Standard IEEE Test Cases Research Articles

Stealthy data integrity attack identification in smart grid networks utilizing deep denoising autoencoder

Smart grids arose as the largest cyber-physical systems with the integration of sophisticated control, computing, and state-of-the-art communications. Like all cyber-physical systems, the smart grids are vulnerable to malicious cyber assaults due to their enormous dependency on communication networks. Various machine learning-based schemes are being investigated in the industry and academia to develop robust defense mechanisms to counter cyber assaults. However, the curse of high dimensionality, which increases with the escalating evolution of an electric power system, infringes upon the efficiency of machine learning models employed to detect such assaults. To this end, this paper proposes a deep denoising autoencoder (DAE)-based framework for dimensionality reduction that learns salient feature representation for high-dimensional, multi-variant smart grid measurement data collected from the smart grids. The latent space apprehended by DAE is then fed to binary support vector machine (SVM) to determine the assaulted data. Various standard IEEE test cases are employed in simulations. The results show that the proposed scheme learns more robust features that reveal the nonlinear properties exhibited in the smart grid measurements, further leading to improved detection accuracy of the classifier as compared to existing approaches.

Data-driven stochastic AC-OPF using Gaussian process regression

At present, electricity generation is responsible for more than a quarter of the greenhouse gas emissions in the US. Integrating significant amounts of renewable energy sources into a power grid is probably the most accessible way to reduce carbon emissions from power grids and slow down climate change. Unfortunately, the most accessible renewable power sources, such as wind and solar, are highly intermittent and thus bring a lot of uncertainty to power grid operation and challenge existing optimization and control policies. The chance-constrained (CC) alternating current optimal power flow (AC-OPF) framework finds the minimum cost of generation dispatch, maintaining the power grid operation within security limits with a prescribed probability. Unfortunately, the AC-OPF problem’s chance-constrained extension is non-convex, computationally challenging, and requires knowledge of system parameters and also needs additional assumptions to be made about the behavior of renewable generation probability distribution. Known linear and convex approximations to the above problems, though tractable, are too conservative for operational practice and do not consider uncertainty in system parameters. This paper presents an alternative data-driven approach for solving the stochastic AC-OPF problem, based on Gaussian process regression (GPR) to close this gap. The Gaussian process (GP) approach learns a simple yet non-convex data-driven approximation to the AC power flow equations that can incorporate uncertain inputs. The latter is then used to determine the solution of CC-OPF efficiently, by accounting for both input and parameter uncertainty. The practical efficiency of the proposed approach using different approximations for GP-uncertainty propagation is validated and illustrated using a number of standard IEEE test cases.

Online Probabilistic Power Flow with Tie-line Power Transfer: A Stacked Denoising Auto-Encoders Method

Based on stacked denoising auto-encoders (SDAE) and combined with the Monte-Carlo simulation (MCS) method, this paper proposes a hybrid algorithm (SDAE-Based-PPF, SPPF) for online calculation of probabilistic power flow (PPF) with tie-line power transfer. By incorporating the deep structure and reconstructive strategy of SDAE, this paper extracts high-level features of nonlinear power flow equations, thereby constructing SDAE-based power flow models. Then, the parameters of SDAE-based power flow models, with improved training speed and accuracy, are optimized by mini-batch gradient descent algorithm, momentum learning rate and introduced cross-entropy loss function. The SDAE-based power flow models are developed to approximate power flow equations with unidirectional extracted high-level features, so as to enable non-iterative solvability judgment and calculation of power flow, therefore fast and accurate. Benefiting from the parallelizability, speed and accuracy of SDAE, the proposed SDAE-based power flow models, with unsolved random samples generated by the MCS method, are able to calculate all samples simultaneously, and this enables PPF to be calculated online. Finally, numerical results are implemented on three standard IEEE test cases to verify the effectiveness of proposed SDAE-based power flow models and SPPF method.

Decentralized Low-Rank State Estimation for Power Distribution Systems

This article considers the low-observability state estimation problem in power distribution networks and develops a decentralized state estimation algorithm leveraging the matrix completion methodology. Matrix completion has been shown to be an effective technique in state estimation that exploits the low dimensionality of the power system measurements to recover missing information. This technique can utilize an approximate (linear) load flow model, or it can be used with no physical models in a network where no information about the topology or line admittance is available. The direct application of matrix completion algorithms requires solving a semi-definite programming (SDP) problem, which becomes computationally challenging for large networks. We therefore develop a decentralized algorithm that capitalizes on the popular proximal alternating direction method of multipliers (proximal ADMM). The method allows us to distribute the computation among different areas of the network, leading to a scalable algorithm. By doing all computations at individual control areas and only communicating with neighboring areas, the algorithm eliminates the need for data to be sent to a central processing unit and thus increases efficiency and contributes to the goal of autonomous control of distribution networks. We illustrate the advantages of the proposed algorithm numerically using standard IEEE test cases.

TOTAL: Optimal Protection Strategy Against Perfect and Imperfect False Data Injection Attacks on Power Grid Cyber–Physical Systems

This article explores the problem of protection against false data injection attacks (FDIAs) on the power system state estimation. Although many research works have been reported previously to solve the same problem, yet most of them are only for perfect FDIAs. To address the problem reasonably, all related factors influencing the success probability and corresponding attack impact of imperfect FDIAs should also be considered. Based on such considerations, a topology, parameter, accuracy, level (TOTAL) protection strategy considering all corresponding factors is proposed. The TOTAL protection strategy minimizes the attack impact of typical imperfect FDIAs (single measurement attacks) while defending against typical perfect FDIAs (single-state variable attacks). Depending on whether the protection scheme contains phasor measurement units (PMUs), we formulate the meter selection as a linear binary programming or integer programming problem, which can be solved by suitable solvers. The proposed strategy is compared with the existing methods in the literature and evaluated using the standard IEEE test cases.

Workload Transfer Strategy of Urban Neighboring Data Centers With Market Power in Local Electricity Market

This paper investigates how to minimize the operational cost of cloud service provider (CSP) that operates urban neighboring data centers (DCs) in the same electricity market and can conduct workload transfer among DCs. Due to the substantial electricity demand of DCs, their market power which can have impact on the locational marginal prices (LMPs) of the electricity market should be taken into consideration. We formulate a bilinear bilevel problem which regards the CSP as a price maker and explores cost-minimizing workload transfer strategies. The upper level is the operational cost minimization problem of CSP and the lower level corresponds to the economic dispatch problem of independent system operator (ISO) of electricity market which determines the electricity prices. It is challenging to directly solve the bilevel problem with bilinear term in the objective function. Hence, we first reformulate the original problem into a single level problem and then based on the property of the problem we develop a polytope cutting algorithm that attains the global optimal solution. The proposed algorithm solves linear optimizations iteratively by cutting the non-convex polytope feasible set into convex sets. In addition, considering the varying communication environment in practice, we analyze the impact of transfer price uncertainty on total cost of CSP, and show that the expected cost surprisingly decreases with the increasing uncertainty. Simulations based on the standard IEEE test cases show that the cost of CSP is significantly reduced and a win-win result for both the CSP and independent system operator (ISO) is possible.

Optimal placement of electric vehicle charging station for unbalanced radial distribution systems

ABSTRACTTransportation is one of the dominant applications where abundant fossil fuel usage can be experienced across the world. To save the earth from carbon emission and depletion of conventional energy resources, alternate energy sources are to be introduced in transportation which will lead to Electric Vehicles (EV) and Hybrid Electric Vehicles (HEV). The infrastructure of the power system is also adaptable to the changes of electrified transportation. In this research work, a methodology is proposed to find the optimal placement of Electric Vehicle Charging Station (EVCS) along with the optimal capacity of charging stations for Unbalanced Radial Distribution System (URDS) by using Particle Swarm Optimization (PSO). This paper also explains the effect of EVCS placement in RDS w.r.t voltage profile and real power losses. Also, the insertion of EVCS to the power system draws additional power from the electrical grid. To make the system more self-sustainable and reliable, this research work proposes additional distributed generators (DGs) at optimal locations to reduce the impact of EVCS on the system by incorporating it. The proposed methodology is validated with two standard unbalanced IEEE test cases such as IEEE 19 bus and IEEE 25 bus URDS.

Priority-Based Protection Against the Malicious Data Injection Attacks on State Estimation

In the modern age, the Internet of Things forms the basis of all the infrastructures for improving efficiency, reliability, and comfort. As applied to the power system, increasing the penetration of information and communication technologies at the device and process level is enabling devices to communicate with each other, thereby, facilitating wide-area situational awareness of the power grid. Dependence on the communication infrastructure has also made the power grid vulnerable to cyber-intrusions. Cybersecurity of the power system is a huge concern, which must be addressed with topmost priority. Securing all the entry points for cyber-attacks may not be economically feasible; hence, a critical set of sensors must be identified and secured to protect the grid against malicious actors. In this article, we propose a defense strategy to select the most critical measurements for securing the power system operation against false data injection attacks. The proposed approach is compared with the existing methodologies in the literature and validated using standard IEEE test cases.

A Geometric Analysis of Power System Loadability Regions

Understanding the feasible power flow region is of central importance to power system analysis. In this paper, we propose a geometric view of the power system loadability problem. By using rectangular coordinates for complex voltages, we provide an integrated geometric understanding of active and reactive power flow equations on loadability boundaries. Based on such an understanding, we develop a linear programming framework to 1) verify if an operating point is on the loadability boundary, 2) compute the margin of an operating point to the loadability boundary, and 3) calculate a loadability boundary point of any direction. The proposed method is computationally more efficient than existing methods since it does not require solving nonlinear optimization problems or calculating the eigenvalues of the power flow Jacobian. Standard IEEE test cases demonstrate the capability of the new method compared to the current state-of-the-art methods. Understanding the feasible power flow region is of central importance to power system analysis. This paper proposes a geometric view of the power system loadability problem. By using rectangular coordinates for complex voltages, this paper provides an integrated geometric understanding of active and reactive power flow equations on loadability boundaries. Based on such an understanding, this paper develops a linear programming framework to 1) verify if an operating point is on the loadability boundary, 2) compute the margin of an operating point to the loadability boundary, and 3) calculate a loadability boundary point of any direction. The proposed method is computationally more efficient than existing methods since it does not require solving nonlinear optimization problems or calculating the eigenvalues of the power flow Jacobian. Standard IEEE test cases demonstrate the capability of the new method compared to the current state-of-the-art methods.

Impact of Stealthy Attacks on Optimal Power Flow: A Simulink-Driven Formal Analysis

Optimal Power Flow (OPF) is a crucial part of the Energy Management System (EMS) as it determines individual generator outputs that minimize generation cost while satisfying transmission, generation, and system level operating constraints. OPF relies on a core EMS routine, namely state estimation, which computes system states, principally bus voltages/phase angles at the buses. However, state estimation is vulnerable to false data injection attacks in which an adversary can alter certain measurements to corrupt the estimator's solution without being detected. It is also shown that such a stealthy attack on state estimation can increase the OPF cost. However, the impact of stealthy attacks on the economic and secure operation of the system cannot be comprehensively analyzed due to the very large size of the attack space. In this paper, we present a hybrid framework that combines formal analytics with Simulink-based system modeling to investigate the feasibility of stealthy attacks and their influence on OPF in a time-efficient manner. The proposed approach is illustrated on synthetic case studies demonstrating the impact of stealthy attacks in different attack scenarios. We also evaluate the impact analysis time by running experiments on standard IEEE test cases and the results show significant scalability of the framework.

Holomorphic Embedding Based Continuation Method for Identifying Multiple Power Flow Solutions

In this paper, we propose an efficient continuation method for locating multiple power flow solutions. We adopt the holomorphic embedding technique to represent solution curves as holomorphic functions in the complex plane. The holomorphicity, which provides global information of the curve at any regular point, enables large step sizes in the path-following procedure such that non-singular curve segments can be traversed with very few steps. When approaching singular points, we switch to the traditional predictor-corrector routine to pass through them and switch back afterward to the holomorphic embedding routine. We also propose a warm starter when switching to the predictor-corrector routine, i.e. a large initial step size based on the poles of the Pad\'{e} approximation of the derived holomorphic function, since these poles reveal the locations of singularities on the curve. Numerical analysis and experiments on many standard IEEE test cases are presented, along with the comparison to the full predictor-corrector routine, confirming the efficiency of the method.

An Integrated Gaussian Process Modeling Framework for Residential Load Prediction

While adding new capabilities, the distributed energy resource (DER) proliferation raises great concern about challenges such as dynamic fluctuations of voltages. For robust and efficient operational planning purposes, we propose an integrated Gaussian process (IGP) modeling framework for reliable hourly load prediction. The proposed IGP modeling framework has the following unique features: 1) the IGP utilizes not only the data streams generated by the target customer, but also those generated by relevant customers in the power system; an effective input space dimension reduction method is proposed to significantly improve the computational efficiency, while maintaining the high predictive accuracy of the IGP; and 2) an adaptive data communication rate controlling scheme is proposed to further enhance the predictive performance of the IGP by optimally and dynamically adjusting the data communication rate used for each customer under the total data communication bandwidth constraint often imposed. Taking into account the highly uncertain load and generation behaviors of DERs, the proposed IGP framework is tested on various standard IEEE test cases with load and renewable generation data collected from real-world power systems with DERs. The superiority and efficacy of the IGP are verified by our simulation results.

Dimension-Adaptive Sparse Grid Interpolation for Uncertainty Quantification in Modern Power Systems: Probabilistic Power Flow

In this paper, the authors firstly present the theoretical foundation of a state-of-the-art uncertainty quantification method, the dimension-adaptive sparse grid interpolation (DASGI), for introducing it into the applications of probabilistic power flow (PPF), specifically as discussed herein. It is well-known that numerous sources of uncertainty are being brought into the present-day electrical grid, by large-scale integration of renewable, thus volatile, generation, e.g., wind power, and by unprecedented load behaviors. In presence of these added uncertainties, it is imperative to change traditional deterministic power flow (DPF) calculation to take them into account in the routine operation and planning. However, the PPF analysis is still quite challenging due to two features of the uncertainty in modern power systems: high dimensionality and presence of stochastic interdependence. Both are traditionally addressed by the Monte Carlo simulation (MCS) at the cost of cumbersome computation; in this paper instead, they are tackled with the joint application of the DASGI and Copula theory (especially advantageous for constructing nonlinear dependence among various uncertainty sources), in order to accomplish the dependent high-dimensional PPF analysis in an accurate and faster manner. Based on the theory of DASGI, its combination with Copula and the DPF for the PPF is also introduced systematically in this work. Finally, the feasibility and the effectiveness of this methodology are validated by the test results of two standard IEEE test cases.

Joint Placement of Phasor and Power Flow Measurements for Observability of Power Systems

We consider the problem of joint optimal placement of phasor measurement units (PMU) and conventional measurements to ensure full observability in power systems. The formulation is initially posed as a nonlinear integer programming problem and then transformed in to an equivalent integer linear programming (ILP) problem by introducing auxiliary variables and constraints. The resulting ILP problem is solved for the optimal solution on IEEE 14-, 57-, and 118-bus systems considering zero-injection buses. To extend the formulation to large-scale systems, two heuristics are proposed where the nonlinear problem is decomposed into two separate problems of lesser complexity. The heuristics are evaluated on standard IEEE test cases and a large 2383-bus Polish system. The heuristics yield solutions close to optimal (difference of 1 PMU) solutions on standard IEEE systems, while substantially reducing problem complexity and run time. The placement results obtained with the proposed formulation require fewer PMUs for observability compared to systems with fixed locations of conventional measurements. The results thus potentially provide a more economical solution to system observability compared to those obtained solely with PMU placement.

Dynamic Load Flow Technique for Power System Simulators

This paper presents a dynamic load flow technique for power system simulators. The approach presented can be applied to a system when there is a net accelerating or decelerating power in the system. It possesses all the attractive features and basic structure of the normal fast decoupled method, and it does not depend on the selected reference bus. The modifications to the standard fast decoupled power flow algorithm are derived, and power system simulator implementation considerations are discussed. The algorithm has been tested on standard IEEE test cases and on a metropolitan utility 559 bus model. A numerical example of the above algorithm on the 559 test case is presented which demonstrates convergence characteristics and computation requirements of the proposed algorithm. These results are compared with those of normal fast decoupled load flow.

Bootstrap Gauss-Seidel load flow

The Gauss-Seidel iterative procedure for load-flow analysis is so well established (and the use of acceleration and extrapolation to hasten convergence so well documented) that the subject might appear to be exhausted. However, a novel variation of the process has now appeared with a convergence rate far superior to conventional accelerated or extrapolated Gauss-Seidel techniques. In this new approach, called ‘bootstrap Gauss-Seidel’, a pseudo-, or fictitious, load flow is set up by making simple changes to the power loading at every node in the network. Since these changes are dependent on the mismatch power (or error) at each node, a ‘bootstrap effect’ results. Conventionally acceptable solutions are reached considerably faster than normal, since convergence is very rapid. Particular benefit is seen on large networks, which tend to converge at a rate up to three times faster than that obtained using optimum real acceleration. The additional mismatch calculation (not normally required in Gauss-Seidel methods) can be made computationally attractive, and is not a serious limitation of the bootstrap approach. Results obtained for about a dozen a.c. load flows, including standard IEEE test cases, have confirmed the power of this method. Detailed results are included for a number of these cases.