Engineering topics

Dvijotham, Krishnamurthy

Publications and source records attributed to Dvijotham, Krishnamurthy.

6 records

DOE OSTI2018

A Framework for Robust Long-Term Voltage Stability of Distribution Systems

Power injection uncertainties in distribution power grids, which are mostly induced by aggressive introduction of intermittent renewable sources, may drive the system away from normal operating regimes and potentially lead to the loss of long-term voltage stability (LTVS). Naturally, there is an ever increasing need for a tool for assessing the LTVS of a distribution system. This paper presents a fast and reliable tool for constructing inner approximations of LTVS regions in multidimensional injection space such that every point in our constructed region is guaranteed to be solvable. Numerical simulations demonstrate that our approach outperforms all existing inner approximation methods in most cases. Furthermore, the constructed regions are shown to cover substantial fractions of the true voltage stability region. In conclusion, the paper will later discuss a number of important applications of the proposed technique, including fast screening for viable injection changes, constructing an effective solvability index and rigorously certified loadability limits.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2018

Constructing Convex Inner Approximations of Steady-State Security Regions

Here, we propose a scalable optimization framework for estimating convex inner approximations of the steady-state security sets. The framework is based on Brouwer fixed point theorem applied to a fixed-point form of the power flow equations. It establishes a certificate for the self-mapping of a polytope region constructed around a given feasible operating point. This certificate is based on the explicit bounds on the nonlinear terms that hold within the self-mapped polytope. The shape of the polytope is adapted to find the largest approximation of the steady-state security region. While the corresponding optimization problem is nonlinear and non-convex, every feasible solution found by local search defines a valid inner approximation. The number of variables scales linearly with the system size, and the general framework can naturally be applied to other nonlinear equations with affine dependence on inputs. Test cases, with the system sizes up to 1354 buses, are used to illustrate the scalability of the approach. The results show that the approximated regions are not unreasonably conservative and that they cover substantial fractions of the true steady-state security regions for most medium-sized test cases.

42 ENGINEERING↗

DOE OSTI2018

Integration of Retail and Wholesale Markets: Modeling Framework and Stability Analysis

As power systems cope with increasing amounts of renewable generation, there is an increasing need to engage flexible demand-side resources and distributed energy resources (DERs) into power systems operations. However engagine millions of DERs in a reliable manner into power systems operations can be a challenging problem. Retail markets can facilitate this by providing a platform to aggregate the flexibility of DERs and bid the aggregate flexibility into wholesale markets. However, unlike generators (which can typically be modeled accurately with capacity constraints and ramping limits), most flexible loads have physical dynamics (like air conditioners) that couples their flexibility over time. This coupling could have unintended undesirable consequences (for example, instability and oscillations in prices and other physical quantities). In this paper, we propose a simple model to capture evolution of load flexibility over time and analyze stability of the interconnection between wholesale and retail electricity markets. We prove that under a natural model of flexibility evolution (assuming a constant base load), oscillations cannot occur and prices converge to a unique equilibrium model quickly.

Ramachandran, Thiagarajan↗

DOE OSTI2017

Real-Time Optimal Power Flow

Future power networks are expected to incorporate a large number of distributed energy resources, which introduce randomness and fluctuations as well as fast control capabilities. But traditional optimal power flow methods are only appropriate for applications that operate on a slow timescale. In this paper, we build on recent work to develop a real-time algorithm for AC optimal power flow, based on quasi-Newton methods. The algorithm uses second-order information to provide suboptimal solutions on a fast timescale, and can be shown to track the optimal power flow solution when the estimated second-order information is sufficiently accurate. We also give a specific implementation based on L-BFGS-B method, and show by simulation that the proposed algorithm has good performance and is computationally efficient.

Tang, Yujie↗

DOE OSTI2017

Integration of wholesale and retail electricity markets: Modeling and stability analysis

The main contribution of this report is to develop a theoretical model of the interaction between retail and wholesale markets and to analyze properties of this dynamical model. The behavior by the flexible loads, when combined with interaction of the retail market with the wholesale market, creates a dynamical system. It is then of interest to understand the behavior of this dynamical system. This analysis will be useful in determining the impact of the market architecture on price volatility, generator dispatch, congestion in the transmission system, etc.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2016

Graphical models for optimal power flow

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 tree-structured graphical model where the nodal variables are low-dimensional vectors. We adapt the standard dynamic programming algorithm for inference over a tree-structured graphical model to the OPF problem. Combining this with an interval discretization of the nodal variables, we develop an approximation algorithm for the OPF problem. Further, we use techniques from constraint programming (CP) to perform interval computations and adaptive bound propagation to obtain practically efficient algorithms. Compared to previous algorithms that solve OPF with optimality guarantees using convex relaxations, our approach is able to work for arbitrary tree-structured distribution networks and handle mixed-integer optimization problems. Further, it can be implemented in a distributed message-passing fashion that is scalable and is suitable for “smart grid” applications like control of distributed energy resources. In conclusion, numerical evaluations on several benchmark networks show that practical OPF problems can be solved effectively using this approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗