Power Loss Model

Losses are important when designing a plant-wide control scheme. Overall losses can be computed as the difference between the input and the output power. The input power to the PCS is the thermal power of the hot oil (Phtf), which depends on the inlet oil temperature (Ti„Tur), outlet oil temperature (ToutTur), and flow (qT) as indicated by Eq. (8.14):

Phtf = qT [1-882 ■ 10-3(T^ – – 0.795{TmTur – ToutTur)] (8.14)

The gross output power of the PCS (Pgross) can be obtained as the difference between the thermal power delivered to the steam generator (Phtf), the thermal power delivered to the refrigeration systems (Prs) and the thermal losses inside the PCS (Lpcs).

The steady state energy balance equation is given by Eq. (8.15):

pgross = Phtf – Ln – Lpcs (8.15)

The following equation was obtained for PSA from experimental data:

Lpcs = 1-56 ■ 10-8 P^tf – 9.31 ■ 10-5 PHTF + 0.21 Phtf – 136 (8.16)

The thermal power delivered to the refrigeration systems were modeled using linear approximations for two operating points at the PCS 290°C (in Eq. (8.11), with a correlation coefficient of 0.99) and 280°C (in Eq. (8.18), with a correlation coefficient of 0.98):

Lrs = 0.618 Phtf + 136 Lrs = 0.169Phtf – 43