In Case 2, due to taking no account of costs of ESS, optimal results tend to the upper bounds of power rating and energy capacity to obtain more extra benefits by the arbitrage.
As the squares of singular values are the bounds of power, energy and power spectral density ratios between the input and output vectors, shaping the singular values of a structure is equivalent to shaping the response of the structure.
As the squares of singular values are the bounds of power, energy and power spectral density ratios between the input and output vectors, shaping the singular values of a composite material is equivalent to shaping the response of the material.
With supreme responsibility thrust on his shoulders, he remained within the bounds of power... Since Sharon's departure, Israel lacks leadership that acknowledges the limits of force, maintains the alliance with America, shows political daring in the territories and won't be deterred by the settlers.
Electricity branch flow constraint underline{S}_{ln}^{elec} le S_{ln}^{elec} le overline{S}_{ln}^{elec} ;;;;;forall l,n in N_{power} (15 where (S_{ln}^{elec}) is power flow between branch (l - n); (underline{S}_{ln}^{elec}) and (overline{S}_{ln}^{elec}) represent lower and upper bounds of power flow; N power is the number of electricity bus node.
Results show that our energy efficient solution obtains higher level of energy efficiency compared to some existing approaches as the upper and lower bounds of power consumption of the NetFPGA Openflow switch are proved to be 30% lower than ones of the commercial HP Enterprise switch.
u_{j,t}^{g} p_{j,s}^{g,l} le p_{j,s,t}^{g} le u_{j,t}^{g} p_{j,s}^{g,u} (14 where (u_{j,t}^{g}) is the binary variable that is equal to 1 if turbine is working; (p_{j,s}^{g,l}) and (p_{j,s}^{g,u}) are the lower bound and upper bound of power generation of s th stage turbine.
u_{j,t}^{c} p_{j,r}^{c,l} le p_{j,r,t}^{c} le u_{j,t}^{c} p_{j,r}^{c,u} (2 where (u_{j,t}^{c}) is the binary variable that is equal to 1 if compressor is working; (p_{j,r}^{c,l}) and (p_{j,r}^{c,u}) are the lower bound and upper bound of power demand of r th stage compressor.
The power consumption of heat pump and circulating water should be limited by: d_{i}^{hp,l} le d_{i,t}^{hp} le d_{i}^{hp,u}, (39 where (d_{i}^{hp,l},d_{i}^{cp,l}) and (d_{i}^{hp,u},d_{i}^{cp,u}) are the lower and upper bound of power consumption of heat pump and circulating water pump equipped at node i. 2) Heat load .
For analysis and comparison, separate curves have been plotted for all the user selection algorithms for two cases: (i) upper bounds of the power using the analytical results derived in previous section and (ii) Monte Carlo simulation curves representing the true average minimum power. .
The president's supporters argue that while his decision may infuriate Republicans, he was acting within the bounds of his power, and only after it became clear that bipartisan legislative reform was off the table.
