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• An integrated gas and electricity network with heat electrification is developed. • Correlated uncertainties of renewable generation and demand are modelled. • Overload probability of power lines and gas pipelines is evaluated. This paper presents a probabilistic method for assessing overload probability of power lines and gas pipelines in integrated gas and electricity networks with the consideration of heat electrification. The proposed model fully considers the correlated uncertainties associated with intermittent generation and fluctuating loads using suitable probability distribution functions and copulas. The effectiveness of the proposed method is verified with application in two test systems: the integrated 9-bus electricity and 8-node gas network, and the integrated IEEE 39-bus and Belgian 20-node gas network. Numerical results show that heat electrification increases the overload probability of some power lines due to a major shift of heat loads to the electricity network. When the correlations of wind and photovoltaic generation as well as electric, gas and heat loads are considered, the overload probability of these power lines further increases showing the importance of correlation modelling for an accurate estimation of power flows and line overload probability. When an uneven distribution of heat loads (i.e., clustering of low-carbon technologies) in the electricity network is considered, the overload probability of some power lines further increases. Heat electrification decreases the overload probability of most gas pipelines, although the probability of overloading a few gas pipelines increases as a result of supplying gas to gas-fired power generators to meet the electrified heat demand. [ABSTRACT FROM AUTHOR]

In recent years, voltage source converter (VSC) HVdc has emerged as an excellent solution for transmitting offshore renewable energy sources and strengthening transmission corridors. It is also reported in the literature that VSC-HVdc is able to enhance specific types of stability. With growing capacity of VSC-HVdc and increasing uncertainty in the current power system, it is essential to perform a rigorous analysis of its impact on the interdependence of power system dynamics. This paper presents a methodology for the thorough assessment of the impact of VSC-HVdc on interdependence among four types of stability: small-disturbance rotor angle, large-disturbance rotor angle, frequency, and voltage. This analysis is performed assuming uncertain conditions for various VSC-HVdc topologies and system loading and generation conditions. The impact of the VSC-HVdc on the interdependence of dynamic performance is assessed using the Spearman correlation coefficient as a quantification tool. The results obtained show that a significant alteration over the interdependence between power system dynamics occurs with the addition of VSC-HVdc. [ABSTRACT FROM AUTHOR]

Abstract The analysis of power systems with a significant share of renewable generation using probabilistic tools is essential to appropriately consider the impact that the variability and intermittency of the renewable generation has on the grid. This paper provides a critical assessment and classification of the available probabilistic computational methods that have been applied to power system stability assessment (including small and large disturbance angular stability, voltage and frequency stability). A probabilistic analysis framework with a state-of-the-art review of the existing literature in the area is presented comprising of a review of (i) input variable modelling, (ii) computational methods and (iii) presentation techniques for the output/results. The most widely used probabilistic methods in power system studies are presented with their specific application areas, advantages, and disadvantages. The purpose of this overview, classification, and assessment of the existing methods is to identify the most appropriate probabilistic methods to be used in their current forms, or suitably modified, for different types of stability studies of power systems containing renewable generation. Highlights • Uncertainty modelling techniques for independent variables. • Uncertainty modelling techniques for correlated variables. • Probabilistic techniques applied to power system stability. • Identification of efficient computational techniques. • Future research needs in this area. [ABSTRACT FROM AUTHOR]

A high level of stochastic dependence (or correlation) exists between different uncertainties (i.e., loads and renewable generation), which is nonlinear and non-Gaussian and it affects power system stability. Accurate modeling of stochastic dependence becomes more important and influential as the penetration of correlated uncertainties (such as renewable generation) increases in the network. The stochastic dependence between uncertainties can be modeled using 1) copula theory and 2) joint probability distributions. These methods have been implemented in this paper and their performances have been compared in assessing the small-disturbance stability of a power system. The value of modeling stochastic dependence with increased renewables has been assessed. Subsequently, the critical uncertainties that most affect the damping of the most critical oscillatory mode have been identified and ranked in terms of their influence using advanced global sensitivity analysis techniques. This has enabled the quantification and identification of the impact of modeling stochastic dependence on the raking of critical uncertainties. The results suggest that multivariate Gaussian copula is the most suitable approach for modeling correlation as it shows consistently low error even at higher levels of renewable energy penetration into the power system. [ABSTRACT FROM PUBLISHER]

This paper evaluates a number of game theoretic (GT) approaches with the aim of assessing their suitability to identify the most influential parameters affecting the small-disturbance stability of a power system. Identification of the most influential parameters affecting system stability will facilitate cost-effective operation and control of a power system in general as it would require limited network monitoring, control and modelling effort by system operators and stakeholders. After identifying the most influential parameters the financial and human resources could be adequately prioritised and deployed to solve or prevent power system stability problems. A priority ranking procedure based on a GT approach has the advantage, compared to other techniques, of considering simultaneously the effect of individual and all possible combinatorial effects of the uncertain parameters (or players in a game context). In this study, the most influential players have been identified through a multi-level approach considering the power flow in the network (by optimal power flow), small disturbance stability aspects (by modal analysis), rational behavior of individual players (by a sensitivity technique) and formation of groups between players (by cooperative game theory). Various GT approaches have been considered namely Shapley Value, Aumann Shapley, Nucleolus, and τ -value approach in order to compare and assess their suitability for power system applications. The results are illustrated using two test networks and considering several approaches of sensitivity analysis and different degrees of variability in the considered uncertainties. [ABSTRACT FROM AUTHOR]

This paper establishes a generic severity function that can be used to produce power system security risk profiles. It is illustrated by analyzing the impacts of system load attributes on the small-disturbance rotor angle stability of a power system. The load attributes contributing to the oscillatory modes can be considered as inherent uncertain variables within power systems and include load power variations, load composition, and load model parameters. Uncertainty in the renewable power generation is also incorporated in the probabilistic modelling and risk assessment to demonstrate the flexibility of the approach. A novel approach is proposed to select the severity functions to logically represent small-disturbance security margin. The risk profile of a power system has been presented considering the probability density functions of power system critical modal damping and a selected set of severity functions. The analysis techniques developed are illustrated with a modified version of the 68-bus NETS-NYPS power system with a high amount of renewable power penetration. The relative importance of the load attributes and the impact of these attributes on stability boundaries have been identified at varying risk levels with respect to their contribution to small-disturbance stability. [ABSTRACT FROM PUBLISHER]

This paper critically evaluates a number of sensitivity analysis (SA) techniques to identify the most influential parameters affecting power system small-disturbance stability. SA of uncertain parameters has attracted increased attention with the adoption of deregulated market structure, intermittent energy resources, and new types of loads. Identification of the most influential parameters affecting system stability using SA techniques will facilitate better operation and control with reduced monitoring (only of the parameters of interest) by system operators and stakeholders. In total, nine SA techniques have been described, implemented, and compared in this paper. These can be categorized into three different types: local, screening, and global SA. This comparative analysis highlights their computational complexity and simulation time. The methods have been illustrated using a two-area power system and 68 bus NETS-NYPS test system. The priority ranking of all uncertain parameters has been evaluated, identifying the most critical parameters with respect to the small-signal stability of the test systems. It is shown that for many applications, the Morris screening approach is most suitable, providing a good balance between accuracy and efficiency. [ABSTRACT FROM AUTHOR]

This paper critically evaluates a number of uncertainty importance measures for use in power system stability studies. Sensitivity analysis of uncertain system parameters is vital as new technologies proliferate and the total level of system uncertainty grows. Accurate assessment of the importance of different uncertainties can guide power system operators towards parameters which will require the greatest levels of mitigation or increased monitoring in order to reduce the uncertainty and its subsequent impact. Local and global sensitivity analysis techniques are described and evaluated within this paper, including nonparametric methods, variance-based approaches, and distribution-based techniques. The techniques are illustrated using a large 295-bus realistic network model of a generic distribution system. Numerical experiments on dynamic models are used in order to assess the impact of uncertainties on the mitigation of system frequency excursions using single-site and distributed energy storage devices. [ABSTRACT FROM AUTHOR]

This paper proposes a methodology to efficiently estimate the probability of small-disturbance rotor angle instability of uncertain power systems. Traditional Monte Carlo (MC) approaches are computationally intensive and inefficient, particularly when used to study low probability conditions which result in small disturbance instabilities and develop into serious outage events high impact. The proposed methodology uses importance sampling to focus on conditions which contain the high information content required to make relevant decisions about low probability events. Latin hypercube sampling (LHS) is used to efficiently bound the search space and identify operating conditions leading to a marginally stable or unstable system response. The proposed approach is demonstrated on a model of a multi-area transmission network with a significant capacity of intermittent generation connected through a multi-terminal voltage source converter-based high voltage direct current (VSC-HVDC) grid. It is demonstrated that the methodology yields accurate results with just a small fraction of the sample points required using a conventional numerical MC approach. [ABSTRACT FROM PUBLISHER]

This paper proposes a new method for the probabilistic risk assessment of rotor angle instability in power systems using fuzzy inference systems (FISs). The novel two-step approach first models the stochastic uncertainties present within the power system to produced probability density functions (pdfs) for stability indicators. These stability indicators are established for both small and large disturbance rotor angle stability analysis. The pdfs produced are subsequently decomposed into regions based on user-specified threshold values. The outputs from this decomposition are analyzed using fuzzy techniques to complete the risk assessment of instability. The methodology is applied to a multi-area test network into which a VSC-MTDC grid has been embedded to support power transfer from a number of large wind farms. This new combination of probabilistic and fuzzy techniques is shown to provide an effective methodology for quantifying the influence of system uncertainties on the risks of rotor angle stability. [ABSTRACT FROM PUBLISHER]

This paper presents a risk-based probabilistic small-disturbance security analysis (PSSA) methodology for use with power systems with uncertainties. This novel addition to existing dynamic security assessment (DSA) techniques can be used to quantify the small-disturbance stability risks associated with forecasted operating conditions. This approach first establishes the probability density functions (PDFs) for the damping of the critical oscillatory electromechanical modes by modeling the stochastic variation of system uncertainties, such as loading levels, intermittent generation sources, and power flows through voltage-source converter–high-voltage direct current (VSC–HVDC) lines. The produced PDFs are then combined with severity measures (either simple risk matrices or continuous functions) in order to quantify the risk of stability issues for the system associated with the forecasted operating scenario. In addition, the PSSA is used to establish risk-based operational limits and the concept of a probabilistic security margin is introduced to more accurately represent the probabilistic operation of uncertain power systems. The proposed techniques are demonstrated using a multiarea meshed power system incorporating two VSC-HVDC systems, one of which is connected to a large wind farm. [ABSTRACT FROM AUTHOR]

This paper presents comparative analysis of the performance of three efficient estimation methods when applied to the probabilistic assessment of small-disturbance stability of uncertain power systems. The presence of uncertainty in system operating conditions and parameters results in variations in the damping of critical modes and makes probabilistic assessment of system stability necessary. The conventional Monte Carlo (MC) approach, typically applied in such cases, becomes very computationally demanding for very large power systems with numerous uncertain parameters. Three different efficient estimation techniques are therefore compared in this paper—point estimation methods, an analytical cumulant-based approach, and the probabilistic collocation method—to assess their feasibility for use with probabilistic small disturbance stability analysis of large uncertain power systems. All techniques are compared with each other and with a traditional numerical MC approach, and their performance illustrated on a multi-area meshed power system. [ABSTRACT FROM PUBLISHER]

• A probabilistic multi-stability operational boundary assessment based on frequency, large-disturbance rotor angle, small-disturbance rotor angle, and voltage stability for varying renewable energy source penetration levels and loading conditions was investigated and established. • Establishing system's operational boundary from a singular stability type is dangerous as the established operational boundary from each stability type is very different. • The established multi-stability operational boundary is heavily influenced by frequency and large-signal disturbance rotor angle stability. • A significant improvement in the system's operational stability boundaries occur when the VSC-HVDC's ability to independently control active and reactive power via V DC - Q control is fully utilized. This paper presents a framework for defining multi-stability operational boundaries of power systems under varying penetration levels of power electronic interfaced generation and uncertain system's loading. Boundaries are established considering the small-disturbance and large-disturbance rotor angle stability, as well as the frequency and voltage stability of the system. Estimating system's operational boundary from multi-stability perspectives will provide invaluable information on how to best operate the system and how to mitigate certain condition that leads to instability especially in the current deregulated market and high penetration of power electronic interfaced generations. A singular stability assessment and its subsequent operational boundary may be valid only for a specific stability study and those may not be true for other types of stability. This paper illustrates the proposed framework in a modified New England Test System using a probabilistic approach. The impact of these varying loading conditions and renewable energy sources penetration levels are quantified on a per -stability-type basis and then aggregated into the multi-stability perspective. The established multi-stability operational boundary is heavily influenced by the frequency and large-signal disturbance rotor angle stability. A significant improvement in the system's operational stability boundaries, particularly for voltage stability and small disturbance rotor angle stability, occur when the voltage source converter high voltage direct current's ability to independently control active and reactive power via V DC - Q control is fully utilized. [ABSTRACT FROM AUTHOR]

This paper explores the feasibility of using the Probabilistic Collocation Method (PCM) in power-system studies in the presence of uncertainties. The application of the PCM is illustrated on small disturbance stability studies and voltage stability studies. First, the PCM is used to determine the effects of a supplementary power oscillation damping (POD) controller installed on a VSC-HVDC line in the presences of parameter and operational uncertainties. Second, it is used to calculate the probabilistic distance to voltage collapse in a distribution system based on measurement errors. The PCM is shown to produce accurate statistical results whilst drastically reducing the computational time of the studies in both cases. Additionally, a ranking process based on eigenvalue sensitivity is presented alongside the small disturbance analysis as an appropriate method for reduction of system complexity for extension to large power systems. This technique is validated through the application of the PCM on a large power-system model, yielding accurate probabilistic results. [ABSTRACT FROM PUBLISHER]

• A generalized framework for transient stability assessment. • Practical for power systems with uncertainties. • Useful in development of probabilistic transient stability assessment frameworks. • Easy to implement on existing practical computational network models. This paper introduces a method for the identification of transient stability boundaries in power systems with multidimensional uncertainties. This method uses a parametric space rather than the state-space to identify the critical operating states. First, different transient stability indices are used to map the state-space of system into the index-specific parametric spaces. Then, these index-specific parametric spaces are characterized to identify their practicality and effectiveness to reflect the system's state-space information accurately and to quantify uncertainties. Finally, the transient stability boundaries are identified using the index-specific parametric spaces considering multidimensional uncertainties. The indices studied in this paper are on basis of rotor-angle difference, transient kinetic energy, and transient potential energy. This method is verified using a 16-machine, 68-bus computer model of the New England Test System and the New York Power System in MATLAB and DigSILENT environments. The uncertainty in this paper is represented in up to 4-dimensions and is modeled in form of loading conditions and generation dispatch uncertainties. This method is further applicable to higher dimensions and other forms of uncertainties and has the utility for probabilistic studies and predictive analytics. [ABSTRACT FROM AUTHOR]