IEEE 30-bus Power System Research Articles

A Scalable PDC Placement Technique for Fast and Resilient Monitoring of Large Power Grids

The Wide Area Measurement System (WAMS) is a key enabler of real-time monitoring of power grids. The essential goals of WAMS design are fast and resilient data transfer from phasor measurement units (PMU) to phasor data concentrators (PDC). We propose a scalable two-stage PDC placement technique for minimizing the end-to-end delay while maintaining resiliency. In the prescreening stage, the plausible candidates of PDC configurations are identified based on a graph theory-based multi-median function (MMF). A computationally efficient meta-heuristic algorithm is used to address scalability. In the candidate selection stage, two different algorithms, namely Suurballe's and Dijkstra's, are employed to identify the best of those plausible PDC configurations as the final design. This technique not only minimizes the hop paths between PMUs and PDCs, but also ensures network resiliency against single PMU, PDC, or communication link failure by incorporating the roles of PMUs in power grid observability into routing policy. Simulation results on the IEEE 57-bus test power system and the 2000-bus test power system demonstrate the effectiveness and scalability of the proposed technique.

Locational detection of the false data injection attacks via semi-supervised multi-label adversarial network

False data injection attacks (FDIAs) pose a significant threat to the healthy and safe operation of smart grids. Traditional fdia detection methods are difficult to deal with complex and harsh scenarios. Considering the increasing demand for attack location services in practical power grid management, this paper proposes a new adversarial scheme called Semi-Supervised Multi-Label Adversarial Network (SMAN). To better adapt to harsh learning conditions with only a few labeled samples, this scheme combines semi-supervised mechanisms with state-of-the-art generative adversarial networks. The showdown between generator and discriminator aims to optimize the model for high detection accuracy in semi-supervised training. Among them, for the non-Euclidean structure of the power system, we propose a graph attention-based generation mechanism to improve the generator and enhance the authenticity of the generated samples. Furthermore, the classification network based on label correlation of FDIAs is proposed to capture the inconsistency and co-occurrence dependency in the measurements due to the potential attacks, which is applied to detect the exact injection locations with high dimension data. To this end, we perform label transformation and hierarchical training on the localization task to quickly localize data attacks based on multi-label classification. Extensive simulations and comparisons implemented on IEEE 14-bus and 118-bus power systems demonstrate the superiority of this scheme in localization detection. And it has been proved that it has high robustness and generalization ability under harsh conditions.

Event-triggered reactive power tracking optimization for second-level power fluctuations of renewables and stochastic loads

The power fluctuations of renewable energy sources and stochastic loads (RESL) makes it difficult for system operators to achieve optimal control. This paper proposes an event-triggered reactive power optimization strategy based on the event-triggered algorithm to rapidly track the optimal operating states for accommodating the second-level power fluctuations of RESL, with less computation and communication. Firstly, on a longer temporal scale, event-triggered multi-stage global optimization (MGO) is performed on a rolling basis to obtain the time-interval optimal operating states according to chance constraint programming, and the system operation security is improved by narrowing the voltage-feasible regions. Next, at each moment within the time interval, event-triggered local tracking optimization (LTO) is performed at each controller of RESL by rapidly regulating reactive power to adapt to its second-level active power fluctuations. The LTO is completed at the local level by using the sensitivity information from MGO, without running the optimal power flow program, to relieve the computation and communication burdens. Then, event-triggered LTOs performed at all controllers synchronously form the system-level real-time optimization. The unnecessary MGO and LTO are skipped by using the event-triggered algorithm when small power fluctuations are occurring. Finally, a case study on the IEEE-39 bus power system validates the feasibility of the proposed strategy.

Frequency control using electric vehicles with adaptive latency compensation and variable speed wind turbines using modified virtual inertia controller

In this paper, to reduce the effect of low inertia consequences, electric vehicle (EV) and variable speed wind turbine (VSWT) are adopted to collaborate in the power system frequency regulation. A virtual inertia controller based on the IEC 61851 standard is proposed to benefit from EV contribution in frequency regulation. In this controller, the rate-of-change-of-frequency (ROCOF) is measured and an appropriate EV current set point is obtained. Furthermore, to decrease the effect of frequency regulation on EVs owners, a stochastic allocation method of the regulation sequence among EVs parking lots is presented. One of the barriers of employing EV in the frequency regulation is the communication latency. To overcome this issue, according to the measured latency, a weighted combination of several compensators which is called adaptive latency compensator (ALC) is utilized. After compensating the delay, the output power of the EVs is calculated and collaborated in frequency regulation. In addition, an algorithm is proposed for collaborating VSWT in frequency control. In the proposed algorithm, according to the wind velocity, the output power of the VSWT increases to the maximum acceptable value and will be fixed. A method is developed to find the maximum acceptable increment power considering VSWT constraints. After a supportive part, a recovery part is started to return VSWT hub speed to a desired value. Two PID controllers are designed in this algorithm for support and recovery parts. During the recovery part, a second frequency dip emerges and a method is introduced which at first identifies the second frequency dip moment and EVs collaboration is applied to alleviate this unfavorable outcome. To evaluate the performance of the proposed algorithms and controllers, different simulation studies are conducted using the modified IEEE 39-bus test power system. Results confirm the effectiveness of the proposed methods in system frequency support.

Distributed energy resource coordination for a microgrid over unreliable communication network with doS attacks

This article studies the coordination economic dispatch problem (EDP) for distributed energy resources. To minimise the total operating cost under various constraints, a switched distributed coordination algorithm is presented to solve the EDP over the unreliable communication network with the Denial-of-Service (DoS) attacks. In this situation, the proposed algorithm integrates the normal mode and the attack mode. The attackers can make the communication network unconnected and destroy the convergence and optimality in the attack mode. In order to explore under what conditions the optimal solution can still be obtained, we model the attack modes by differential inclusions and use an average dwell-time automaton and time-ratio monitor to limit the DoS attacks. Then, the switched distributed algorithm is modelled as a hybrid dynamical system. Furthermore, some conditions are derived to guarantee the exponential convergence of the proposed algorithm under DoS attacks. Finally, simulation results tested on the IEEE 30-bus power system illustrate the effectiveness of the proposed algorithm.

Low-carbon economic dispatch of integrated energy systems that incorporate CCPP-P2G and PDR considering dynamic carbon trading price

To address the challenge of global warming stemming from excessive fossil fuel combustion, the exploration of low-carbon technologies and improvements to carbon trading mechanisms stand out as vital strategies. An effective conduit for these strategies is the integrated energy system (IES), which has garnered increasing attention for its potential. To realize low-carbon advancements within energy systems, this study proposes a low-carbon economic scheduling framework for the IES that integrates the coupled operation of carbon-capture power plants, power-to-gas (CCPP–P2G) unit and the price-based demand response (PDR) considering dynamic carbon trading mechanisms. The proposed approach firstly concurrently considers source-side CCPP-P2G and load-side PDR to achieve coordinated low-carbon operation, elucidating the underlying mechanisms. Subsequently, a dynamic carbon trading model for the IES is formulated, flexibly capturing the ebb and flow of supply and demand in the carbon trading market. Amidst the uncertainty of the system, a bi-level optimization model is constructed to minimize the operational cost. Finally the effectiveness of the proposed method is demonstrated on an IES consisting of the IEEE-30 bus power system, 6-bus natural gas system and 6-bus district heating system. The findings indicate that the proposed dynamic carbon trading mechanism is able to effectively provide time-varying carbon trading price signals to fully reflect the supply and demand relationship of carbon emission allowance. Furthermore, the synchronized operation of CCPP-P2G and PDR yields substantial benefits, compared to the benchmark. Specifically for the test case, the proposed framework reduces system operational costs, wind power curtailment, and carbon emissions by $87,160, 1,410 MWh, and 4,849t, respectively.

Economic environmental operation in bulk AC/DC hybrid interconnected systems via enhanced artificial hummingbird optimizer

Innovative technologies of multi-terminal high voltage direct current (HVDC), often known as “MTDC,” represent additional features for better active and reactive power control when hybridized with traditional AC power systems. In this sequence, optimal operation in hybrid AC and MTDC power systems becomes highly economically and environmentally necessary. This paper presents an Improved Artificial Hummingbird Optimizer (IAHO) technique for reducing total generation fuel costs, environmental pollution, and whole power losses in AC-MTDC power systems. The proposed IAHO includes a variety of territorial foraging tactics (TFTs) and a Linear Control Process (LCP) which improve both local and universal searching capabilities. The proposed IAHO and AHO are performed on modified IEEE 57-bus and 30-bus hybrid AC and multi-terminal HVDC power systems. The simulation findings declare high economic, environmental, and technical benefits based on the proposed IAHO. A significant reduction in fuel costs, emissions, and losses with 22%, 59.51%, and 71.83% compared to the initial case for the IEEE 57-bus hybrid AC-MTDC power system. Also, the IEEE 30-bus hybrid AC-MTDC power system significantly reduced fuel costs, emissions, and losses by 17.01%, 16.04%, and 28.49% compared to the initial case. Moreover, the significant outperformance of the proposed IAHO is demonstrated over several reported algorithms.

Debiased Uncertainty Quantification Approach for Probabilistic Transient Stability Assessment

System instability does not occur often in practice and thus the historical data for training a machine learning method has to address the imbalanced and multi-modal probabilistic distribution in the probabilistic transient stability assessment (PTSA). This letter proposes a transient stability index (TSI) density-based weighting scheme and feature-TSI similarity regularization to address that, yielding debiased uncertainty quantification for PTSA in the presence of uncertain wind generations and loads. Numerical results on the IEEE 39-bus and Illinois 200-bus power systems demonstrate the significantly improved performance of the proposed method over other state-of-the-art machine learning approaches in PTSA.

A self-healing restoration of power grid based on two-stage adaptive decision-making strategy to enhance grid resilience

Large-scale power outages can affect the economy of the country and jeopardize the lives of millions of people, so there is a need for a fast, reliable, and self-healing tool to reduce these losses. Hence, the power system restoration performance can be improved by considering both restoring and operating performance, however, current restoration strategies only consider the restoring performance but ignore the operational performance which can enhance the power system resiliency. Given this background, challenging tasks such as optimal restoration planning (ORP) and optimal real-time operation (ORO) are planned to be tackled by developing an adaptive decision-making strategy (ADMS). In order to reduce the effects of emergency power outages on power systems, this study presents the ADMS, a two-stage self-healing restoration approach. Moreover, a novel metric of capacity accessibility (NMCA) is developed to determine the capacity adequacy status during severe events. The proposed ADMS has two steps, each of which is conducted at a certain time, and is referred to as ORP for the first stage and ORO functions for the second stage. The goal of the ORP optimization model is to maximize system-wide power capacity for electricity demand under extreme events by considering practical constraints, including non-black-start generators (NBSGs) constraints, network topology constraints, and power balance constraints. In order to reduce generation costs, the ORO optimization model adjusts the generated output power to enhance one or more operating performance metrics. The first stage problem is formulated using mixed-integer linear programming (MILP), and it is resolved using the branch-and-bound technique. Moreover, the interior point method solves AC optimal power flow for the second stage. Finally, simulation studies are performed on the modified IEEE 118-bus power systems. The outcomes demonstrate the effectiveness of the proposed strategy for planning (ORP) and real-time operation (ORO); the proposed two-stage strategy is capable of providing an optimal solution for a high-performance online restoration decision support system; the proposed strategy can adapt against the system conditions and contingencies.

Controlled Power System Separation Using Generator PMU Data and System Kinetic Energy

With the growing number of severe system disturbances and blackouts around the world, controlled system separation is becoming an increasingly important system integrity protection scheme (SIPS) to save the electric power system from a complete or partial disintegration. A successful controlled splitting approach should at least tackle the following two well-known and interrelated problems: "when to split?" and "where to split?". Multiple previous publications consider these problems separately, and even those pursuing a combined approach propose solutions with limited applicability. In this paper, we are proposing a novel PMU-based detector of loss of synchronism that utilizes generator rotor angles and speeds to promptly detect rotor angle instabilities over a wide area. Moreover, we are showing how our loss of synchronism detection principle can be coupled with the known controlled splitting techniques to form an integrated defense scheme against unintentional loss of synchronism. The performance of this wide-area SIPS is demonstrated on the IEEE 39-bus test power system for various types of unstable conditions.

Determining optimal generator start-up sequence in bulk power system restoration considering uncertainties: A confidence gap decision theory based robust optimization approach

A reasonable start-up sequence of generators considering renewable energy generation integration can effectively improve the restoration efficiency of the power system concerned. The restoration strategy of generators is time-sensitive, however, the computation procedure of existing methods is not fast enough to meet the requirements of practical applications. In this paper, the generator start-up sequence optimization (GSSO) problem is addressed with the integration of wind-solar hybrid systems (WSSs) considered in bulk power systems. Specifically, a deterministic model for GSSO is formulated to maximize the total generation capability during the restoration procedure, in which fewer auxiliary variables are required to promote the computational efficiency. On this basis, in order to deal with the inherent and significant uncertainties of WSSs, a confidence gap decision theory (CGDT) based approach is proposed combining the advantages of stochastic optimization and the information gap decision theory based method while considering the worst-case realization of unknown probability distributions, so that a chance-constrained robust generator start-up solution is thereby attained. Moreover, the formulated CGDT based model is transformed into a mixed integer linear programming problem. Finally, the IEEE 39-bus power system and a modified version of an actual power system in China are employed to demonstrate the feasibility and efficiency of the proposed method.

NSGA-III integrating eliminating strategy and dynamic constraint relaxation mechanism to solve many-objective optimal power flow problem

Increasing optimizing criteria in modern power systems promotes the birth of many-objective optimal power flow (Ma-OPF) problems in which more than three optimizing objective functions are considered. The increasing optimizing objectives as well as complex constraints of power balance and other system limits bring a decrease in selection pressure and challenges of constraint handling techniques for traditional multi-objective evaluation algorithms. Aiming at the solving difficulties of Ma-OPF problems, an improved NSGA-III integrating eliminating strategy and dynamic constraint relaxation mechanism (NSGA-III-EDR) is proposed. In the proposed approach, a new elimination strategy that eliminates the associated points having the largest angle with the corresponding reference line is employed to increase the selection pressure of the algorithm. An integrated constraint handling method, which employs a repair strategy based on assigning decision variables to feasible values and a penalty function approach together to handle power flow equality constraints, is also introduced into the NSGA-III-EDR. Aiming at lacking feasible solutions of the algorithm in the early searching stage, a strategy of relaxing constraint violations as well as a dynamic updating strategy for the tolerated threshold value of distinguishing feasible and infeasible solutions at the early evolution is proposed. Moreover, an improved domination sorting rule based on the proposed constraint handling method and the relaxing strategy to constraint violations is employed to promote the generation of feasible solutions. The effectiveness and feasibility of the proposed improved NSGA-III-EDR approach are studied and evaluated on different test cases of a famous standard IEEE 30-bus power system as well as the larger power systems of IEEE 57-bus and IEEE 118-bus. The numerical results show that the proposed NSGA-III-EDR method can provide solutions to many-objective OPF problems with tremendous potential compared with the traditional NSGA-III and other algorithms illustrated in the literature.

Investing in Wind Energy Using Bi-Level Linear Fractional Programming

Investing in wind energy is a tool to reduce greenhouse gas emissions without negatively impacting the environment to accelerate progress towards global net zero. The objective of this study is to present a methodology for efficiently solving the wind energy investment problem, which aims to identify an optimal wind farm placement and capacity based on fractional programming (FP). This study adopts a bi-level approach whereby a private price-taker investor seeks to maximize its profit at the upper level. Given the optimal placement and capacity of the wind farm, the lower level aims to optimize a fractional objective function defined as the ratio of total generation cost to total wind power output. To solve this problem, the Charnes-Cooper transformation is applied to reformulate the initial bi-level problem with a fractional objective function in the lower-level problem as a bi-level problem with a fractional objective function in the upper-level problem. Afterward, using the primal-dual formulation, a single-level linear FP model is created, which can be solved via a sequence of mixed-integer linear programming (MILP). The presented technique is implemented on the IEEE 118-bus power system, where the results show the model can achieve the best performance in terms of wind power output.

Optimal Deployment in Moving Target Defense against Coordinated Cyber–Physical Attacks via Game Theory

This work proposes a method for the intelligent deployment of distributed flexible AC transmission system (D-FACTS) devices. In recent years, in the field of moving target defense (MTD) strategies to detect coordinated cyber–physical attacks (CCPAs), establishing how to deploy D-FACTS devices has become an important research point. Although some research results have been proposed, the obtained deployment solutions are unintelligent due to not carefully considering smart attackers’ behaviors. A method for achieving the intelligent deployment of D-FACTS devices is proposed in this paper. First, the basic concept of corrupting CCPAs is summarized; second, based on considering practical constraints and the basic concept, a protected transmission line set is confirmed; and third, a zero-sum game model is formulated, and a robust Nash equilibrium solution is computed. Due to the game’s characteristics, this solution reflects the smart attackers’ sense of action. Relying on the solution, those lines that are most likely to be tripped form a new protected transmission line set. Finally, a comprehensive algorithm using a metric proposed in previous studies is proposed for finding an intelligent solution for the deployment of D-FACTS devices. We validated our results through extensive simulations using IEEE 14-bus, 30-bus, and 118-bus power systems provided by MATPOWER and the real-world load profiles from New York State. Our work, in tracking the targets that attackers are most likely to attack, opens up new ideas for the intelligent deployment of D-FACTS devices.

An efficient model for capturing gas transients in the energy flow of integrated electricity–gas systems

Gas-fired units provide great flexibility to accommodate the intermittent nature of renewable energy sources and are also considered to be an ideal substitute for retiring coal-fired generations. However, the increasing deployment of gas-fired units deepens interdependency between electric power and natural gas, calling for efficient modeling of the heterogeneous energy flow in the integrated electricity–gas systems (IEGS). Plenty of research works show the necessity of considering gas flow transients in the IEGS, which can be described by a set of partial differential equations (PDEs). To ensure a tractable optimization, the PDEs are often discretized using the finite/infinite difference method, which may result in a large computational scale for achieving good precision. To this end, this paper proposes an efficient model for capturing gas flow transients in the IEGS, which can be taken as the operational constraints in the optimal energy flow model for IEGS coordinated planning, scheduling, and control. For improving the computational efficiency, the PDE-based transient gas flow model is discretized using a space–time orthogonal collocation (OC) method, which provides high-quality results using fewer spatial–temporal discrete points than differential methods. Further, aiming at the difficulty in the determination of the number of space–time collocation points, an adaptive strategy is proposed and embedded in the proposed model utilizing the local fitting errors of state variables related to pipelines. Case studies show the superiority in computational accuracy and efficiency of the proposed model over the existing models based on Wendorff difference and global OC. And an illustrative case based on the modified IEGS benchmark system composed of the IEEE 118-bus power system and the Belgian 20-node gas network exhibits the application value of the proposed model in the optimization and control of the IEGS.

Robust coupled single-port method based on PMU-based state estimation method for voltage stability assessment

Real-time monitoring of voltage stability margin is an essential issue to warrant secure operation of electrical power systems. One of the important tools for real-time monitoring of voltage stability margin is the PMU-based state estimation method. This paper presents a novel PMU-based State Estimation method based on the continuous Levenberg Marquardt (CLM) method and fourth-order Runge–Kutta (RK4) formulation, which is named as PSECLR method. Moreover, based on the proposed PSECLR method, a novel Robust Coupled Single-Port (RCSP) method for real-time monitoring of voltage stability margin in power systems is presented in this paper. To determine the efficiency of the proposed methods, detailed simulation results are presented and analyzedfor IEEE 14-bus, IEEE 30-bus, IEEE 118-bus and IEEE 300-bus power systems.

A robust bi-level optimization framework for participation of multi-energy service providers in integrated power and natural gas markets

This paper presents a bi-level scheduling model for a new energy system under the concept of multi-energy service providers (MESPs) to participate in the integrated power and natural gas market (IPNGM). While the presented bi-level model takes full consideration of the unit commitment constraints of the power network and line pack constraints of the gas network into consideration at the lower level, the MESPs minimize the cost of purchasing power and natural gas by operating energy storage systems as well as the demand response program (DRP) as flexible technologies at the upper level. In order to solve the bi-level problem, an iterative-based two-step algorithm is developed. Moreover, since the MESPs cannot accurately predict other participants in the IPNGM, especially renewable energy sources (RESs), the power price determined by IPNGM is considered an uncertain parameter, and a robust optimization (RO) method is employed to capture this uncertainty. The proposal is formulated as a mixed-integer linear programming (MILP) and carried out on the IEEE 6-bus power system integrated with the 6-node natural gas network and considering one MES using the CPLEX solver in the general algebraic modeling system (GAMS) environment. Further, to show the model flexibility, simulation results are extended to the IEEE 118-bus power system integrated with the 10-node natural gas network by considering six MESs. The obtained results verified the effectiveness of the model by reducing the cost of the purchased power and natural gas up to 4.39% by employing flexible energy sources.

Coordinated Power Oscillation Damping From a VSC-HVDC Grid Integrated With Offshore Wind Farms: Using Capacitors Energy

This paper proposes a novel coordinated control strategy for a voltage source converter (VSC) based high-voltage direct current (HVDC) grid integrated offshore wind farms (OWFs) to damp the power system oscillations. A feature of this strategy is aiming to use the DC-link capacitor energy of offshore wind turbines (WTs) to reduce interactions between power oscillations and HVDC grid voltage when onshore grid-side VSCs (GSVSCs) modulate the active and reactive power injections. Unlike the previous communication-based method, the coordination from offshore WTs in this strategy depends on the local measurements of the HVDC grid voltage instead of the remote communication data from the onshore AC grid. A modified IEEE 39-bus power system with a 5-terminal VSC-HVDC grid connected to two OWFs has been developed to validate the effectiveness of this proposed strategy. Both the eigenvalue analysis and time-domain simulation results indicate that this strategy can significantly improve the power oscillation damping (POD). Comparative simulation studies also conclude that the proposed strategy has similar POD improvements to the previous communication-based method without the negative impact of communication delay from onshore to offshore.

Analysis of Failure Propagation in Cyber-Physical Power Systems Based on an Epidemic Model

From the perspective of propagation dynamics in complex networks, failure propagation in cyber-physical power systems is analogous to the spread of diseases; subsequently, the cyber nodes and power nodes are regarded as individuals in each of their groups. In this study, a two-layer interdependent network model of the cyber-physical power system is proposed, where each subnetwork adopts the Susceptible-Infected-Susceptible (SIS) epidemic-spreading model. On this basis, we construct a failure cooperation propagation model of cyber-physical power systems. Furthermore, we introduce the node protection mechanism to ensure the normal operation of key nodes. The generated scale-free cyber network and IEEE118-bus power system are used for simulation to analyze the influence of the coupling effect between them on the final failure scale.

Data-Driven Time-Varying Inertia Estimation of Inverter-Based Resources

This letter proposes a data-driven inertia estimator for inverter-based resources (IBRs) with grid-forming control. It is able to track both constant and time-varying inertia. By utilizing the Thevenin equivalent, the virtual frequency inside IBRs is first estimated with only its terminal voltage and current phasor measurements. The virtual frequency and the measurements are then used together to derive the state-space swing equation model. Then, an enhanced adaptive Unscented Kalman filter (EAUKF) is developed to estimate IBR inertia. Numerical results on the modified IEEE 39-bus power system demonstrate that the proposed inertia estimator remarkably outperforms the existing state-of-art methods both in tracking speed and accuracy.