Thermal Component Base

The ThermalComponentBase class provides common functionality for thermal power plant components in Hercules. It serves as a base class for multiple thermal plant types including:

• Reciprocating internal combustion engines (RICE)

• Open-cycle gas turbines (OCGT)

• Combined-cycle gas turbines (CCGT)

• Coal-fired power plants

The parameterized model is based primarily on [1], with additional parameters and naming conventions from [2] and [3]. Table 1 on page 48 of [1] provides many of the default values used in subclasses.

Note: All efficiency values throughout this module are HHV (Higher Heating Value) net plant efficiencies, consistent with the data in Exhibit ES-4 of [5].

State Machine

The thermal component operates as a state machine with six states:

State Transitions

The decision between hot, warm, and cold starting is based on how long the unit has been off. The cutoff times are hardcoded based on reference [5]: less than 8 hours triggers a hot start, 8-48 hours triggers a warm start, and 48+ hours triggers a cold start.

From State	To State	Diagram Label	Condition
OFF (0)	HOT STARTING (1)	start (hot)	power_setpoint > 0 AND time_in_state >= min_down_time AND time_in_state < 8 hours
OFF (0)	WARM STARTING (2)	start (warm)	power_setpoint > 0 AND time_in_state >= min_down_time AND time_in_state >= 8 hours AND time_in_state < 48 hours
OFF (0)	COLD STARTING (3)	start (cold)	power_setpoint > 0 AND time_in_state >= min_down_time AND time_in_state >= 48 hours
HOT STARTING (1)	OFF (0)	abort	power_setpoint <= 0
HOT STARTING (1)	ON (4)	P >= P_min	power_output >= P_min (after hot_startup_time)
WARM STARTING (2)	OFF (0)	abort	power_setpoint <= 0
WARM STARTING (2)	ON (4)	P >= P_min	power_output >= P_min (after warm_startup_time)
COLD STARTING (3)	OFF (0)	abort	power_setpoint <= 0
COLD STARTING (3)	ON (4)	P >= P_min	power_output >= P_min (after cold_startup_time)
ON (4)	STOPPING (5)	shutdown	power_setpoint <= 0 AND time_in_state >= min_up_time
STOPPING (5)	OFF (0)	P = 0	power_output <= 0

Parameters

All parameters below are defined in the Hercules input YAML file. The base class does not provide default values—subclasses (such as OpenCycleGasTurbine) supply defaults based on References [1-3].

Required Parameters

Parameter	Units	Description
rated_capacity	kW	Maximum power output (P_max)
min_stable_load_fraction	fraction (0-1)	Minimum operating point as fraction of rated capacity
ramp_rate_fraction	fraction/min	Maximum rate of power change during normal operation, as fraction of rated capacity per minute
run_up_rate_fraction	fraction/min	Maximum rate of power increase during startup ramp, as fraction of rated capacity per minute
hot_startup_time	s	Time to reach P_min from off (hot start). Includes both readying time and ramping time
warm_startup_time	s	Time to reach P_min from off (warm start). Includes both readying time and ramping time
cold_startup_time	s	Time to reach P_min from off (cold start). Includes both readying time and ramping time
min_up_time	s	Minimum time unit must remain on before shutdown is allowed
min_down_time	s	Minimum time unit must remain off before restart is allowed
initial_conditions.power	kW	Initial power output. State is derived automatically: power > 0 sets ON, power == 0 sets OFF. When ON, time_in_state = min_up_time (ready to stop). When OFF, time_in_state = min_down_time (ready to start).
hhv	J/m³	Higher heating value of fuel
fuel_density	kg/m³	Fuel density for mass calculations
efficiency_table	dict	Dictionary containing power_fraction and efficiency arrays (see below). Efficiency values must be HHV net plant efficiencies.

Derived Parameters

The following parameters are computed from the input parameters:

Parameter	Formula	Description
P_max	rated_capacity	Maximum power output
P_min	min_stable_load_fraction × rated_capacity	Minimum stable power output
ramp_rate	ramp_rate_fraction × rated_capacity / 60	Ramp rate in kW/s
run_up_rate	run_up_rate_fraction × rated_capacity / 60	Run-up rate in kW/s
ramp_time	P_min / run_up_rate	Time to ramp from 0 to P_min
hot_readying_time	hot_startup_time - ramp_time	Preparation time before hot start ramp begins
warm_readying_time	warm_startup_time - ramp_time	Preparation time before warm start ramp begins
cold_readying_time	cold_startup_time - ramp_time	Preparation time before cold start ramp begins

Startup and Ramp Behavior

The following diagram illustrates the startup sequence and ramp behavior, showing how the input and derived parameters relate to each other:

During startup:

1. The unit receives a positive power_setpoint while in the OFF state

2. If min_down_time is satisfied, the unit transitions to HOT STARTING, WARM STARTING, or COLD STARTING (depending on how long it has been off: <8h = hot, 8-48h = warm, >48h = cold)

3. The unit remains at zero power during the readying time (hot_readying_time, warm_readying_time, or cold_readying_time)

4. After readying, the unit ramps up to P_min using run_up_rate

5. Once P_min is reached, the unit transitions to ON state

During normal operation (ON state):

• Power changes are constrained by ramp_rate

• Power output is constrained between P_min and P_max

• The unit must remain on for at least min_up_time before shutdown is allowed

During shutdown:

• The unit ramps down to zero using ramp_rate

• Once power reaches zero, the unit transitions to OFF

Efficiency and Fuel Consumption

The base class calculates HHV net plant efficiency and fuel consumption based on the efficiency_table and hhv parameters.

Efficiency Table Format

The efficiency_table parameter specifies how HHV net plant efficiency varies with load. All efficiency values must be HHV (Higher Heating Value) net plant efficiencies:

efficiency_table:
  power_fraction:  # fraction of rated_capacity (0-1)
    - 1.0
    - 0.75
    - 0.50
    - 0.25
  efficiency:  # HHV net plant efficiency, fraction (0-1), e.g., 0.39 = 39%
    - 0.39
    - 0.37
    - 0.325
    - 0.245

Both arrays must have the same length and values must be in the range [0, 1]. The arrays are sorted by power_fraction internally.

Efficiency Interpolation

HHV net efficiency is calculated by linear interpolation from the table based on current power fraction (power_output / rated_capacity). Values outside the table range are clamped to the nearest endpoint.

Fuel Rate Calculation

Fuel volume rate is calculated as:

\[ \text{fuel\_volume\_rate} = \frac{\text{power}}{\text{efficiency} \times \text{hhv}} \]

Where:

• power is in W (converted from kW internally)

• efficiency is the interpolated HHV net efficiency (0-1)

• hhv is the higher heating value in J/m³

• Result is fuel volume rate in m³/s

The fuel mass rate is then computed from the volume rate using the fuel density:

\[ \text{fuel\_mass\_rate} = \text{fuel\_volume\_rate} \times \text{fuel\_density} \]

Where:

• fuel_volume_rate is in m³/s

• fuel_density is in kg/m³

• Result is fuel mass rate in kg/s

Outputs

The base class outputs are returned in h_dict:

Output	Units	Description
power	kW	Actual power output
state	integer	Current operating state (0-5), corresponding to the STATES enum
efficiency	fraction (0-1)	Current HHV net plant efficiency
fuel_volume_rate	m³/s	Fuel volume flow rate
fuel_mass_rate	kg/s	Fuel mass flow rate (computed from volume rate using fuel_density)

References

1. Agora Energiewende (2017): “Flexibility in thermal power plants - With a focus on existing coal-fired power plants.”

2. “Impact of Detailed Parameter Modeling of Open-Cycle Gas Turbines on Production Cost Simulation”, NREL/CP-6A40-87554, National Renewable Energy Laboratory, 2024.

3. Deane, J.P., G. Drayton, and B.P. Ó Gallachóir. “The Impact of Sub-Hourly Modelling in Power Systems with Significant Levels of Renewable Generation.” Applied Energy 113 (January 2014): 152–58. https://doi.org/10.1016/j.apenergy.2013.07.027.

4. IRENA (2019), Innovation landscape brief: Flexibility in conventional power plants, International Renewable Energy Agency, Abu Dhabi.

5. M. Oakes, M. Turner, “Cost and Performance Baseline for Fossil Energy Plants, Volume 5: Natural Gas Electricity Generating Units for Flexible Operation,” National Energy Technology Laboratory, Pittsburgh, May 5, 2023.

6. I. Staffell, “The Energy and Fuel Data Sheet,” University of Birmingham, March 2011. https://claverton-energy.com/cms4/wp-content/uploads/2012/08/the_energy_and_fuel_data_sheet.pdf