A pinboard by
Yu Zhang

Postdoc, Lawrence Berkeley National Laboratory


My research focuses on advancing the design, modeling, and analysis of electric power systems

To meet the urgent need of renovating the aging infrastructure, power systems are undergoing dramatic transformations due to high penetration of renewable generation, large numbers of flexible loads, along with the growing deployment of automated two-way communications. Consequently, we are facing grand challenges in the form of increased uncertainty and cybersecurity threats at multiple time scales. In this context, my research thrusts focus on advancing the design, modeling, and optimization of electric power grids by developing novel computational frameworks and efficient algorithmic solutions. Capitalizing on contemporary techniques from optimization theory, machine learning, and signal processing, I have been working on a number of research projects for improving the efficiency and resilience of the future power grids. The novelty and merits of my research are outlined as follows, which includes the topics of grid learning, monitoring, and management.

(1) Big Energy Data Analytics I leveraged state-of-the-art machine learning techniques to forecast electricity prices and wind power generation. By uniquely exploiting domain knowledge, novel approaches were developed to capture the underlying spatio-temporal correlation. Real-data numerical tests corroborated their superior prediction accuracy of the proposed approaches.

(2) Enhanced Power Grid Monitoring Power system state estimation (SE) constitutes the core of the monitoring module that provides real-time system conditions. Given a set of noisy measurements including power injections and line flows, the task is to estimate the voltage magnitude and phase angle at every bus of the network. I recently developed efficient convexification frameworks for the SE. My main contribution lies in the strong theoretical results that quantify the quality of the obtained suboptimal solution.

(3) Energy Management for Sustainable Power Grids A focused endeavor is still required to make technological breakthroughs in energy management problems. In this context, I developed decentralized economic dispatch for grid-connected microgrids with high-penetration renewables and demand-side management. To address the major challenge of maintaining power supply-demand balance, the novel optimization framework involves the actual and committed wind power. The resulting problem, which minimizes the microgrid net cost, was optimized in a distributed fashion by all local controllers.


Alternative Linear and Second-order Cone Approximation Approaches for Polynomial Optimization

Abstract: In theory, hierarchies of semidefinite programming (SDP) relaxations based on sum of squares (SOS) polynomials have been shown to provide arbitrarily close approximations to general polynomial optimization problems (POP). However, due to the computational challenge of solving SDPs, it becomes difficult to use SDP hierarchies for large-scale problems. To address this, hierarchies of second-order cone programming (SOCP) relaxations resulting from a restriction of the SOS polynomial condition have been recently proposed to approximate POPs. Here, we consider alternative ways to use these SOCP restriction of the SOS condition. In particular, we show that SOCP hierarchies can be effectively used to strengthen hierarchies of linear programming (LP) relaxations for POPs. Specifically, we show that this solution approach is substantially more effective in finding solutions of certain POPs for which the more common hierarchies of SDP relaxations are known to perform poorly. Also, we use hierarchies of LP relaxations for POPs that allows us to show that the SOCP approach can be used to obtain hierarchies of SOCPs that converge to the optimal value of the POP when its feasible set is compact. Additionally, we show that the SOCP approach can be used to address the solution of the fundamental alternating current optimal power flow (ACOPF) problem. In particular, we show that the first-order SOCP hierarchy obtained by weakening the more common hierarchy of SDP relaxations for this problem is equivalent to solving the conic dual of the SOCP approximations recently proposed to address the ACOPF problem. Through out the article, we illustrate our findings with relevant experimental results. In the case of the ACOPF problem, we use well-known instances of the problem that appear in the related literature.

Pub.: 22 Oct '15, Pinned: 30 Jun '17

Strong SOCP Relaxations for the Optimal Power Flow Problem

Abstract: This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem. These three relaxations are incomparable to each other and two of them are incomparable to the standard SDP relaxation of OPF. Extensive computational experiments show that these relaxations have numerous advantages over existing convex relaxations in the literature: (i) their solution quality is extremely close to that of the SDP relaxations (the best one is within 99.96% of the SDP relaxation on average for all the IEEE test cases) and consistently outperforms previously proposed convex quadratic relaxations of the OPF problem, (ii) the solutions from the strong SOCP relaxations can be directly used as a warm start in a local solver such as IPOPT to obtain a high quality feasible OPF solution, and (iii) in terms of computation times, the strong SOCP relaxations can be solved an order of magnitude faster than standard SDP relaxations. For example, one of the proposed SOCP relaxations together with IPOPT produces a feasible solution for the largest instance in the IEEE test cases (the 3375-bus system) and also certifies that this solution is within 0.13% of global optimality, all this computed within 157.20 seconds on a modest personal computer. Overall, the proposed strong SOCP relaxations provide a practical approach to obtain feasible OPF solutions with extremely good quality within a time framework that is compatible with the real-time operation in the current industry practice.

Pub.: 30 Oct '15, Pinned: 30 Jun '17

Conic Relaxations for Power System State Estimation with Line Measurements

Abstract: This paper deals with the non-convex power system state estimation (PSSE) problem, which plays a central role in the monitoring and operation of electric power networks. Given a set of noisy measurements, PSSE aims at estimating the vector of complex voltages at all buses of the network. This is a challenging task due to the inherent nonlinearity of power flows, for which existing methods lack guaranteed convergence and theoretical analysis. Motivating by these limitations, we propose a novel convexification framework for the PSSE using semidefinite programming (SDP) and second-order cone programming (SOCP) relaxations. We first study a related power flow (PF) problem as the noiseless counterpart, which is cast as a constrained minimization program by adding a suitably designed objective function. We study the performance of the proposed framework in the case where the set of measurements includes: (i) nodal voltage magnitudes, and (ii) branch active power flows over a spanning tree of the network. It is shown that the SDP and SOCP relaxations both recover the true PF solution as long as the voltage angle difference across each line of the network is not too large (e.g., less than 90 degrees for lossless networks). By capitalizing on this result, penalized SDP and SOCP problems are designed to solve the PSSE, where a penalty based on the weighted least absolute value is incorporated for fitting noisy measurements with possible bad data. Strong theoretical results are derived to quantify the optimal solution of the penalized SDP problem, which is shown to possess a dominant rank-one component formed by lifting the true voltage vector. An upper bound on the estimation error is also derived as a function of the noise power, which decreases exponentially fast as the number of measurements increases.

Pub.: 01 Apr '17, Pinned: 30 Jun '17