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``````Advanced Topics 449
LP technology
• EachratesectionwithintheLPareacontributesapartofanLPequationforarecalcula- tion. The purpose of the recalculation is to determine the maximum effective flow rates in the system, given the constraints defined by block settings and the structure of the model. The result is the set of effective rates for each section in the LP area at that point in the sim- ulation. The system is optimized such that only the rate sections in the LP area are recalcu- lated; all the other effective rates in the system don’t need to recalculate at that moment and won’t.
• Amongotherthings,theLPcalculationstakeintoconsiderationeachblock’s:
• Critical constraints, which place an upper bound on rate sections connected to that block.
• Relational constraints, which define the way rate sections are related to each other. • Bias, which is a block’s preference that flow travel one route rather than another.
The LP area
The LP area is made up of one or more rate sections linked together by the fact that their effective rates could change at that point in the simulation – a change in the effective rates in one section might impact effective rates in the other sections. The rates, constraints, and biases within the LP area are used by the LP Solver to calculate the optimal set of effective rates for the rate sections contained within that area.
The effective rate of one section can affect the effective rate of another section through rela- tional constraints. When an event occurs that causes a rate section’s effective rate to be reeval- uated, blocks propagate “rate block flow” messages (see “Block messages” on page 459) throughout the model to determine which other rate sections might be impacted by the new event. The affected rate sections constitute the LP area and rate sections outside of the LP area are not included in the recalculation, reducing redundant computations.
The boundaries of the LP area are determined through the propagation of messages between Rate library blocks. A change in a block’s constraints during the simulation run causes the block to notify the Executive and send messages which propagate through all the rate sections whose effective rates might change as a result. Whether the block is the originator of the recal- culation request or receives a propagation message:
• TheblockdeclareswhichofitsconnectedratesectionsareintheLParea.Thepropagation process then creates a global list of rate sections to include in the current LP area.
• If the block provides a relational constraint connection between two or more rate sections, the effective rates connected to that block are dependent on one another. The block then con- tinues the message propagation to all the dependent block(s), who propagate the message to their dependent blocks, and so forth.
The change in the originating block will definitely cause a recalculation of the effective rates for all directly connected rate sections, and (depending on relational constraints between the sections) might cause a recalculation of the effective rates for other rate sections.
☞ The boundaries of the LP area will change dynamically during the simulation depending on which effective rates are involved in the recalculation and which relational constraint depen- dencies occur between rate sections.
Discrete Rate

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