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and the auxiliary heat source supplied 9.3 MMBtu (about C O P = ⎡⎣ c 1 + c 2 ( T s ) ⎤⎦ + c 3 ( T a m b ) + c 4 ( T a m b ) 95% of load by heat pump seasonal heating cost = ⎡ 0.95 × 194.3 × 43.66 ⎤ + ⎡ 0.05 × 194.3 × 43.66 ⎤ = $2, 733 ⎢⎣ 3.49 ⎥⎦ ⎢⎣ 1 ⎥⎦ ⎛ 293KWHR ⎞ ⎛ $0.11 ⎞ 45.2%2M)MofBtuotal. =$136/season seasonal average COP ⎜⎝ M M B t u ⎟⎠ ⎜⎝ K W H R ⎟⎠ As of this writing, the cost of electricity supplied to provided by heat pump aux elec. The current price of natural gas in Boston is about $1.55 pertherm,whichatanassumed92%seasonparolvaidvedrabyge boiler efficiency equates to $16.85/MMBtu. The cost of heat source residential customers just west of Boston, where the heating the example house for an average winter using natural gas at this rate and conversion efficiency would be: In this project, the cost of space heating energy using the air-to-water heat pump was 16.5% lower than using L =Qd(T−T)−Q bldg iouti buildin∆gT is located, is $0.149/kwhr. This is slightly higher d than the current U.S. national average rate of $0.118/kwhr. If electricity costing $0.149/kwhr was directly converted to heat⎛,Tsu−cTh ⎞as in an electric boiler, the cost per million Btus Ts =⎜ sd in ⎟(Tin −Tout)+Tin wou⎝ldT b−eT $⎠43.66/MMBtu. This would make the estimated in od seasonal heating cost of the building $8,483. Q=⎡k+k(T)⎤+k(T )+k(T )2 natuqra=lkg(Tas.−FTurth)ermore, if a basic service charge of $20 wa room As h 1 2 s 3 out 4 out ater heat pump, operating at a per month for having a natural gas meter on the building was eliminated so that the house was all electric, an additional savings of $240 per year would be achieved. The total annual savings would be $781 per year. su⎣m ing th a⎦ t t h e air-t o-w seasonal average COP of 3.49, supplies 95% of the seasonal heat — both of which were projected by the spreadsheet aCnOaPlys=is⎡c—+ ca(nTd)⎤t+hca(tTan) +elcec(Ttric)2boiler supplies the remaining ⎣12s⎦3amb 4amb 5%, the estimated seasonal heat cost would be: seasonalheatingcost=⎛ $16.85⎞×⎛194.3MMBtu⎞=$3,274 ⎜⎝ MMBtu⎟⎠ ⎜⎝ season ⎟⎠ q=k(Twa −Troom) This example has shown that the majority (95%) of the space heating energy for a house near Boston with a 75,000 Btu/hr design load, and a hydronic distribution system that requires 120oF water at design conditions, can be supplied by a nominal 4-ton low-ambient air-to- water heat pump, and at seasonal cost about 16% lower than if the heating was done using a high-efficiency boiler operating on natural gas. 45 seasonalheatingcost=⎛ $16.85⎞×⎛194.3MMBtu⎞=$3,274 ⎜⎝ MMBtu⎟⎠ ⎜⎝ season ⎟⎠ 95% of load by heat pump ⎢⎣ 3.49 seasonal average COP provided by heat pump seasonal heating cost = ⎡ 0.95 × 194.3 × 43.66 ⎤ + ⎡ 0.05 × 194.3 × 43.66 ⎤ = $2, 733 ⎥⎦ ⎢⎣ 1 ⎥⎦ provided by aux elec. heat sourcePDF Image | Heat Pump Systems 2020
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