Loading Margin Research Articles

Information gap decision theory to deal with long-term wind energy planning considering voltage stability

This paper proposes a novel approach for long-term planning of wind energy considering its inherent uncertainty. The uncertainty of wind energy is handled via information gap decision theory (IGDT) method. Additionally, due to the importance of security considerations, loading margin is employed as an index of voltage stability to guarantee the security of power system. The operational constraints (such as power flow equations) in initial operation point considered along with those at the voltage collapse point, simultaneously. Accordingly, the IGDT-based voltage stability constrained wind energy-planning model is proposed that can be used for ensuring the safe operation of power networks. The main feature of this model is to handle the uncertainty of wind energy in the long-term wind energy planning via IGDT technique, by considering voltage stability constraints. In order to evaluate the capability of the IGDT technique for uncertainty handling of wind energy, the obtained results are compared with Monte Carlo simulations. To demonstrate the effectiveness of proposed model, it is applied to the New-England 39-bus test system. The obtained results validated the applicability of the proposed model for optimal wind energy planning. The proposed methodology could help wind farm investors to make optimal large-scale wind energy investment decisions.

A Novel Load Margin Sensitivity Method for Predicting Load Margin of Line Outage with Wind Power Generation Systems

Abstract In this paper, a novel load margin sensitivity method based on the proposed novel direct method have been studied with wind power generation systems. In the beginning, a bidirectional sweep approach is applied for power flow analysis when wind power generators are linked to the main power grid. Fixed-speed and doubly-fed induction generators are included in the analysis. Then, the proposed novel direct method, based on a bordered system, is employed to predict the load margin in order to decrease computational complexities. Moreover, the novel direct method can be successfully integrated with the bi-directional sweep approach to form the distributed load margin estimation. Finally, the load margin sensitivity based on the proposed novel direct method is employed to estimate the load margin deviation under the outage of transmission lines. The numerical demonstration on the IEEE 300 bus system have been verified the effectiveness of the proposed load margin estimation approach.

Thermodynamic assessment of the pseudoternary Na2O–Al2O3–SiO2 system

AbstractVitrified high‐level radioactive waste that contains high concentrations of Na2O and Al2O3, such as the waste stored at the Hanford site, can cause nepheline to precipitate in the glass upon cooling in the canisters. Nepheline formation removes oxides such as Al2O3 and SiO2 from the host glass, which can reduce its chemical durability. Uncertainty in the extent of precipitated nepheline necessitates operating at an enhanced waste loading margin, which increases operational costs by extending the vitrification mission as well as increasing waste storage requirements. A thermodynamic evaluation of the Na2O–Al2O3–SiO2 system that forms nepheline was conducted by utilizing the compound energy formalism and ionic liquid model to represent the solid solution and liquid phases, respectively. These were optimized with experimental data and used to extrapolate phase boundaries into regions of temperature and composition where measurements are unavailable. The intent is to import the determined Gibbs energies into a phase field model to more accurately predict nepheline phase formation and morphology evolution in waste glasses to allow for the design of formulations with maximum loading.

Toward Online Bus-Bar Splitting for Increasing Load Margins to Static Stability Limit

The effect of bus-bar splitting on the static stability limit is studied in this paper. A novel online bus-bar splitting methodology is developed to increase the static stability limit of a look-ahead (i.e., short term, say, 30 minutes ahead) power system. The proposed methodology, designed for online application, is based on a strategy consisting of screening, ranking, and decision stages. A tailored model of bus-bar splitting is developed to accurately model bus-bar splitting scenarios. The effectiveness of the proposed online bus-bar splitting methodology is evaluated on the IEEE 118-bus, 1648-bus, and 3120-bus power systems. Results indicate that significant load margin increases can be achieved by bus-bar splitting.

Optimal wind power generation investment, considering voltage stability of power systems

Studies show that improper sizing and placement of wind farms (WFs) lead to undesired investment and operation costs as well as the risk of voltage instability. Thus, optimal placement of WFs and enough loading margin (LM) are important factors which ensure the voltage stability of system as well as optimal investment and expenditure for WFs development. In this paper, modal analysis is used to determine the optimal place of WFs from the voltage stability viewpoint. Moreover, a new voltage stability constrained wind energy planning (VSC-WEP) model is proposed to determine the optimal yearly wind power penetration while satisfying voltage stability constraints. A 10-years horizon is considered and the net profit from the energy procurement via the WFs' installed optimally, is maximized. Furthermore, the added capacity of WFs and the net profit are analyzed by sensitivity analyzes to investigate the impact of various technical and financial factors on the obtained results. The proposed VSC-WEP model is implemented on the IEEE New-England 39-bus test system, and solved by General Algebraic Modeling System (GAMS) optimization package. The simulation results demonstrate the capability of the proposed model for optimal determination of WFs capacity while preserving a proper LM of system.

Dual AC Boosting Compensation Scheme for Multistage Amplifiers

In this brief, a dual AC boosting compensation (DACBC) scheme is presented for multistage amplifiers with low power and a large capacitive load. Dual AC boosting paths are introduced to move the zero from the right-half-plane to the left-half-plane as compared with conventional AC boosting compensation (ACBC) scheme, which helps to improve the phase margin and gain bandwidth (GBW) product of the amplifier. Two three-stage amplifiers with DACBC and ACBC, respectively, are both fabricated in 65-nm CMOS technology for comparison. The amplifier with proposed DACBC drives a 3200 pF||25 $\text{k}\boldsymbol {\Omega }$ load and achieves a GBW of 0.52 MHz with 58° phase margin, consuming only $60~\boldsymbol {\mu }\text{W}$ of power from a ±0.8 V supply, while ACBC achieves 0.26 MHz GBW with the same load, power consumption, and phase margin. These results imply a doubled figure of merit of DACBC versus its ACBC counterpart without an extra power penalty, while the core chip area of DACBC is reduced by a half of that of ACBC due to a smaller compensation capacitance.

A PMU-Based Method for Smart Transmission Grid Voltage Security Visualization and Monitoring

With the rapid growth of usage of phasor measurement units (PMUs) for modern power grids, the application of synchronized phasors (synchrophasors) to real-time voltage security monitoring has become an active research area. This paper presents a novel approach for fast determination of loading margin using PMU data from a wide-area monitoring system (WAMS) to construct the voltage stability boundary (VSB) of a transmission grid. Specifically, a new approach for online loading margin estimation that considers system load trends is proposed based on the Thevenin equivalent (TE) technique and the Mobius transformation (MT) technique. A VSB is then computed by means of real-time PMU measurements and is presented in a complex load power space. VSB can be utilized as a visualization tool that is able to provide real-time visualization of the current voltage stability situation. The proposed method is fast and adequate for online voltage security assessment. Furthermore, it enables us to significantly increase a system operator’s situational awareness for operational decision making. Simulation studies were carried out using different sized power grid models under various operating conditions. The simulation results are shown to validate the capability of the proposed method.

Calculation of optimal load margin based on improved continuation power flow model

This study proposed an improved continuation power flow (CPF) model to calculate the load margin for voltage stability. A self-adjusting step-size controlling scheme of CPF, which is based on the iterations in the corrector and the reactive power reserve of generator buses, is presented. The load margin here is defined either by encountering the saddle node bifurcation (SNB) or the limit-induced bifurcation (LIB). To confirm the LIB, a rapid approach is proposed to calculate the sensitivity of voltage magnitude to reactive power injection change for load buses. Because CPF with distributed slack bus (DSB) could generate different load margin results corresponding to various allocations of imbalanced power, optimization techniques should be adopted in the search for maximizing the load margin. Therefore, the improved CPF is integrated with an evolutionary mechanism-based particle swarm optimization (PSO) method via coordinate transformation. Furthermore, parallel processing is deployed in the programming for high-performance computing. The case studies for the IEEE 5-bus and IEEE 14-bus test systems demonstrate the efficiency of the proposed approaches.

Impact of Coupled Transmission-Distribution on Static Voltage Stability Assessment

With the rapid growth of distributed generators, the distribution static voltage stability assessment (D-VSA) becomes as important as the transmission voltage stability assessment (T-VSA). However, the T-VSA and D-VSA normally treat the transmission and distribution separately, neglecting the interactions between transmission and distribution (T-D). This letter studies the impact of coupled T-D on VSA via physical analysis and numerical simulation. We observe that without considering the T-D interaction, D-VSA may exaggerate the actual load margin significantly, and T-VSA may either exaggerate or underestimate the actual load margin, both of which are unreliable. Hence, the coupled T-D interactions must be considered in both T-VSA and D-VSA.

A new interactive sine cosine algorithm for loading margin stability improvement under contingency

In this paper, a new method called sine cosine algorithm is adapted in coordination with an interactive process to improve the power system security considering loading margin stability and faults at specified important branches. In this study, the loading margin stability is optimized in coordination with total cost, total power loss, total voltage deviation and voltage stability index. In order to locate the best loading margin stability, an initial global database containing suboptimized control variables is generated based on two indices named global and local critical reactive margin security related to generating units. The optimized loading margin stability is improved in coordination with the availability of reactive power of different shunt FACTS devices installed at particular locations. The robustness of the proposed planning strategy is validated on a small test system, the IEEE 30-Bus and to a large test system, the IEEE 118-Bus. Optimized results found confirmed clearly the improvement of loading margin stability at critical situations such as faults at specified branches.

QV interaction evaluation and pilot voltage‐reactive power coupling area partitioning in bulk power systems

This study presents a novel methodology to evaluate the QV interactions among buses and to partition the pilot voltage-reactive power coupling areas (VRPCAs) using relative gain (RG). According to the concept of a multi-input multi-output system, the QV coupling RG is first calculated based on the QV matrix, which is extracted from power flow Jacobian matrix, to evaluate the QV interactions among different buses and then to determine the VRPCAs. The voltage stability critical buses are first identified through a modified loading margin. For each critical bus, the other buses that have strong QV coupling are detected via the cross RG and are clustered into a VRPCA piloted by the corresponding critical bus. New England 39-bus system and Polish power system are used to test the performance of the proposed approach. Simulation results verify the effectiveness of the proposed approach in evaluating the QV interactions and partitioning the VRPCAs.

Load-Dependent Cascading Failures in Finite-Size Erdös-Rényi Random Networks

Large-scale cascading failures can be triggered by very few initial failures, leading to severe damages in complex networks. This paper studies load-dependent cascading failures in random networks consisting of a large but finite number of components. Under a random single-node attack, a framework is developed to quantify the damage at each stage of a cascade. Estimations and analyses for the fraction of failed nodes are presented to evaluate the time-dependent system damage due to the attack. The results provide guidelines for choosing the load margin to avoid a cascade of failures. Furthermore, the analysis reveals a phase transition behavior in the extent of the damage as the load margin grows, i.e., the fraction of the damaged components drops from near one to near zero over a slight change in the load margin. The critical value of the load margin and the short interval over which such an abrupt change occurs are derived to characterize the network reaction to small network load variations. Our findings provide design principles for enhancing the network resiliency in load-dependent complex networks with practical sizes.

An evaluation of our experience in position verification of catheters used for interstitial high-dose-rate brachytherapy of solitary bladder tumors

PurposeThe goal of this study was to verify the position of catheters used over 4 days for brachytherapy of solitary bladder tumors. Methods and MaterialsThe study covered three phases. Shifting of catheters was studied using daily position verification CT scans of 20 patients. The possibility to omit the CT scan on Day 2 by adding a loading margin of 4 mm on each side was studied using data of 5 patients. Whether the Day 4 verification CT scan could be omitted if this margin was used, was studied for another group of 10 patients, comparing the Day 3 treatment plan to the Day 4 CT scan. ResultsAn average catheter shift on Days 2, 3, and 4 of, respectively, −0.3 mm (−8 to 10 mm), −0.5 mm (−14 to 10 mm), and −0.1 mm (−16 to 28 mm) was found over the measurements at both sites of the catheter. Including only shifts causing underdosing of the clinical target volume (CTV), the average shift on Days 2, 3, and 4 was, respectively, −3.6 mm (−1 to −8 mm), −5.4 mm (−1 to −14 mm), and −5.3 mm (−1 to −16 mm). After adding a loading margin, the CTV was covered on Day 2; however, the margin was not sufficient for Days 3 and 4. On Day 4, in 2/10 patients, the CTV was not completely covered. In 5/10 patients, an increased 200% isodose volume was found. ConclusionsPosition verification is necessary in bladder brachytherapy. If a 4-mm margin on each side of the loading pattern was added, position verification on Day 2 could be omitted. The verification CT scan of Days 3 and 4 is still necessary.

Information gap decision theory for voltage stability constrained OPF considering the uncertainty of multiple wind farms

This study deals with the voltage stability constrained optimal power flow (VSC-OPF) problem considering the wind power generation uncertainty. The main feature of the proposed model is to handle the uncertainty of multiple wind farms (WFs) in a way that for a given worsening of total cost, maximum tolerable uncertainty of wind power generation is achieved for all WFs. This maximum uncertainty is determined in a way that a required loading margin (LM), is preserved. It is worth noting that LM is the most important measure of voltage stability which reflects the distance from the current operating point to the voltage collapse point. For this aim, information gap decision theory (IGDT) is utilised to handle the uncertainty of wind power generation. The proposed model is implemented on IEEE 39-bus standard test system. In order to evaluate the effectiveness of the proposed VSC-OPF model for uncertainty handling of multiple WFs, the results obtained by IGDT technique are compared with Monte Carlo simulations and scenario-based approach. The simulation results imply that the uncertainty radius and the desired LM are inversely related, such that for a given tolerable increase of cost, the radius of uncertainty decreases by increasing the desired LM.

Robustness Area Technique Developing Guidelines for Power System Restoration

This paper proposes a novel energy based technique called the Robustness Area (RA) technique that measures power system robustness levels, as a helper for planning Power System Restorations (PSRs). The motivation is on account of the latest blackouts in Brazil, where the local Independent System Operator (ISO) encountered difficulties related to circuit disconnections during the restoration. The technique identifies vulnerable and robust buses, pointing out system areas that should be firstly reinforced during PSR, in order to enhance system stability. A Brazilian power system restoration area is used to compare the guidelines adopted by the ISO with a more suitable new plan indicated by the RA tool. Active power and reactive power load margin and standing phase angle show the method efficiency as a result of a well balanced system configuration, enhancing the restoration performance. Time domain simulations for loop closures and severe events also show the positive impact that the proposed tool brings to PSRs.

Initiative Control Capability of Electric Vehicle and New Energy Consumptive Control Strategy

Abstract For the parked electric vehicle (EV)load in a specific area, its initiativecontrollability was studied and make targeted optimization and control within controllability to achieve the goal of using EVs to consume new energy output and improve the regional load characteristics. In the premise of the reliable two-way communication system, the upper dispatch department can monitor the real-time controllability of EVs based on the EV load margin boundary in this paper, so as to provide load balancing for the area by usingtheEVs’ load.

Voltage stability monitoring of power systems using reduced network and artificial neural network

This paper presents network reduction based methodologies to monitor voltage stability of power systems using limited number of measurements. In a multi-area power system, artificial neural networks (ANNs) are used to estimate the loading margin of the overall system, based on measurements from the internal area only. Information regarding the important measurements from the external areas is considered in measurement transformation through the network reduction process, to enhance the estimation accuracy of the ANNs. A Z-score based bad or missing data processing algorithm is implemented to make the methodologies robust. To account for changing operating conditions, adaptive training of the ANNs is also suggested. The proposed methods are successfully implemented on IEEE 14-bus and 118-bus test systems.

Extreme Learning Machine Approach for Real Time Voltage Stability Monitoring in a Smart Grid System using Synchronized Phasor Measurements

Online voltage stability monitoring using real-time measurements is one of the most important tasks in a smart grid system to maintain the grid stability. Loading margin is a good indicator for assessing the voltage stability level. This paper presents an Extreme Learning Machine (ELM) approach for estimation of voltage stability level under credible contingencies using real-time measurements from Phasor Measurement Units (PMUs). PMUs enable a much higher data sampling rate and provide synchronized measurements of real-time phasors of voltages and currents. Depth First (DF) algorithm is used for optimally placing the PMUs. To make the ELM approach applicable for a large scale power system problem, Mutual information (MI)-based feature selection is proposed to achieve the dimensionality reduction. MI-based feature selection reduces the number of network input features which reduces the network training time and improves the generalization capability. Voltage magnitudes and phase angles received from PMUs are fed as inputs to the ELM model. IEEE 30-bus test system is considered for demonstrating the effectiveness of the proposed methodology for estimating the voltage stability level under various loading conditions considering single line contingencies. Simulation results validate the suitability of the technique for fast and accurate online voltage stability assessment using PMU data.

Research on Voltage Stability Boundary under Different Reactive Power Control Mode of DFIG Wind Power Plant

A novel method is proposed to construct the voltage stability boundary of power system considering different Reactive Power Control Mode (RPCM) of Doubly-Fed Induction Generator (DFIG) Wind Power Plant (WPP). It can be used for reflecting the static stability status of grid operation with wind power penetration. The analytical derivation work of boundary search method can expound the mechanism and parameters relationship of different WPP RPCMs. In order to improve the load margin and find a practical method to assess the voltage security of power system, the approximate method of constructing voltage stability boundary and the critical points search algorithms under different RPCMs of DFIG WPP are explored, which can provide direct and effective reference data for operators.

Cascading Failures in Load-Dependent Finite-Size Random Geometric Networks

The problem of cascading failures in cyber-physical systems is drawing much attention in lieu of different network models for a diverse range of applications. While many analytic results have been reported for the case of large networks, very few of them are readily applicable to finite-size networks. This paper studies cascading failures in load-dependent finite-size geometric networks where the number of nodes is on the order of hundreds as in many real-life networks. In such networks, every node carries a certain amount of load in normal conditions, and maintains a load margin that enables handling a higher load up to a limit, if necessary. We investigate the impact of design parameters such as load margin, node density, and connectivity radius on network reaction to initial disturbances of different sizes. We quantify the damage imposed on the network, and derive lower and upper bounds on the size of this damage. Our finite-size analysis reveals the decisiveness and criticality of taking action within the first few stages of failure propagation in preventing a cascade. Furthermore, studying the trend of the bounds as the number of nodes increases indicates a phase transition behavior in the size of the cascade with respect to the load margin. We derive the critical value of the load margin at which such a transition occurs. The findings of this paper, in particular, shed light on how to choose the load margin appropriately such that a cascade of failures could be avoided.