Page 322 - Sustainable On-Site CHP Systems Design, Construction, and Operations

Sustaining Operational Ef ficiency of a CHP System 295

where metricnum and metricdenom are the numerator and denominator of the effi-
ciency, effectiveness or utilization factor. For example, applying Eq. (17-61) to the fuel
utilization efficiency,

24 hours
∫ (W elec + ∑ Q th, j )dt
Average daily η = 0 j
F 24
∫ Q Fuel dt
0
(17-62)
24 ⎛ ⎞
∑ ⎜ ⎝ W elec ∑ Q th, ⎟ ⎠
+
c
k
≈ = j 1 k j
24
∑ Q Fuel,j
= j 1
where the sum over the index j is for the 24 hours of the day and the sum over index k
is over all useful thermal outputs of the CHP system.

Average Value for the Last n Hours
t
∫ (metricnum )dt
Average metric value over last n hours = − tn
t
∫ (metricdenom )dt
− tn
(17-63)
t
∑ metrricnum j
=−
≈ jt n
t
∑ metricdenom j
=−
jt n
As an example, applying Eq. (17-63) to the value-weighted energy utilization factor
(EUF ),
VW
t
∫ (W elec elec + ∑ Q th, k th, k )dt
Y
Y
Average EUF over last 8 hours = − t 8 k
VW t
∫ ( ∑ Q Fuel, l Pricce Fuel,l ) dt
t−8 l
(17-64)
0
∑
∑ ( W elec elec ∑ Q th,k Y th,k )
+
Y
≈ j =−8 0 k j
∑ ( ∑ Q Price )
j =−8 l Fuel, l Fuel, l j
Here, the summation over j is for each of the last 8 hours, the summation over k is for
all useful thermal energy outputs from the system, and the summation over l is for all