49 research outputs found
Digital Grid: Transforming the Electric Power Grid into an Innovation Engine for the United States
The electric power grid is one of the largest and most complex
infrastructures ever built by mankind. Modern civilization depends on it for
industry production, human mobility, and comfortable living. However, many
critical technologies such as the 60 Hz transformers were developed at the
beginning of the 20th century and have changed very little since then.1 The
traditional unidirectional power from the generation to the customer through
the transmission-distribution grid has also changed nominally, but it no longer
meets the need of the 21st century market energy customers. On one hand, 128m
US residential customers pay $15B/per month for their utility bill, yet they
have no option to select their energy supplier. In a world of where many
traditional industries are transformed by digital Internet technology (Amazon,
Ebay, Uber, Airbnb), the traditional electric energy market is lagging
significantly behind. A move towards a true digital grid is needed. Such a
digital grid requires a tight integration of the physical layer (energy and
power) with digital and cyber information to allow an open and real time market
akin to the world of e-commerce. Another major factor that is pushing for this
radical transformation are the rapidly changing patterns in energy resources
ownership and load flow. Driven by the decreasing cost in distributed solar,
energy storage, electric vehicle, on site generation and microgrids, the high
penetration of Distributed Energy Resource (DER) is shifting challenges
substantially towards the edge of grid from the control point of view. The
envisioned Digital Grid must facilitate the open competition and open
innovation needed to accelerate of the adoption of new DER technologies while
satisfying challenges in grid stability, data explosion and cyber security.Comment: A Computing Community Consortium (CCC) white paper, 3 page
Hierarchical H2 Control of Large-Scale Network Dynamic Systems
Standard H2 optimal control of networked dynamic systems tend to become
unscalable with network size. Structural constraints can be imposed on the
design to counteract this problem albeit at the risk of making the solution
non-convex. In this paper, we present a special class of structural constraints
such that the H2 design satisfies a quadratic invariance condition, and
therefore can be reformulated as a convex problem. This special class consists
of structured and weighted projections of the input and output spaces. The
choice of these projections can be optimized to match the closed-loop
performance of the reformulated controller with that of the standard H2
controller. The advantage is that unlike the latter, the reformulated
controller results in a hierarchical implementation which requires
significantly lesser number of communication links, while also admitting model
and controller reduction that helps the design to scale computationally. We
illustrate our design with simulations of a 500-node network.Comment: Submitted to 2018 American Control Conferenc
Sparsity-Promoting Optimal Control of Cyber-Physical Systems over Shared Communication Networks
Recent years have seen several new directions in the design of sparse control
of cyber-physical systems (CPSs) driven by the objective of reducing
communication cost. One common assumption made in these designs is that the
communication happens over a dedicated network. For many practical
applications, however, communication must occur over shared networks, leading
to two critical design challenges, namely - time-delays in the feedback and
fair sharing of bandwidth among users. In this paper, we present a set of
sparse H2 control designs under these two design constraints. An important
aspect of our design is that the delay itself can be a function of sparsity,
which leads to an interesting pattern of trade-offs in the H2 performance. We
present three distinct algorithms. The first algorithm preconditions the
assignable bandwidth to the network and produces an initial guess for a
stabilizing controller. This is followed by our second algorithm, which
sparsifies this controller while simultaneously adapting the feedback delay and
optimizing the H2 performance using alternating directions method of
multipliers (ADMM). The third algorithm extends this approach to a multiple
user scenario where optimal number of communication links, whose total sum is
fixed, is distributed fairly among users by minimizing the variance of their H2
performances. The problem is cast as a difference-of-convex (DC) program with
mixed-integer linear program (MILP) constraints. We provide theorems to prove
convergence of these algorithms, followed by validation through numerical
simulations.Comment: Preliminary version appeared at American Control Conference (ACC)
201
Locating Power Flow Solution Space Boundaries: A Numerical Polynomial Homotopy Approach
The solution space of any set of power flow equations may contain different
number of real-valued solutions. The boundaries that separate these regions are
referred to as power flow solution space boundaries. Knowledge of these
boundaries is important as they provide a measure for voltage stability.
Traditionally, continuation based methods have been employed to compute these
boundaries on the basis of initial guesses for the solution. However, with
rapid growth of renewable energy sources these boundaries will be increasingly
affected by variable parameters such as penetration levels, locations of the
renewable sources, and voltage set-points, making it difficult to generate an
initial guess that can guarantee all feasible solutions for the power flow
problem. In this paper we solve this problem by applying a numerical polynomial
homotopy based continuation method. The proposed method guarantees to find all
solution boundaries within a given parameter space up to a chosen level of
discretization, independent of any initial guess. Power system operators can
use this computational tool conveniently to plan the penetration levels of
renewable sources at different buses. We illustrate the proposed method through
simulations on 3-bus and 10-bus power system examples with renewable
generation.Comment: 9 pages, 5 figure
Reduced-Dimensional Reinforcement Learning Control using Singular Perturbation Approximations
We present a set of model-free, reduced-dimensional reinforcement learning
(RL) based optimal control designs for linear time-invariant singularly
perturbed (SP) systems. We first present a state-feedback and output-feedback
based RL control design for a generic SP system with unknown state and input
matrices. We take advantage of the underlying time-scale separation property of
the plant to learn a linear quadratic regulator (LQR) for only its slow
dynamics, thereby saving a significant amount of learning time compared to the
conventional full-dimensional RL controller. We analyze the sub-optimality of
the design using SP approximation theorems and provide sufficient conditions
for closed-loop stability. Thereafter, we extend both designs to clustered
multi-agent consensus networks, where the SP property reflects through
clustering. We develop both centralized and cluster-wise block-decentralized RL
controllers for such networks, in reduced dimensions. We demonstrate the
details of the implementation of these controllers using simulations of
relevant numerical examples and compare them with conventional RL designs to
show the computational benefits of our approach
Exploring the Impact of Wind Penetration on Power System Equilibrium Using a Numerical Continuation Approach
In this paper we investigate how the equilibrium characteristics of
conventional power systems may change with an increase in wind penetration. We
first derive a differential-algebraic model of a power system network
consisting of synchronous generators, loads and a wind power plant modeled by a
wind turbine and a doubly-fed induction generator (DFIG). The models of these
three components are coupled via nonlinear power flow equations. In contrast to
the traditional approach for solving the power flows via iterative methods that
often lead to only local solutions, we apply a recently developed
parameter-homotopy based numerical continuation algorithm to compute all
possible solutions. The method solves the power flow equations over multiple
values of the wind penetration level with far less computational effort instead
of solving them at each value individually. We observe that depending on the
penetration limit and the setpoint value for the magnitude of the wind bus
voltage, the system may exhibit several undesired or even unstable equilibria.
We illustrate these results through a detailed simulation of a 5-machine power
system model with wind injection, and highlight how the solutions may be
helpful for small-signal stability assessment.Comment: 7 pages, 14 figures. Submitted to a Special Session of American
Control Conference to be held in Palmer House Hilton, Chicago, IL, USA, in
July 201
Game-Theoretic Multi-Agent Control and Network Cost Allocation under Communication Constraints
Multi-agent networked linear dynamic systems have attracted attention of
researchers in power systems, intelligent transportation, and industrial
automation. The agents might cooperatively optimize a global performance
objective, resulting in social optimization, or try to satisfy their own
selfish objectives using a noncooperative differential game. However, in these
solutions, large volumes of data must be sent from system states to possibly
distant control inputs, thus resulting in high cost of the underlying
communication network. To enable economically-viable communication, a
game-theoretic framework is proposed under the \textit{communication cost}, or
\textit{sparsity}, constraint, given by the number of communicating
state/control input pairs. As this constraint tightens, the system transitions
from dense to sparse communication, providing the trade-off between dynamic
system performance and information exchange. Moreover, using the proposed
sparsity-constrained distributed social optimization and noncooperative game
algorithms, we develop a method to allocate the costs of the communication
infrastructure fairly and according to the agents' diverse needs for feedback
and cooperation. Numerical results illustrate utilization of the proposed
algorithms to enable and ensure economic fairness of wide-area control among
power companies
A New Cyber-Secure Countermeasure for LTI systems under DoS attacks
This paper presents a new counter-measure to mitigate denial-of-service
cyber-attacks in linear time-invariant (LTI) systems. We first design a sparse
linear quadratic regulator (LQR) optimal controller for a given LTI plant and
evaluate the priority of the feedback communication links in terms of the loss
of closed-loop performance when the corresponding block of the feedback gain
matrix is removed. An attacker may know about this priority ordering, and
thereby attack the links with the highest priority. To prevent this, we present
a message rerouting strategy by which the states that are scheduled to be
transmitted through the high priority links can be rerouted through lower
priority ones in case the former get attacked. Since the attacked link is not
available for service, and the states of the low priority links can no longer
be accommodated either, we run a structured control algorithm
to determine the post-attack optimal feedback gains. We illustrate various
aspects of the proposed algorithms by simulations
Co-Design of Delays and Sparse Controllers for Bandwidth-Constrained Cyber-Physical Systems
We address the problem of sparsity-promoting optimal control of
cyber-physical systems with feedback delays. The delays are categorized into
two classes - namely, intra-layer delay, and inter-layer delay between the
cyber and the physical layers. Our objective is to minimize the H2-norm of the
closed-loop system by designing an optimal combination of these two delays
along with a sparse state-feedback controller, while respecting a given
bandwidth constraint. We propose a two-loop optimization algorithm for this.
The inner loop, based on alternating directions method of multipliers (ADMM),
handles the conflicting directions of decreasing H2-norm and increasing
sparsity of the controller. The outer loop comprises of semidefinite program
(SDP)-based relaxations of non-convex inequalities necessary for stable
co-design of the delays with the controller. We illustrate this algorithm using
simulations that highlight various aspects of how delays and sparsity impact
the stability and \mc{H}_2 performance of a LTI system
Control Inversion: A Clustering-Based Method for Distributed Wide-Area Control of Power Systems
Wide-area control (WAC) has been shown to be an effective tool for damping
low-frequency oscillations in power systems. In the current state of art, WAC
is challenged by two main factors - namely, scalability of design and
complexity of implementation. In this paper we present a control design called
control inversion that bypasses both of these challenges using the idea of
clustering. The basic philosophy behind this method is to project the original
power system model into a lower-dimensional state-space through clustering and
aggregation of generator states, and then designing an LQR controller for the
lower-dimensional model. This controller is finally projected back to the
original coordinates for wide-area implementation. The main problem is,
therefore, posed as finding the projection which best matches the closed-loop
performance of the WAC controller with that of a reference LQR controller for
damping low-frequency oscillations. We verify the effectiveness of the proposed
design using the NPCC 48-machine power system model.Comment: Submitted to IEEE Transactions on Control of Network System