CHP plants¶

Description¶

Set Combined heat and power (CHP) plant heat to power operational zones. There are three types of CHP that can be described by the following constraints:

CHPs with extraction (condensing) turbines, where some electrical efficiency can be sacrificed by diverting high-temperature steam to provide more heat (following the extraction (cv) line). At maximum electrical efficiency, some heat can still be generated from the low-temperature steam output (following the backpressure (cb) line). The following figure shows the 2D plane of electricity and heat generation; there is a third dimension not shown here: fuel consumption.

Along the cv line, fuel consumption remains constant.
^
|Electricity
|
|----
|    \-------   Cv
|            \-------
|                    \-------
|                            \------
|                              --/
|    operating region       --/
|                        --/
|                     --/
|                  --/
|               --/
|            --/   Cb
|         --/
|      --/
|   --/
| -/                              Heat
-------------------------------------->

CHPs without extraction turbines, but with auxiliary boilers that can be used to divert fuel use for direct heat generation. At maximum electrical efficiency, some heat can be generated from the low-temperature steam output (following the backpressure (cb) line). For the same fuel input, electricity output can be sacrificed by diverting some fuel to direct use in a boiler, with its own efficiency. This leads to two sources of heat output (E = electricity output): H1 = E / cb; H2 / boiler_eff + E / turbine_eff = fuel_consumption. Total heat output H is then H1 + H2. The following figure shows the 2D plane of electricity and heat generation; there is a third dimension not shown here: fuel consumption.
```
^
|Electricity
|
|                  --/
|         Cb    --/   \-
|            --/        \-
|         --/             \-
|      --/                  \-
|   --/        operating      \-
| -/            region          \-  Heat
---------------------------------------->
```

CHPs without extraction turbines and without an auxiliary boiler. Here, there is no operating region; the output must follow the backpressure line.

^
|Electricity
|
|                          /--
|                       /--
|               Cb   /--
|                 /--
|               /-
|            /--
|         /--
|      /--
|    /-
| /--                             Heat
-------------------------------------->

Note

These constraints clash with the base math balance_conversion constraint. To mitigate this, we also need to update that constraint's "where" string so it doesn't build for cases (1) and (2) above. For case (3), we change the balance_conversion constraint to link gas input with only electricity output.

New technology-level parameters:

turbine_type (used to group constraints together)
power_loss_factor
power_to_heat_ratio
boiler_eff

YAML definition¶

Download the YAML example

constraints:

# Update the base math `balance_conversion` constraint (see note above).
# ~~
  balance_conversion:
    equations:
      - where: NOT turbine_type
        expression: sum(flow_out_inc_eff, over=carriers) == sum(flow_in_inc_eff, over=carriers)
      - where: turbine_type=backpressure AND NOT boiler_eff
        expression: flow_out_inc_eff[carriers=electricity] == sum(flow_in_inc_eff, over=carriers)
# ~~

# Extraction turbine constraints
# ~~
  chp_extraction_line:
    description: >
      Set the extraction line for combined heat and power plants with extraction
      turbines. `power_loss_factor` is also referred to as simply `cv`.
    foreach: [nodes, techs, timesteps]
    where: turbine_type=extraction
    equations:
      - expression: >
          flow_out[carriers=electricity]
          <= (sum(flow_in_inc_eff, over=carriers) * flow_out_eff[carriers=electricity])
             - (flow_out[carriers=heat] * power_loss_factor)

  chp_backpressure_line_min:
    description: >
      Set the backpressure line as a lower bound for electricity generation in
      combined heat and power plants with extraction turbines.
      `power_to_heat_ratio` is also referred to as the `backpressure ratio`
      or simply `cb`.
    foreach: [nodes, techs, timesteps]
    where: turbine_type=extraction
    equations:
      - expression: >
          flow_out[carriers=electricity] >=
          flow_out[carriers=heat] * power_to_heat_ratio
# ~~

# Backpressure with direct boiler option
# ~~
  chp_backpressure_line_max:
    description: >
      Set the backpressure line as a lower bound for heat generation in
      combined heat and power plants without extraction turbines,
      but with the option to divert fuel to use in direct heat generation
      (e.g., via a boiler). `power_to_heat_ratio` is also referred to as the
      `backpressure ratio` or simply `cb`.
    foreach: [nodes, techs, timesteps]
    where: turbine_type=backpressure AND boiler_eff
    equations:
      - expression: >
          flow_out[carriers=electricity] <=
          flow_out[carriers=heat] * power_to_heat_ratio

  chp_divert_fuel_to_boiler:
    description: >
      Divert fuel input from use in combined heat and power generation to be
      used in direct heat generation (e.g., via a boiler).
      `heat_eff` is the boiler efficiency. `power_to_heat_ratio` is also
      referred to as the `backpressure ratio` or simply `cb`.
    foreach: [nodes, techs, timesteps]
    where: turbine_type=backpressure AND boiler_eff
    equations:
      - expression: >-
          flow_out[carriers=heat]
          <= (sum(flow_in_inc_eff, over=carriers) * boiler_eff) - (
                flow_out[carriers=electricity] * (
                  (boiler_eff / flow_out_eff[carriers=electricity])
                  - (1 / power_to_heat_ratio)
                )
              )
# ~~

# Backpressure only
  chp_backpressure_line_equals:
    description: >
      Fix the backpressure line for combined heat and power plants without
      extraction turbines. `power_to_heat_ratio` is also referred to as the
      `backpressure ratio` or simply `cb`.
    foreach: [nodes, techs, timesteps]
    where: turbine_type=backpressure AND NOT boiler_eff
    equations:
      - expression: >
          flow_out[carriers=electricity] ==
          flow_out[carriers=heat] * power_to_heat_ratio