Load/Unload Stage Power and Energy

Let \(P_{max,mod}=f_{P,FL}P_{max}\). The average modulation power is found from the average modulation pressure \(\bar P_{mod,g}\):

\begin{equation}\label{eq:load-unload-average-mod-pressure} \bar P_{mod,g}=P_{max,g}+\Delta P_{mod}-\frac{Q\Delta P_{mod}}{Q_{FL}} +\left(\frac{Q\Delta P_{mod}}{Q_{FL}}-\Delta P_{mod}\right) \frac{\Delta P_{mod}V_s}{P_{atm}Q_{FL}} \frac{1-e^{-P_{atm}Q_{FL}t_{mod}/(60\Delta P_{mod}V_s)}}{t_{mod}}60 \end{equation}

\begin{equation}\label{eq:load-unload-average-mod-power} \bar P_{mod}=(P_{max}-P_{max,mod}) \left(\frac{P_{max,g}+\Delta P_{mod}-\bar P_{mod,g}}{\Delta P_{mod}}\right)^m +P_{max,mod} \end{equation}

\begin{equation}\label{eq:load-unload-average-blowdown-power} \bar P_{bd}=P_{NL}+\left([(P_{UL}-P_{max,mod})e^{-t_{bd}/\tau_{sd}}+P_{max,mod}]-P_{NL}\right) \left(1-e^{-t_{bd}/\tau_{bd}}\right)\frac{\tau_{bd}}{t_{bd}} \end{equation}

\begin{equation}\label{eq:load-unload-minimum-blowdown-power} P_{bd,min}=\begin{cases} P_{NL}, & t_{bd}=t_{bd,set}\\ P_{NL}+\left([(P_{UL}-P_{max,mod})e^{-t_{bd}/\tau_{sd}}+P_{max,mod}]-P_{NL}\right)e^{-t_{bd}/\tau_{bd}}, & t_{bd}<t_{bd,set} \end{cases} \end{equation}

\begin{equation}\label{eq:load-unload-other-stage-powers} P_{off}=P_{NL},\qquad \bar P_{reload}=\frac{P_{bd,min}+P_{FL}}{2},\qquad \bar P_{pump}=\frac{[1-P_{atm}Qt_{reload}/(60V_sP_{ref})]P_{FL}+P_{max}}{2} \end{equation}

\begin{equation}\label{eq:load-unload-stage-energies} E_{bd}=t_{bd}\bar P_{bd},\quad E_{off}=t_{off}P_{off},\quad E_{reload}=t_{reload}\bar P_{reload},\quad E_{pump}=t_{pump}\bar P_{pump},\quad E_{mod}=t_{mod}\bar P_{mod} \end{equation}

\(P_{max,mod}\)	Modulation power floor \([\unit{ \kilo\watt}]\)
\(f_{P,FL}\)	Control-specific modulation floor fraction, including 0.92 for injected load/unload \([\unit{ \unitless}]\)
\(P_{max}\)	Maximum package power \([\unit{ \kilo\watt}]\)
\(P_{UL}\)	Package power at unload airflow \([\unit{ \kilo\watt}]\)
\(P_{NL}\)	No-load package power \([\unit{ \kilo\watt}]\)
\(P_{FL}\)	Full-load package power \([\unit{ \kilo\watt}]\)
\(\bar P_{mod}\)	Average modulation-stage package power \([\unit{ \kilo\watt}]\)
\(\bar P_{bd}\)	Average blowdown-stage package power \([\unit{ \kilo\watt}]\)
\(P_{bd,min}\)	Package power at the end of blowdown \([\unit{ \kilo\watt}]\)
\(P_{off}\)	Off-load package power \([\unit{ \kilo\watt}]\)
\(\bar P_{reload}\)	Average reload-transition package power \([\unit{ \kilo\watt}]\)
\(\bar P_{pump}\)	Average receiver pump-up package power \([\unit{ \kilo\watt}]\)
\(\bar P_{mod,g}\)	Average modulation gauge pressure \([\unit{ \psig}]\)
\(m\)	Modulation exponent, 1 for modulation and 2 for variable displacement \([\unit{ \unitless}]\)
\(P_{ref}\)	Named legacy receiver pump-up reference pressure, 200 \([\unit{ \psig}]\)
\(E_{bd},E_{off},E_{reload},E_{pump},E_{mod}\)	Energy terms for the five stages \([\unit{ \kilo\watt\second}]\)

Symbols for time, airflow, storage, and pressure are defined in Load/Unload Stage Runtimes.