Ying Jun Zhang

Liping Qian, Ying Jun Zhang, Jianwei Huang

Achieving weighted throughput maximization (WTM) through power control has been a long standing open problem in interference-limited wireless networks. The complicated coupling between the mutual interferences of links gives rise to a non-convex optimization problem. Previous work has considered the WTM problem in the high signal to interference-and-noise ratio (SINR) regime, where the problem can be approximated and transformed into a convex optimization problem through proper change of variables. In the general SINR regime, however, the approximation and transformation approach does not work. This paper proposes an algorithm, MAPEL, which globally converges to a global optimal solution of the WTM problem in the general SINR regime. The MAPEL algorithm is designed based on three key observations of the WTM problem: (1) the objective function is monotonically increasing in SINR, (2) the objective function can be transformed into a product of exponentiated linear fraction functions, and (3) the feasible set of the equivalent transformed problem is always normal although not necessarily convex. The MAPLE algorithm finds the desired optimal power control solution by constructing a series of polyblocks that approximate the feasible SINR region in increasing precision. Furthermore, by tuning the approximation factor in MAPEL, we could engineer a desirable tradeoff between optimality and convergence time. MAPEL provides an important benchmark for performance evaluation of other heuristic algorithms targeting the same problem. With the help of MAPEL, we evaluate the performance of several respective algorithms through extensive simulations.

Wei Yuan, Jianwei Huang, Ying Jun Zhang

This paper considers the problem of charging station pricing and plug-in electric vehicles (PEVs) station selection. When a PEV needs to be charged, it selects a charging station by considering the charging prices, waiting times, and travel distances. Each charging station optimizes its charging price based on the prediction of the PEVs' charging station selection decisions and the other station's pricing decision, in order to maximize its profit. To obtain insights of such a highly coupled system, we consider a one-dimensional system with two competing charging stations and Poisson arriving PEVs. We propose a multi-leader-multi-follower Stackelberg game model, in which the charging stations (leaders) announce their charging prices in Stage I, and the PEVs (followers) make their charging station selections in Stage II. We show that there always exists a unique charging station selection equilibrium in Stage II, and such equilibrium depends on the charging stations' service capacities and the price difference between them. We then characterize the sufficient conditions for the existence and uniqueness of the pricing equilibrium in Stage I. We also develop a low complexity algorithm that efficiently computes the pricing equilibrium and the subgame perfect equilibrium of the two-stage Stackelberg game.

Wanrong Tang, Ying Jun Zhang

With the increasing adoption of plug-in electric vehicles (PEVs), it is critical to develop efficient charging coordination mechanisms that minimize the cost and impact of PEV integration to the power grid. In this paper, we consider the optimal PEV charging scheduling, where the non-causal information about future PEV arrivals is not known in advance, but its statistical information can be estimated. This leads to an "online" charging scheduling problem that is naturally formulated as a finite-horizon dynamic programming with continuous state space and action space. To avoid the prohibitively high complexity of solving such a dynamic programming problem, we provide a Model Predictive Control (MPC) based algorithm with computational complexity $O(T^3)$, where $T$ is the total number of time stages. We rigorously analyze the performance gap between the near-optimal solution of the MPC-based approach and the optimal solution for any distributions of exogenous random variables. Furthermore, our rigorous analysis shows that when the random process describing the arrival of charging demands is first-order periodic, the complexity of proposed algorithm can be reduced to $O(1)$, which is independent of $T$. Extensive simulations show that the proposed online algorithm performs very closely to the optimal online algorithm. The performance gap is smaller than $0.4\%$ in most cases.

Suzhi Bi, Ying Jun Zhang

Smart power grid enables intelligent automation at all levels of power system operation, from electricity generation at power plants to power usage at households. The key enabling factor of an efficient smart grid is its built-in information and communication technology (ICT) that monitors the real-time system operating state and makes control decisions accordingly. As an important building block of the ICT system, power system state estimation is of critical importance to maintain normal operation of the smart grid, which, however, is under mounting threat from potential cyber attacks. In this article, we introduce a graph-based framework for performing cyber-security analysis in power system state estimation. Compared to conventional arithmetic-based security analysis, the graphical characterization of state estimation security provides intuitive visualization of some complex problem structures and enables efficient graphical solution algorithms, which are useful for both defending and attacking the ICT system of smart grid. We also highlight several promising future research directions on graph-based security analysis and its applications in smart power grid.

Suzhi Bi, Ying Jun Zhang

Accurate state estimation is of paramount importance to maintain the power system operating in a secure and efficient state. The recently identified coordinated data injection attacks to meter measurements can bypass the current security system and introduce errors to the state estimates. The conventional wisdom to mitigate such attacks is by securing meter measurements to evade malicious injections. In this paper, we provide a novel alternative to defend against false-data injection attacks using covert power network topological information. By keeping the exact reactance of a set of transmission lines from attackers, no false data injection attack can be launched to compromise any set of state variables. We first investigate from the attackers' perspective the necessary condition to perform injection attack. Based on the arguments, we characterize the optimal protection problem, which protects the state variables with minimum cost, as a well-studied Steiner tree problem in a graph. Besides, we also propose a mixed defending strategy that jointly considers the use of covert topological information and secure meter measurements when either method alone is costly or unable to achieve the protection objective. A mixed integer linear programming (MILP) formulation is introduced to obtain the optimal mixed defending strategy. To tackle the NP-hardness of the problem, a tree pruning-based heuristic is further presented to produce an approximate solution in polynomial time. The advantageous performance of the proposed defending mechanisms is verified in IEEE standard power system testcases.

Suzhi Bi, Xiaojun Yuan, Ying Jun Zhang

Conventionally, secrecy is achieved using cryptographic techniques beyond the physical layer. Recent studies raise the interest of performing encryption within the physical layer by exploiting some unique features of the physical wireless channel. Following this spirit, we present a novel physical layer encryption (PLE) scheme that randomizes the radio signal using a secret key extracted from the wireless channel under the assumption of channel reciprocity. Specifically, we propose to jointly design the encryption function and the secret-key generation method. On one hand, we establish a sufficient and necessary condition for the encryption function to achieve perfect secrecy. Based on that, several candidate encryption functions are proposed and compared. We show that, given the secret key available to the legitimate users, perfect secrecy can be achieved without compromising the capability of the communication channel. On the other hand, we study the practical design of the secret-key generation method based on the channel reciprocity. We show that, by introducing marginal system overhead, the key agreement between the legitimate users can be done with a high success probability. The performance advantages of the proposed PLE method is verified through comparisons against other existing PLE methods.