Ток кабеля при ограничении температуры и обратной связи сопротивления

"""Самостоятельная лабораторная работа курса FEMM 5.
Запуск: встроенный MicroPython FEMM 5, команды FEMM доступны непосредственно.
Геометрические координаты и глубина — мм; результаты интегралов — единицы СИ.
Данные, допущения, аналитические ориентиры и ход исследования заданы в README.md.
Каждая серия записывается в новую calculated-XX; прежние результаты сохраняются.
Сохранённая модель закрывается и открывается до расчёта, включая русские имена.
"""

import os
import sys
import json
import math

script = globals().get("__file__", "") or (sys.argv[0] if sys.argv else "")
base = os.path.dirname(os.path.abspath(script)) if script else os.getcwd()
index = 1
while "calculated-%02d" % index in os.listdir(base):
    index += 1
directory = base + "/calculated-%02d" % index
os.mkdir(directory)
records = []
checks = []


def real(value):
    if isinstance(value, (tuple, list)):
        return real(value[0])
    return complex(value).real


def check(name, value, limit):
    checks.append(
        {
            "name": name,
            "value": value,
            "limit": limit,
            "passed": math.isfinite(value) and value <= limit,
        }
    )


def polygon(prefix, points):
    for x, y in points:
        globals()[prefix + "_addnode"](x, y)
    for i, (x, y) in enumerate(points):
        x2, y2 = points[(i + 1) % len(points)]
        globals()[prefix + "_addsegment"](x, y, x2, y2)


def geometry(prefix, job, mesh):
    if job.get("polygon"):
        polygon(prefix, job["polygon"])
    for x1, y1, x2, y2 in job.get("interfaces", []) + job.get("segments", []):
        globals()[prefix + "_addnode"](x1, y1)
        globals()[prefix + "_addnode"](x2, y2)
        globals()[prefix + "_addsegment"](x1, y1, x2, y2)
    for x1, y1, x2, y2, angle, name in job.get("arcs", []):
        globals()[prefix + "_addnode"](x1, y1)
        globals()[prefix + "_addnode"](x2, y2)
        globals()[prefix + "_addarc"](x1, y1, x2, y2, angle, 1)
        cx, cy = job.get("arc_center", (0, 0))
        mx = (x1 + x2) / 2 - cx
        my = (y1 + y2) / 2 - cy
        radius = math.sqrt((x1 - cx) ** 2 + (y1 - cy) ** 2)
        factor = radius / math.sqrt(mx * mx + my * my)
        globals()[prefix + "_selectarcsegment"](cx + mx * factor, cy + my * factor)
        if prefix == "ci":
            ci_setarcsegmentprop(1, "<None>", 0, 0, name or "<None>")
        else:
            hi_setarcsegmentprop(1, name or "<None>", 0, 0, "<None>")
        globals()[prefix + "_clearselected"]()
    for x, y, radius, name in job.get("circles", []):
        globals()[prefix + "_addnode"](x - radius, y)
        globals()[prefix + "_addnode"](x + radius, y)
        globals()[prefix + "_addarc"](x - radius, y, x + radius, y, 180, 1)
        globals()[prefix + "_addarc"](x + radius, y, x - radius, y, 180, 1)
        globals()[prefix + "_selectarcsegment"](x, y + radius)
        globals()[prefix + "_selectarcsegment"](x, y - radius)
        if prefix == "ci":
            ci_setarcsegmentprop(1, "<None>", 0, 0, name or "<None>")
        else:
            hi_setarcsegmentprop(1, name or "<None>", 0, 0, "<None>")
        globals()[prefix + "_clearselected"]()
    for x, y, name, group in job["blocks"]:
        globals()[prefix + "_addblocklabel"](x, y)
        globals()[prefix + "_selectlabel"](x, y)
        globals()[prefix + "_setblockprop"](
            name,
            0,
            mesh
            * job.get("block_mesh_multipliers", {}).get(
                str(group), job.get("mesh_multipliers", {}).get(name, 1)
            ),
            group,
        )
        globals()[prefix + "_clearselected"]()


def current(job, mesh, stem):
    newdocument(3)
    ci_probdef("millimeters", job.get("type", "planar"), 0, 1e-10, job["depth"], 30)
    for name, sx, sy in job["materials"]:
        ci_addmaterial(name, sx, sy, 1, 1, 0, 0)
    for name, voltage, amperes, kind in job["terminals"]:
        ci_addconductorprop(name, voltage, amperes, kind)
    geometry("ci", job, mesh)
    for x, y, name in job.get("electrode_segments", []):
        ci_selectsegment(x, y)
        ci_setsegmentprop("<None>", mesh, 0, 0, 0, name)
        ci_clearselected()
    path = directory + "/" + stem + ".fec"
    ci_saveas(path)
    ci_close()
    opendocument(path)
    ci_analyze(1)
    ci_loadsolution()
    co_smooth("off")
    terminals = {}
    terminal_power = 0
    balance = 0
    current_scale = 0
    for name, voltage, amperes, kind in job["terminals"]:
        u, i = co_getconductorproperties(name)
        terminals[name] = {"U_V": real(u), "I_A": real(i)}
        terminal_power += real(complex(u) * complex(i).conjugate())
        balance += complex(i)
        current_scale = max(current_scale, abs(complex(i)))
    powers = {}
    power = 0
    for x, y, name, group in job["blocks"]:
        if name == "<No Mesh>":
            continue
        co_groupselectblock(group)
        powers[str(group)] = real(co_blockintegral(0))
        power += powers[str(group)]
        co_clearblock()
    samples = []
    for x, y in job.get("samples", []):
        values = co_getpointvalues(x, y)
        samples.append(
            {
                "x_mm": x,
                "y_mm": y,
                "U_V": real(values[0]),
                "J_A_m2": math.sqrt(
                    abs(complex(values[1])) ** 2 + abs(complex(values[2])) ** 2
                ),
            }
        )
    row = {
        "model": stem + ".fec",
        "mesh_mm": mesh,
        "nodes": co_numnodes(),
        "elements": co_numelements(),
        "terminals": terminals,
        "P_W": power,
        "group_power_W": powers,
        "samples": samples,
        "current_balance_relative": abs(balance) / current_scale,
        "power_balance_relative": abs(power - terminal_power) / max(power, 1e-30),
    }
    check(stem + ": баланс токов", row["current_balance_relative"], 1e-6)
    check(stem + ": баланс мощности", row["power_balance_relative"], 1e-6)
    co_close()
    ci_close()
    return row


def heat(job, mesh, stem):
    newdocument(2)
    hi_probdef("millimeters", job.get("type", "planar"), 1e-10, job["depth"], 30)
    for name, kx, ky, q in job["materials"]:
        hi_addmaterial(name, kx, ky, q, 0)
    for boundary in job["boundaries"]:
        name, kind, temp, ambient, h = boundary[:5]
        beta = boundary[5] if len(boundary) > 5 else 0
        hi_addboundprop(name, kind, temp, 0, ambient, h, beta)
    geometry("hi", job, mesh)
    for x, y, name in job.get("boundary_segments", []):
        hi_selectsegment(x, y)
        hi_setsegmentprop(name, job.get("boundary_mesh", mesh), 0, 0, 0, "<None>")
        hi_clearselected()
    path = directory + "/" + stem + ".feh"
    hi_saveas(path)
    hi_close()
    opendocument(path)
    hi_analyze(1)
    hi_loadsolution()
    ho_smooth("off")
    averages = {}
    generated = 0
    for x, y, name, group in job["blocks"]:
        ho_groupselectblock(group)
        averages[str(group)] = real(ho_blockintegral(0))
        volume = real(ho_blockintegral(2))
        q = [m[3] for m in job["materials"] if m[0] == name][0]
        generated += q * volume
        ho_clearblock()
    samples = []
    for x, y in job.get("samples", []):
        samples.append({"x_mm": x, "y_mm": y, "T_K": real(ho_getpointvalues(x, y)[0])})
    convection = 0
    for x1, y1, x2, y2, ambient, h in job.get("convection_edges", []):
        count = 200
        total = 0
        for n in range(count + 1):
            t = real(
                ho_getpointvalues(
                    x1 + (x2 - x1) * n / count, y1 + (y2 - y1) * n / count
                )[0]
            )
            total += (0.5 if n in (0, count) else 1) * (t - ambient)
        length = math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2) * 0.001
        convection += total / count * length * job["depth"] * 0.001 * h
    row = {
        "model": stem + ".feh",
        "mesh_mm": mesh,
        "nodes": ho_numnodes(),
        "elements": ho_numelements(),
        "samples": samples,
        "group_average_K": averages,
        "generated_W": generated,
        "convection_W": convection,
    }
    if job.get("convection_edges") and not job.get("skip_convection_balance"):
        check(
            stem + ": баланс конвективного теплоотвода",
            abs(convection - generated) / max(generated, 1e-30),
            0.005,
        )
    ho_close()
    hi_close()
    return row


JOB = {
    "depth": 1000,
    "materials": [],
    "blocks": [[0, 0, "Медная жила", 1], [7, 0, "Изоляция", 2]],
    "circles": [[0, 0, 5, ""], [0, 0, 8, "Конвекция"]],
    "boundaries": [["Конвекция", 2, 0, 293.15, 10]],
    "samples": [[0, 0]],
}
area = math.pi * 0.005**2
resistance20 = 1 / (5.8e7 * area)
alpha = 0.00393
analytic_rth = (
    1 / (4 * math.pi * 380)
    + math.log(8 / 5) / (2 * math.pi * 0.2)
    + 1 / (2 * math.pi * 0.008 * 10)
)
limit_temperature = 363.15
reference_current = math.sqrt(70 / (resistance20 * analytic_rth * (1 + alpha * 70)))
for level, mesh in enumerate((0.4, 0.2, 0.1)):
    job = json.loads(json.dumps(JOB))
    job["materials"] = [["Медная жила", 380, 380, 1 / area], ["Изоляция", 0.2, 0.2, 0]]
    unit = heat(job, mesh, "mesh-%d-unit" % (level + 1))
    rth = unit["samples"][0]["T_K"] - 293.15
    maximum_current = math.sqrt(70 / (resistance20 * rth * (1 + alpha * 70)))
    operating_current = 0.8 * maximum_current
    temperature = 293.15
    history = []
    for iteration in range(1, 61):
        conductivity = 5.8e7 / (1 + alpha * (temperature - 293.15))
        q = (operating_current / area) ** 2 / conductivity
        job["materials"] = [["Медная жила", 380, 380, q], ["Изоляция", 0.2, 0.2, 0]]
        result = heat(job, mesh, "mesh-%d-feedback-%02d" % (level + 1, iteration))
        new_temperature = result["samples"][0]["T_K"]
        residual = abs(new_temperature - temperature)
        history.append(
            {"iteration": iteration, "T_K": new_temperature, "residual_K": residual}
        )
        if residual < 0.001:
            break
        temperature = (temperature + new_temperature) / 2
    check("Итерационная сходимость, сетка %d" % (level + 1), residual, 0.001)
    check(
        "Ток температурного ограничения против аналитики",
        abs(maximum_current / reference_current - 1),
        0.002,
    )
    analytic_delta = (
        operating_current**2
        * resistance20
        * analytic_rth
        / (1 - operating_current**2 * resistance20 * analytic_rth * alpha)
    )
    check(
        "Итерационная температура против аналитики, К",
        abs(new_temperature - 293.15 - analytic_delta),
        0.1,
    )
    q = (maximum_current / area) ** 2 / (5.8e7 / (1 + alpha * 70))
    job["materials"] = [["Медная жила", 380, 380, q], ["Изоляция", 0.2, 0.2, 0]]
    limit_result = heat(job, mesh, "mesh-%d-limit" % (level + 1))
    check(
        "Достижение заданной температуры, К",
        abs(limit_result["samples"][0]["T_K"] - limit_temperature),
        0.01,
    )
    records.append(
        {
            "mesh_mm": mesh,
            "model": limit_result["model"],
            "I_limit_A": maximum_current,
            "I_operating_A": operating_current,
            "operating_model": result["model"],
            "unit_model": unit["model"],
            "T_operating_K": new_temperature,
            "iterations": iteration,
            "history": history,
        }
    )
check(
    "Сходимость предельного тока",
    abs(records[-1]["I_limit_A"] / records[-2]["I_limit_A"] - 1),
    0.002,
)

result = {
    "runtime": "FEMM 5; embedded MicroPython",
    "records": records,
    "checks": checks,
    "passed": all(item["passed"] for item in checks),
}
with open(directory + "/result.json", "w") as output:
    json.dump(result, output)
print(json.dumps(result))
assert result["passed"]