Power System Uncertainties Research Articles

A computational framework for uncertainty integration in stochastic unit commitment with intermittent renewable energy sources

The penetration of intermittent renewable energy sources (IRESs) into power grids has increased in the last decade. Integration of wind farms and solar systems as the major IRESs have significantly boosted the level of uncertainty in operation of power systems. This paper proposes a comprehensive computational framework for quantification and integration of uncertainties in distributed power systems (DPSs) with IRESs. Different sources of uncertainties in DPSs such as electrical load, wind and solar power forecasts and generator outages are covered by the proposed framework. Load forecast uncertainty is assumed to follow a normal distribution. Wind and solar forecast are implemented by a list of prediction intervals (PIs) ranging from 5% to 95%. Their uncertainties are further represented as scenarios using a scenario generation method. Generator outage uncertainty is modeled as discrete scenarios. The integrated uncertainties are further incorporated into a stochastic security-constrained unit commitment (SCUC) problem and a heuristic genetic algorithm is utilized to solve this stochastic SCUC problem. To demonstrate the effectiveness of the proposed method, five deterministic and four stochastic case studies are implemented. Generation costs as well as different reserve strategies are discussed from the perspectives of system economics and reliability. Comparative results indicate that the planned generation costs and reserves are different from the realized ones. The stochastic models show better robustness than deterministic ones. Power systems run a higher level of risk during peak load hours.

A Flexible Dispatch Margin for Wind Integration

Integrating wind power into power systems contributes to existing variability in system operations. Current methods to mitigate this variability and uncertainty focus on using conventional generator ramping capability. There is also the option of using wind power itself to mitigate the variability and uncertainty that it introduces into the system. This paper introduces the concept of a flexible dispatch margin as a means for wind to participate in mitigating net variability and net uncertainty. In providing a flexible dispatch margin, wind generators under-schedule in the hour-ahead energy market in order to have additional expected flexibility available for the real-time market. The implementation of the flexible dispatch margin is analyzed in a two-stage optimization model with recourse to the flexible dispatch margin, flexible demand and generator ramping. This modeling framework combines Monte Carlo simulations with AC OPF analysis, using the IEEE 39-bus test system. Results show that use of the flexible dispatch margin decreases the reliance on peaking generators to mitigate net variability and uncertainty, and also decreases the frequency of price spike events, particularly as wind penetration increases from 10% to 30%. The analysis emphasizes the importance of increasing flexible resource capability as power system variability and uncertainty increase.

Enhancing Corrected Transient Energy Margin in Electricity Energy Market Operation Using Stochastic Multiobjective Mathematical Programming

In this paper, a new stochastic multiobjective model for the market clearing of the joint energy and reserve auctions is proposed wherein both supply and demand sides can participate as reserves. The proposed framework considers the dynamic security aspect of the power system in the scenario-based market operation. To solve the problem, first, on the basis of lattice Monte Carlo simulation, different scenarios are generated to model the uncertainties of power system (including generating units and transmission line contingencies). Then, the competing objective functions of the proposed framework, including the expected social welfare function and expected corrected transient energy margin (CTEM), are simultaneously optimized for each scenario in the multiobjective framework. To calculate the CTEM, a sensitivity analysis based on the ac power flow formulation is incorporated before solving the optimization problem of the market clearing. The optimization problem is solved considering dc power flow constraints and system reserve requirements. Eventually, the scenarios are aggregated based on the expected value of decision variables to produce the final results of the market clearing framework. The model is applied to the New England test system, and simulation studies are implemented to demonstrate the effectiveness of the proposed method.

Optimal power flow based TU/CHP/PV/WPP coordination in view of wind speed, solar irradiance and load correlations

This paper addresses a novel probabilistic optimisation framework for handling power system uncertainties in the optimal power flow (OPF) problem that considers all the essential factors of great impact in the OPF problem. The object is to study and model the correlation and fluctuation of load demands, photovoltaic (PV) and wind power plants (WPPs) which have an important influence on transmission lines and bus voltages. Moreover, as an important tool of saving waste heat energy in the thermoelectric power plant, the power networks share of combined heat and power (CHP) has increased dramatically in the past decade. So, the probabilistic OPF (POPF) problem considering valve point effects, multi-fuel options and prohibited zones of thermal units (TUs) is firstly formulated. The PV, WPP and CHP units are also modeled. Then, a new method utilizing enhanced binary black hole (EBBH) algorithm and 2m+1 point estimated method is proposed to solve this problem and to handle the random nature of solar irradiance, wind speed and load of consumers. The correlation between input random variables is considered using a correlation matrix. Finally, numerical results are presented and considered regarding the IEEE 118-busses, including PV, WPP, CHP and TU at several busses. The simulation and comparison results obtained demonstrate the broad advantages and feasibility of the suggested framework in the presence of dependent non-Gaussian distribution of random variables.

A Multi-Objective Transmission Expansion Planning Framework in Deregulated Power Systems With Wind Generation

Integration of renewable energy resources into the power system has increased the financial and technical concerns for the market-based transmission expansion planning. This paper proposes a stochastic framework for transmission grid reinforcement studies in a power system with wind generation. A multi-stage multi-objective transmission network expansion planning (TNEP) methodology is developed which considers the investment cost, absorption of private investment and reliability of the system as the objective functions. A non-dominated sorting genetic algorithm (NSGA II) optimization approach is used in combination with a probabilistic optimal power flow (POPF) to determine the Pareto optimal solutions considering the power system uncertainties. Using a compromise-solution method, the best final plan is then realized based on the decision-maker preferences. The proposed methodology is applied to the IEEE 24-bus Reliability Tests System (RTS) to evaluate the feasibility and practicality of the developed planning strategy.

An inexact programming approach for urban electric power systems management under random-interval-parameter uncertainty

In electric power management problems, a number of system parameters are subjected to many powerful and unpredictable influences (e.g. economic situation, technologies in energy conservation). This leads to the difficulty in accurately qualifying them through conventional approaches. In this paper, a concept of random-boundary interval (RBI) whose upper and lower bounds are random variables is introduced to account for the high-uncertain components, like electricity demand, in electric power systems. A fuzzy integer programming model with RBI parameters is developed to support effective planning of urban electric power systems (UEPS). A case study is then provided for demonstrating the applicability of the proposed model. The obtained solutions can be used for generating efficient electricity-supply and capacity-expansion schemes under various situations. Compared with the existing methods, the proposed model could tackle the complex parameter uncertainty in electric power systems, and the potential system-failure risks arising from such uncertainty could be quantified by means of violation levels and satisfaction levels.

Application of linear stability via Lyapunov exponents in high dimensional electrical power systems

Abstract Applications of linear stability via Lyapunov exponents in high dimensional test systems are presented. The stochastic disturbance model is given by a bounded Markov diffusion process, as it appears in the description of load or generation uncertainties of power systems, for example. For such systems, the Lyapunov exponents describe necessary and sufficient conditions for almost sure asymptotic stability. The present article reports results obtained by applying the proposed methodology to four-machine ten-bus, ten-machine thirty-nine-bus, and sixteen-machine sixty-eight-bus international test systems.

Coefficient Diagram Method Based Load Frequency Control for a Modern Power System

With the increasing penetration of renewable energy sources with a wide range of operating conditions causing power system uncertainties, conventional controllers are incapable of providing proper performance to keep the system stable. However, controllable or dispatchable loads such as electric vehicles (EVs) and heat pumps (HPs) can be utilized for supplementary frequency control. This paper shows the ability of plug-in hybrid EVs, HPs, and batteries (BTs) to contribute in the frequency control of an isolated power system. Moreover, we propose a new online intelligent approach by using a coefficient diagram method (CDM) to enhance the system performance and robustness against uncertainties. The performance of the proposed intelligent CDM control has been compared with the proportional-integral (PI) controller and the superiority of the proposed scheme has been verified in Matlab/Simulink programs.

Coordinated Robust Control of DFIG Wind Turbine and PSS for Stabilization of Power Oscillations Considering System Uncertainties

Uncertainties in power systems, such as intermittent wind power, generating and loading conditions may cause the malfunction of power system stabilizing controllers, which are designed without considering such uncertainties. To enhance the robustness of stabilizing controllers against system uncertainties, this paper proposes a new coordinated robust control of doubly fed induction generator (DFIG) wind turbine equipped with power oscillation damper (POD) and synchronous generator installed with power system stabilizer (PSS) for stabilization of power system oscillations. Without the difficulty of mathematical representation, the inverse output multiplicative perturbation is used to model system uncertainties. The structure of POD and PSS is specified as a practical second-order lead/lag compensator with single input. The parameters optimization of POD and PSS is conducted so that the stabilizing performance and robustness of POD and PSS are augmented. The improved firefly algorithm is applied to solve the optimization problem and achieve the POD and PSS parameters automatically. Simulation study in the modified IEEE-39 bus New England system included with DFIG wind turbines ensures that the robustness and stabilizing performance of the proposed coordinated DFIG with POD and PSS are much superior to those of the conventional DFIG with POD and PSS under various severe disturbances and system uncertainties.

A Fuzzy Model with Thermodynamic Based Consequents and a Niching Swarm-Based Supervisor to Capture the Uncertainties of Damavand Power System

In this investigation, a novel fuzzy mathematical program based on thermodynamic principles is implemented to capture the uncertainties of a practical power system, known as Damavand power plant. The proposed intelligent machine takes the advantages of a niching bio-inspired learning mechanism to be reconciled to the requirements of the problem at hand. The aim of the bio-inspired fuzzy based intelligent system is to yield a model capable of recognizing different operating parameters of Damavand power system under different operating conditions. To justify the privileges of using a niching metaheuristic over gradient descend methods, the authors use the data, derived through data acquisition, together with a machine learning based approach to estimate the multi-modality associated with the training of the proposed fuzzy model. Moreover, the niching bio-inspired metaheuristic, niching particle swarm optimization (NPSO), is compared to canonical PSO (CPSO), stochastic social PSO (SSPSO), unified PSO (UPSO), comprehensive learning PSO (CLPSO), PSO with constriction factor (PSOCF) and fully informed PSO (FIPSO). Through experiments and analysis of the characteristics of the problem being optimized, it is proved that NPSO is not only able to tackle the deficiencies of the learning process, but also can effectively adjust the fuzzy approach to conduct the identification process with a high degree of robustness and accuracy.

MIP-Based Stochastic Security-Constrained Daily Hydrothermal Generation Scheduling

This paper presents the application of a mixed-integer programming (MIP) approach for solving stochastic security-constrained daily hydrothermal generation scheduling (SCDHGS). Power system uncertainties including generating units and branch contingencies and load uncertainty are explicitly considered in the stochastic programming of SCDHGS. The roulette wheel mechanism and lattice Monte Carlo simulation (LMCS) are first employed for random scenario generation wherein the stochastic SCDHGS procedure is converted into its respective deterministic equivalents (scenarios). Then, the generating units are scheduled through MIP over the set of deterministic scenarios for the purpose of minimizing the cost of supplying energy and ancillary services over the optimization horizon (24 h) while satisfying all the operating and network security constraints. To a more realistic modeling of the DHGS problem, in the proposed MIP formulation, the nonlinear valve loading effect, cost, and emission function are modeled in linear form, and prohibited operating zones (POZs) of thermal units are considered. Furthermore, a dynamic ramp rate of thermal units is used, and for the hydro plants, the multiperformance curve with spillage and time delay between reservoirs is considered. To assess the efficiency and powerful performance of the aforementioned method, a typical case study based on the standard IEEE-118 bus system is investigated, and the results are compared to each other in different test systems.

Modeling Uncertainties in Power System by Generalized Lambda Distribution

AbstractThis paper employs the generalized lambda distribution (GLD) to model random variables with various probability distributions in power system. In the context of the probability weighted moment (PWM), an optimization-free method is developed to assess the parameters of GLD. By equating the first four PWMs of GLD with those of the target random variable, a polynomial equation with one unknown is derived to solve for the parameters of GLD. When employing GLD to model correlated multivariate random variables, a method of accommodating the dependency is put forward. Finally, three examples are worked to demonstrate the proposed method.

Probabilistic multi-objective transmission investment and expansion planning

Summary In market-based planning studies, the financial aspects of transmission grids have been posed as a major challenge since these are important keys to provide a non-discriminative and competitive environment for energy market participants. In this respect, this paper proposes a probabilistic multi-objective transmission expansion planning algorithm considering private investors' preferences, technical concerns, and random nature of power system uncertainties. The combination of Non-Dominated Sorting Genetic Algorithm II, as a widely-used robust multi-objective optimization technique, and point estimation method is employed to handle non-commensurable probabilistic objective functions. The IEEE Reliability Test System is taken into consideration as the test system to verify and address the different aspects of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.

Short-term load and wind power forecasting using neural network-based prediction intervals.

Electrical power systems are evolving from today's centralized bulk systems to more decentralized systems. Penetrations of renewable energies, such as wind and solar power, significantly increase the level of uncertainty in power systems. Accurate load forecasting becomes more complex, yet more important for management of power systems. Traditional methods for generating point forecasts of load demands cannot properly handle uncertainties in system operations. To quantify potential uncertainties associated with forecasts, this paper implements a neural network (NN)-based method for the construction of prediction intervals (PIs). A newly introduced method, called lower upper bound estimation (LUBE), is applied and extended to develop PIs using NN models. A new problem formulation is proposed, which translates the primary multiobjective problem into a constrained single-objective problem. Compared with the cost function, this new formulation is closer to the primary problem and has fewer parameters. Particle swarm optimization (PSO) integrated with the mutation operator is used to solve the problem. Electrical demands from Singapore and New South Wales (Australia), as well as wind power generation from Capital Wind Farm, are used to validate the PSO-based LUBE method. Comparative results show that the proposed method can construct higher quality PIs for load and wind power generation forecasts in a short time.

Stochastic security constrained unit commitment incorporating demand side reserve

Increasing the social welfare and achieving real competitive markets are the main purposes of consumers participation in electricity markets. Hence, Demand Response Programs (DRPs) have been designed to consider the consumers participation. One of these programs named Emergency Demand Response Program (EDRP) is based on consumers’ responses to high electricity prices and to the incentives that are paid by Independent System Operators (ISOs) in the critical hours. In this paper, a model has been proposed for EDRP participation in the Stochastic Security Constrained Unit Commitment (SCUC) program. Both the spinning reserve and the demand side reserve, which is modeled as EDRP, are taken into account as the operating reserve services. The effects of EDRP and its parameters on the system operation cost have been investigated under power system uncertainties. The two-stage stochastic SCUC model has been utilized for simultaneous clearing of energy and reserve markets. Mixed Integer Linear Programming (MILP) has been used for modeling the proposed method in the GAMS (General Algebraic Modeling System) environment. The proposed model is applied to a 6-bus test system and a modified IEEE Reliability Test System (RTS) to demonstrate its effectiveness.

Probabilistic Assessment and Sensitivity Analysis of Marginal Price of Different Services in Power Markets

Different sources of uncertainty in power systems, i.e., the uncertainties associated with bus loading and component availability is reflected in uncertainties in different system variables through system physical and economical relationships. A stochastic power flow algorithm can be used to model the stochastic nature of power systems. The algorithm introduced in this paper calculates the probability density function (pdf) of marginal prices of different market services. These pdfs provide the market participant with some valuable information to reduce the risk of their decisions and actions. The algorithm linearizes the optimal power flow formulation and uses the Gram-Charlier method to find the pdf of the marginal prices based on the statistical moments of these prices. The market clearing equation is linearized instead of the power flow equations. It is essential for different market participants to reduce the risk of their actions in both planning and operation modes. Application of the mentioned PDFs can help them in this way. The great advantage of the proposed method is that the program execution time is very short. The proposed method is illustrated using the IEEE Reliability Test System and the results are presented and discussed in detail to show the effectiveness of the proposed method.

A Novel Prediction Method for Electric Power Demand Based on Markov Chain Model with a Fuzzy Probability

In this study, a novel prediction method for electric power demand based on markov chain model with a fuzzy probability has been developed. The model improves upon the existing prediction methods with advantages in uncertainty reflection, such as the uncertainties in electric power system which reflect the vague and ambiguous during the process of power load forecasting through allowing uncertainties expressed as fuzzy parameters and discrete intervals. The developed model is applied to predict the electric power demand of a virtual city from 2011 to 2016. Different satisfaction degrees of fuzzy parameters are considered as different levels of detail of the statistic data. The results indicate that the model can reflect the high uncertainty of long term power demand, which could support the programming and management of power system.

Linear Stability via Lyapunov Exponents in Electrical Power Systems

This paper deals with linear systems under sustained random perturbations. The stochastic perturbation model is given by a bounded Markov diffusion process, as it appears, e.g., in the description of load or generation uncertainties of power systems. For such systems, the Lyapunov exponents describe necessary and sufficient conditions for almost sure asymptotic stability. The present article reviews several numerical methods for the computation of Lyapunov exponents and applies this methodology to international test systems: four machines - ten bus and ten machines -thirty nine bus.

Robust digital design of continuous-time nonlinear control systems using adaptive prediction and random-local-optimal NARMAX model

In this paper the time-delay and uncertainty of continuous-time (CT) systems are considered, and it is suggested that input and output of a discrete-time (DT) Neural Plant Model (NPM) and recursive neural controller have scaling factors which limit the value zone of measured data from a system. Adapted scaling factors cause the tuned parameters to converge to obtain a robust control performance. However, the proposed Random-Local-Optimization (RLO) design for a model/controller uses off-line initialization to obtain a near global optimal model/controller. Other important issues are the considerations of cost, greater flexibility, and highly reliable digital products for these control problems. This issue of DT control design for CT plant is more difficult than that of CT control design for CT plant, because of the need to process the modeling error between the CT plant and DT model. The input-delay, uncertainty, and sampling distortion of a CT nonlinear power system need to be solved by developing a digital model-based controller. Here, this is called the DT tracking control design of CT systems (DT–CT).Therefore, the DT structure of the adaptive controller for the CT nonlinear power system should be designed as a kind of feed-forward-Recursive-Predictive controller (FRP). First, due to the problem of delays, a digital neural controller with feed-forward of the reference signal and a Nonlinear Auto-Regressive Moving Average eXogenous (NARMAX) neural model design is adopted to reduce this difficulty. The most important contribution is that the more reasonable and systematic two-stage control design, the CT nonlinear delayed system to be controlled is modeled using a NARMAX technique with the first-stage (off-line) method by the proposed global optimal network algorithm and second-stage (on-line) adaptive steps. Second, the dynamic response of the system is controlled by an adaptive NARMAX neural controller via a sensitivity function. A theorizing method is then proposed to replace the sensitivity calculation, which reduces the calculation of Jacobin matrices of the BP method. Finally, the feed-forward input of reference signals helps the digital neural controller to improve the control performance, and the technique works to control the CT systems precisely.

Risk Assessment of a Line Outage Based on Fuzzy Membership

There are many uncertainties in power system. It is significant to consider the impact of uncertainties when comparing the importance of lines. The fuzzy set theory was applied and the fuzzy load flow calculation on the basis of line outage which had taken into account the generator output and load uncertainties were deduced. Overload, low voltage, and load shedding were selected as risk indexes. Then combined with the severity functions in the risk theory, the risk assessment models based on fuzzy membership have been put forward. Finally, the results of the three indexes and their comprehensive risk index about IEEE 118-bus system were given, and then the importance of each line in the system was compared, which confirms the value of the approach introduced in this paper.