Modified IEEE 30-bus System Research Articles

Regional Sensitivity Analysis for Maximum Static Transfer Capability of Power Systems by Dimension-Adaptive Sparse Grid Interpolation

The maximum static transfer capability (MSTC) can be regarded as a measure of the power transmission ability of power systems in steady-state operation. These emerging uncertainty sources pose a difficult challenge for the efficient analysis and effective control of MSTC. To address this challenge, the dimension-adaptive sparse grid interpolation (DASGI) method is applied with modified boundaries of the collocation points to establish a surrogate model for the faster calculation of the MSTC based on AC optimal power flow (AC-OPF), thus accelerating its probabilistic analysis as well. Subsequently, the regional sensitivity analysis (RSA) is introduced in terms of contribution to the sample mean (CSM) and to the sample variance (CSV) to identify the critical regions of the uncertainty sources. Hence, an adjustment strategy is developed to increase the mean or decrease the variance of MSTC for secure and stable power transmission. Furthermore, the total CSM (TCSM) and total CSV (TCSV) are proposed as indicators to select the most influential random inputs as the preliminary step of RSA, which reduces the analytical burden. The effectiveness of this proposition is illustrated on the modified IEEE 118-bus system and the Polish 2383-bus power system, where the Monte Carlo simulation method, in combination with the AC-OPF-based MSTC model, provides an accuracy reference and a traditional sensitivity index provides the term for comparison.

A systematic approach for risk assessment and mitigation of wind integrated electricity markets

A risk-based double auction mechanism with dispatchable loads is one of the most cost-efficient trading mechanisms in the modern real-time electricity markets. Risks in the system due to various uncertainties, such as line failure, generator failure, load changes and other severe contingencies causes non-systematic execution of real-time electricity markets. This paper presents a simple and systematic procedure for reducing system risks in deregulated power markets considering wind power integrations. For maximizing the considerable system social welfare and minimizing the system’s economic risk, the optimal placement and operation of wind power producers (WPP) have been suggested. The critical buses have been identified by accessing the different assessment tools e.g., Value at Risk (VaR), Conditional Value at Risk (CVaR), and locational marginal pricing (LMP) based Marginal Pricing Index (MPI). The presented approach has been evaluated and validated on modified IEEE 30-bus system.

Probabilistic Optimal Power Flow Computation Using Stratified Quadrature Rule

In this paper, the probabilistic optimal power flow (POPF) problem is modeled as a black box uncertainty quantification problem. If distribution functions of POPF inputs are unknown, only samples are available, the multivariate Gaussian mixture model is suggested to recover the joint cumulative distribution function of POPF inputs, and a probability selection method is introduced to relate POPF inputs to an independent standard normal vector. Then, moment matching equations are proposed to characterize the uncertainty effects of POPF inputs on outputs, whereby some properties of the POPF problem are revealed, and a stratified quadrature rule (SQR) is proposed for POPF computation by combining a Hadamard matrix based quadrature rule and a discrete sine transformation matrix based quadrature rule. This newly developed SQR has a computational burden linear with the number of POPF inputs, and performs well in estimating means and standard deviations POPF outputs. Finally, case studies are conducted on a modified IEEE 118-bus system to illustrate the accuracy and efficiency of the proposed method.

Feasibility Layer Aided Machine Learning Approach for Day-Ahead Operations

Day-ahead operation involves a complex and computationally intensive optimization process to determine the generator commitment schedule and dispatch. The optimization process is a mixed-integer linear program (MILP) also known as security-constrained unit commitment (SCUC). Independent system operators (ISOs) run SCUC daily and require state-of-the-art algorithms to speed up the process. Existing patterns in historical information can be leveraged for model reduction of SCUC, which can provide significant time savings. In this paper, machine learning (ML) based classification approaches, namely logistic regression, neural networks, random forest and K-nearest neighbor, were studied for model reduction of SCUC. The ML was then aided with a feasibility layer (FL) and post-process technique to ensure high quality solutions. The proposed approach is validated on several test systems namely, IEEE 24-Bus system, IEEE-73 Bus system, IEEE 118-Bus system, South-Carolina (SC) synthetic grid 500-Bus system, and Polish 2383-Bus system. Moreover, model reduction of a stochastic SCUC (SSCUC) was demonstrated utilizing a modified IEEE 24-Bus system with renewable generation. Simulation results demonstrate a high training accuracy to identify commitment schedule while FL and post-process ensure ML predictions do not lead to infeasible solutions with minimal loss in solution quality.

Cyberattack on Phase-Locked Loops in Inverter-Based Energy Resources

This article reveals power grid vulnerabilities by manipulating the phase-locked loop (PLL) in an inverter-based energy resource (IBER). An attacker can exploit the off-nominal frequency operation of a power grid coupled with stability and tracking properties of an IBER PLL to manipulate the inverter and grid operations during strong and weak grid conditions. Employing a modified IEEE-14 bus system, simulation studies show that PLL-based attacks can cause: (i) revenue losses to IBER operators in weak and strong grid conditions, (ii) voltage limit violations and voltage profile deterioration at IBER bus under weak grid condition, and (iii) system-wide power-angle instability under weak and strong grid conditions. To detect the PLL-based attack, we propose attack severity index (ASI) by generating a detection error signal from local grid voltage measurements and PLL estimation. The attack is mitigated by incorporating security as an integral part of the PLL design, yielding a security-aware PLL.

Multi-objective distributed control of WT-PV-BESS integrated weak grid via finite time containment

This paper proposes a finite time containment control scheme to achieve distributed control of a weak grid which is integrated with photovoltaic (PV), wind turbine (WT) and battery energy storage system (BESS). Taking advantage of the containment control in multi-dimensional control, we proposed a multi-objective control scheme of the WT-PV-BESS system in a weak grid, wherein four control objectives are specified, namely, bus voltage regulation, grid frequency control, peak load shaving and economic benefits optimization for the system operator. Firstly, the sizing approach of BESSs to fulfill the operation mission requirements is proposed; meanwhile, the general coordination strategy for the PV, WT and BESS to achieve the demand–supply balance is proposed. Subsequently, the predefined four control objectives are modeled and transferred into the long/short time frame operational constraints of the BESSs. Afterwards, the finite time containment control algorithm is proposed to force the BESSs into achieving containment status within prescribed time. Simulation case studies are conducted on a modified IEEE 9-bus system to show the effectiveness and performance of the proposed scheme.

Stochastic model for active distribution networks planning: An analysis of the combination of active network management schemes

The widespread adoption of distributed generation (DG) is changing the operation of distribution networks. To increase the control of power flows and avoid the detriments of DG intermittency, active distribution networks (ADN) emerge as a feasible solution. In this paper, we propose a convex model for ADN expansion planning. Four active network management (ANM) schemes are considered: DG active power curtailment, DG reactive power control, on-load tap changer (OLTC) tap adjustment, and shunt compensation device control. The problem is formulated as a mixed integer second-order cone programming problem (MISOCP) using the distflow equations and second-order cone relaxations (SOCR). By scenario analysis, we address the uncertainty associated with power demand, renewable generation, and electricity prices. The proposed model is used to study the benefits of different combinations of ANM schemes to a modified IEEE 33-bus system and compare them with the individual benefits of each scheme. The results indicate that ANM schemes can reduce total network costs, reduce losses, delay network reinforcement, and improve the voltage profile. In addition, some combinations of schemes develop synergies in which the combined economic benefits are greater than the sum of the individual benefits.

Robust Optimal Scheduling of Microgrid with Electric Vehicles Based on Stackelberg Game

With increasing penetration of distributed generators (DG), the uncertainty and intermittence of renewable energy has brought new challenges to the economic dispatch and promotion of environment sustainability of microgrids. Active loads, especially in electric vehicles (EVs), are thought to be an efficient way to deal with the uncertainty and intermittence of renewable energy. One of the most important features of EVs is that their demand will vary in response to the electricity price. How to determine the real-time charging price to guide the orderly charging of EVs and operate with an uncertain renewable energy output represents an important topic for the microgrid operator (MGO). To this end, this paper formulates the optimal pricing and robust dispatch problem of the MGO as a Stackelberg game, in which the upper level minimizes the MGO’s cost, while the lower level minimizes the charging cost of each EV. In the problem, the approximate linear relationship between the node voltage and equivalent load is modeled, and the approximate linear expression of the node voltage security constraint is derived. Using dual optimization theory, the robust optimal dispatch model is transformed into a linear programming model without uncertain variables. Then, the Stackelberg game model is transformed into a mixed integer linear program by using the duality theorem of linear programming. Finally, the effectiveness of the proposed method is proved by simulation within the modified IEEE33-bus system.

Congestion forecast framework based on probabilistic power flow and machine learning for smart distribution grids

The increase in renewable energy sources and new technologies such as electric vehicles and storage can generate uncertainties in distribution grid operations, increasing the likelihood of congestions in power lines. Distribution system operators (DSOs) face several challenges while operating their grids in such conditions. These congestions deteriorate the electrical equipment in the long term, reducing its life span. This work proposes a framework to predict grid asset congestions on a daily basis. A congestion forecast framework is proposed by combining probabilistic power flows and machine learning algorithms to support DSOs in their daily decision-making. The framework is tested on a modified IEEE-33 bus system and CINELDI MV Reference system with hourly synthetic data. The results showed that the framework is able to closely predict the congestions on the lines. Computational capabilities are reported and discussed. The study indicates that the framework is a suitable tool for day-to-day congestion predictions in smart distribution grids yielding low error in expected values.

Preventive–corrective stability constrained OPF in microgrids for accommodating DG plug-and-play

To accommodate unpredictable plug-and-play (PnP) of distributed generators (DGs) in droop controlled microgrids, this paper proposes a preventive–corrective stability constrained optimal power flow (SC-OPF). Firstly, considering that DG droops are restricted by load sharing, we introduce the battery energy storage system (BESS) with adjustable droops, which acts as a new control resource. Secondly, we propose a bi-level optimization problem, where the upper level ensures minimizing the preventive–corrective coordinated cost and accommodating DG PnPs without violating stability constraints and the lower level focuses on the stability index given by semi-definite program (SDP) based on the Lyapunov equation. With the previously proposed analytical stability sensitivity, the lower level problem is reformulated by a series of linear constraints through the Benders decomposition method, and hence the entire bilevel problem can be solved efficiently and accurately. We apply the modified IEEE 33-bus system to validate the proposed SC-OPF model. From simulation results, the proposed model significantly improves the economic cost, stability, and computational efficiency compared to other SC-OPF models without considering BESS droop control or PnPs.

Coordination of protective relays in distribution systems considering uncertainty caused by renewables and demands based on orthogonal experiments

The operations of distribution systems are more challenging than in past decades because of the penetration of distributed generation (DG). Several serious problems may be caused by DG, such as bi-directional power flow in a distribution line, different levels of fault currents and uncertainty in power generation. This paper investigates the coordination of inverse-time overcurrent relays (OCRs) in distribution systems with uncertain distributed power generation and loads. A novel method is presented in this work, considering different scenarios along with two levels of uncertainty caused by DGs (photovoltaics and wind) and bus loads, to determine fault currents using Taguchi orthogonal experiments. Nonlinear optimization is then employed to find the optimal settings of inverse-time OCRs in distribution systems and to identify infeasible current transformer ratios. Simulation results obtained from a 9-bus system and a modified IEEE 33-bus system show that the proposed method outperforms the traditional point-estimation method (PEM). For the 33-bus system, the mean values of similarity indices based on the probability density function are obtained by the proposed method, and they are 0.979 and 0.975, which are closer to unity, for time multiplier setting (TMS) and pick-up setting (PS), respectively, than those (0.953 and 0.951 for TMS and PS, respectively) obtained by the PEM. The mean values of error indices based on the cumulative distribution function are obtained by the proposed method, and they are only 0.0007 and 0.0085 for TMS and PS, respectively, while those obtained by the PEM are 0.0011 and 0.0110 for TMS and PS, respectively.

Market Mechanism Design of Inertia and Primary Frequency Response With Consideration of Energy Market

The shortage of inertia and primary frequency response (IPFR) will be more severe in future power systems since conventional fossil-based synchronous generators are gradually being replaced by variable renewable energy (VRE) generators. To relieve the shortage of IPFR, corresponding market mechanisms should be designed and incorporated to motivate appropriate provision from various sources. The mechanism of IPFR provision from different types of generators and its tight relation with energy production should receive particular attention. This paper proposes a novel IPFR market mechanism in which the energy market is taken into joint consideration. The virtual inertia and droop factor provided by VRE generators are defined and introduced, considering its dominant share in future power systems. A differentiated pricing scheme is designed towards incentive compatibility, considering provision from different types of generators with different quality levels and opportunity costs. Then, the proposed IPFR market mechanism is formulated, and a modified piecewise linearization method is utilized to simplify the non-linear nadir constraints. Finally, the model is tested on a modified IEEE 30-bus system according to historical data in CAISO. The results indicate the proposed mechanism could increase the utilization of VREs, decrease system operation costs, and guarantee reasonable payback for various types of generators.

Method to Quantify Modal Interactions Between Converter Interfaced Generators and Synchronous Generators

The aim of this paper is to quantify the interactions between the oscillation modes of power systems within the realm of small-signal stability. This paper focuses on the interactions between Converter Interfaced Generator (CIG) oscillation modes and electromechanical oscillation modes of Synchronous Generators (SGs). It is difficult to determine the modal interactions using the existing analysis such as mode sensitivity, mode loci and participation factors. This paper proposes an extension to eigenvalue sensitivity analysis in order to determine the interaction between modes and impact of the interaction on system stability. Interaction coefficients are proposed to quantify the interaction between the modes. A modified IEEE 39-bus system with CIGs is considered to carry out the proposed analysis. The analysis is carried out to investigate the impact of PLL parameters on the interaction among the oscillation modes. The analysis is also carried out considering renewable energy penetration levels of 50-70%. It is observed that the interaction between CIG and electromechanical modes of SG results in increased participation of SGs' states in CIG modes. This increased participation of SG states in CIG modes results in reduced damping of oscillations in SG states.

Parameter Calibration of Wind Farm With Error Tracing Technique and Correlated Parameter Identification

With the increasing penetrations of wind power in power systems, periodical calibration of the large-scale Wind Farm (WF) model is crucial to maintaining high-quality model performance for stability investigations. However, the existing calibration methods mainly focus on correcting synchronous generators, not the more dynamical WF model. Challenges in tracing errors of inaccurate models and identifying the correlated parameters would further restrain the calibrating performance. To address such limitations, a novel parameter calibration approach for the WF model is developed explicitly in this article. With the development of a trajectory sensitivity based dominant parameters selection strategy, the parameters which significantly impact the model responses can be precisely located. Then, for discriminating the ill-conditioned parameters (deviating from their actual values), an improved error tracing method incorporating Hybrid Dynamic Simulation (HDS) and Hilbert-Huang Transform (HHT) is proposed. Lastly, to enhance the model performance, the ill-conditioned parameters are iteratively tuned by a well-designed multistage identification approach, with the consideration of parameter correlations. Additionally, theoretical proof of the error tracing technique is provided to guarantee the proposed method's validity mathematically. With realistic WF and a modified IEEE 39-bus system, the proposed method demonstrated its excellent performance in tracing and tuning inaccurate parameters.

Profit enhancement and grid frequency control by energy level scheduling of CAES system in wind-connected electrical system

The maintenance of power balance poses significant challenges in renewable combined deregulated power systems due to the unpredictable nature of renewable energy sources. This situation leads to economic instability within the system. However, an energy storage system can help maintain energy supply and control system stability for renewable incorporated thermal power plants. Unlike in regulated markets, energy prices in deregulated markets are not fixed by any government body or particular company. Instead, the Independent System Operator (ISO) serves as the main entity in the electrical market, gathering tenders from Generation Companies (GENCOs), Distribution Companies (DISCOs), and Transmission Companies (TRANSCOs). The market controller regulates energy prices using Nodal Pricing (NP), which provides economic benefits to both GENCOs and DISCOs. However, the unpredictability of renewable sources often results in a decline in system profit due to the production of an imbalance price (CostIMC) caused by a mismatch in contracted power generation from the renewable power plant. To address these issues, this study proposes a novel combined system that utilizes a suitable scheduling technique for the optimum operation of a wind farm-compressed air energy storage (CAES) system to maximize profit and revenue while maintaining grid frequency. The CAES system’s energy level is divided into four different levels, and an optimal strategy has been developed to efficiently utilize the CAES system to maintain grid frequency. This work has been conducted in both regulated and deregulated environments using a modified IEEE 30-bus system. The proposed method has been compared with an existing approach and has yielded better results in all aspects.

A Data-Driven Approach for Reactive Power Optimization Incorporating Interval Values for Renewable Power Generation

The increasing integration of renewable energy sources into modern electric grids has led to a rise in uncertain factors that must be managed to maintain voltage security during reactive power optimization (RPO). Traditional deterministic RPO methods fail to account for these uncertainties, which can result in power grid security issues such as voltage violations. To address these challenges, this paper proposes a data-driven interval-based reactive power optimization method (IRPOM). The IRPOM represents the uncertainties associated with renewable power generation and load demands as intervals within the RPO problem formulation. The proposed method uses an improved particle swarm optimization algorithm to solve the RPO problem. In each iteration, the uncertain power flow is solved using the optimizing-scenarios method- (OSM-) based interval power flow (IPF) algorithm. This approach calculates the real power losses and checks whether state quantities, including voltage, power flow, and generator output, exceed their limits. Furthermore, a data-driven modeling approach is introduced to reduce the conservativeness of the IRPOM solutions. The effectiveness of the proposed method is demonstrated through detailed computational analysis on a modified IEEE 30-bus system. The results show that the proposed approach ensures economic efficiency while maintaining a low bus voltage threshold crossing probability close to zero.

A Multilevel Model of Energy Market Considering Coupon Incentive Based Demand Response with Wind Power Uncertainty

Demand response (DR) can decrease or increase energy consumption and has the ability to use generating assets more efficiently. Because of the increased power consumption, it has become necessary for the power system networks either to update or upgrade the already existing power system or to inculcate some schemes to minimize the load through effective customer engagement. To address this issue incentive-based demand response proved to be an effective tool to change the pattern of consumption. This work proposes a novel multilevel energy market considering coupon incentive based DR (C-IBDR). The proposed model is operated on a modified PJM 5-Bus system where the independent service operator (ISO) using economic dispatch (ED) computes the localized marginal pricing (LMP) and the load serving entity (LSE) issues coupons to consumers and procures the demand reduction from them. Two wind generators are incorporated into the test system and their effect on the localized marginal pricing with and without demand response is analyzed. The optimization problems are modeled using particle swarm optimization (PSO) and linear programming (LP) in MATLAB. The results demonstrate that the proposed C-IBDR reduces peak demand from 900 to 860 MW through the utilization of wind and DR. This alteration modifies the load curve, increases the power factor from 0.524 to 0.555, raises the revenue of LSEs from $106,646 to $106,946, reduces generation costs from $473,291 to $214,651, and procures a total of 262 MW of demand from the consumer side in the form of demand reduction. The system is further tested for scalability. The practicality of the suggested approach in handling more extensive systems is vividly demonstrated through its application to the modified IEEE 118-bus system.

Profit Extension of a Wind-Integrated Competitive Power System by Vehicle-to-Grid Integration and UPFC Placement

Profit maximization is critical in the control of power system networks for both power providers and users. Electrical energy is freely accessible in the electrical grid during off-peak hours, with storage units helping to store excess energy and assist the electrical grid during high-demand situations. Such techniques promote grid stability and ensure safe operation. Because renewable resources are intermittent, energy storage technologies are especially significant in renewable-associated power systems. Vehicle-to-grid (V2G) technology has recently acquired popularity in preserving power grid stability in the presence of renewable resources.V2G technology employs automobiles as mobile storage devices and focuses on the efficient utilization of extra power available during off-peak hours. The goal of this work is to improve the functioning of a V2G system in a power network to reduce energy production costs while increasing system profitability. This study for deregulated power environments also depicts the influence of V2G mixing on system voltage profile and locational marginal pricing (LMP), as well as the performance of the Unified Power Flow Controller (UPFC) on system economics. The MiPower simulation program is used in the study to find the best placement of the power storage unit for the modified IEEE 14-bus system.

Source-load cooperative multi-modal peak regulation and cost compensation mechanism in China’s ancillary service electricity market

To enhance the market participation initiatives from the power source and load sides, we propose a novel power system optimal scheduling and cost compensation mechanism for China’s peak regulation ancillary service market. Owing to China’s energy structure, thermal power accounts for nearly half of the country’s installed power generation capacity. Although the willingness of thermal power units to participate in peak regulation auxiliary services is low, we propose a peak regulation cost compensation and capacity-proportional allocation mechanism. This mechanism comprehensively considers the source-load initiative. From the source side, it encourages entities to participate in peak regulation, and the restriction of the peak regulation initiative is set to ensure that each entity benefits from the peak regulation transaction. From the load side, it takes the shiftable and sheddable load as the hybrid demand response and uses the price information to influence the power consumption behavior of the user side. Subsequently, a peak regulation scheduling model was constructed with the multi-objective minimum thermal power output fluctuation of the lowest system operating cost and minimum renewable energy abandonment. This was solved using a mixed-integer linear programming model and CPLEX. Finally, a power system consisting of wind-solar-hydro-thermal-storage and hybrid demand response with a modified IEEE 30-bus system was tested to verify the effectiveness. It was proven that the proposed method improves the utilization rate of renewable energy and optimizes the scheduling of the economic benefit system of each power generation entity.

Stochastic optimal scheduling strategy of cross-regional carbon emissions trading and green certificate trading market based on Stackelberg game

Under the urgent goal of "carbon peaking and carbon neutralization" in China and based on the distribution characteristics of renewable energy, it is essential to promote the large-scale consumption of renewable energy and increase the proportion of large-scale renewable energy in market transactions. Therefore, a stochastic optimal scheduling model that combines the Stackelberg game, cross-regional carbon emissions trading, and tradable green certificate transaction to consider the uncertainty of renewable energy power generation is proposed. To encourage more market participants to participate in the tradable green certificate trading, the model uses Stackelberg game theory to analyze the complex interest relationship between different market participants and obtain a scheduling scheme that balances the interests of different participants. To give full play to the role of the trading mechanism on the cross-regional system, the tradable green certificate trading mechanism and the carbon emission trading mechanism are combined to optimize the overall allocation of green certificates and carbon emission rights, to stimulate renewable energy generation, limit the carbon emission of traditional thermal power units and promote energy conversion. Finally, the modified IEEE 39-bus system and Hami power grid (in Western China) are used as examples to illustrate the feasibility and effectiveness of the proposed scheduling model. The results show that the proposed strategy improves the cross-regional system economy and reduces emissions, fully reflects the monetary value of the external characteristics of renewable energy, guides renewable energy investment and power grid planning, and promotes the consumption of renewable energy.