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//! Voltage-dependent load laws, expressed as multipliers of nominal P and Q.
use crate::DistLoadVoltageModel;
impl DistLoadVoltageModel {
/// Evaluate active/reactive power multipliers at a nonnegative voltage
/// magnitude in volts. Coefficient and nominal-voltage arrays follow
/// active load branches, rather than bus conductor order.
///
/// For a bounded ZIP law, let `u = voltage / v_nom`. Below `v_low_pu`,
/// both factors are `u²`. Between that threshold and `v_min_pu`, the
/// constant-power/current contributions interpolate current magnitude
/// from `v_low_pu` to respectively `1/v_min_pu` and `1`; the impedance
/// term stays `u²`. Above `v_max_pu`, their power factors are respectively
/// `(u/v_max_pu)²` and `u²/v_max_pu`. Inside the band they are `1` and `u`.
/// Above the low threshold, a positive cutoff multiplies the result by
/// `(1 + tanh(500 * (u - cutoff_pu))) / 2`.
///
/// For a bounded exponential law the middle-band factors are
/// `u^gamma_p` and `u^gamma_q`. Both factors become `u²` below the low
/// threshold, `u * (low + (1/min - low) * (u-low)/(min-low))` between
/// low and min, and `(u/max)²` above max (using `u²` when max is zero).
/// These continuations need not join the exponential law continuously.
///
/// For bounded constant power, the scale is `(u/min)²` at or below
/// min, `1` inside the band, and `(u/max)²` above max. An optional
/// current limit caps this scale at `u * current_limit_pu`.
///
/// Returns an error for missing coefficients, invalid parameters or
/// nonfinite evaluation instead of manufacturing a nominal load law.
#[expect(
clippy::too_many_lines,
reason = "keep all branches of the bounded voltage law together for comparison with its documented equations"
)]
pub fn power_scale(&self, phase: usize, voltage: f64) -> Result<[f64; 2], String> {
if !voltage.is_finite() || voltage < 0.0 {
return Err("load voltage magnitude must be finite and nonnegative".into());
}
if matches!(self, Self::ConstantPower { .. }) {
return Ok([1.0; 2]);
}
let nominal = *self
.v_nom()
.get(phase)
.ok_or("missing nominal load voltage")?;
if !nominal.is_finite() || nominal <= 0.0 {
return Err("nominal load voltage must be positive and finite".into());
}
let voltage_pu = voltage / nominal;
let at = |v: &[f64]| -> Result<f64, String> {
v.get(phase)
.copied()
.filter(|v| v.is_finite())
.ok_or_else(|| "missing or nonfinite load coefficient".into())
};
let value = match self {
Self::ConstantPower { .. } => unreachable!(),
Self::ConstantCurrent { .. } => [voltage_pu; 2],
Self::ConstantImpedance { .. } => [voltage_pu * voltage_pu; 2],
Self::Exponential {
gamma_p, gamma_q, ..
} => [voltage_pu.powf(at(gamma_p)?), voltage_pu.powf(at(gamma_q)?)],
Self::BoundedConstantPower {
v_min_pu,
v_max_pu,
current_limit_pu,
..
} => {
if !v_min_pu.is_finite()
|| *v_min_pu <= 0.0
|| !v_max_pu.is_finite()
|| *v_max_pu < *v_min_pu
|| current_limit_pu.is_some_and(|v| !v.is_finite() || v <= 0.0)
{
return Err("constant-power bounds and current limit must be positive, finite and ordered".into());
}
let scale = if voltage_pu <= *v_min_pu {
(voltage_pu / v_min_pu).powi(2)
} else if voltage_pu > *v_max_pu {
(voltage_pu / v_max_pu).powi(2)
} else {
1.0
};
[current_limit_pu.map_or(scale, |limit| scale.min(voltage_pu * limit)); 2]
}
Self::BoundedExponential {
gamma_p,
gamma_q,
v_low_pu,
v_min_pu,
v_max_pu,
..
} => bounded_exponential_scale(
voltage_pu,
[at(gamma_p)?, at(gamma_q)?],
[*v_low_pu, *v_min_pu, *v_max_pu],
)?,
Self::Zip {
alpha_z,
alpha_i,
alpha_p,
beta_z,
beta_i,
beta_p,
..
}
| Self::BoundedZip {
alpha_z,
alpha_i,
alpha_p,
beta_z,
beta_i,
beta_p,
..
} => {
let active = [at(alpha_z)?, at(alpha_i)?, at(alpha_p)?];
let reactive = [at(beta_z)?, at(beta_i)?, at(beta_p)?];
let (impedance_scale, current_scale, power_scale, dropout) =
if let Self::BoundedZip {
v_low_pu: low,
v_min_pu: min,
v_max_pu: max,
cutoff_pu: cutoff,
..
} = self
{
if [low, min, max, cutoff]
.iter()
.any(|v| !v.is_finite() || **v < 0.0)
{
return Err(
"load voltage thresholds must be finite and nonnegative".into()
);
}
if voltage_pu <= *low {
// Native low-voltage continuation is the full nominal
// impedance, even when ZIP coefficients do not sum to one.
return if (voltage_pu * voltage_pu).is_finite() {
Ok([voltage_pu * voltage_pu; 2])
} else {
Err("load power evaluation became nonfinite".into())
};
}
let (current_scale, power_scale) = if voltage_pu <= *min {
let weight = (voltage_pu - low) / (min - low);
(
voltage_pu * (low + (1.0 - low) * weight),
voltage_pu * (low + (1.0 / min - low) * weight),
)
} else if voltage_pu > *max {
(
voltage_pu * voltage_pu / if *max == 0.0 { 1.0 } else { *max },
voltage_pu * voltage_pu / if *max == 0.0 { 1.0 } else { max * max },
)
} else {
(voltage_pu, 1.0)
};
let dropout = if *cutoff > 0.0 {
f64::midpoint(1.0, (500.0 * (voltage_pu - cutoff)).tanh())
} else {
1.0
};
(voltage_pu * voltage_pu, current_scale, power_scale, dropout)
} else {
(voltage_pu * voltage_pu, voltage_pu, 1.0, 1.0)
};
[
active[0] * impedance_scale
+ active[1] * current_scale
+ active[2] * power_scale,
reactive[0] * impedance_scale
+ reactive[1] * current_scale
+ reactive[2] * power_scale,
]
.map(|v| v * dropout)
}
};
if value.iter().any(|v| !v.is_finite()) {
Err("load power evaluation became nonfinite".into())
} else {
Ok(value)
}
}
/// Nominal law without voltage bounds: the middle-band law, with the
/// low-voltage transitions, high-voltage continuation and dropout removed.
/// Any other law is returned unchanged. A caller uses this only with an
/// explicit diagnostic when the destination cannot carry the full law.
#[must_use]
#[allow(clippy::float_cmp)] // Only exact coefficient identities permit this projection.
pub fn without_voltage_bounds(&self) -> Self {
if let Self::BoundedConstantPower { v_nom, .. } = self {
return Self::ConstantPower {
v_nom: v_nom.clone(),
};
}
if let Self::BoundedExponential {
v_nom,
gamma_p,
gamma_q,
..
} = self
{
return Self::Exponential {
v_nom: v_nom.clone(),
gamma_p: gamma_p.clone(),
gamma_q: gamma_q.clone(),
};
}
let Self::BoundedZip {
v_nom,
alpha_z,
alpha_i,
alpha_p,
beta_z,
beta_i,
beta_p,
cutoff_pu,
..
} = self
else {
return self.clone();
};
let all = |xs: &[f64], x| !xs.is_empty() && xs.iter().all(|v| *v == x);
if *cutoff_pu == 0.0 && all(alpha_z, 0.0) && all(beta_z, 0.0) {
if all(alpha_i, 0.0) && all(beta_i, 0.0) && all(alpha_p, 1.0) && all(beta_p, 1.0) {
return Self::ConstantPower {
v_nom: v_nom.clone(),
};
}
if all(alpha_p, 0.0) && all(beta_p, 0.0) && all(alpha_i, 1.0) && all(beta_i, 1.0) {
return Self::ConstantCurrent {
v_nom: v_nom.clone(),
};
}
}
Self::Zip {
v_nom: v_nom.clone(),
alpha_z: alpha_z.clone(),
alpha_i: alpha_i.clone(),
alpha_p: alpha_p.clone(),
beta_z: beta_z.clone(),
beta_i: beta_i.clone(),
beta_p: beta_p.clone(),
}
}
}
fn bounded_exponential_scale(
u: f64,
gamma: [f64; 2],
bounds: [f64; 3],
) -> Result<[f64; 2], String> {
if bounds.iter().any(|v| !v.is_finite() || *v < 0.0) {
return Err("load voltage thresholds must be finite and nonnegative".into());
}
let [low, min, max] = bounds;
// Preserve the native branch order even when thresholds overlap.
let scale = if u <= low {
u * u
} else if u <= min {
u * (low + (1.0 / min - low) * (u - low) / (min - low))
} else if u > max {
u * u / if max == 0.0 { 1.0 } else { max * max }
} else {
return Ok(gamma.map(|exponent| u.powf(exponent)));
};
Ok([scale; 2])
}