# Sidhant Misra's research while affiliated with Los Alamos National Laboratory and other places

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## Publications (74)

A prominent challenge to the safe and optimal operation of the modern power grid arises due to growing uncertainties in loads and renewables. Stochastic optimal power flow (SOPF) formulations provide a mechanism to handle these uncertainties by computing dispatch decisions and control policies that maintain feasibility under uncertainty. Most SOPF...

Non-convexities induced by the non-linear power flow equations challenge solution algorithms for many power system optimization and control problems. Linear approximations are often used to address these challenges by trading off modeling accuracy for tractability. The accuracy of a power flow linearization depends on the characteristics of the pow...

Stochastic fluctuations in power injections from distributed energy resources (DERs) combined with load variability can cause constraint violations (e.g., exceeded voltage limits) in electric distribution systems. To monitor grid operations, sensors are placed to measure important quantities such as the voltage magnitudes. In this paper, we conside...

Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of much debate. Thus far, experimental benchmarking studies have indicated that quantum annealing hardware does not provide an irrefutable performance gain over state-of-the-art optimization methods. However, as this hardware conti...

A prominent challenge to the safe and optimal operation of the modern power grid arises due to growing uncertainties in loads and renewables. Stochastic optimal power flow (SOPF) formulations provide a mechanism to handle these uncertainties by computing dispatch decisions and control policies that maintain feasibility under uncertainty. Most SOPF...

Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for learning graphical models with least amount of data remains an active research topic. Reconstruction of graphical models that describe the statistics of discrete variables is a particularly challenging prob...

Estimating the structure of physical flow networks such as power grids is critical to secure delivery of energy. This paper discusses statistical structure estimation in power grids in the under-excited regime, where a subset of internal nodes have zero injection fluctuations. Prior estimation algorithms based on nodal voltages fail for such grids...

In many engineered systems, optimization is used for decision making at time scales ranging from real-time operation to long-term planning. This process often involves solving similar optimization problems over and over again with slightly modified input parameters, often under tight latency requirements. We consider the problem of using the inform...

The usual setting for learning the structure and parameters of a graphical model assumes the availability of independent samples produced from the corresponding multivariate probability distribution. However, for many models the mixing time of the respective Markov chain can be very large and i.i.d. samples may not be obtained. We study the problem...

We address the problem of learning of continuous exponential family distributions with unbounded support. While a lot of progress has been made on learning of Gaussian graphical models, we are still lacking scalable algorithms for reconstructing general continuous exponential families modeling higher-order moments of the data beyond the mean and th...

We examine the problem of optimal transport capacity expansion planning for a gas pipeline network to service the growing demand of gas-fired power plants that are increasingly used to provide base load, flexibility, and reserve generation for bulk electric system. The aim is to determine the minimal cost set of additional pipes and gas compressors...

This paper presents novel formulations and algorithms for
$N-k$
interdiction problem in transmission networks. In particular, it formulates spatial and topological resource constraints on attackers for
$N-k$
interdiction problems and illustrates the formulation with two new classes of
$N-k$
attacks: (i) Spatial
$N-k$
attacks where the attac...

Growing uncertainty from renewable energy integration and distributed energy resources motivate the need for advanced tools to quantify the effect of uncertainty and assess the risks it poses to secure system operation. Polynomial chaos expansion (PCE) has been recently proposed as a tool for uncertainty quantification in power systems. The method...

In traditional power system operations real-time control policies are based on simple control policies such as automatic generation control and/or local voltage control. Although these simple policies have worked well in the past, the increased variability associated with higher penetrations of renewable energy strengthens the case for more general...

There is an emerging need for efficient solutions to stochastic AC Optimal Power Flow (AC-OPF) to ensure optimal and reliable grid operations in the presence of increasing demand and generation uncertainty. This paper presents a highly scalable data-driven algorithm for stochastic AC-OPF that has extremely low sample requirement. The novelty behind...

In many parts of the world, electric power systems have seen a significant shift toward generation from renewable energy and natural gas. Because of their ability to flexibly adjust power generation in real time, gas-fired power plants are frequently seen as the perfect partner for variable renewable generation. However, this reliance on gas genera...

We derive conditions for monotonicity properties that characterize general flows of a commodity over a network, where the flow is described by potential and flow dynamics on the edges, as well as potential continuity and the Kirchhoff-Neumann mass balance requirements at nodes. The transported commodity may be injected or withdrawn at any of the ne...

We derive conditions for monotonicity properties that characterize general flows of a commodity over a network, where the flow is described by potential and flow dynamics on the edges, as well as potential continuity and Kirchhoff-Neumann mass balance requirements at nodes. The transported commodity may be injected or withdrawn at any of the networ...

In many parts of the world, electric power systems have seen a significant shift towards generation from renewable energy and natural gas. Because of their ability to flexibly adjust power generation in real time, gas-fired power plants are frequently seen as the perfect partner for variable renewable generation. However, this reliance on gas gener...

Graphical models are widely used in science to represent joint probability distributions with an underlying conditional dependence structure. The inverse problem of learning a discrete graphical model given i.i.d samples from its joint distribution can be solved with near-optimal sample complexity using a convex optimization method known as General...

Diffusion and Seeding in Random Networks

Estimating the structure of physical flow networks such as power grids is critical to secure delivery of energy. This paper discusses statistical structure estimation in power grids in the "under-excited" regime, where a subset of internal nodes do not have external injection. Prior estimation algorithms based on nodal potentials or voltages fail i...

There is an emerging need for efficient solutions to stochastic AC Optimal Power Flow (OPF) to ensure optimal and reliable grid operations in the presence of increasing demand and generation uncertainty. This paper presents a highly scalable data-driven algorithm for stochastic AC-OPF that has extremely low sample requirement. The novelty behind th...

Growing uncertainty from renewable energy integration and distributed energy resources motivate the need for advanced tools to quantify the effect of uncertainty and assess the risks it poses to secure system operation. Polynomial chaos expansion (PCE) has been recently proposed as a tool for uncertainty quantification in power systems. The method...

As renewable wind energy penetration rates continue to increase, one of the major challenges facing grid operators is the question of how to control transmission grids in a reliable and a cost-efficient manner. The stochastic nature of wind forces an alteration of traditional methods for solving day-ahead and look-ahead unit commitment and dispatch...

As the share of renewables in the grid increases, the operation of power systems becomes more challenging. The present paper proposes a method to formulate and solve chance-constrained optimal power flow while explicitly considering the full nonlinear AC power flow equations and stochastic uncertainties. We use polynomial chaos expansion to model t...

This paper presents novel formulations and algorithms for the $N$-$k$ interdiction problem in transmission networks. In particular, it models two new classes of $N$-$k$ attacks: (i) Spatial $N$-$k$ attacks where the attack is constrained to be within a specified distance of a bus chosen by an attacker and (ii) Topological $N$-$k$ attacks where the...

The optimal power flow is an optimization problem used in power systems operational planning to maximize economic efficiency while satisfying demand and maintaining safety margins. Due to uncertainty and variability in renewable energy generation and demand, the optimal solution needs to be updated in response to observed uncertainty realizations o...

Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for learning graphical models with least amount of data remains an active research topic. Reconstruction of graphical models that describe the statistics of discrete variables is a particularly challenging prob...

This article develops a strengthened convex quadratic convex (QC) relaxation of the AC Optimal Power Flow (AC-OPF) problem and presents an optimization-based bound-tightening (OBBT) algorithm to compute tight, feasible bounds on the voltage magnitude variables for each bus and the phase angle difference variables for each branch in the network. The...

Word of Mouth (WoM) is known as a powerful marketing force, as numerous empirical studies reveal that consumers' purchasing decisions are based on the advice of those in their social networks rather than on direct advertising. A recent international survey by Nielsen reports that 92% of consumers around the world count on recommendations from frien...

We review new ideas and the first results from the application of the graphical models approach, which originated from statistical physics, information theory, computer science, and machine learning, to optimization problems of network flow type with additional constraints related to the physics of the flow. We illustrate the general concepts on a...

Many engineered systems, such as energy and transportation infrastructures, are networks governed by non-linear physical laws. A primary challenge for operators of these networks is to achieve optimal utilization while maintaining safety and feasibility, especially in the face of uncertainty regarding the system model. To address this problem, we f...

In many engineered systems, optimization is used for decision making at time-scales ranging from real-time operation to long-term planning. This process often involves solving similar optimization problems over and over again with slightly modified input parameters, often under stringent time requirements. We consider the problem of using the infor...

The optimal power flow problem plays an important role in the market clearing and operation of electric power systems. However, with increasing uncertainty from renewable energy operation, the optimal operating point of the system changes more significantly in real-time. In this paper, we aim at developing control policies that are able to track th...

This paper outlines an optimization framework for choosing fast and reliable control actions in a transmission grid emergency situation. We consider contractual load shedding and generation re-dispatch as exemplary emergency actions. To achieve computational efficiency and scalability, this novel formulation of the robust corrective action optimiza...

As renewable wind energy penetration rates continue to increase, one of the major challenges facing grid operators is the question of how to control transmission grids in a reliable and a cost-efficient manner. The stochastic nature of wind forces an alteration of traditional methods for solving day-ahead and look-ahead unit commitment and dispatch...

We study the problem of reconstructing the graph of a sparse Gaussian Graphical Model from independent observations, which is equivalent to finding non-zero elements of an inverse covariance matrix. For a model of size $p$ and maximum degree $d$, information theoretic lower bounds established in prior works require that the number of samples needed...

In this manuscript we review new ideas and first results on application of the Graphical Models approach, originated from Statistical Physics, Information Theory, Computer Science and Machine Learning, to optimization problems of network flow type with additional constraints related to the physics of the flow. We illustrate the general concepts on...

Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In this paper, we formulate the optimal power flow problem over tree networks as an inference problem over a tre...

Reconstruction of structure and parameters of a graphical model from binary samples is a problem of practical importance in a variety of disciplines, ranging from statistical physics and computational biology to image processing and machine learning. The focus of the research community shifted towards developing universal reconstruction algorithms...

Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In this paper, we formulate the optimal power flow problem over tree networks as an inference problem over a tre...

Higher shares of electricity generation from renewable energy sources and market liberalization is increasing uncertainty in power systems operation. At the same time, operation is becoming more flexible with improved control systems and new technology such as phase shifting transformers (PSTs) and high voltage direct current connections (HVDC). Pr...

Many products and innovations become well-known and widely adopted through the social interactions of individuals in a population. The Bass diffusion model has been widely used to model the temporal evolution of adoption in such social systems. In the model, the likelihood of a new adoption is proportional to the number of previous adopters, implic...

Over the past years, the share of electricity production from wind power plants has increased to significant levels in several power systems across Europe and the United States. In order to cope with the fluctuating and partially unpredictable nature of renewable energy sources, transmission system operators (TSOs) have responded by requiring wind...

We derive a monotonicity property for general, transient flows of a commodity transferred throughout a network, where the flow is characterized by density and mass flux dynamics on the edges with density continuity and mass balance conditions at the nodes. The dynamics on each edge are represented by a general system of partial differential equatio...

We consider the problem of learning the underlying graph of an unknown Ising model on p spins from a collection of i.i.d. samples generated from the model. We suggest a new estimator that is computationally efficient and requires a number of samples that is near-optimal with respect to previously established information-theoretic lower-bound. Our s...

We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past. We establish that when the underlying matrix has rank $r=1$, has positive bounded entries, and the graph $\mathcal{G}$ underlying the revealed ent...

As renewable wind energy penetration rates continue to increase, one of the major challenges facing grid operators is the question of how to control transmission grids in a reliable and a cost-efficient manner. The stochastic nature of wind forces an alteration of traditional methods for solving day-ahead and look-ahead unit commitment and dispatch...

We derive conditions for the propagation of monotone ordering properties for
a class of nonlinear parabolic partial differential equation (PDE) systems on
metric graphs. For such systems, PDE equations with a general nonlinear
dissipation term define evolution on each edge, and balance laws create
Kirchhoff-Neumann boundary conditions at the vertic...

Over the past years, the share of electricity production from wind power
plants has increased to significant levels in several power systems across
Europe and the United States. In order to cope with the fluctuating and
partially unpredictable nature of renewable energy sources, transmission system
operators (TSOs) have responded by increasing thei...

We study the problem of the existence of a giant component in a random multipartite graph. We consider a random multipartite graph with p parts generated according to a given degree sequence [Formula: see text] which denotes the number of vertices in part i of the multipartite graph with degree given by the vector d in an n-node graph. We assume th...

We derive a monotonicity property for general, transient flows of a commodity
transferred throughout a network, where the flow is characterized by density
and mass flux dynamics on the edges with density continuity and mass balance
conditions at the nodes. The dynamics on each edge are represented by a general
system of partial differential equatio...

Model-based compressed sensing refers to compressed sensing with extra structure about the underlying sparse signal known a priori. Recent work has demonstrated that both for deterministic and probabilistic models imposed on the signal, this extra information can be successfully exploited to enhance recovery performance. In particular, weighted '1-...

The development of hydraulic fracturing technology has dramatically increased
the supply and lowered the cost of natural gas in the United States, driving an
expansion of natural gas-fired generation capacity in several electrical
inter-connections. Gas-fired generators have the capability to ramp quickly and
are often utilized by grid operators to...

We consider balanced flows in a natural gas transmission network and discuss
computationally hard problems such as establishing if solution of the
underlying nonlinear gas flow equations exists, if it is unique, and finding
the solution. Particular topologies, e.g. trees, are known to be easy to solve
based on a variational description of the gas f...

We consider a dissipative flow network that obeys the standard linear nodal
flow conservation, and where flows on edges are driven by potential difference
between adjacent nodes. We show that in the case when the flow is a
monotonically increasing function of the potential difference, solution of the
network flow equations is unique and can be equi...

We consider general, steady, balanced flows of a commodity over a network
where an instance of the network flow is characterized by edge flows and nodal
potentials. Edge flows in and out of a node are assumed to be conserved, thus
representing standard network flow relations. The remaining freedom in the flow
distribution over the network is constr...

Due to the increasing amount of electricity generated from renewable sources,
uncertainty in power system operation will grow. This has implications for
tools such as Optimal Power Flow (OPF), an optimization problem widely used in
power system operations and planning, which should be adjusted to account for
this uncertainty. One way to handle the...

Natural gas transmission pipelines are complex systems whose flow
characteristics are governed by challenging non-linear physical behavior. These
pipelines extend over hundreds and even thousands of miles with gas injected
into the system at a constant rate. A series of compressors are distributed
along the pipeline to boost the gas pressure to mai...

The property of spatial mixing and strong spatial mixing in spin systems has
been of interest because of its implications on uniqueness of Gibbs measures on
infinite graphs and efficient approximation of counting problems that are
otherwise known to be #P hard. In the context of coloring, strong spatial
mixing has been established for regular trees...

We study the problem of the existence of a giant component in a random
multipartite graph. We consider a random multipartite graph with $p$ parts
generated according to a given degree sequence $n_i^{\mathbf{d}}(n)$ which
denotes the number of vertices in part $i$ of the multipartite graph with
degree given by the vector $\mathbf{d}$. We assume that...

Model-based compressed sensing refers to compressed sensing with extra
structure about the underlying sparse signal known a priori. Recent work has
demonstrated that both for deterministic and probabilistic models imposed on
the signal, this extra information can be successfully exploited to enhance
recovery performance. In particular, weighted $\e...

## Citations

... In [77], the relation between the LVDS feeder and the hosting capacity (HC) is mapped using a linear regression function based on the features of the feeder. Machine learning tools like neural networks are recently used for minimizing the cost of generation under uncertainties as in [78]. In [79], a deep neural network (DNN) is used to approximate the power flow calculation, making a surrogate model to reduce computational effort of MC based methods. ...

... Due to the nonlinear nature of the AC power flow equations, computing a globally optimal solution is challenging. We utilize conservative linear approximations of the power flow equations to convert the lower-level problem to a linear program [10]. This bilevel problem can be reformulated to a single-level problem using the Karush-Kuhn-Tucker (KKT) conditions with binary variables via a big-M formulation [11]- [13]. ...

... Pearl [1988], Lauritzen [1996], Jordan [2004], Koller and Friedman [2009] for an introduction to graphical models, their uses, and associated inference algorithms, and see e.g. Chow and Liu [1968], Chow and Wagner [1973], Narasimhan and Bilmes [2004], Ravikumar et al. [2010], Tan et al. [2011], Jalali et al. [2011], Santhanam and Wainwright [2012], Bresler [2015], Vuffray et al. [2016], 1 Klivans and Meka [2017], Hamilton et al. [2017], , Kandiros et al. [2021], Daskalakis and Pan [2021], Bhattacharyya et al. [2021], Vuffray et al. [2022] and the references in the previous paragraph for some classical work and some recent theoretical progress on learning and testing graphical models as well as other types of statistical inference with them. ...

... Further, these methods also extend to meshed grids with ZIBs (zero-injection buses), where the voltage covariance matrix is non-invertible. In that case, reference [69] first identifies ZIBs and their neighbors using flow conservation-based voltage regression, and then, discovers the remaining topology using properties of the inverse voltage covariance at non-ZIBs. ...

... Reinforcement learning [41] has been used in [29] to solve a diverse range of combinatorial problems defined over graphs where a neural network is trained to learn a heuristic algorithm which suggests the next node to visit contributing towards the optimal solution. In [39], a statistical approach is developed to uncover the set of optimal active constraints-i.e., constraints that hold with equality in the optimal solution-for parametric optimisation problems. The algorithm needs to be fine-tuned for every problem and is limited to continuous optimisation problems-the paper claims that it can capture mixed-integer and non-convex problem but, no numerical evidence has been reported supporting that claim. ...

... The natural gas transmission networks expanded with time due to the addition of the new demand centers and the enhanced load at the existing ones. The flow dynamics of natural gas through a pipeline are very complex due to the nonlinear relationship between the natural gas pressure and flow [2]. Further, the combinatorial nature of pipeline diameters makes the problem mixed-integer in nature [3]. ...

Reference: Reinforcement of a Gas Transmission Network

... Analytical methods like Polynomial Chaos Expansion (PCE) expansion have gained increasing interest in PPF calculations. It has been shown that PCE outweighs other analytical methods used for PPF calculation as this method preserves the non-linearity of the power flow equation [16]. In this thesis, different PPF for LVDS hosting capacity (HC) calculations are compared, and PCE is proposed as a viable solution to reduce the computational cost compared to alternative probabilistic methods such as MC methods. ...

... Several studies have established uniqueness of solutions for boundary value problems on physical flow networks, including for compressible [18], [30], [31] and incompressible fluid flow [32] with actuators. Each of these proofs considers transport of a homogeneous fluid, and relies on the monotonicity of the flow equation on each individual edge. ...

... PCE methods propagate uncertainty distributions through non-linear equations by decomposing onto a set of non-linear basis functions, resulting in a hierarchy of increasingly accurate, but more computationally challenging problems. PCE was first applied to power flow problems [86,195] and then to chance-constrained optimal power flow problems [80], with modeling, computational, and other improvements subsequently developed in [35,[196][197][198]. Despite these improvements, PCE methods remain computationally challenging. ...

... Instead, we assume that the linear relation A 0 x 0 + a A a x a = b holds inexactly. Specifically, motivated by data-driven approaches for power flow models [28], we assume that there exists a random variable ξ with bounded support such that ...