Standards

popo.standards represents voltage limits and inverter characteristics as named standards. A study selects a standard by name, so its results record which standard was applied. This module needs no solver.

Voltage limits

A VoltageLimits holds a band and the rule for applying it: the share of samples that must lie inside the band (the coverage) and, where the standard sets one, an extreme bound that no sample may cross.

from dataclasses import asdict

from popo.standards import VoltageLimits

standards = [
    VoltageLimits.en_50160(),
    VoltageLimits.ansi_c84_1_range_a(),
    VoltageLimits.ansi_c84_1_range_b(),
]
pd.DataFrame([asdict(limits) for limits in standards]).set_index("name")

	lower_pu	upper_pu	coverage	extreme_lower_pu	extreme_upper_pu	reference
name
EN 50160	0.900	1.100	0.95	0.85	1.1	EN 50160:2022, clause 4.2.2
ANSI C84.1 Range A	0.950	1.050	1.00	NaN	NaN	ANSI C84.1-2020, Table 1, service voltage
ANSI C84.1 Range B	0.917	1.058	1.00	NaN	NaN	ANSI C84.1-2020, Table 1, service voltage

EN 50160 requires 95 % of the ten-minute mean voltages in a week to lie within ±10 % of nominal, and none below 0.85 pu. Its extreme upper bound equals its band, so any sample above 1.10 pu fails. ANSI C84.1 Range A requires every sample to lie within ±5 %.

Checking a series

check() applies the full rule to a series and returns a ComplianceReport. The example below is one week of ten-minute means: near nominal, with a dip to 0.88 pu from 18:00 to 18:40 each day.

import numpy as np

samples = np.arange(7 * 144)  # one week of ten-minute means
voltage = 1.0 + 0.015 * np.sin(2 * np.pi * samples / 144)
time_of_day = samples % 144
voltage[(time_of_day >= 108) & (time_of_day < 112)] = 0.88  # 18:00 to 18:40, four samples a day

pd.DataFrame([asdict(limits.check(voltage)) for limits in standards]).set_index("standard")

	compliant	n_samples	fraction_within	fraction_below	fraction_above	worst_low_pu	worst_high_pu	extreme_breach
standard
EN 50160	True	1008	0.972	0.028	0.0	0.88	1.015	False
ANSI C84.1 Range A	False	1008	0.972	0.028	0.0	0.88	1.015	False
ANSI C84.1 Range B	False	1008	0.972	0.028	0.0	0.88	1.015	False

The same series complies with EN 50160 and fails both ANSI ranges. EN 50160 permits 5 % of samples outside its band, and 97.2 % lie inside; ANSI permits none. summary() states the verdict in one line:

print(VoltageLimits.en_50160().check(voltage).summary())

EN 50160: compliant; 97.22 % within band, range 0.8800 to 1.0150 pu

Where and for how long

violations() returns the readings outside the band, with the side and the distance past the bound. It takes any frame with a vmag_pu column, such as the output of bus_voltages().

readings = pd.DataFrame({"bus": ["a", "b", "c", "d"], "vmag_pu": [0.93, 1.0, 1.06, 1.12]})
VoltageLimits.ansi_c84_1_range_a().violations(readings)

	bus	vmag_pu	side	severity_pu
0	a	0.93	low	0.02
2	c	1.06	high	0.01
3	d	1.12	high	0.07

event_summary() takes one voltage trace per customer and counts the steps outside the band, their mean severity and the longest unbroken run. Two customers with the same maximum voltage can differ in duration:

traces = {
    "brief": [1.02, 1.04, 1.12, 1.04, 1.02, 1.02, 1.02, 1.02],
    "sustained": [1.02, 1.11, 1.12, 1.12, 1.11, 1.11, 1.04, 1.02],
}
VoltageLimits.en_50160().event_summary(traces)

	name	v_mean_pu	v_min_pu	v_max_pu	v_std_pu	over_steps	over_severity_pu	over_longest_steps	under_steps	under_severity_pu	under_longest_steps
0	brief	1.038	1.02	1.12	0.032	1	0.020	1	0	0.0	0
1	sustained	1.081	1.02	1.12	0.043	5	0.014	5	0	0.0	0

Inverter characteristics

InverterCapability is the reactive power an inverter must be able to supply, as a fraction of its rating: 0.44 under IEEE 1547 category B and 0.33 under EREC G99. VoltVarCurve sets reactive power against voltage, and VoltWattCurve sets the share of active power allowed against voltage. Both have an IEEE 1547 default.

import matplotlib.pyplot as plt

from popo.plotting import line_style, style, tokens
from popo.standards import VoltVarCurve, VoltWattCurve

line_style.configure(latex=False)
volts = np.linspace(0.88, 1.12, 241)
volt_var = VoltVarCurve.ieee_1547_default()
volt_watt = VoltWattCurve.ieee_1547_default()

fig, (left, right) = plt.subplots(1, 2, figsize=style.panel(0.8, 0.37))
left.plot(volts, volt_var.reactive_power_pu(volts), color=tokens.PRIMARY, lw=line_style.LINE_WIDTH)
left.set_title("Volt-VAr", fontsize=10)
left.set_ylabel("Reactive power (pu)")
right.plot(volts, volt_watt.active_power_pu(volts), color=tokens.PRIMARY, lw=line_style.LINE_WIDTH)
right.set_title("Volt-Watt", fontsize=10)
right.set_ylabel("Active power limit (pu)")
for ax in (left, right):
    ax.set_xlabel("Voltage (pu)")
    line_style.finish(ax)
line_style.show(fig)

The Volt-VAr curve supplies reactive power below 0.98 pu and absorbs it above 1.02 pu, reaching the 0.44 pu capability at 0.92 and 1.08 pu. The Volt-Watt curve starts curtailing at 1.06 pu and reaches its 0.2 pu floor at 1.10 pu. Scenarios installs both on a feeder.

Limitations

• check treats each sample as given. EN 50160 is defined on ten-minute means over a week; a simulation in 30-minute steps over two days is an approximation of that rule.

• The limits apply to the voltage at the customer’s connection. A voltage at the substation busbar says little about compliance further along the feeder (see Power flow).

• The standards here cover steady-state voltage magnitude. Flicker, unbalance and harmonics, which EN 50160 also limits, are not modelled.