고온 초전도 한류기(SFCL) 전력망 단락 사고 방호 & 1,000Hz 0-Alloc C# 퀜치(Quench) 저항 급변 비선형 유동 엔진

using System;
using System.Runtime.CompilerServices;

namespace ZeliDesk.Stem.SmartGridSuperconductor;

/// 

/// 초전도 한류기(SFCL) 전기-열 상태 구조체 (100% Stack Allocation)
/// 
public readonly ref struct SfclState
{
    public readonly double FaultCurrentKiloAmp;   // 고장 전류 (kA)
    public readonly double LimitedCurrentKiloAmp; // 한류된 전류 (kA)
    public readonly double QuenchResistanceOhm;   // SFCL 퀜치 저항 (Ω)
    public readonly double TapeTemperatureKelvin; // 초전도 선재 온도 (K)
    public readonly double FaultLimitingRatio;    // 고장 전류 제한율 (%)
    public readonly double JouleHeatJoules;       // 누적 줄 발열량 (J)

    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public SfclState(
        double faultCurrentKiloAmp,
        double limitedCurrentKiloAmp,
        double quenchResistanceOhm,
        double tapeTemperatureKelvin,
        double faultLimitingRatio,
        double jouleHeatJoules)
    {
        FaultCurrentKiloAmp = faultCurrentKiloAmp;
        LimitedCurrentKiloAmp = limitedCurrentKiloAmp;
        QuenchResistanceOhm = quenchResistanceOhm;
        TapeTemperatureKelvin = tapeTemperatureKelvin;
        FaultLimitingRatio = faultLimitingRatio;
        JouleHeatJoules = jouleHeatJoules;
    }
}

/// 

/// 1,000Hz 0-Alloc C# 저항형 고온 초전도 한류기 수치 시뮬레이터
/// 
public static class SuperconductingLimiterEngine
{
    private const double CriticalTempTc = 92.0;       // YBCO Tc (K)
    private const double CriticalCurrent77K = 350.0;  // 77K 임계전류 Ic (A)
    private const double TapeLengthM = 120.0;         // 총 선재 길이 (m)
    private const double StabResistanceOhm = 12.5;    // 안정화 금속층 저항 (Ω)
    private const double NValue = 28.0;               // n-value
    private const double HeatCapacityCp = 2.4e6;      // 부피 비열 (J/m^3·K)
    private const double TapeVolumeM3 = 1.2e-4;       // 선재 체적

    /// 

    /// 1ms 타임스텝 단락 고장 전류 억제 연산 (0-Alloc)
    /// 
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static SfclState StepFaultLimiting(
        double gridVoltageVolts,
        double prospectiveFaultCurrentKa,
        double currentTempKelvin,
        double dtSec = 0.001)
    {
        // 1. 선재 온도에 따른 임계 전류 저하: Ic(T) = Ic0 * (1 - T/Tc)
        double icTemp = currentTempKelvin < CriticalTempTc 
            ? CriticalCurrent77K * (1.0 - (currentTempKelvin - 77.0) / (CriticalTempTc - 77.0))
            : 0.0;
        icTemp = Math.Max(icTemp, 0.0);

        // 2. 비선형 E-J 모델 기반 초전도 저항 산출
        double prospectiveAmps = prospectiveFaultCurrentKa * 1e3;
        double currentRatio = icTemp > 0.0 ? prospectiveAmps / icTemp : 10.0;

        double rSc = 0.0;
        if (currentRatio > 1.0)
        {
            // 퀜치 발생: 지수적 저항 급증
            rSc = 0.1 * Math.Pow(Math.Min(currentRatio, 3.0), NValue) * TapeLengthM * 1e-3;
        }

        // 안정화층 병렬 저항
        double rSfcl = (rSc * StabResistanceOhm) / (rSc + StabResistanceOhm + 1e-6);
        rSfcl = Math.Clamp(rSfcl, 0.0, StabResistanceOhm);

        // 3. 한류된 실제 전류 계산 (계통 임피던스 약 0.5Ω 가정)
        double gridImpedance = 0.55;
        double limitedAmps = gridVoltageVolts / (gridImpedance + rSfcl);
        double limitedKa = limitedAmps * 1e-3;

        // 4. 줄 발열 및 온도 갱신: dT = (I^2 * R * dt) / (C_p * V)
        double joulePower = limitedAmps * limitedAmps * rSfcl;
        double coolingPower = 180.0 * (currentTempKelvin - 77.0); // 액체질소 비등 냉각
        double netHeat = Math.Max(joulePower - coolingPower, 0.0);
        double nextTemp = currentTempKelvin + (netHeat * dtSec) / (HeatCapacityCp * TapeVolumeM3);

        // 5. 한류율 계산 (%)
        double limitingRatio = (1.0 - (limitedKa / prospectiveFaultCurrentKa)) * 100.0;

        return new SfclState(
            prospectiveFaultCurrentKa,
            limitedKa,
            rSfcl,
            nextTemp,
            Math.Clamp(limitingRatio, 0.0, 99.0),
            netHeat * dtSec);
    }
}