rrrlr POS & PROPERTY & UNIT & DESCRIPTION & VALUE 1 & V & L & Volume & Var 2 & U & W/m²·K & Tank’s Heat Transfer Coefficient & Var 3 & H & m & Height & Var 4 & D & m & Diameter & Var 5 & Cdhw & J/K & Thermal Capacity & Var 6 & A & m² & Tank’s surface area & Var 7 & $_{l,st}$ & W & Standard Tank’s Heat Losses & Var 8 & CAPEXtank & CHF & Tank’s capital expenditure & Var 9 &Pnom & W & Nominal Electric Power & Var 10 & d₀ & Unitless & Independent COP coefficient & 5.593 11 & d₁ & Unitless & Tamb-dependent COP coefficient & 0.569 12 & d₂ & Unitless & Ttank-dependent COP coefficient & -0.0661 13 & a₁ & Unitless & 1st order part-load efficiency coefficient & 8.335 14 & a₂ & Unitless & 2nd order part-load efficiency coefficient & -38.0747 15 & a₃ & Unitless & 3rd order part-load efficiency coefficient & 104.6758 16 & a₄ & Unitless & 4th order part-load efficiency coefficient & -159.6927 17 & a₅ & Unitless & 5th order part-load efficiency coefficient & 121.4477 18 & a₆ & Unitless & 6th order part-load efficiency coefficient & -35.9697 19 & CAPEXhp & CHF & Heat Pump’s capital expenditure & Var 20 & Prated & W & Rated Power & Var 21 & p₀ & Unitless & Standby losses coefficient & 0.0072 22 & k & Unitless & Load losses coefficient & 0.0345 23 & c₁ & Unitless & Fitting curve coefficient & -0.2418 24 & c₂ & Unitless & Fitting curve coefficient & -1.127 25 & c₃ & Unitless & Fitting curve coefficient & 96.1 26 & PPV & kWp & Size of Photovoltaic Array & Var 27 & PPV, DC & W & Photovoltaic DC-production & M525601x1 28 & Pload & W & Household’s electric consumption profile & M525601x1 39 & $_d$ & l/min & Domestic Hot Water Demand & M361423x1 30 & Tws & °C & Domestic hot water consumption temperature & 55 31 & Tamb & °C & Ambient Temperature & M525601x1 32 & Tcold & °C & Cold Water Temperature for DHW & 15 33 & Troom & °C & Tank’s Room Temperature & 20 34 & Cb & cts/kWh & Buying price of electricity & M525601x1 35 & Cs & cts/kWh & Selling price of electricity & M525601x1 36 & FiL & W & Feed-in power limit & Var 37 & t & min & Elapsed simulation time & tϵ [1, 525601] 38 & topt & min & Discrete optimization time & toptϵ [1, 96] 39 & tendopt & min & End of Optimization Time & 96 40 & tend & min & End of Simulation Time & tendϵ [1, 525601] 41 & tstep & min & Simulation time step & 1 42 & tstepopt & min & Optimization time step & 30 43 & tlengthopt & min & Time horizon for predictive control & 2880 44 & t₀ & min & Starting time of simulation & t₀ϵ [1, 525601] 45 & AOP & binary & 1: Auxiliary/Extra HP operation | 0: Optimized HP Operation & M525601x1 46 & COP & Unitless & Heat pump’s coefficient of performance & M525601x1 47 & COPm & Unitless & COPm = COP · fc & M525601x1 48 & fc & Unitless & HP’s part-load correction factor & M525601x1 49 & fICA & CHF & Accumulated cost of real system operation & Var 50 & Gf & W & Net grid power flux & M525601x1 51 & Plossinv & W & Inverter Power Losses & M525601x1 52 & Pexp & W & Exporting grid flux & M525601x1 53 & Php & W & Heat Pump Electric Power & M525601x1 54 & PhpAOP & W & HP auxiliary power supplied when AOP = 1 & M525601x1 55 & Pimp & W & Importing grid flux & M525601x1 56 & Pload & W & Household’s electricity consumption & M525601x1 57 & Ploss & W & Power Curtailment due to FiL & M525601x1 58 & PPV, AC & W & Photovoltaic-AC production & M525601x1 59 & $_{hp}$ & Wth & Heat pump’s thermal power & M525601x1 60 & $_{l}$ & Wth & Tank’s conductive heat losses & M525601x1 61 & Roff & binary & 1: HP off | 0: HP can be turned on & M525601x1 62 & Tmax & °C & Maximum heat pump supply temperature & 65 63 & Tmin & °C & Minimum tank’s temperature & 55 64 & Ttank & °C & Tank’s temperature & M525601x1 65 & Cbopt & cts/kWh & Buying electricity price & M96x1 66 & COPopt & Unitless & Optimized heat pump’s coefficient of performance & M96x1 67 & COPmopt & Unitless & COPmopt = COPopt · fcopt & M96x1 68 & costvec & CHF & Optimized OPEX cost values for all tested heating states & Mqxj 69 & Csopt & cts/kWh & Selling electricity price & M96x1 70 & fcopt & Unitless & Optimized HP’s part-load correction factor & M96x1 71 & fHCA & CHF & Optimized OPEX cost value & Var 72 & Gfopt & W & Optimized net grid power flux PPV, ACopt − Ploadopt − Phpopt & M96x1 73 & j & Unitless & Iteration number from i=0 until iteration i where Ttankopt(i)<Tmin & Zϵ[1, i] 74 & $_d^{opt}$ & l/min & OptStep-min DHW mass flow usage forecast & M96x1 75 & MO & Binary & Maximum Operation: 1/0 = unavailable/available heating states until the current iteration i & M96x1 76 & Pexpopt & W & Optimized exporting grid flux & M96x1 77 & $_{hp}^{opt}$ & Unitless & Optimized heat pump power profile normalized to Pnom & M96x1 78 & $_{hp_{old}}^{opt}$ & Unitless & $_{hp}^{opt}$ vector taken from the last decision as reference & M96x1 79 & Pimpopt & W & Optimized importing grid flux & M96x1 80 & Ploadopt & W & tstepopt-min electric consumption forecast & M96x1 81 & Plossopt & W & Optimized power curtailment value & M96x1 82 & PPV, DCopt & W & tstepopt-min PV production forecast & M96x1 83 & q & Unitless & HP discrete power state & Zϵ[1, 5] 84 & $_{hp}^{opt}$ & Wth & Optimized heat pump thermal power & M96x1 85 & Ropt & Binary & Optimized Heat Pump Running State (1:on|0:off) & M96x1 86 & Solver & case & Fmincon;GlobalSearch;Heuristic algorithm;Intlinprog & - 87 & Sopt & Binary & Optimized HP start-up (1:Switch on, 0:otherwise) & M96x1 88 & Tambopt & °C & tstepopt-min Tamb forecast & M96x1 89 & Tmaxopt & °C & Maximum temperature value of Ttankopt vector & Var 90 & Ttankopt & °C & Optimized tank temperature profile & M96x1 91 & eopt(t) & Binary & Slack variable for the MILP optimization & M96x1 92 & OBopt(t) & Binary & OB=1/0 Temperature Out/within Boundaries & M96x1