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This paper introduces a novel multi-control area framework for explicit modeling, managing, and accounting of simultaneous bilateral transactions with specified contract paths. Our framework provides a modular and multi-layered electrical network representation with zooming-in and zooming-out capabilities. The zoomed-out representation concerns interconnections and inter-area transactions, while the zoomed-in representation concerns a single area and its internal transactions. The framework allows explicit modeling of bilateral transactions with contract paths through a transformation of a meshed electrical network into a spanning tree. Loop flows are introduced to represent a deviation between the contract paths of bilateral transactions and physical line flows. The effects of both intra-area and inter-area bilateral transactions and loop flows can be graphically traced in the framework. Moreover, these tracing methods allocate bilateral transactions to line flows and loop flows, essential for accounting and flow control. Our tracing methods differ from the distribution factor based method because the distribution factor matrix handles nodal injections only and it cannot account for contract paths of bilateral transactions and the resulting loop flows. The multi-layered network transformations and tracing methods are illustrated on the IEEE 14-bus system. [ABSTRACT FROM AUTHOR]

This paper defines flow control algorithms for loop flow cancellation based on the allocation and tracing of bilateral transactions and loop flows. In Part I of this paper, we have shown that the main difference between transportation and electrical networks is caused by the existence of loop flows. We have introduced a distributed framework for the modeling and tracing of bilateral transactions and the corresponding loop flows. Its zooming-out capability provides a valuable mechanism for representing external (inter-area) loop flows based on simplified topologies of individual areas. The tracing information accurately allocates bilateral transactions with associated contract paths to line flows and loop flows. Furthermore, this information can be used for determining the set points of control equipment so that loop flows are minimized. In this framework, phase angle regulators (PARs), commonly used for line flow control, are represented through their effects on loop flows. We define sufficient conditions for achieving complete loop flow cancellation. A new distributed algorithm for determining PAR set points in a coordinated way without revealing operating conditions of individual areas is introduced in this part. Finally, complete loop flow cancellation and the distributed algorithm for finding PAR set points are demonstrated in the Reliability Test System (RTS) 96-bus system with wheeling loop flows. [ABSTRACT FROM AUTHOR]