Linear Generator

Linear Generator#

The LinearGenerator class models a Mainspring linear generator — a free-piston linear engine that burns fuel to produce electricity directly, without a rotating shaft. It is a subclass of ThermalComponentBase and inherits all state machine behavior, ramp constraints, and operational logic from the base class.

Set component_type: LinearGenerator in the component’s YAML section. The section key is a user-chosen component_name (e.g. linear_generator); see Component Names, Types, and Categories for details.

For details on the state machine, startup/shutdown behavior, and base parameters, see Thermal Component Base.

Default Linear Generator-Specific Parameter Values#

The LinearGenerator class provides default values for all base class parameters. Only rated_capacity and initial_conditions are required in the YAML configuration. All defaults are defined in the class-level DEFAULTS dict.

Parameter

Default Value

Source

Notes

min_stable_load_fraction

0.0 (0%)

—

Minimum stable load fraction of the generator

ramp_rate_fraction

1.2 (120%/min)

[2]

Ramp rate fraction of the generator

run_up_rate_fraction

Same as ramp_rate_fraction

—

Run-up rate fraction of the generator

hot_startup_time

90 s (1.5 minutes)

—

Time required for a hot start

warm_startup_time

450 s (7.5 minutes)

—

Time required for a warm start

cold_startup_time

900 s (15 minutes)

—

Time required for a cold start

min_up_time

300 s (5 minutes)

—

Note below

min_down_time

300 s (5 minutes)

—

Minimum down time of the generator

hot_to_warm_time

2700 s (45 minutes)

—

Assumptions documented below

hot_to_cold_time

10800 s (3 hours)

—

Assumptions documented below

hhv

39050000 J/m³ (39.05 MJ/m³)

[3]

Higher heating value of the fuel

fuel_density

0.768 kg/m³

[3]

Density of the fuel

efficiency_table

41.44% HHV peak, with roll-off at extremes (see below)

[1]

Efficiency of the generator, converted from LHV

Notes:

  • min_up_time is often determined by thermal and mechanical stress management considerations, as the generator may need to remain on for a minimum duration to avoid excessive wear from frequent cycling.

  • hot_to_warm_time and hot_to_cold_time are estimated based on catalyst cooling characteristics; see the section below for details on how these values were derived.

Estimating hot_to_warm_time and hot_to_cold_time#

These two parameters can be interpreted as catalyst cooling thresholds, similar to the \tau_{hot} and \tau_{warm} transition times used in conventional unit commitment startup models:

  • hot_to_warm_time: time offline after which a hot start can no longer be assumed

  • hot_to_cold_time: time offline after which a cold start must be assumed

For the linear generator, a reasonable first estimate is based on how long the catalyst takes to cool below its light-off temperature, typically about 200-300 °C. A simple lumped thermal model treats the catalyst assembly as cooling approximately exponentially after shutdown:

\[ T(t) = T_{amb} + (T_{op} - T_{amb}) e^{-t/\tau} \]

where T_amb is ambient temperature, T_op is the catalyst operating temperature, and \tau is the thermal time constant of the catalyst assembly, approximately equal to thermal mass divided by heat loss conductance.

Using rough screening values:

  • catalyst operating temperature: 400-600 °C

  • ambient temperature: about 20 °C

  • catalyst light-off temperature: about 250 °C

  • catalyst thermal time constant: about 30-60 minutes for a relatively small, modestly insulated substrate

For example, if the catalyst is at 500 °C when the unit shuts down and the hot-to-warm threshold is taken as 250 °C, then:

\[ 250 = 20 + (500 - 20)e^{-t/\tau} \]

which gives:

\[ \frac{230}{480} = e^{-t/\tau}, \qquad t = \tau \ln\left(\frac{480}{230}\right) \approx 0.74\tau \]

If \tau = 45 minutes, this yields a hot-to-warm transition time of about 33 minutes after shutdown. The warm-to-cold transition, defined more conservatively as the catalyst approaching near-ambient conditions such as within 50 °C of ambient, would usually occur after several time constants, on the order of 2-4 hours.

This supports a reasonable first-guess range of:

Transition

Estimated threshold

Hot -> Warm

30-60 minutes offline

Warm -> Cold

2-4 hours offline

These thresholds are much shorter than those of many conventional thermal generators because the catalyst assembly has much lower thermal mass. More accurate values would require vendor-specific information about catalyst substrate mass, heat capacity, insulation, and enclosure heat loss.

Linear Generator Fuel Parameters#

The LinearGenerator class currently uses default values for natural gas properties from [3]:

Parameter

Units

Default

Description

hhv

J/m³

39050000

Higher heating value of natural gas (39.05 MJ/m³) [3]

fuel_density

kg/m³

0.768

Fuel density for mass calculations [3]

Linear generators are also capable of mixed-fuel operation. To model a different fuel, simply override the hhv and fuel_density parameters in the YAML configuration; in this case the efficiency_table should also be updated to reflect the new fuel’s combustion characteristics. The efficiency_table parameter is optional. If not provided, the default HHV net plant efficiency from the Mainspring Energy Linear Generator datasheet [1] is used. All efficiency values are HHV (Higher Heating Value) net plant efficiencies. See Thermal Component Base for details on the efficiency table format.

Default Efficiency Table#

The default HHV net plant efficiency table is sourced from the Mainspring Energy Linear Generator datasheet [1]:

Power Fraction

HHV Net Efficiency

1.00

0.40 (40%)

0.90

0.4144 (41.44%)

0.30

0.4144 (41.44%)

0.20

0.35 (35%)

Mainspring reports a single peak efficiency value of 41.44% HHV, which is representative of most of the operating range. The table adds a modest drop-off at the extremes: a small reduction at high load (above ~90% of rated) reflecting thermal losses, and a larger reduction at low load (below ~30% of rated) reflecting fixed auxiliary and parasitic losses. The boundary values at 0.90 and 0.30 are chosen conservatively to preserve the reported peak efficiency across the broad mid-load range; the actual roll-off shape is uncertain without part-load test data, so users with site-specific measurements should override the efficiency_table accordingly.

Linear Generator Outputs#

The linear generator model provides the following outputs (inherited from base class):

Output

Units

Description

power

kW

Actual power output

state

integer

Operating state number (0-7), 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 using fuel_density [3])

YAML Configuration#

Minimal Configuration#

Required parameters only (uses all defaults):

linear_generator:
  component_type: LinearGenerator
  rated_capacity: 250  # kW
  initial_conditions:
    power: 0  # 0 kW means OFF; power > 0 means ON

Full Configuration#

All parameters explicitly specified:

linear_generator:
  component_type: LinearGenerator
  rated_capacity: 250  # kW
  min_stable_load_fraction: 0.0
  ramp_rate_fraction: 1.2  # 120%/min
  run_up_rate_fraction: 1.2  # 120%/min
  hot_startup_time: 90.0  # 1.5 minutes
  warm_startup_time: 450.0  # 7.5 minutes
  cold_startup_time: 900.0  # 15 minutes
  min_up_time: 300  # 5 minutes
  min_down_time: 300  # 5 minutes
  hot_to_warm_time: 2700.0  # 45 minutes
  hot_to_cold_time: 10800.0  # 3 hours
  hhv: 39050000  # J/m³ for natural gas (39.05 MJ/m³) [3]
  fuel_density: 0.768  # kg/m³ for natural gas [3]
  efficiency_table:
    power_fraction:
      - 1.00
      - 0.90
      - 0.30
      - 0.20
    efficiency:  # HHV net plant efficiency from [1]; peak ±roll-off at extremes
      - 0.40
      - 0.4144
      - 0.4144
      - 0.35
  log_channels:
    - power
    - fuel_volume_rate
    - fuel_mass_rate
    - state
    - efficiency
    - power_setpoint
  initial_conditions:
    power: 250  # kW; power > 0 means ON

Multi-Unit Configuration (via ThermalPlant)#

Multiple linear generators can be combined using the ThermalPlant component:

thermal_power_plant:
  component_type: ThermalPlant
  units: ["linear_generator_ms", "linear_generator_ms", "linear_generator_ms", "linear_generator_ms"]
  unit_names: ["lg_1", "lg_2", "lg_3", "lg_4"]

  linear_generator_ms:
    component_type: LinearGenerator
    rated_capacity: 250  # kW
    initial_conditions:
      power: 250  # Start ON at rated capacity

Logging Configuration#

The log_channels parameter controls which outputs are written to the HDF5 output file.

Available Channels:

  • power: Actual power output in kW (always logged)

  • state: Operating state number (0-7), corresponding to the STATES enum

  • fuel_volume_rate: Fuel volume flow rate in m³/s

  • fuel_mass_rate: Fuel mass flow rate in kg/s (computed using fuel_density [3])

  • efficiency: Current HHV net plant efficiency (0-1)

  • power_setpoint: Requested power setpoint in kW

References#

  1. Mainspring Energy, “Linear Generator Datasheet,” Rev. R30313.3, March 16, 2026. https://linear-power.files.svdcdn.com/production/Mainspring-Linear-Generator-Datasheet-R30313.3_2026-03-16-205457_psod.pdf

  2. https://www.energy.ca.gov/sites/default/files/2024-05/CEC-500-2024-037.pdf

  3. 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