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StatusParameters

StatusParameters add on/off behavior to flows — startup costs, minimum run times, cycling limits.

Basic: Binary Status

A status variable \(s(t) \in \{0, 1\}\) controls whether equipment is active:

generator = fx.Flow(
    label='power', bus=elec_bus, size=100,
    relative_minimum=0.4,  # 40% min when ON
    status_parameters=fx.StatusParameters(
        effects_per_startup={'costs': 25000},  # €25k per startup
    ),
)

When \(s(t) = 0\): flow is zero. When \(s(t) = 1\): flow bounds apply.

Startup Tracking

Detect transitions: \(s^{start}(t) - s^{stop}(t) = s(t) - s(t-1)\)

fx.StatusParameters(
    effects_per_startup={'costs': 25000},
)

fx.StatusParameters(
    effects_per_active_hour={'costs': 100},  # €/h while on
)

fx.StatusParameters(
    startup_limit=20,  # Max 20 starts per period
)

Duration Constraints

Once on, must stay on for minimum duration:

\(s^{start}(t) = 1 \Rightarrow \sum_{j=t}^{t+k} s(j) \geq T_{up}^{min}\)

fx.StatusParameters(min_uptime=8)  # 8 hours minimum

Once off, must stay off for minimum duration:

\(s^{stop}(t) = 1 \Rightarrow \sum_{j=t}^{t+k} (1 - s(j)) \geq T_{down}^{min}\)

fx.StatusParameters(min_downtime=4)  # 4 hours cooling

Force shutdown after limit:

\(\sum_{j=t-k}^{t} s(j) \leq T_{up}^{max}\)

fx.StatusParameters(max_uptime=18)  # Max 18h continuous

Limit total operating hours per period:

\(H^{min} \leq \sum_t s(t) \cdot \Delta t \leq H^{max}\)

fx.StatusParameters(
    active_hours_min=2000,
    active_hours_max=5000,
)

Reference

Symbol Type Description
\(s(t)\) \(\{0, 1\}\) Binary status (0=off, 1=on)
\(s^{start}(t)\) \(\{0, 1\}\) Startup indicator
\(s^{stop}(t)\) \(\{0, 1\}\) Shutdown indicator
\(T_{up}^{min}\) \(\mathbb{R}_{\geq 0}\) Min uptime in hours (min_uptime)
\(T_{up}^{max}\) \(\mathbb{R}_{\geq 0}\) Max uptime in hours (max_uptime)
\(T_{down}^{min}\) \(\mathbb{R}_{\geq 0}\) Min downtime in hours (min_downtime)
\(H^{min}\) \(\mathbb{R}_{\geq 0}\) Min total active hours (active_hours_min)
\(H^{max}\) \(\mathbb{R}_{\geq 0}\) Max total active hours (active_hours_max)
\(\Delta t\) \(\mathbb{R}_{> 0}\) Timestep duration (hours)

Classes: StatusParameters, StatusModel