5,679 research outputs found
New Congruences Modulo 2, 4, and 8 for the Number of Tagged Parts Over the Partitions with Designated Summands
Recently, Lin introduced two new partition functions PD and
PDO, which count the total number of tagged parts over all partitions of
with designated summands and the total number of tagged parts over all
partitions of with designated summands in which all parts are odd. Lin also
proved some congruences modulo 3 and 9 for PD and PDO, and
conjectured some congruences modulo 8. Very recently, Adansie, Chern, and Xia
found two new infinite families of congruences modulo 9 for PD. In this
paper, we prove the congruences modulo 8 conjectured by Lin and also find many
new congruences and infinite families of congruences modulo some small powers
of 2.Comment: 19 page
Optimal Ensemble Control of Loads in Distribution Grids with Network Constraints
Flexible loads, e.g. thermostatically controlled loads (TCLs), are
technically feasible to participate in demand response (DR) programs. On the
other hand, there is a number of challenges that need to be resolved before it
can be implemented in practice en masse. First, individual TCLs must be
aggregated and operated in sync to scale DR benefits. Second, the uncertainty
of TCLs needs to be accounted for. Third, exercising the flexibility of TCLs
needs to be coordinated with distribution system operations to avoid
unnecessary power losses and compliance with power flow and voltage limits.
This paper addresses these challenges. We propose a network-constrained,
open-loop, stochastic optimal control formulation. The first part of this
formulation represents ensembles of collocated TCLs modelled by an aggregated
Markov Process (MP), where each MP state is associated with a given power
consumption or production level. The second part extends MPs to a multi-period
distribution power flow optimization. In this optimization, the control of TCL
ensembles is regulated by transition probability matrices and physically
enabled by local active and reactive power controls at TCL locations. The
optimization is solved with a Spatio-Temporal Dual Decomposition (ST-D2)
algorithm. The performance of the proposed formulation and algorithm is
demonstrated on the IEEE 33-bus distribution model.Comment: 7 pages, 6 figures, accepted PSCC 201
Exact Topology and Parameter Estimation in Distribution Grids with Minimal Observability
Limited presence of nodal and line meters in distribution grids hinders their
optimal operation and participation in real-time markets. In particular lack of
real-time information on the grid topology and infrequently calibrated line
parameters (impedances) adversely affect the accuracy of any operational power
flow control. This paper suggests a novel algorithm for learning the topology
of distribution grid and estimating impedances of the operational lines with
minimal observational requirements - it provably reconstructs topology and
impedances using voltage and injection measured only at the terminal (end-user)
nodes of the distribution grid. All other (intermediate) nodes in the network
may be unobserved/hidden. Furthermore no additional input (e.g., number of grid
nodes, historical information on injections at hidden nodes) is needed for the
learning to succeed. Performance of the algorithm is illustrated in numerical
experiments on the IEEE and custom power distribution models
One Breaker is Enough: Hidden Topology Attacks on Power Grids
A coordinated cyber-attack on grid meter readings and breaker statuses can
lead to incorrect state estimation that can subsequently destabilize the grid.
This paper studies cyber-attacks by an adversary that changes breaker statuses
on transmission lines to affect the estimation of the grid topology. The
adversary, however, is incapable of changing the value of any meter data and
can only block recorded measurements on certain lines from being transmitted to
the control center. The proposed framework, with limited resource requirements
as compared to standard data attacks, thus extends the scope of cyber-attacks
to grids secure from meter corruption. We discuss necessary and sufficient
conditions for feasible attacks using a novel graph-coloring based analysis and
show that an optimal attack requires breaker status change at only ONE
transmission line. The potency of our attack regime is demonstrated through
simulations on IEEE test cases.Comment: 5 pages, 5 figures, Accepted to the IEEE PES General Meeting 201
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