Page 319 - Sustainable On-Site CHP Systems Design, Construction, and Operations

292 Op erations

CHP System-Level Performance Monitoring Calculations
The monitoring algorithms are based on Eqs. (17-1), (17-54), and the expressions for
other monitored variables given earlier. The density, specific heat, and heating value of
each fuel stream (j) must be specified. Although the density and heating value of the
fuels are assumed to vary slowly compared to the time between samples of the mea-
sured inputs and, therefore, are considered fixed inputs, they could be varied by chang-
ing their values periodically based on measurement of them or information from the
fuel supplier. All individual useful thermal outputs (j) must be specified to ensure
proper crediting of outputs and their values (Y ). System-level monitoring provides
th,j
top-level indicators of the performance of the CHP plant and is supplemented by com-
ponent monitoring, which provides greater detail and resolution.

Summary of Equations for Metrics
In this section we present the summary of equations for system-level metrics. Equations
for these metrics are summarized in Table 17-2. The rates can be integrated to obtain
average values over selected time periods, and average efficiencies and utilization fac-
tors can be determined by integrating the numerator and denominator in the corre-
sponding expression separately and then taking their ratio. Some generic example
expressions for time-integrated quantities follow.

Rates
Average value for time period t to t
0 1
t 1
∫
dt
Average quantity over last n hours = (current-rate ) / (t 1 − )t 0
t 0
(17-56)
n 1
≈ ∑ current-hourlly-rate / n( 1 − n )
j
0
=
jn 0
where t and t represent the start and end times for the time interval of interest for time
0 1
measured from any arbitrary origin t = 0; n and n are the corresponding time interval
0 1
indices corresponding to times t and t ; n − n = (t − t )/Δt, and Δt is the length of the time
0 1 1 0 1 0
interval (e.g., 1 hour). Some specific example expressions based on Eq. (17-56) follow.
Daily Average Value
24 hours
Average value = ∫ (current-rate )dt
0
(17-57)
24
≈ ∑
current-hourly-raate /24
j
j=1
Average Value for the Last n Hours
t
dt
Average quantity over last n hours = ∫ (current-rate ) /n
− tn
(17-58)
t
≈ ∑ current-hourly-ratee/n
=−
jt n j