The composed model

What the surface, generators and loads make together:

import math_spec as ms

model = ms.merge({'surface': 'surface.yaml', 'generator': 'generator.yaml', 'load': 'load.yaml'})
spec = ms.to_spec(model)

The file below is model, the mapping merge returns, written as YAML. No fragment holds it, and nothing in the repository commits it. Port_p is one declaration here. Each component fragment read it under given:, and merging folded those readings into the surface's own declaration.

The objective is the generator's, carried as it was written, since no other fragment prices anything. A second priced fragment would add its term to this one, each term in parentheses.

The math under the file has a tab per formulation. As composed is the model above. With commitment lays variants/commitment.yaml over it with override, which makes the generator a committed unit:

spec = ms.to_spec(ms.override(model, {'commitment': 'variants/commitment.yaml'}))

A patch is refused on its own, since it edits declarations it does not declare. So the model it lands on is the only place its math exists, and the tab prints the patch beside that math.

dimensions:
  snapshot: {dtype: datetime, description: dispatch periods}
  bus: {dtype: str, description: network nodes}
  port: {dtype: str, description: 'the connections components make, one label per connection'}
  generator: {dtype: str, description: 'generating units, each on one port'}
  load: {dtype: str, description: 'demands, each on one port'}
relations:
  Port_bus: {key: port, values: bus}
  Generator_port: {key: generator, values: port}
  Load_port: {key: load, values: port}
parameters:
  Generator_p_nom:
    dims: [generator]
    description: nominal power
  Generator_marginal_cost:
    dims: [generator]
    description: cost of one unit of output
  Load_p_set:
    dims: [snapshot, load]
    description: '`Load-p_set` — what a load takes in a snapshot'
variables:
  Port_p:
    dims: [snapshot, port]
    description: what a port puts into its bus in a snapshot, negative for a withdrawal
  Generator_p:
    dims: [snapshot, generator]
    bounds: {lower: 0, upper: Generator_p_nom}
    description: '`Generator-p` — what a generator produces in a snapshot'
constraints:
  Bus_nodal_balance:
    description: '`Bus-nodal_balance` — what the ports on a bus put in nets to nothing'
    dims: [snapshot, bus]
    expression: sum(Port_p, by=Port_bus, over=port, into=bus) == 0
  Generator_injection:
    description: 'what a generator produces is what its port injects. No PyPSA row stands for this: PyPSA
      writes the generator into the balance instead'
    dims: [snapshot, generator]
    expression: at(Port_p, by=Generator_port, over=port, into=generator) == Generator_p
  Load_withdrawal:
    description: 'what a load takes is what its port withdraws. No PyPSA row stands for this: PyPSA writes
      the load into the balance instead'
    dims: [snapshot, load]
    expression: at(Port_p, by=Load_port, over=port, into=load) == -Load_p_set
objective: {sense: minimize, expression: sum(Generator_p * Generator_marginal_cost)}

As composedWith commitment

Sets

Symbol	Meaning
\(\mathcal{T}\)	index \(t\) — snapshot — dispatch periods
\(\mathcal{N}\)	index \(n\) — bus with \(\mathrm{Port\_bus}: \mathcal{J} \to \mathcal{N}\) — network nodes
\(\mathcal{J}\)	index \(j\) — port with \(\mathrm{Port\_bus}: \mathcal{J} \to \mathcal{N},\ \mathrm{Generator\_port}: \mathcal{G} \to \mathcal{J},\ \mathrm{Load\_port}: \mathcal{D} \to \mathcal{J}\) — the connections components make, one label per connection
\(\mathcal{G}\)	index \(g\) — generator with \(\mathrm{Generator\_port}: \mathcal{G} \to \mathcal{J}\) — generating units, each on one port
\(\mathcal{D}\)	index \(d\) — load with \(\mathrm{Load\_port}: \mathcal{D} \to \mathcal{J}\) — demands, each on one port

Parameters

Symbol	Meaning
\(\mathrm{p}^{\mathrm{nom}}\)	Generator_p_nom over \(\mathcal{G}\) — nominal power
\(\mathrm{c}\)	Generator_marginal_cost over \(\mathcal{G}\) — cost of one unit of output
\(\mathrm{load}\)	Load_p_set over \(\mathcal{T} \times \mathcal{D}\) — Load-p_set — what a load takes in a snapshot

Variables

Symbol	Meaning
\(f\)	Port_p over \(\mathcal{T} \times \mathcal{J}\) — what a port puts into its bus in a snapshot, negative for a withdrawal
\(p\)	Generator_p over \(\mathcal{T} \times \mathcal{G}\) — Generator-p — what a generator produces in a snapshot

Objective

\[ \min \sum_{t \in \mathcal{T},\ g \in \mathcal{G}} p_{t,g} \cdot \mathrm{c}_{g} \]

Subject to

Bus_nodal_balance

\[ \sum_{j \in \mathcal{J} \,:\, \mathrm{Port\_bus}(j) = n} f_{t,j} = 0 \qquad \forall\, t \in \mathcal{T},\ n \in \mathcal{N} \]

Generator_injection

\[ f_{t,\mathrm{Generator\_port}(g)} = p_{t,g} \qquad \forall\, t \in \mathcal{T},\ g \in \mathcal{G} \]

Load_withdrawal

\[ f_{t,\mathrm{Load\_port}(d)} = -\mathrm{load}_{t,d} \qquad \forall\, t \in \mathcal{T},\ d \in \mathcal{D} \]

Variable domains

Port_p

\[ f_{t,j} \in \mathbb{R} \qquad \forall\, t \in \mathcal{T},\ j \in \mathcal{J} \]

Generator_p

\[ 0 \le p_{t,g} \le \mathrm{p}^{\mathrm{nom}}_{g} \qquad \forall\, t \in \mathcal{T},\ g \in \mathcal{G} \]

variants/commitment.yaml

parameters:
  Generator_p_min_pu: { dims: [generator], description: "least output, per unit of nominal power" }
variables:
  Generator_status:
    dims: [snapshot, generator]
    domain: binary
    description: "`Generator-status` — whether a unit is on in a snapshot"
  Generator_p: { bounds: { upper: null } }
constraints:
  Generator_com_p_upper:
    description: "`Generator-com-p-upper` — a committed unit outputs at most its nominal power; off, at most nothing"
    dims: [snapshot, generator]
    expression: Generator_p <= Generator_p_nom * Generator_status
  Generator_com_p_lower:
    description: "`Generator-com-p-lower` — a committed unit outputs at least its minimum; off, at least nothing"
    dims: [snapshot, generator]
    expression: Generator_p >= Generator_p_min_pu * Generator_p_nom * Generator_status

Sets

Symbol	Meaning
\(\mathcal{T}\)	index \(t\) — snapshot — dispatch periods
\(\mathcal{N}\)	index \(n\) — bus with \(\mathrm{Port\_bus}: \mathcal{J} \to \mathcal{N}\) — network nodes
\(\mathcal{J}\)	index \(j\) — port with \(\mathrm{Port\_bus}: \mathcal{J} \to \mathcal{N},\ \mathrm{Generator\_port}: \mathcal{G} \to \mathcal{J},\ \mathrm{Load\_port}: \mathcal{D} \to \mathcal{J}\) — the connections components make, one label per connection
\(\mathcal{G}\)	index \(g\) — generator with \(\mathrm{Generator\_port}: \mathcal{G} \to \mathcal{J}\) — generating units, each on one port
\(\mathcal{D}\)	index \(d\) — load with \(\mathrm{Load\_port}: \mathcal{D} \to \mathcal{J}\) — demands, each on one port

Parameters

Symbol	Meaning
\(\mathrm{p}^{\mathrm{nom}}\)	Generator_p_nom over \(\mathcal{G}\) — nominal power
\(\mathrm{c}\)	Generator_marginal_cost over \(\mathcal{G}\) — cost of one unit of output
\(\mathrm{load}\)	Load_p_set over \(\mathcal{T} \times \mathcal{D}\) — Load-p_set — what a load takes in a snapshot
\(\underline{\mathrm{p}}\)	Generator_p_min_pu over \(\mathcal{G}\) — least output, per unit of nominal power

Variables

Symbol	Meaning
\(f\)	Port_p over \(\mathcal{T} \times \mathcal{J}\) — what a port puts into its bus in a snapshot, negative for a withdrawal
\(p\)	Generator_p over \(\mathcal{T} \times \mathcal{G}\) — Generator-p — what a generator produces in a snapshot
\(u\)	Generator_status over \(\mathcal{T} \times \mathcal{G}\) — Generator-status — whether a unit is on in a snapshot

Objective

\[ \min \sum_{t \in \mathcal{T},\ g \in \mathcal{G}} p_{t,g} \cdot \mathrm{c}_{g} \]

Subject to

Bus_nodal_balance

\[ \sum_{j \in \mathcal{J} \,:\, \mathrm{Port\_bus}(j) = n} f_{t,j} = 0 \qquad \forall\, t \in \mathcal{T},\ n \in \mathcal{N} \]

Generator_injection

\[ f_{t,\mathrm{Generator\_port}(g)} = p_{t,g} \qquad \forall\, t \in \mathcal{T},\ g \in \mathcal{G} \]

Load_withdrawal

\[ f_{t,\mathrm{Load\_port}(d)} = -\mathrm{load}_{t,d} \qquad \forall\, t \in \mathcal{T},\ d \in \mathcal{D} \]

Generator_com_p_upper

\[ p_{t,g} \le \mathrm{p}^{\mathrm{nom}}_{g} \cdot u_{t,g} \qquad \forall\, t \in \mathcal{T},\ g \in \mathcal{G} \]

Generator_com_p_lower

\[ p_{t,g} \ge \underline{\mathrm{p}}_{g} \cdot \mathrm{p}^{\mathrm{nom}}_{g} \cdot u_{t,g} \qquad \forall\, t \in \mathcal{T},\ g \in \mathcal{G} \]

Variable domains

Port_p

\[ f_{t,j} \in \mathbb{R} \qquad \forall\, t \in \mathcal{T},\ j \in \mathcal{J} \]

Generator_p

\[ p_{t,g} \ge 0 \qquad \forall\, t \in \mathcal{T},\ g \in \mathcal{G} \]

Generator_status

\[ u_{t,g} \in \{0, 1\} \qquad \forall\, t \in \mathcal{T},\ g \in \mathcal{G} \]