 UTC] Creating optimization model
[ Info: [2026-11-04T07:48:06.897 UTC] Preparing optimization model
[ Info: [2026-11-04T07:48:06.901 UTC] Preparing model parameters
[ Info: [2026-11-04T07:48:06.902 UTC] Adding flow variables
[ Info: [2026-11-04T07:48:06.904 UTC] Adding vintage flow variables
[ Info: [2026-11-04T07:48:06.905 UTC] Adding investment variables
[ Info: [2026-11-04T07:48:06.905 UTC] Adding decommission variables
[ Info: [2026-11-04T07:48:06.905 UTC] Adding unit commitment variables
[ Info: [2026-11-04T07:48:06.906 UTC] Adding start-up and shut-down variables
[ Info: [2026-11-04T07:48:06.906 UTC] Adding power flow variables
[ Info: [2026-11-04T07:48:06.906 UTC] Adding storage variables
[ Info: [2026-11-04T07:48:06.906 UTC] Adding conditional value-at-risk variables
[ Info: [2026-11-04T07:48:06.906 UTC] Adding expressions to constraints
[ Info: [2026-11-04T07:48:07.246 UTC] Creating model expressions
[ Info: [2026-11-04T07:48:07.246 UTC] Creating multi-year expressions
[ Info: [2026-11-04T07:48:07.259 UTC] Adding storage expressions
[ Info: [2026-11-04T07:48:07.261 UTC] Preparing objective tables
[ Info: [2026-11-04T07:48:07.283 UTC] Adding operational cost expressions
[ Info: [2026-11-04T07:48:07.301 UTC] Adding objective
[ Info: [2026-11-04T07:48:07.312 UTC] Adding scenario tail excess expressions
[ Info: [2026-11-04T07:48:07.313 UTC] Adding capacity constraints
[ Info: [2026-11-04T07:48:07.330 UTC] Adding energy constraints
[ Info: [2026-11-04T07:48:07.332 UTC] Adding consumer constraints
[ Info: [2026-11-04T07:48:07.336 UTC] Adding storage constraints
[ Info: [2026-11-04T07:48:07.365 UTC] Adding conversion constraints
[ Info: [2026-11-04T07:48:07.366 UTC] Adding transport constraints
[ Info: [2026-11-04T07:48:07.367 UTC] Adding investment group constraints
[ Info: [2026-11-04T07:48:07.373 UTC] Adding available asset units constraints
[ Info: [2026-11-04T07:48:07.376 UTC] Adding ramping constraints
[ Info: [2026-11-04T07:48:07.391 UTC] Adding minimum output flow constraints
[ Info: [2026-11-04T07:48:07.394 UTC] Adding flow relationship constraints
[ Info: [2026-11-04T07:48:07.396 UTC] Adding DC power flow constraints
[ Info: [2026-11-04T07:48:07.399 UTC] Adding vintage flow sum constraints
[ Info: [2026-11-04T07:48:07.401 UTC] Adding unit commitment logic constraints
[ Info: [2026-11-04T07:48:07.403 UTC] Adding scenario tail excess constraints
[ Info: [2026-11-04T07:48:07.403 UTC] Adding minimum up time constraints
[ Info: [2026-11-04T07:48:07.406 UTC] Adding minimum down time constraints
[ Info: [2026-11-04T07:48:07.412 UTC] Optimization model creation finished

• By restricting the capacity, we accepted bids will eventually change. The first breakpoint is at capacity = 50, because bids 2 and 4 requires 50 KW at time steps 2 and 3.

When capacity is slightly less than 50, bid 3 is dropped:

_, _, accepted_bids = full_bid_run(bid_blocks; capacity = 49.9, operational_cost = 0.0)
@assert accepted_bids == [1, 2]

[ Info: [2026-11-04T07:48:07.741 UTC] Creating EnergyProblem internal tables
[ Info: [2026-11-04T07:48:08.026 UTC] Computing variable indices
[ Info: [2026-11-04T07:48:08.051 UTC] Computing constraint indices
[ Info: [2026-11-04T07:48:08.111 UTC] Preparing profiles
[ Info: [2026-11-04T07:48:08.116 UTC] Creating optimization model
[ Info: [2026-11-04T07:48:08.116 UTC] Preparing optimization model
[ Info: [2026-11-04T07:48:08.121 UTC] Preparing model parameters
[ Info: [2026-11-04T07:48:08.121 UTC] Adding flow variables
[ Info: [2026-11-04T07:48:08.123 UTC] Adding vintage flow variables
[ Info: [2026-11-04T07:48:08.124 UTC] Adding investment variables
[ Info: [2026-11-04T07:48:08.124 UTC] Adding decommission variables
[ Info: [2026-11-04T07:48:08.124 UTC] Adding unit commitment variables
[ Info: [2026-11-04T07:48:08.124 UTC] Adding start-up and shut-down variables
[ Info: [2026-11-04T07:48:08.125 UTC] Adding power flow variables
[ Info: [2026-11-04T07:48:08.125 UTC] Adding storage variables
[ Info: [2026-11-04T07:48:08.125 UTC] Adding conditional value-at-risk variables
[ Info: [2026-11-04T07:48:08.125 UTC] Adding expressions to constraints
[ Info: [2026-11-04T07:48:08.468 UTC] Creating model expressions
[ Info: [2026-11-04T07:48:08.469 UTC] Creating multi-year expressions
[ Info: [2026-11-04T07:48:08.481 UTC] Adding storage expressions
[ Info: [2026-11-04T07:48:08.483 UTC] Preparing objective tables
[ Info: [2026-11-04T07:48:08.505 UTC] Adding operational cost expressions
[ Info: [2026-11-04T07:48:08.523 UTC] Adding objective
[ Info: [2026-11-04T07:48:08.532 UTC] Adding scenario tail excess expressions
[ Info: [2026-11-04T07:48:08.533 UTC] Adding capacity constraints
[ Info: [2026-11-04T07:48:08.549 UTC] Adding energy constraints
[ Info: [2026-11-04T07:48:08.552 UTC] Adding consumer constraints
[ Info: [2026-11-04T07:48:08.555 UTC] Adding storage constraints
[ Info: [2026-11-04T07:48:08.583 UTC] Adding conversion constraints
[ Info: [2026-11-04T07:48:08.583 UTC] Adding transport constraints
[ Info: [2026-11-04T07:48:08.585 UTC] Adding investment group constraints
[ Info: [2026-11-04T07:48:08.591 UTC] Adding available asset units constraints
[ Info: [2026-11-04T07:48:08.593 UTC] Adding ramping constraints
[ Info: [2026-11-04T07:48:08.607 UTC] Adding minimum output flow constraints
[ Info: [2026-11-04T07:48:08.610 UTC] Adding flow relationship constraints
[ Info: [2026-11-04T07:48:08.612 UTC] Adding DC power flow constraints
[ Info: [2026-11-04T07:48:08.615 UTC] Adding vintage flow sum constraints
[ Info: [2026-11-04T07:48:08.617 UTC] Adding unit commitment logic constraints
[ Info: [2026-11-04T07:48:08.619 UTC] Adding scenario tail excess constraints
[ Info: [2026-11-04T07:48:08.619 UTC] Adding minimum up time constraints
[ Info: [2026-11-04T07:48:08.622 UTC] Adding minimum down time constraints
[ Info: [2026-11-04T07:48:08.627 UTC] Optimization model creation finished

• We also expect bid 4 to be dropped if the price is not higher than the operational cost:

_, _, accepted_bids = full_bid_run(bid_blocks; capacity = 999.9, operational_cost = 1.0)
@assert accepted_bids == [1, 2]

[ Info: [2026-11-04T07:48:08.753 UTC] Creating EnergyProblem internal tables
[ Info: [2026-11-04T07:48:09.029 UTC] Computing variable indices
[ Info: [2026-11-04T07:48:09.053 UTC] Computing constraint indices
[ Info: [2026-11-04T07:48:09.115 UTC] Preparing profiles
[ Info: [2026-11-04T07:48:09.119 UTC] Creating optimization model
[ Info: [2026-11-04T07:48:09.119 UTC] Preparing optimization model
[ Info: [2026-11-04T07:48:09.124 UTC] Preparing model parameters
[ Info: [2026-11-04T07:48:09.125 UTC] Adding flow variables
[ Info: [2026-11-04T07:48:09.127 UTC] Adding vintage flow variables
[ Info: [2026-11-04T07:48:09.128 UTC] Adding investment variables
[ Info: [2026-11-04T07:48:09.128 UTC] Adding decommission variables
[ Info: [2026-11-04T07:48:09.128 UTC] Adding unit commitment variables
[ Info: [2026-11-04T07:48:09.128 UTC] Adding start-up and shut-down variables
[ Info: [2026-11-04T07:48:09.128 UTC] Adding power flow variables
[ Info: [2026-11-04T07:48:09.128 UTC] Adding storage variables
[ Info: [2026-11-04T07:48:09.128 UTC] Adding conditional value-at-risk variables
[ Info: [2026-11-04T07:48:09.128 UTC] Adding expressions to constraints
[ Info: [2026-11-04T07:48:09.462 UTC] Creating model expressions
[ Info: [2026-11-04T07:48:09.462 UTC] Creating multi-year expressions
[ Info: [2026-11-04T07:48:09.473 UTC] Adding storage expressions
[ Info: [2026-11-04T07:48:09.476 UTC] Preparing objective tables
[ Info: [2026-11-04T07:48:09.495 UTC] Adding operational cost expressions
[ Info: [2026-11-04T07:48:09.512 UTC] Adding objective
[ Info: [2026-11-04T07:48:09.521 UTC] Adding scenario tail excess expressions
[ Info: [2026-11-04T07:48:09.522 UTC] Adding capacity constraints
[ Info: [2026-11-04T07:48:09.536 UTC] Adding energy constraints
[ Info: [2026-11-04T07:48:09.538 UTC] Adding consumer constraints
[ Info: [2026-11-04T07:48:09.541 UTC] Adding storage constraints
[ Info: [2026-11-04T07:48:09.566 UTC] Adding conversion constraints
[ Info: [2026-11-04T07:48:09.567 UTC] Adding transport constraints
[ Info: [2026-11-04T07:48:09.568 UTC] Adding investment group constraints
[ Info: [2026-11-04T07:48:09.573 UTC] Adding available asset units constraints
[ Info: [2026-11-04T07:48:09.576 UTC] Adding ramping constraints
[ Info: [2026-11-04T07:48:09.588 UTC] Adding minimum output flow constraints
[ Info: [2026-11-04T07:48:09.591 UTC] Adding flow relationship constraints
[ Info: [2026-11-04T07:48:09.593 UTC] Adding DC power flow constraints
[ Info: [2026-11-04T07:48:09.595 UTC] Adding vintage flow sum constraints
[ Info: [2026-11-04T07:48:09.597 UTC] Adding unit commitment logic constraints
[ Info: [2026-11-04T07:48:09.598 UTC] Adding scenario tail excess constraints
[ Info: [2026-11-04T07:48:09.599 UTC] Adding minimum up time constraints
[ Info: [2026-11-04T07:48:09.601 UTC] Adding minimum down time constraints
[ Info: [2026-11-04T07:48:09.606 UTC] Optimization model creation finished

• Decreasing the capacity to slightly less than 40 KW, also makes us drop bid 2, but allows us to have more space to accept bids 3 and 4:

_, _, accepted_bids = full_bid_run(bid_blocks; capacity = 39.9, operational_cost = 0.0)
@assert accepted_bids == [1, 3, 4]

[ Info: [2026-11-04T07:48:09.729 UTC] Creating EnergyProblem internal tables
[ Info: [2026-11-04T07:48:10.006 UTC] Computing variable indices
[ Info: [2026-11-04T07:48:10.031 UTC] Computing constraint indices
[ Info: [2026-11-04T07:48:10.091 UTC] Preparing profiles
[ Info: [2026-11-04T07:48:10.096 UTC] Creating optimization model
[ Info: [2026-11-04T07:48:10.096 UTC] Preparing optimization model
[ Info: [2026-11-04T07:48:10.100 UTC] Preparing model parameters
[ Info: [2026-11-04T07:48:10.101 UTC] Adding flow variables
[ Info: [2026-11-04T07:48:10.103 UTC] Adding vintage flow variables
[ Info: [2026-11-04T07:48:10.104 UTC] Adding investment variables
[ Info: [2026-11-04T07:48:10.104 UTC] Adding decommission variables
[ Info: [2026-11-04T07:48:10.104 UTC] Adding unit commitment variables
[ Info: [2026-11-04T07:48:10.104 UTC] Adding start-up and shut-down variables
[ Info: [2026-11-04T07:48:10.104 UTC] Adding power flow variables
[ Info: [2026-11-04T07:48:10.104 UTC] Adding storage variables
[ Info: [2026-11-04T07:48:10.104 UTC] Adding conditional value-at-risk variables
[ Info: [2026-11-04T07:48:10.104 UTC] Adding expressions to constraints
[ Info: [2026-11-04T07:48:10.433 UTC] Creating model expressions
[ Info: [2026-11-04T07:48:10.433 UTC] Creating multi-year expressions
[ Info: [2026-11-04T07:48:10.444 UTC] Adding storage expressions
[ Info: [2026-11-04T07:48:10.446 UTC] Preparing objective tables
[ Info: [2026-11-04T07:48:10.465 UTC] Adding operational cost expressions
[ Info: [2026-11-04T07:48:10.481 UTC] Adding objective
[ Info: [2026-11-04T07:48:10.490 UTC] Adding scenario tail excess expressions
[ Info: [2026-11-04T07:48:10.491 UTC] Adding capacity constraints
[ Info: [2026-11-04T07:48:10.505 UTC] Adding energy constraints
[ Info: [2026-11-04T07:48:10.507 UTC] Adding consumer constraints
[ Info: [2026-11-04T07:48:10.510 UTC] Adding storage constraints
[ Info: [2026-11-04T07:48:10.535 UTC] Adding conversion constraints
[ Info: [2026-11-04T07:48:10.535 UTC] Adding transport constraints
[ Info: [2026-11-04T07:48:10.537 UTC] Adding investment group constraints
[ Info: [2026-11-04T07:48:10.542 UTC] Adding available asset units constraints
[ Info: [2026-11-04T07:48:10.544 UTC] Adding ramping constraints
[ Info: [2026-11-04T07:48:10.557 UTC] Adding minimum output flow constraints
[ Info: [2026-11-04T07:48:10.559 UTC] Adding flow relationship constraints
[ Info: [2026-11-04T07:48:10.562 UTC] Adding DC power flow constraints
[ Info: [2026-11-04T07:48:10.564 UTC] Adding vintage flow sum constraints
[ Info: [2026-11-04T07:48:10.565 UTC] Adding unit commitment logic constraints
[ Info: [2026-11-04T07:48:10.567 UTC] Adding scenario tail excess constraints
[ Info: [2026-11-04T07:48:10.568 UTC] Adding minimum up time constraints
[ Info: [2026-11-04T07:48:10.570 UTC] Adding minimum down time constraints
[ Info: [2026-11-04T07:48:10.575 UTC] Optimization model creation finished

• In fact, because bid 3 can be curtailed to 80%, we can further decrease the capacity. Up to 35 KW, the same bids are still accepted:

a, b, accepted_bids = full_bid_run(bid_blocks; capacity = 35.0, operational_cost = 0.0)
@assert accepted_bids == [1, 3, 4]

[ Info: [2026-11-04T07:48:10.696 UTC] Creating EnergyProblem internal tables
[ Info: [2026-11-04T07:48:10.966 UTC] Computing variable indices
[ Info: [2026-11-04T07:48:10.990 UTC] Computing constraint indices
[ Info: [2026-11-04T07:48:11.048 UTC] Preparing profiles
[ Info: [2026-11-04T07:48:11.053 UTC] Creating optimization model
[ Info: [2026-11-04T07:48:11.053 UTC] Preparing optimization model
[ Info: [2026-11-04T07:48:11.057 UTC] Preparing model parameters
[ Info: [2026-11-04T07:48:11.058 UTC] Adding flow variables
[ Info: [2026-11-04T07:48:11.060 UTC] Adding vintage flow variables
[ Info: [2026-11-04T07:48:11.060 UTC] Adding investment variables
[ Info: [2026-11-04T07:48:11.061 UTC] Adding decommission variables
[ Info: [2026-11-04T07:48:11.061 UTC] Adding unit commitment variables
[ Info: [2026-11-04T07:48:11.061 UTC] Adding start-up and shut-down variables
[ Info: [2026-11-04T07:48:11.061 UTC] Adding power flow variables
[ Info: [2026-11-04T07:48:11.061 UTC] Adding storage variables
[ Info: [2026-11-04T07:48:11.061 UTC] Adding conditional value-at-risk variables
[ Info: [2026-11-04T07:48:11.061 UTC] Adding expressions to constraints
[ Info: [2026-11-04T07:48:11.388 UTC] Creating model expressions
[ Info: [2026-11-04T07:48:11.389 UTC] Creating multi-year expressions
[ Info: [2026-11-04T07:48:11.399 UTC] Adding storage expressions
[ Info: [2026-11-04T07:48:11.402 UTC] Preparing objective tables
[ Info: [2026-11-04T07:48:11.421 UTC] Adding operational cost expressions
[ Info: [2026-11-04T07:48:11.437 UTC] Adding objective
[ Info: [2026-11-04T07:48:11.446 UTC] Adding scenario tail excess expressions
[ Info: [2026-11-04T07:48:11.447 UTC] Adding capacity constraints
[ Info: [2026-11-04T07:48:11.460 UTC] Adding energy constraints
[ Info: [2026-11-04T07:48:11.462 UTC] Adding consumer constraints
[ Info: [2026-11-04T07:48:11.465 UTC] Adding storage constraints
[ Info: [2026-11-04T07:48:11.488 UTC] Adding conversion constraints
[ Info: [2026-11-04T07:48:11.489 UTC] Adding transport constraints
[ Info: [2026-11-04T07:48:11.491 UTC] Adding investment group constraints
[ Info: [2026-11-04T07:48:11.496 UTC] Adding available asset units constraints
[ Info: [2026-11-04T07:48:11.498 UTC] Adding ramping constraints
[ Info: [2026-11-04T07:48:11.510 UTC] Adding minimum output flow constraints
[ Info: [2026-11-04T07:48:11.512 UTC] Adding flow relationship constraints
[ Info: [2026-11-04T07:48:11.514 UTC] Adding DC power flow constraints
[ Info: [2026-11-04T07:48:11.517 UTC] Adding vintage flow sum constraints
[ Info: [2026-11-04T07:48:11.518 UTC] Adding unit commitment logic constraints
[ Info: [2026-11-04T07:48:11.520 UTC] Adding scenario tail excess constraints
[ Info: [2026-11-04T07:48:11.520 UTC] Adding minimum up time constraints
[ Info: [2026-11-04T07:48:11.522 UTC] Adding minimum down time constraints
[ Info: [2026-11-04T07:48:11.527 UTC] Optimization model creation finished

• Slight less capacity forces the model to drop another bid. Although bid 4 is cheaper per KW, is requests more energy, to it is better.

a, b, accepted_bids = full_bid_run(bid_blocks; capacity = 34.9, operational_cost = 0.0)
@assert accepted_bids == [3, 4]

[ Info: [2026-11-04T07:48:11.649 UTC] Creating EnergyProblem internal tables
[ Info: [2026-11-04T07:48:11.921 UTC] Computing variable indices
[ Info: [2026-11-04T07:48:11.945 UTC] Computing constraint indices
[ Info: [2026-11-04T07:48:12.003 UTC] Preparing profiles
[ Info: [2026-11-04T07:48:12.008 UTC] Creating optimization model
[ Info: [2026-11-04T07:48:12.009 UTC] Preparing optimization model
[ Info: [2026-11-04T07:48:12.013 UTC] Preparing model parameters
[ Info: [2026-11-04T07:48:12.014 UTC] Adding flow variables
[ Info: [2026-11-04T07:48:12.015 UTC] Adding vintage flow variables
[ Info: [2026-11-04T07:48:12.016 UTC] Adding investment variables
[ Info: [2026-11-04T07:48:12.016 UTC] Adding decommission variables
[ Info: [2026-11-04T07:48:12.016 UTC] Adding unit commitment variables
[ Info: [2026-11-04T07:48:12.017 UTC] Adding start-up and shut-down variables
[ Info: [2026-11-04T07:48:12.017 UTC] Adding power flow variables
[ Info: [2026-11-04T07:48:12.017 UTC] Adding storage variables
[ Info: [2026-11-04T07:48:12.017 UTC] Adding conditional value-at-risk variables
[ Info: [2026-11-04T07:48:12.017 UTC] Adding expressions to constraints
[ Info: [2026-11-04T07:48:12.345 UTC] Creating model expressions
[ Info: [2026-11-04T07:48:12.345 UTC] Creating multi-year expressions
[ Info: [2026-11-04T07:48:12.355 UTC] Adding storage expressions
[ Info: [2026-11-04T07:48:12.358 UTC] Preparing objective tables
[ Info: [2026-11-04T07:48:12.377 UTC] Adding operational cost expressions
[ Info: [2026-11-04T07:48:12.392 UTC] Adding objective
[ Info: [2026-11-04T07:48:12.401 UTC] Adding scenario tail excess expressions
[ Info: [2026-11-04T07:48:12.402 UTC] Adding capacity constraints
[ Info: [2026-11-04T07:48:12.416 UTC] Adding energy constraints
[ Info: [2026-11-04T07:48:12.418 UTC] Adding consumer constraints
[ Info: [2026-11-04T07:48:12.421 UTC] Adding storage constraints
[ Info: [2026-11-04T07:48:12.444 UTC] Adding conversion constraints
[ Info: [2026-11-04T07:48:12.444 UTC] Adding transport constraints
[ Info: [2026-11-04T07:48:12.446 UTC] Adding investment group constraints
[ Info: [2026-11-04T07:48:12.451 UTC] Adding available asset units constraints
[ Info: [2026-11-04T07:48:12.453 UTC] Adding ramping constraints
[ Info: [2026-11-04T07:48:12.465 UTC] Adding minimum output flow constraints
[ Info: [2026-11-04T07:48:12.467 UTC] Adding flow relationship constraints
[ Info: [2026-11-04T07:48:12.470 UTC] Adding DC power flow constraints
[ Info: [2026-11-04T07:48:12.472 UTC] Adding vintage flow sum constraints
[ Info: [2026-11-04T07:48:12.473 UTC] Adding unit commitment logic constraints
[ Info: [2026-11-04T07:48:12.475 UTC] Adding scenario tail excess constraints
[ Info: [2026-11-04T07:48:12.475 UTC] Adding minimum up time constraints
[ Info: [2026-11-04T07:48:12.477 UTC] Adding minimum down time constraints
[ Info: [2026-11-04T07:48:12.482 UTC] Optimization model creation finished

• But if the generation cost is too high, then bid 4 is dropped in favour of bid 1.

a, b, accepted_bids = full_bid_run(bid_blocks; capacity = 34.9, operational_cost = 1.0)
@assert accepted_bids == [1, 3]

[ Info: [2026-11-04T07:48:12.604 UTC] Creating EnergyProblem internal tables
[ Info: [2026-11-04T07:48:12.876 UTC] Computing variable indices
[ Info: [2026-11-04T07:48:12.900 UTC] Computing constraint indices
[ Info: [2026-11-04T07:48:12.957 UTC] Preparing profiles
[ Info: [2026-11-04T07:48:12.963 UTC] Creating optimization model
[ Info: [2026-11-04T07:48:12.963 UTC] Preparing optimization model
[ Info: [2026-11-04T07:48:12.967 UTC] Preparing model parameters
[ Info: [2026-11-04T07:48:12.968 UTC] Adding flow variables
[ Info: [2026-11-04T07:48:12.969 UTC] Adding vintage flow variables
[ Info: [2026-11-04T07:48:12.970 UTC] Adding investment variables
[ Info: [2026-11-04T07:48:12.971 UTC] Adding decommission variables
[ Info: [2026-11-04T07:48:12.971 UTC] Adding unit commitment variables
[ Info: [2026-11-04T07:48:12.971 UTC] Adding start-up and shut-down variables
[ Info: [2026-11-04T07:48:12.971 UTC] Adding power flow variables
[ Info: [2026-11-04T07:48:12.971 UTC] Adding storage variables
[ Info: [2026-11-04T07:48:12.971 UTC] Adding conditional value-at-risk variables
[ Info: [2026-11-04T07:48:12.971 UTC] Adding expressions to constraints
[ Info: [2026-11-04T07:48:13.297 UTC] Creating model expressions
[ Info: [2026-11-04T07:48:13.297 UTC] Creating multi-year expressions
[ Info: [2026-11-04T07:48:13.307 UTC] Adding storage expressions
[ Info: [2026-11-04T07:48:13.310 UTC] Preparing objective tables
[ Info: [2026-11-04T07:48:13.329 UTC] Adding operational cost expressions
[ Info: [2026-11-04T07:48:13.344 UTC] Adding objective
[ Info: [2026-11-04T07:48:13.353 UTC] Adding scenario tail excess expressions
[ Info: [2026-11-04T07:48:13.354 UTC] Adding capacity constraints
[ Info: [2026-11-04T07:48:13.367 UTC] Adding energy constraints
[ Info: [2026-11-04T07:48:13.369 UTC] Adding consumer constraints
[ Info: [2026-11-04T07:48:13.372 UTC] Adding storage constraints
[ Info: [2026-11-04T07:48:13.394 UTC] Adding conversion constraints
[ Info: [2026-11-04T07:48:13.395 UTC] Adding transport constraints
[ Info: [2026-11-04T07:48:13.397 UTC] Adding investment group constraints
[ Info: [2026-11-04T07:48:13.402 UTC] Adding available asset units constraints
[ Info: [2026-11-04T07:48:13.404 UTC] Adding ramping constraints
[ Info: [2026-11-04T07:48:13.416 UTC] Adding minimum output flow constraints
[ Info: [2026-11-04T07:48:13.418 UTC] Adding flow relationship constraints
[ Info: [2026-11-04T07:48:13.420 UTC] Adding DC power flow constraints
[ Info: [2026-11-04T07:48:13.422 UTC] Adding vintage flow sum constraints
[ Info: [2026-11-04T07:48:13.424 UTC] Adding unit commitment logic constraints
[ Info: [2026-11-04T07:48:13.425 UTC] Adding scenario tail excess constraints
[ Info: [2026-11-04T07:48:13.426 UTC] Adding minimum up time constraints
[ Info: [2026-11-04T07:48:13.428 UTC] Adding minimum down time constraints
[ Info: [2026-11-04T07:48:13.433 UTC] Optimization model creation finished

Visualization of the results

To help visualize the use of bids, we will vary the value of generator's capacity and the operational cost to get from the generator to the bid and create a few plots of the solutions. We are doing the same as in the previous section, but systematically.

We will use some longer code that we'll hide, but that can be inspected in the code for this file. The code simply loops over many cases, like the section above, and saves data to be used in the plots below:

# plts and dim2 are defined in the hidden code
plot(
    plts...;
    size = (300 * dim2, 3 * 200),
    layout = grid(3, dim2),
    leftmargin = 5Plots.mm,
    bottommargin = 4Plots.mm,
)

The plot has three columns and three rows. The columns vary in operational cost, and the rows show three different kinds of plots. The x-axis of all plots is the capacity.

The first row of plots show the profit made accepting these bids, per capacity. The second row of plots show the accepted bids per capacity. The plots in the third row show the profit made per capacity, but grouped per bid.

Some noteworthy points in the plots above:

• For operational cost = $ 0.1 / KW, around capacity 35, bid 1 is slightly less profitable than bid 4, and there is only capacity for one of them (and bid 3), so the accepted bids change accordingly.
• For operational cost = $ 0.6 / KW, this is not the case anymore, and thus bid 1 is always accepted.
• For operational cost = $ 1.1 / KW, then it is never profitable to accept bid 4.
• The profit generated by bid 3 around capacity 16 to 20, and 31 to 35 is linearly increasing, since the bid 3 can be curtailed.