Load Uncertainty Research Articles

Frequency Control of Interconnected Power System via SBO assisted Simultaneous Tuning Strategy in Presence of DFIG

To achieve the objectives of the automatic generation control (AGC) of wind integrated interconnected power system (WIIPS), better tuning and control strategies are required. This paper suggests simultaneous tuning strategy for the AGC and wind system controllers to improve the stability of the WIIPS. The bulk amount of wind is integrated into the grid using the doubly fed induction generator (DFIG) and its simplified model is used to simulate the WIIPS. Initially, classical controllers are opted in AGC mechanism to reduce the frequency disturbances caused by the load and wind generation uncertainties. Further, classical controllers of WIIPS are replaced with cascade controllers to enhance the system frequency profile during the disturbances. The optimal set of solutions of the classical and cascade controllers are examined by the satin bowerbird optimizer (SBO) with the help of integral square error as fitness function of the optimization problem. Comparisons are provided to show the merits of the WIIPS over normal interconnected power system, cascade controller over classical controller and simultaneous tuning strategy over regular tuning mechanism.

Probabilistic analysis of lateral behaviour of offshore wind turbine monopile considering uncertainties of geological model and loads

Due to the complex geological, meteorological and hydrological conditions, along with the limited availability of field measurements, multiple uncertainties are related to the performance analysis of the offshore wind turbine. The main sources of uncertainty are the geological model and the environmental loads. However, the geological model uncertainty and loads uncertainty were often characterized separately in previous studies. To this end, this article proposes a novel framework for the coupled characterization of the geological model and loads uncertainties. With this new framework, the geological model is generated using a conditional random field method, in which the stratigraphic and geo-properties uncertainties are characterized simultaneously. Next, environmental parameters are considered as random variables, and the cross correlation between different environmental parameters is captured with the Pearson correlation coefficient. Then, multiple realizations of the geological model and these of environmental parameters are sampled with Monte Carlo simulation. With these generated realizations as inputs, the monopile foundation performance could then be analyzed probabilistically considering uncertainties of the geological model and loads. To demonstrate the effectiveness of the new framework, a case study of an offshore site in Taiwan is conducted. Further, a comparative study is performed to quantitatively reveal the influence of different uncertainty sources on site characterization and monopile behaviour assessment, through which the superiority of the presented framework is demonstrated.

Reliability-driven time-of-use tariffs for efficient plug-in electric vehicle integration

Demand response (DR) plays a crucial role in balancing electricity supply and demand, but existing studies on price-based DR for plug-in electric vehicle (PEV) load management lack comprehensive considerations. Therefore, this study designs reliability-driven time-of-use (TOU) tariffs for the integration of PEVs, considering various factors such as random component failures, the stochastic characteristics of non-dispatchable components, and fluctuations in load patterns and uncertainties. The proposed framework employs advanced stochastic simulation models to assess generation facility reliability amidst extensive PEV deployment in three steps. First, individual components, including conventional generation capacity, renewable energy sources, and demand, as well as PEV load models, are developed. Then, a system reserve margin assessment is carried out via the generation of seasonal synthetic time series data. During this step, innovative techniques, including box-plot methods and expert rules, are used to simplify the representation of the system reserve margin at each hour. Finally, optimized TOU pricing schedules for PEVs are generated. These pricing hours are initially categorized as off-peak, mid-peak, or on-peak, streamlining scenario analysis and aligning PEV charging profiles with predefined pricing schedules for grid reliability evaluation. Case studies have shown that the proposed method can improve the reliability indices by effectively mitigating the impacts.

A risk‐averse strategy based on information gap decision theory for optimal placement of service transformers in distribution networks

AbstractIn distribution networks, among the planning problems, optimal placement of medium voltage to low voltage (MV/LV) transformers is a vital and challenging issue. Electrical load uncertainty is an important factor that affects the result of this planning problem. This paper investigates optimal allocation of service transformers with respect to the load uncertainty modelled by information gap decision theory (IGDT). For this aim, the planning problem is solved in risk‐neutral (RN) and risk‐averse (RA) frameworks. In RN strategy, objective function is defined to minimize the cost of service transformers and low voltage feeders as well as the cost of power losses. On the other hand, in RA strategy, objective function is defined to maximize the radius of the uncertainty in such a way that any deviation of the uncertain parameter results in an objective function value that is not worse than the critical limit. The optimization problem is solved by crow search algorithm (CSA) and particle swarm optimization (PSO) and the results are compared. In mid‐term planning, with respect to the deviation factors of 0.05, 0.1, 0.15, 0.2, 0.25 and 0.3, optimal values of the uncertainty radius are 5.89%, 13.64%, 21.37%, 28.97%, 34.39% and 43.46%, respectively. In long‐term planning, with respect to the deviation factors of 0.05, 0.1, 0.15, 0.2, 0.25 and 0.3, optimal values of the uncertainty radius are 6.92%, 13.33%, 20.39%, 27.03%, 34% and 40.46%, respectively. Moreover, on average, CSA finds more promising results than PSO.

Leveraging Transformer-Based Non-Parametric Probabilistic Prediction Model for Distributed Energy Storage System Dispatch

In low-voltage distribution networks, distributed energy storage systems (DESSs) are widely used to manage load uncertainty and voltage stability. Accurate modeling and estimation of voltage fluctuations are crucial to informed DESS dispatch decisions. However, existing parametric probabilistic approaches have limitations in handling complex uncertainties, since they always rely on predefined distributions and complex inference processes. To address this, we integrate the patch time series Transformer model with the non-parametric Huberized composite quantile regression method to reliably predict voltage fluctuation without distribution assumptions. Comparative simulations on the IEEE 33-bus distribution network show that the proposed model reduces the DESS dispatch cost by 6.23% compared to state-of-the-art parametric models.

Carbon-oriented pricing scheme in digitalized power transmission networks utilizing carbon-driven demand response program under risk investigation

The main challenge for future sustainable societies is dealing with the high portion of released CO2 throughout smart power transmission systems; consequently, a comprehensive carbon-based framework is required that directly calculates stakeholders' contribution to the network's CO2 emissions. In this case, this paper proposes a mechanism driven by the carbon-tracing (CTR) process to tackle carbon emissions in smart transmission networks. Using the CTR mechanism enables the digitalized independent system operator (ISO) to allocate the total emissions among participants using the real-time data received from smart grid infrastructures. Furthermore, a carbon-based nodal pricing mechanism for gas and power systems is proposed, which reflects the received data from CTR analysis. To reduce carbon emissions in the smart power transmission network, a carbon-based demand response (DR) procedure is suggested, under which consumers will receive higher incentives for reducing their consumption, especially in high-carbon-intensity buses. In addition, in this paper, for effective management of carbon pollution, the uncertainties of wind and loads and leading risks to carbon and operation costs have been modeled. Hence, the conditional value-at-risk (CVaR) method is utilized for modeling the risks related to uncertainties. It can be seen that applying the proposed CVaR-based risk assessment framework and carbon-incentive-based DR programs led to a decrease in daily total carbon and operation costs by 0.66% and 1.02%, respectively.

An integrated energy system day-ahead scheduling method based on an improved dynamic time warping algorithm

With the construction and development of the new energy system, the integrated energy system (IES) has garnered significant attention as a crucial energy carrier in recent years. Therefore, to address the scheduling challenges of IES influenced by uncertainty in source load and mitigate the conservatism of scheduling schemes while enhancing clustering accuracy, a method for day-ahead top-note scheduling of IES is proposed. First, by improving dynamic time warping (DTW) for hierarchical clustering of wind, solar, and load data in IES, typical scenarios of IES are derived. Second, using the interval method to model wind, solar, and load data in IES along with their coupled devices and considering the conservatism issue of interval optimization, the established IES interval model undergoes affine processing. Finally, with the goal of minimizing the operating costs of IES, a day-ahead interval affine scheduling model is established, which is solved using the CPLEX Solver and INTLAB toolbox, and scheduling schemes for all typical scenarios are provided. Through comparative analysis of calculation examples, it is found that the method proposed in this paper can enhance clustering accuracy and reduce the conservatism of system scheduling schemes.

Safe Reinforcement Learning-Based Balance Control for Multi-Cylinder Hydraulic Press

Abstract Considering the load uncertainty and unmodeled dynamics in multicylinder hydraulic systems, this paper proposes a balance control algorithm based on safe reinforcement learning to release the restrictions of classical model-based control methods that depend on fixed gain. In this paper, the hydraulic press is controlled by a trained agent that directly maps the system states to control commands in an end-to-end manner. By introducing an action modifier into the algorithm, the system states are kept within security constraints from the beginning of training, making safe exploration possible. Furthermore, a normalized exponential reward function has been proposed. Compared with a quadratic reward function, the precision is greatly improved under the same training steps. The experiment shows that our algorithm can achieve high precision and fast balance for multicylinder hydraulic presses while being highly robust. To the best of our knowledge, this research is the first to attempt the application of a reinforcement learning algorithm to multi-execution units of hydraulic systems.

Sensitivity of fatigue reliability in wind turbines: effects of design turbulence and the Wöhler exponent

Abstract. Fatigue assessment of wind turbines involves three main sources of uncertainty: material resistance, load, and the damage accumulation model. Many studies focus on increasing the accuracy of fatigue load assessment to improve the fatigue reliability. Probabilistic modeling of the wind's turbulence standard deviation is an example of an approach used for this purpose. Editions 3 and 4 of the IEC standard for the design of wind energy generation systems (IEC 61400-1) suggest different probability distributions as alternatives for the representative turbulence in the normal turbulence model (NTM) of edition 1. There are debates on whether the suggested distributions provide conservative reliability levels, as the established design safety factors are calibrated based on the representative turbulence approach. The current study addresses the debate by comparing annual reliability based on different scenarios of NTM using a probabilistic approach. More importantly, it elaborates on the relative importance of load assessment accuracy in defining the fatigue reliability. Using the DTU 10 MW reference wind turbine and the first-order reliability method (FORM), we study the changes in the annual reliability level and its sensitivity to the three main random inputs. We perform the study considering the blade root flapwise and the tower base fore–aft moments, assuming different fatigue exponents in each load channel. The results show that integration over distributions of turbulence in each mean wind speed results in less conservative annual reliability levels than representative turbulence. The difference in the reliability levels varies according to turbulence distribution and the fatigue exponent. In the case of the tower base, the difference in the annual reliability index after 20 years can be up to 50 %. However, the model and material uncertainty have much higher effects on the reliability levels compared to load uncertainty. Knowledge about such differences in the reliability levels due to the choice of turbulence distribution is especially important, as it impacts the extent of lifetime extension through reliability reassessments.

Short-term load forecasting based on CEEMDAN and dendritic deep learning

Short-term load forecasting (STLF) plays a key role in improving the operational efficiency of real-time electricity markets by reducing load uncertainty, optimising the allocation of generation resources and increasing the reliability of electricity supply. Despite significant advances in the field, achieving high accuracy in STLF remains a challenge due to the inherent complexity and volatility of load data. This study proposes a novel STLF method that synergistically combines the strengths of a dendritic neuron model (DNM), long short-term memory, and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) to address these challenges. First, historical load data is decomposed into components of different frequencies using CEEMDAN. Then, LSTM is used to extract the temporal characteristics of these load subsequence components in combination with various influencing factors such as temperature and humidity. Uniquely, this study innovatively integrates a dendritic neuron model instead of the traditional fully connected layer, a structural innovation that enhances the model’s ability to explore the intrinsic correlations of the time series data in depth. This allows the model to process and predict each component individually, and then later reconstruct and sum these independent prediction results to obtain a final prediction value with higher accuracy. Experiments are conducted on the Panama electricity load dataset to compare the proposed dendritic learning model with several state-of-the-art models, including CrossFormer and Transformer. The results confirm that the proposed model has significantly better prediction accuracy.

Entirely Coupled Recurrent Neural Network-Based Backstepping Control for Global Stability of Power System Networks

In an interconnected power system network, global performance is affected by various unknown power system parameters subjected to system uncertainties. These unknown parameters in the control expression deteriorate the performance of the power system network. Therefore, these terms associated with the control expression must be estimated precisely. This paper proposes an adaptive backstepping scheme using an entirely coupled recurrent neural network (ECRNN) to estimate these control terms. Three continuous differentiable functions are used to design control input, virtual signals, and adaptive control laws to achieve global performance. The objective of ECRNN is to reduce the control complexity by estimating the associated nonlinear term in the control expression. It will facilitate the complex formulation of the controller and improve system performance. The robust functional estimation ability of ECRNN will make the system immune to uncertainties that may appear due to external disturbances. In ECRNN, feedback loops are added to each neuron layer to achieve additional estimation accuracy. The proposed adaptive law enhances the online weight update speed and accuracy. Verification of the proposed scheme is carried out in MATLAB/Simulink. It is also verified in the real-time digital simulator (RTDS) platform using the IEEE standard New England 39-bus, 10-machine power system model. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the existing limitations in the global performance of a multimachine power system network due to uncertainty in the system parameters. Uncertainties in the power system network primarily appeared due to penetration of renewable power sources, load uncertainty, or occurrence of an uncertain fault in the network. As power system networks are complex nonlinear interconnected systems, these perturbations in the generator states may cause economic losses, load demand uncertainty, or electric scarcity. Thus, a control scheme is required to address the global performance of such networks. This article proposes uniform ultimate bounded stability of synchronous generators in a multimachine power system network with a robust ECRNN-based backstepping control design. The other available technique has not adequately addressed the global performance under uncertainties. The efficacy of the proposed scheme is verified in a real-time environment via a real-time digital simulator which may be a feasible solution for designing excitation control for the synchronous machine in an extensive industrial network.

Optimal operation of multiple energy system considering load management approach and uncertainty

In recent years, the advancement of technology has led to the development of energy networks' infrastructure, resulting in the transformation of conventional networks into smart networks. By incorporating communication equipment, each component of the network can now exchange information with other components, creating an environment where innovative ideas can be implemented. One such idea is the utilization of multi-carrier energy systems, also known as Energy Hubs. Integrating energy hubs into traditional networks used to be a challenging task. However, with the expansion and enhancement of smart networks, the potential for incorporating and locating energy hubs within the power grid has significantly increased. In these systems, the focus shifts from optimizing a single energy carrier to ensuring the optimal operation of a system that encompasses multiple energy carriers, such as natural gas, electric grid, and thermal energy. Energy hubs act as intermediaries between energy supply companies and various consumers, including residential, commercial, and industrial sectors. These energy suppliers can encompass different energy networks, such as electricity, gas, and local heating. The integration of residential and commercial energy hubs has become a crucial aspect of modern energy systems, particularly in the context of load response applications. This paper proposes a novel approach for effectively utilizing residential and commercial energy hubs, taking into account the time of use (ToU) load response program. In the proposed system, the inherent uncertainties of the system are addressed using the two-point estimation method of the model. To achieve the desired objective, the Cuckoo optimization algorithm, a well-established meta-heuristic algorithm for solving optimization problems, is employed. This algorithm aids in determining the optimal scheduling of energy resources while considering ToU tariffs and load management plan signals. The results demonstrate that the proposed approach can significantly reduce energy costs for the energy system.

Residential net load interval prediction based on stacking ensemble learning

In response to the high uncertainty associated with residential net load due to the coupling of distributed photovoltaic generation and user demand, this paper proposed a novel cluster-based stacking ensemble learning model for net load interval prediction. Firstly, the k-means algorithm is employed to discover the similarity in user electricity consumption patterns. Then, a RIME optimization algorithm with local enhancement (LRIME) is developed to optimize the parameters and weights of the base learners in stacking ensemble learning. Subsequently, base learners with strong predictive capabilities and significant diversity are chosen as the first-layer predictive models, extreme learning machine (ELM) is utilized as the second-layer predictive model, ultimately resulting in the proposed stacking ensemble learning prediction model. And utilizing the bootstrap method to fit the volatility of point predictions, different prediction intervals are obtained at varying confidence levels, aiming to quantify the integrated uncertainty in photovoltaic generation and load. Testing on the open Ausgrid electricity load data in Australia provided robust validation of the proposed method's effectiveness. In comparison with other outstanding prediction models, the proposed ensemble model can effectively capture the uncertainty in integrating photovoltaic generation and user load.

Parameterized Reduced-Order Models for Probabilistic Analysis of Thermal Protection System Based on Proper Orthogonal Decomposition

The thermal protection system (TPS) represents one of the most critical subsystems for vehicle re-entry. However, due to uncertainties in thermal loads, material properties, and manufacturing deviations, the thermal response of the TPS exhibits significant randomness, posing considerable challenges in engineering design and reliability assessment. Given that uncertain aerodynamic heating loads manifest as a stochastic field over time, conventional surrogate models, typically accepting scalar random variables as inputs, face limitations in modeling them. Consequently, this paper introduces an effective characterization approach utilizing proper orthogonal decomposition (POD) to represent the uncertainties of aerodynamic heating. The augmented snapshots matrix is used to reduce the dimension of the random field by the decoupling method of independently spatial and temporal bases. The random variables describing material properties and geometric thickness are also employed as inputs for probabilistic analyses. An uncoupled POD Gaussian process regression (UPOD-GPR) model is then established to achieve highly accurate solutions for transient heat conduction. The model takes random heat flux fields as inputs and thermal response fields as outputs. Using a typical multi-layer TPS and thermal structure as two examples, probabilistic analyses are conducted. The mean square relative error of a typical multi-layer TPS is less than 4%. For the thermal structure, the averaged absolute error of the radiation and insulation layer is less than 25 °C and 6 °C when the maximum reaches 1200 °C and 150 °C, respectively. This approach can provide accurate and rapid predictions of thermal responses for TPS and thermal structures throughout their entire operating time when furnished with input heat flux fields and structural parameters.

Hybrid uncertainty approach for management of energy storage-embedded soft open points in distribution grids

Energy storage-embedded soft open point (ESOP) is an innovative electronic device that incorporates energy storage capabilities and is designed to interconnect two or three neighboring distribution feeders. Its primary functions include active power control, reactive power compensation, and grid voltage regulation. On the other hand, distribution grids have been equipped with other distributed energy resources (DERs) such as smart PV inverters, renewable energy sources (solar and wind), and so on. Therefore, this article proposes a novel management scheme for the mentioned devices in distribution grids based on a convex formulation to take powerful solvers like CPLEX into account. Since there are a set of uncertainties associated with the model, including renewable resources, loads, and market price, a hybrid framework is developed based on the unscented transformation (UT) method and information gap decision theory (IGDT). In other words, the uncertainties of renewable resources and loads are captured by the UT method which could provide a correlation among uncertain parameters, while the IGDT method is employed to model the uncertainty associated with the market price. The hybridization of these methods assists in reducing the discrepancy between the actual and predicted values of uncertain parameters. The model is applied to a 33-bus grid, considering various case studies. The proposed method results in a substantial operational cost reduction of approximately 26.82 %. Additionally, it ensures a flatter voltage profile across the network, with the minimum voltage reaching 0.985 p.u.

Belbic frequency control of provisional microgrid with hybrid AC/DC microgrid and renewable energy sources

Nowadays, intelligent control methods play an important role in the advancement of technology and the human movement towards further evolution. The development of new frameworks for power generation and distribution systems by designing a microgrid structure with economic capabilities is one of these areas of progress. Therefore, this paper introduces a new practical method for controlling the frequency of provisional microgrid and is able to cover the following issues at the same time including (1) It considers the nonlinear model of provisional microgrid which has a hybrid structure (AC and DC) in addition to renewable energy sources; (2) Introduces a method for microgrid frequency control under different operational conditions that performs based on the brain emotional learning; (3) Ensures the operation and applicability of the control method for the provisional microgrid through implementation of FPGA for the first time; (4) Confirms the robustness of the proposed method under severe load changes and generation from renewable sources. So, the effects of wind turbines and solar energy are considered in the simulation scenario and under the influence of various changes in load and system uncertainties, the robustness and efficiency of the proposed method are well demonstrated.

Optimal scheduling of a microgrid based on renewable resources and demand response program using stochastic and IGDT-based approach

Optimal economic scheduling of microgrids with photovoltaic (PV) and wind generation has gained increased attention during recent years. Integration of renewable energy resources in microgrids requires increasingly active control and management of energy storages and demand response (DR). In this paper, a risk-based stochastic optimal energy management model is developed for microgrid with renewables, energy storage and load control by time-of-use-based DR programs. Microgrid includes PV system, wind system, micro-turbine, fuel cell, electric vehicle (EV), and energy storage. Information-gap decision theory (IGDT) is employed to address the uncertainty of loads and to provide the operating strategies for the microgrid controllable energy resources. This proposed model has been solved as a mixed-integer non-linear programming (MINLP) in General Algebraic Modeling System (GAMS) software and simulation results in different conditions are studied and discussed. Three different risk management strategies have been studied such as risk-averse, risk-neutral and risk-seeker mode. The simulation results indicate that the impacts of risk-averseness or risk-seeker of the decision maker affect the system operation. For instance, the results showed the DR program's role in risk-averse and risk-taking strategies, impacting consumption and costs. The proposed model ensures the risk-averse decision-maker that if the uncertain parameter deviates within the optimum robustness region, the final cost will not exceed the critical cost. On the other hand, the risk-seeking decision-maker can reach lower final costs by accepting the risks if the uncertain parameter deviates favorably within the opportunity region. Decision-makers can manage risks by adjusting consumption. Thus, considering the cost of risk management is crucial, as it increases with robust or opportunistic approaches.

Enhanced energy balancing and optimal load curtailment strategy for DC microgrid integration in hybrid AC/DC distribution networks

AbstractUnleashing the potential of distributed renewable energy sources (RESs), intelligent and autonomous microgrids are becoming pivotal in attaining net‐zero carbon emission goals. Hybrid AC/DC microgrids rise as cutting‐edge microgrid topologies, capitalising on the best of both AC and DC systems. However, the integration of intermittent renewables and uncertainties in loading poses stability challenges. Advanced bidirectional converter controls provide efficient power exchange, but in extreme contingencies, a resilient supervisory control framework (load management/load curtailment approach) is inevitable to withstand/avoid unplanned renewable disruptions/blackouts. Moreover, the operational paradigm shift towards achieving net‐zero emissions, isolated operation of RESs, and conventional load shedding methods are anticipated to encounter substantial challenges, necessitating the development of alternative strategies. In order to improve the stability of hybrid microgrid systems in islanding scenarios, this research presents an energy balancing and load curtailment strategy. The proposed method aims at optimising resource utilisation, prioritising essential loads, and executing an optimal load curtailment strategy (if required), thereby augmenting the stability of systems. Unlike a meta‐heuristic or exhaustive search, which depends on 2n − 1 possible combinations and become unworkable as load numbers increase, the suggested methodology is based on a mathematically modelled load restriction method. By including load criticality, this strategy effectively prevents blackouts even with an increasing number of loads, providing a significantly more useful and practical solution. Additionally, the proposed charging algorithm ensures that the energy storage system imports energy from the grid during off‐peak hours and maximises power generation from the DC subgrid. The efficacy of the proposed strategy is validated using a modified IEEE‐33 bus system as a test case for a hybrid AC/DC microgrid. Simulation results demonstrate the effectiveness of the MILP‐based load curtailment approach in maintaining system stability and preventing blackouts during unforeseen events.

Attractive Ellipsoid Technique for a Decentralized Passivity-Based Voltage Tracker for Islanded DC Microgrids

A new passivity-based voltage tracker for islanded Direct Current (DC) microgrids is presented in this paper. The proposed design develops a new sufficient condition for passivity-based state feedback with proportional and integral control using the attracting ellipsoid method. In this paper, we consider the time behavior of the extended vector, which completely describes the principle properties of the closed-loop system such as the boundedness of the trajectories within some ellipsoid and the dependence of its “size” on the feedback gains. The next step, which we are realizing in this paper, is the minimization of the attractive ellipsoid by selecting the “best” admissible feedback parameters. Here, it is important to note that the applied feedback is of PD-type (proportional differential) on the system state and I-type (integral) on the output. This is a new construction of the suggested feedback which gives several advantages for a designer. The suggested control is decentralized and uses only the local states; it is cost-effective and avoids the time delays in the communication networks which are needed if centralized control is used. The suggested control is carried out in the bilinear matrix inequality (BMI) framework. Extensive simulation is performed on a test system composed of renewable energy sources, under plug and play (PnP) operations, and uncertainties in distribution lines and loads. The performance of the proposed decentralized voltage controller is compared with that of a voltage tracker present in the literature. The comparison shows the improvements introduced by the proposed control ensure the stability of the dc bus voltage and a quick response under different scenarios of operating conditions.

A Pushover analysis approach considering structural and loading uncertainties for seismic performance assessment

This paper proposes an approach for evaluating the seismic performance of buildings. By considering the uncertainties in material and geometrical properties of the structural elements as well as those related to the seismic loading, this method aims to delimit the performance zone of the structure rather than focusing on a single performance point commonly used in pushover analysis. This zone makes it possible to identify the probable levels of performance of the building linked to uncertainties and to indicate the most severe level of damage. Reasoning by performance points leads to an answer that gives a single state of damage. The performance zone is defined by capacity curves and response spectrum representing the mean values plus and minus standard deviation obtained by Monte Carlo simulations. These simulations consider the stiffnesses of the structural elements, the natural periods, and the damping ratio of the response spectrum as random variables. The application of the procedure to a case of a building made it possible to identify the upper limit of damage corresponding to the most unfavourable scenario of uncertainties, as well as the situation of the response value of the studied structure in the performance zone, indicating a less critical level of damage (minor damage) to the building. The calculation of the performance point revealed a level of damage oscillating between Immediate Occupancy (IO) and Life Safety (LS). Considering the uncertainties in the material and geometric properties of the structural elements as well as those linked to the response spectrum, the probable extreme damage state is between the LS and CP levels (severe damage).