IEEE 30-bus Test System Research Articles

Bandwidth-Aware Event-Triggered Load Frequency Control For Power Systems Under Time-Varying Delays

Networked Load frequency control (LFC) inevitably subjects to constrained bandwidth and time delays. However, the network traffic essentially varies from time to time and then the bandwidth status may be only busy during some specific peak periods but idle during others. This paper proposes a bandwidth-aware event-triggered load frequency control (ETLFC) scheme for multi-area power systems under time-varying delays by incorporating bandwidth-aware adaptive regulation scheme into decentralized ETLFC scheme. Different from existing time-delay ETLFC model, a model of aperiodic sampled-data system with time delay is constructed for the ETLFC scheme to obtain less conservative stability and co-design conditions based on looped Lyapunov functional. The regulation scheme is designed to adaptively adjust the threshold parameter of the ETLFC scheme based on variable bandwidth status and system output change in order to lessen communication burden while ensuring desired control performance. For fixed output change, a better bandwidth status generates a smaller threshold parameter to raise the triggering frequency in order to utilize available communication resources to improve control performance rather than unilaterally reduce data transmissions in the existing research. Case studies are undertaken by an IEEE 39-bus test system to show the effectiveness and advantages of the proposed scheme.

Optimal placement of battery energy storage systems with energy time shift strategy in power networks with high penetration of photovoltaic plants

This paper introduces a novel approach for the optimal placement of battery energy storage systems (BESS) in power networks with high penetration of photovoltaic (PV) plants. Initially, a fit-for-purpose steady-state, power flow BESS model with energy time shift strategy is formulated following fundamental operation principles. The optimal BESS placement methodology is subsequently developed in the realm of incremental modelling of power system losses, which permits to identify the best candidate node for the BESS connection that reduces the total power losses. And for practical results, daily varying patterns of nodal demand, generation dispatch and solar irradiance are considered, all this accompanied by the BESS operating strategy, i.e., electric energy time shift, which is one of the most sounding strategic applications in current BESS facilities. In addition to providing a suitable validation proof using the standard IEEE 5-bus test system, two practical test power network models with 24 and 118 nodes are used to showcase the usefulness of the incremental modelling approach for optimal BESS placement in power grids with high penetration of PV plants.

Laplace-Domain Hybrid Distribution Model Based FDIA Attack Sample Generation in Smart Grids

False data injection attack (FDIA) is a deliberate modification of measurement data collected by the power grid using vulnerabilities in power grid state estimation, resulting in erroneous judgments made by the power grid control center. As a symmetrical defense scheme, FDIA detection usually uses machine learning methods to detect attack samples. However, existing detection models for FDIA typically require large-scale training samples, which are difficult to obtain in practical scenarios, making it difficult for detection models to achieve effective detection performance. In light of this, this paper proposes a novel FDIA sample generation method to construct large-scale attack samples by introducing a hybrid Laplacian model capable of accurately fitting the distribution of data changes. First, we analyze the large-scale power system sensing measurement data and establish the data distribution model of symmetric Laplace distribution. Furthermore, a hybrid Laplace-domain symmetric distribution model with multi-dimensional component parameters is constructed, which can induce a deliberate deviation in the state estimation from its safe value by injecting into the power system measurement. Due to the influence of the multivariate parameters of the hybrid Laplace-domain distribution model, the sample deviation generated by this model can not only obtain an efficient attack effect, but also effectively avoid the recognition of the FDIA detection model. Extensive experiments are carried out over IEEE 14-bus and IEEE 118-bus test systems. The corresponding results unequivocally demonstrate that our proposed attack method can quickly construct large-scale FDIA attack samples and exhibit significantly higher resistance to detection by state-of-the-art detection models, while also offering superior concealment capabilities compared to traditional FDIA approaches.

Incorporating catastrophe insurance in power distribution systems investment and planning for resilience enhancement

Severe damage and high economic losses caused by frequent extreme disasters are becoming unbearable for distribution system operators (DSOs) under climate change. In order to cope with extreme disasters, this paper proposes an investment portfolio and planning framework of multi-resource for resilience enhancement. In the investment portfolio and planning framework, insurance is incorporated to mitigate high economic losses as a risk sharing and resilience enhancement supplementary strategy, and co-optimized with security investment from the perspective of DSOs. Firstly, the insurance investment is modelled based on Gordon-Loeb model according to insurance industry principles and formulated as constraints by piecewise linearization techniques. Secondly, the investment portfolio and planning framework proposed in this paper is modeled as a scenario-based two-stage stochastic mixed integer linear optimization program (MILP). In the first stage, DSO makes investment and planning decisions including energy storage (ESS) allocation, line hardening strategy and insurance investment. Both operation strategies of normal operation scenarios and extreme disaster scenarios under climate change are optimized in the second stage. Finally, progressive hedging (PH) algorithm is applied to solve the two-stage stochastic MILP model. The proposed model and algorithm are tested on the modified IEEE 33-bus test system. The results verify the validity of investment portfolio and planning framework, and the results show that portfolio investment considering insurance can realize resilience enhancement in both load shedding and economic losses.

A Multi-objective Optimization Planning Framework for Active Distribution System Via Reinforcement Learning

The effective planning of active distribution networks is crucial for utility companies to make informed decisions regarding investments in distributed generation, reliability assessment, reactive power planning, substation revisions, and feeder repositioning. However, the dynamic nature of the solution space makes it challenging for model-based optimization methods to ensure computational performance in active distribution network planning. To address this issue, this study proposes a planning method that focuses on improving computational performance through the continuous updating of the planning model’s solution space during the reinforcement learning training process. Based on simulations conducted on the IEEE 33-bus test system, the proposed planning strategy successfully enhances computational performance while minimizing investment costs compared to other strategies. With the proposed method, the investment cost and the operation cost are reduced by 32.42% and 23.91%, respectively.

A recursive system identification inertia estimator for traditional and converter-interfaced generators

This paper proposes a method to estimate the inertia constant of synchronous generators (SGs) and the virtual inertia provided by converter-interfaced generators (CIGs). It can be applied when the system is under normal operating conditions or after power imbalance events. The algorithm is based on a recursive system identification approach and uses the active power and bus frequency measurements proceeding from phasor measurement units. The measurements are preprocessed to improve the estimation accuracy. Subsequently, a model-independent rotor speed estimator is used to compute rotor speed variations (or internal frequency variations, in the case of CIGs). Afterwards, a recursive least-square equation error formulation is implemented to compute the SG and CIG parameters in the z-domain, which are later converted into their respective counterparts in the s-domain. The method is applied to several generation devices in the IEEE 39-bus and IEEE 118-bus test systems, including traditional SGs and CIGs providing virtual inertia. Numerical results show the accuracy and the low computational burden of the proposed method.

Optimal power flow using a hybridization algorithm of arithmetic optimization and aquila optimizer

In this paper, a hybridization method based on Arithmetic optimization algorithm (AOA) and Aquila optimizer (AO) solver namely, the AO-AOA is applied to solve the Optimal Power Flow (OPF) problem to independently optimize generation fuel cost, power loss, emission, voltage deviation, and L index. The proposed AO-AOA algorithm follows two strategies to find a better optimal solution. The first strategy is to introduce an energy parameter (E) to balance the transition between the individuals’ procedure of exploration and exploitation in AO-AOA swarms. Next, a piecewise linear map is employed to reduce the energy parameter’s (E) randomness. To evaluate the performance of the proposed AO-AOA algorithm, it is tested on two well-known power systems i.e., IEEE 30-bus test network, and IEEE 118-bus test system. Moreover, to validate the effectiveness of the proposed (AO-AOA), it is compared with a famous optimization technique as a competitor i.e., Teaching-learning-based optimization (TLBO), and recently published works on solving OPF problems. Furthermore, a robustness analysis was executed to determine the reliability of the AO-AOA solver. The obtained result confirms that not only the AO-AOA is efficient in optimization with significant convergence speed, but also denotes the dominance and potential of the AO-AOA in comparison with other works.

Daily scheduling of generating units with natural-gas market constraints

We address the daily scheduling of generating units (unit commitment) in a system whose production mix includes a large number of natural-gas-fired units. We assume that the natural-gas system, operating under market conditions, does its best to supply the natural-gas for electricity production required by the power system. We formulate this problem as a bi-level model whose upper-level problem represents the scheduling of generating units under a second-order conic relaxation of the AC network constraints, and whose lower-level one represents the clearing of the natural-gas market. The upper-level problem is mixed-integer second-order conic, while the lower-level one is second-order conic as well, but continuous. We replace the lower-level problem by its optimality conditions in the form of primal constraints, dual constraints, and strong duality equality, which results in a single-level nonconvex mixed-integer nonlinear optimization problem. To improve the computational tractability of such formulation, we derive a mixed-integer second-order conic relaxation of the single-level nonconvex mixed-integer nonlinear optimization problem. Such problem is solved using a Benders-type outer-approximation decomposition framework with a master mixed-integer linear problem and two subproblems that are nonlinear but convex. The communication between the master problem and the subproblems is enhanced by incorporating into the master problem linearized information pertaining to the subproblems and valid linear inequalities. The benefits of the proposed model and the effectiveness of the solution procedure are illustrated using the IEEE 24-bus test system coupled with a 20-node natural-gas system and the Central Illinois 200-bus power system coupled with a 48-node natural-gas system.

Equilibrium Optimizer Algorithm for Optimal Reactive Power Dispatch

Optimal Reactive Power Dispatch (ORPD) is a significant research area in terms of maintaining the reliability and safety of the power system and operating it more economically. ORPD problem can be formed from a variety of perspectives including the minimization of the active power losses and voltage deviation, and improving the voltage stability performance. The majority of methods so as to deal with ORPD problem is meta-heuristic techniques because of the complex, non-linear and non-convex nature of the problem. In this paper, a new physic-based meta-heuristic algorithm, Equilibrium Optimizer (EO), is proposed for ORPD problem to reach the optimal settings of control variables such as voltage magnitudes in PV buses, tap positions of transformers and reactive power support of shunt devices. The introduced algorithm is evaluated on IEEE 30-bus test system by using various objectives, and a comparison of the implemented method to other optimization techniques described in the literature is utilized to assess its efficacy. Simulation results and statistical indicators demonstrate that the EO algorithm validates its computational efficacy and robustness in handling the ORPD problem.

Expansion planning of the transmission network with high penetration of renewable generation: A multi-year two-stage adaptive robust optimization approach

This paper addresses the multi-year two-stage expansion planning of the transmission network of a power system with high penetration of renewable generation modeling long-term uncertainty by using adaptive robust optimization. The multi-year nature of the problem is modeled by considering a comprehensive view of the planning horizon. A cardinality-constrained uncertainty set is used to model the future worst-case uncertainty realization of the peak power consumption of loads, along with the capacity and marginal production cost of generating units. Unlike previous works, we model certain features of the operation that are typically ignored in multi-year robust transmission network expansion planning problems, namely, the operational variability of renewable generating units, the operational flexibility of conventional generating units, and the non-convex operational feasibility sets of storage facilities. The solution procedure employed for this multi-year two-stage robust problem, which is formulated as a three-level problem, is based on the combination of the nested column-and-constraint generation algorithm with two exact acceleration techniques. We analyze the performance of the proposed model through the use of the IEEE 24-bus Reliability Test System and the IEEE 118-bus Test System. Numerical results show that the use of the multi-year approach leads to reductions in the total worst-case cost of up to 7% in comparison with the static and sequential static procedures. Moreover, an underestimation of the total worst-case cost of more than 8% is attained when ignoring certain operational constraints of conventional generating units and storage facilities. Lastly, a sensitivity analysis is presented in order to illustrate the impact of the maximum deviations of the uncertain parameters on the total worst-case cost.

Congestion Management Using an Optimized Deep Convolution Neural Network in Deregulated Environment

The technical issue of congestion, which is predominantly found in deregulated power systems, is caused by the failure of transmission networks to satisfy load power demands. This failure is primarily caused due to an increase in loads or loss of transmission lines or generators in modern restructured power networks. This work introduces a CM approach using Deep Convolution Neural Network (DCNN) for minimizing congestion and supporting Independent System Operators (ISOs). The purpose of the work is to generate enhanced prediction outputs for congestion management with reduced error values. These objectives were achieved through the actual power rescheduling of generators. The proposed work adopts DCNN which is optimized using an Improved Lion Algorithm (LA) and aids in providing significant outcomes for congestion management with reduced error. By implementing customized IEEE 57-bus, IEEE 30-bus, and IEEE 118-bus test systems, the suggested approach has been successfully verified for its performance on test systems of varied sizes. This analysis incorporates restrictions such as line loads, bus voltage influence, generator, line limits, etc. The most important results for the test system indicating convergence profile, congestion cost, and change in real-power and voltage magnitude are obtained by the simulation in MATLAB, and on the basis of the obtained simulation outcomes, it is evident that the proposed Improved Lion Algorithm optimized Deep Convolution Neural Network displays phenomenal computation performance in minimizing congestion losses at minimum congestion costs. When compared to several contemporary optimization techniques, the suggested technique performs better in terms of congestion cost and losses by generating improved prediction outputs with reduced errors.

Multivariate Spectral Analysis and Hypothesis Testing-Based Robust Attack Detection for Multiarea Frequency Control

Frequency control is one of the critical systems responsible for maintaining grid stability, making it a vulnerable and attractive choice for cyber-attacks. This article presents a multivariate singular spectrum analysis (MSSA) for extracting the system’s dynamics under normal operation and proposes a projection-based distance tracking and hypothesis testing method to detect multiarea load frequency control (MA-LFC) attacks. The proposed methodology is robust, adaptive, and computationally efficient, especially, when system and measurement noises are considered. The three main features of the proposed method are that: 1) it uses standard SCADA data and does not require attack data; 2) it can be integrated with the existing grid control system with minimal hardware; and 3) it is independent of system configuration and upgrades. The attack detection algorithm can successfully detect different types of false data injection attacks (FDIAs), including stealth attacks on multiple sensors. The algorithm is tested on an IEEE 39-bus New England test system, 300 bus test system, and 1888 bus RTE system. The attack detection algorithm was found to be reliable, fast, robust, and scalable under noisy measurements compared to the existing methods.

Wide-Area Backup Protection Using Sparse Synchronized/Unsynchronized PMU Measurements

This paper proposes a wide-area backup protection (WABP) method for transmission systems using sparse synchronized/unsynchronized PMU measurements. The method is aimed at addressing practical challenges such as temporary loss of the time-synchronization signal (LTSS), sparse PMU coverage, and communication failures and latencies. A linear and computationally efficient formulation is proposed to identify the faulted line in near real-time based on the superimposed-circuit concept. An index is proposed that quantifies the mismatch degrees between the expected and observed superimposed phasors without requiring full network observability. The method can work well with unsynchronized measurements without imposing a significant computational burden. This is achieved by canceling out the effect of angle drifts caused by LTSS from the equations. Since no matrix inversion is involved, sparse PMU measurements do not result in singularity, and thus, the unsolvability of the equations. A technique is proposed to assess the feasibility of faulted-line identification by a given set of PMUs. Being robust against measurement and parameter errors, the method performs well with PMUs of different reporting rates regardless of the fault distance, type, and resistance. More than 200,000 simulations conducted on the IEEE 39-bus test system verify the effectiveness of the proposed WABP method.

A novel loss allocation method applicable for any desired network topology

Due to the expansion of power networks in response to the increase in total load demand, the complexity regarding power systems transmission networks’ configuration has been increased. Similarly, with the advent of local energy markets and transactive energy concept, power distribution networks are undergoing a fundamental change. In this respect, numerous agents are transacting power within both distribution and transmission networks. Therefore, as more power is transacted among agents in different energy networks, power networks face higher power losses. Dealing with the financial outcomes of these losses, a general accurate yet fast method for loss allocation in power networks is of utmost importance. In response, this paper proposes a novel loss allocation framework based on the power tracking method that is applicable for any desired network topology within both transmission and distribution networks. In this regard, at first, a new method is proposed to obtain how the optimal scheduled generation of each production unit should be allocated to each specific load of the network. Then, it is obtained that how these transactions are flown in each line of the network. In the next step, the exact losses in each line resulted from distinct transactions between each pair of agents in the network are obtained. Finally, how each specific transaction contributes to the total losses of the network can be calculated. By implementing the proposed framework on a modified IEEE 14-bus test system and a 69-bus IEEE distribution network, the applicability and effectiveness of the proposed method is demonstrated by the numerical results. The results indicate that the proposed method can be implemented in any network and with any scale.

On-line tracking of inertia constants using ambient measurements

In this paper, a new method for on-line inertia estimation is developed. The proposed method is based on the sliding window concept and uses ambient responses, i.e., responses obtained during the normal operation of the power system, to identify inertia constants of generation devices. The effectiveness of the developed method is evaluated by means of simulations on two benchmark power system models, namely the IEEE 9-Bus Test System and the IEEE 39-Bus Test System. The conducted analysis reveals that the proposed method can accurately identify inertia constants of conventional synchronous generators (SGs), converter-interfaced units operated as virtual SGs, and virtual power plants. The performance of the proposed method is also evaluated under noisy conditions, by performing Monte Carlo simulations. Finally, comparisons with conventional methods are performed, demonstrating the superior performance of the developed method.

Optimal real-time Voltage/Var control for distribution network: Droop-control based multi-agent deep reinforcement learning

The photovoltaics (PVs) known as clean power generation has been highly penetrated in distribution networks, which motivates the network develops towards high uncertainty with complex real-time operation status. In this paper, an optimal real-time Voltage/Var control (ORT-VVC) method is proposed to reduce power losses and mitigate voltage fluctuations by optimizing the reactive power output of the PV inverter. And the ORT-VVC is implemented via a novelly proposed droop-control based multi-agent deep reinforcement learning (DC-MADRL). The VVC structure is constructed in distributed pattern with network partition and the multi-agents are established to rule the sub-networks via rare information communication between neighbors. Then, the PV control model is established as a Q-V droop control model with adjustable parameters. The MADRL is employed to optimize the PV controlling parameters instead of optimizing PV reactive power output directly, which aims to improve the real-time VVC performance for distribution network. The DC-MADRL model is established and solved via the multi-agent deep deterministic policy gradient (MADDPG) algorithm. Finally, numerical simulations are performed on the IEEE 123-bus test system to demonstrate the effectiveness of the proposed method.

Enhanced Multi-Objective Power Flow Optimization for IEEE-118 Bus Test System using Advanced Grey Wolf Optimization Algorithm

This research article thoroughly examines the implementation of an enhanced Grey Wolf Optimization (GWO) method for Multi-Objective Power Flow Optimization (MO-PFO) in the IEEE-118 bus test system. Given the growing complexity and uncertainty in modern power systems, power flow optimization presents a crucial challenge. The suggested enhanced GWO algorithm improves the performance of the traditional GWO for MO-PFO issues while addressing its inherent flaws.
 The goal of this study is to obtain optimal solutions concurrently for multiple objectives, including the reduction of power losses, voltage variations, and the enhancement of system stability. In the Related Works section, I review the research on power flow optimization in the literature, which also showcases the improvements achieved by applying various optimization techniques and discusses the benefits and drawbacks of traditional optimization methods and their effectiveness in dealing with MO-PFO issues.
 The improved GWO algorithm, designed specifically for MO-PFO, is described in detail in the Methodology section. I explain the adjustments made to the regular GWO algorithm and introduce a cutting-edge method for handling multiple objectives. In the IEEE-118 bus test system, I present the mathematical model of the MO-PFO problem and develop fitness functions for each objective.
 Furthermore, I describe the implementation of the enhanced GWO algorithm, including parameter settings and termination criteria. The proposed algorithm demonstrates its capability to effectively handle the multi-objective nature of power flow optimization, thereby paving the way for future power system operations that are more dependable and sustainable

Identification and classification for multiple cyber attacks in power grids based on the deep capsule CNN

Cyber-attacks have become one of the main threats to the security, reliability, and economic operation of power systems. Detection and classification of multiple cyber-attacks pose challenges for ensuring the stability and security of power systems. To address this issue, this study proposes an automatic identification and classification method for multiple cyber-attacks based on the deep capsule convolution neural network. Spatial correlations among different nodes and temporal features from history operation status in the transmitted data packets are extracted by the convolution neural network. Capsules in the proposed structure have important implications for maintaining the topological consistency contained in the measurement matrix. Furthermore, the proposed method is model-free and avoids the impact of system parameters uncertainties on detection performance. Multiple kinds of typical cyber-attacks, including false data injection attacks, replay attacks, denial of service attacks, time-delay attacks, and deception attacks, are considered and modeled in this paper. Numerical results on the IEEE 39-bus test system show that the proposed method can achieve 99.97% detection accuracy on single cyber-attacks and 96.25% detection accuracy on multiple cyber-attacks. Comparative results illustrate the proposed method outperforms than traditional neural networks. This approach provides a solution for the problem of multiple cyber-attack detection and classification.

A Novel Adaptive Restarting Genetic Algorithm for Transmission Congestion Alleviation in the Deregulated Power Market

A key concern in a deregulated power market (DPM) scenario is congestion on electricity transmission lines, which is one of the most pressing problems. The independent system operator (ISO) manages congestion to ensure the power system framework operates reliably and securely. Considering the context of the restructured power system’s inherent uncertainties, congestion management (CM) is critical in the operation and security of DPM. CM aims to ease congestion on the transmission lines while meeting all system constraints at the lowest possible congestion cost. This study employs a novel adaptive restarting genetic algorithm (ARGA) for rescheduling the generation to alleviate transmission congestion in the energy market. This work uses the proposed ARGA CM technique to reduce congestion costs by rescheduling generators’ active power output most cost-effectively. The participation of generation units in the CM is made possible by considering the generator sensitivity factors (GSF). IEEE 57-bus and IEEE 118-bus test systems are employed to evaluate the suggested methodology’s accuracy. The acquired results are contrasted using several contemporary optimization approaches to validate the suggested technique’s validity. The proposed algorithm was tested in Python, and power flow analysis was done using the PANDAPOWER tool.

Fault diagnosis and protection strategy based on spatio-temporal multi-agent reinforcement learning for active distribution system using phasor measurement units

Active distribution system (ADS) requires intelligent sensors to provide real-time data. Due to the harmonic distortion and sparse reward function, the multi-agent reinforcement learning strategy has the fuzzy characteristic and slow convergence. This work proposes a model-free spatio-temporal multi-agent reinforcement learning (STMARL) strategy for the spatio-temporal fault diagnosis and protection. The augmented-state extended Kalman filter tracks spatial–temporal sequences measured by phasor measurement unit (PMU) and feed into the diagnosis model. The supervised multi-residual generation learning (SMGL) model is constructed to diagnose the single-phase-to-ground fault. Based on spatio-temporal sequences, the SMGL diagnosis model integrates the ADS protection as a Markov decision process and the protection operation is quantified as the STMARL reward. In the hybrid multi-agent framework, the STMARL protection strategy converges faster based on the higher-level agent suggestion without the global reward. The STMARL protection strategy is validated in the IEEE 34-bus distribution test system with 10 PMUs. Comparing with the SOGI, WNN, Sarsa and DDPG algorithms, in the common fault conditions, the STMARL protection strategy shows better performance in the high dynamic environment with the response time 1.274 s and the diagnosis accuracy rate 97.125%. The STMARL diagnosis and protection strategy guides ADS in a stable operation coordinate with all PMUs, which lays foundation for the synchronous measurement application in the smart grid.