Engineering topics
DeMarco, Christopher L.
Publications and source records attributed to DeMarco, Christopher L..
Convex relaxation of Sparse Tableau Formulation for the AC optimal power flow
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Advanced modeling of $\mathrm{DER}$s and $\mathrm{UPFC}$ devices with Sparse Tableau Formulation for $\mathrm{ACOPF}$
Distributed energy resources (DERs) are projected to be significant contributors in electric power grid modernization efforts. Yet many distribution and transmission system operators are concerned about potential reliability and security impacts of high penetration of DERs, and cite the need of greater visibility and controllability of decision variables associated with these DERs. Tractable modeling of DERs in AC optimal power flow (ACOPF) is one of the barriers to their integration into the existing operation, planning and market paradigm. Similarly, as more intermittent renewable resources are deployed, power flow control becomes more valuable, and accurate representation of Flexible AC Transmission System (FACTS) devices in ACOPF will likely grow in importance. Here this paper focuses on the detailed representation of substations with the high penetration of DERs, and on the Unified Power Flow Controller (UPFC) FACTS devices, in OPF. To this end, a novel Sparse Tableau Formulation (STF) for ACOPF is used to accurately model such features as substation reconfiguration to accommodate DERs, and to represent decision variables appropriate to the voltage source converters within UPFCs. Numerical studies are provided to demonstrate the impacts of detailed DER and UPFC representations on optimal operation, and the computational efficiency.
Benefits of Sparse Tableau Over Nodal Admittance Formulation for Power-Flow Studies
Assembly of power-flow equations has traditionally begun from a nodal analysis formulation of the underlying transmission circuit's behavior. Most power-flow formulations encapsulate network constraints in the bus admittance matrix, Y bus . From a circuit perspective, this admittance representation restricts the network elements to be voltage controlled; resulting drawbacks treating zero-impedance branches in such applications as state estimation have long been recognized. This paper explores the advantages of the alternatives to Y bus -based formulations in power flow. It proposes a sparse tableau formulation (STF), and it demonstrates its computational efficiency, robustness, and generality in detailed comparison to traditional Y bus -based solution algorithms. In the examples of power networks ranging from 1888 to 82 000 buses, computational case studies indicate that STF provides comparable computational speed, while allowing simple treatment of zero-impedance branches and more reliably converging to solutions in many cases for which Y bus -based Newton algorithms diverge.
A Sparse Tableau Formulation for Node-Breaker Representations in Security-Constrained Optimal Power Flow
Realistic representations of contingencies in AC optimal power flow (ACOPF) often challenge traditional bus-branch network models. Derived from nodal analysis, such approaches represent network constraints in terms of the familiar bus admittance matrix, Ybus. A fixed Ybus is unable to represent common circuit breaker actions such as bus splitting. Work-arounds for Ybus-based analysis typically rely on topology processing, switching between different Ybus matrices depending on breaker settings. In this paper, we propose a very general node-breaker approach, employing multi-port element models and using a sparse tableau formulation (STF) for network constraints. Instead of treating breaker action as altering network topology, and hence changing the structure of Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL) equations, this approach represents a breaker’s position as impacting only constraints associated with a single component, thereby maintaining fixed structure in the KVL and KCL constraints. While larger numbers of variables are required, STF proves sparser than Ybus formulations. Numerical case studies herein demonstrate that STF provides computational efficiency comparable to a Ybus-based ACOPF at the scale of several hundred buses, and lower computational cost in an example of over one thousand buses.