Risk-Cost Minimization in Optimal Reactive Power Dispatch Problem in the DFIG Integrated System

In this paper, a novel method for a multi-objective and risk-based optimal reactive power dispatch is proposed. The method includes two main objective functions: technical and economic. The technical objective involves minimizing the risks of voltage instability, voltage deviation, and flow violation, and the economic objective involves minimizing the costs of reactive power generation, active power losses, load shedding, and active power rescheduling. Using these functions and assigning different weighting factors for each sub-objective, the risk of the events or uncertainties to customers or the grid can be managed. In addition, moment matching is used to discretize and create scenarios from continues probability distribution functions of wind speed and electrical energy uncertainties. As the number of uncertain variables increases, so does the number of scenarios and the simulation time. Therefore, the fast-forward selection algorithm is applied to reduce the number of scenarios. To reduce the computational complexity and the number of topological scenarios, a new contingency filtering method based on high-risky events is proposed. A modified multi-objective PSO algorithm based on a hybrid PSO with sine-cosine acceleration coefficients is proposed to find the Pareto front of solutions. The method is implemented on the modified IEEE 30-bus test system. To demonstrate the effectiveness of the proposed method, the results are compared with previously published literature. The results show that risk-based scheduling increases system reliability and cost-effectiveness compared to traditional scheduling

Multiobjective Transmission Network Planning considering the Uncertainty and Correlation of Wind Power

In order to consider the uncertainty and correlation of wind power in multiobjective transmission network expansion planning (TNEP), this paper presents an extended point-estimation method to calculate the probabilistic power flow, based on which the correlative power outputs of wind farm are sampled and the uncertain multiobjective transmission network planning model is transformed into a solvable deterministic model. A modified epsilon multiobjective evolutionary algorithm is used to solve the above model and a well-distributed Pareto front is achieved, and then the final planning scheme can be obtained from the set of nondominated solutions by a fuzzy satisfied method. The proposed method only needs the first four statistical moments and correlation coefficients of the output power of wind farms as input information; the modeling of wind power is more precise by considering the correlation between wind farms, and it can be easily combined with the multiobjective transmission network planning model. Besides, as the self-adaptive probabilities of crossover and mutation are adopted, the global search capabilities of the proposed algorithm can be significantly improved while the probability of being stuck in the local optimum is effectively reduced. The accuracy and efficiency of the proposed method are validated by IEEE 24 as well as a real system

Economic operational analytics for energy storage placement at different grid locations and contingency scenarios with stochastic wind profiles

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The placement of energy storage systems (ESS) in smart grids is challenging due to the high complexity of the underlying model and operational datasets. In this paper, non-parametric multivariate statistical analyses of the energy storage operations in base and contingency scenarios are carried out to address these issues. Monte Carlo simulations of the optimization process for the overall cost involving unit commitment and dispatch decisions are performed with different wind and load demand ensembles. The optimization is performed for different grid contingency scenarios like transmission line trips and generator outages along with the location of the ESS in different parts of the grid. The stochastic mixed-integer programming technique is used for optimization. The stochastic model load demand and wind power are obtained from real data. The uncertainty in the operational decisions is obtained, considering the different stochastic realizations of load demand and wind power. The data analytics is performed on ESS operations in the base and its corresponding contingency scenarios with different locations in the grid. Moreover, it is aided by non-parametric multivariate hypothesis tests to understand their dependence amongst various parameters and locations in the grid. The numerical analysis has been shown on a simple 3-bus system considering all the locational and contingency scenarios.F ERDF Cornwall New Energy (CNE

Stochastic Operation of Distribution Networks with Voltage Dependent Load

Uncertainties in load and renewable generations impose new challenges on the operation of distribution networks due to the complexity of physical models and the randomness at the distribution level. This topic has been increasingly studied due to the growing accessibility of real-time data at the distribution level and the increasing uncertainties from high-penetration of renewable generations and the integration of electric vehicles. This work starts with the formulation of adequate network and load models in a deterministic problem. Then the uncertainties are included in these models to find the probability distribution function (PDF) of the state of the system in a probabilistic load flow (PLF). The uncertainty model of the PLF is later used to formulate an optimal power flow (OPF) to find the optimal input of the controllable sources in a typical distribution network. Finally, battery energy storage systems (BESS) are added to the OPF problem, which is further generalized through a distributionally robust approach by considering more realistic randomness with an uncertain PDF. The oncoming permanently close operation of normal open switches between feeders in distribution systems results in larger and meshed networks, which imposes challenges for the real-time operation now required for the supervisory control and data acquisition. This has accelerated the development of decentralized and fast tools for the analysis of new larger distribution networks. In this work, a three-phase decentralized load flow method is developed for distribution networks based on a novel extended current injection model (CIM) with the voltage dependence of the load expressed by the constant-impedance, constant-current and constant-power (ZIP) load model. A hybrid method that combines the good behavior of the Newton-Raphson method over constant power loads and the fixed-point method over constant current load is presented to solve the proposed extended CIM. To consider unbalanced uncertainties from voltage-sensitive loads and photovoltaic (PV) generation in distribution networks, this work proposes a fully analytic second-order probabilistic load flow (PLF) method to realize an accurate and fast three-phase load flow analysis based on the bus injection model (BIM), which is a derivation of the CIM. The load flow equations are modeled using an accurate quadratic expression. To work at the distribution level, the voltage dependence of the load is considered. The uncertainties are modeled in time series as conditional probabilities, reducing the complexity of their PDFs. The PLF is modeled in a fully analytic second-order second-moment (SOSM) stochastic formulation, which can accurately and easily handle PDFs of voltage and current by computing the first two moments. The computation is accelerated by an analytical calculation of the quadratic coefficients over the ZIP parameters. With the proposed SOSM model, this work develops a stochastic AC optimal power flow (SOPF) method. It considers the load voltage dependence, unbalance, and correlation that exist in distribution systems. The proposed SOPF handles the uncertainties of PV sources and loads as voltage sensitive parameters, caused by communication delays. The SOPF method optimizes the active and reactive power of BESS in a static model, as well as the reactive power of PV generators and static var compensators (SVCs). As ZIP parameters are random variables in the PLF, the accurate SOSM model is applied to map the complex uncertainties over the complex voltage to handle the strongly nonlinear relation between the voltage and random ZIP parameters. A second-moment chance constraint is formulated to tackle the voltage and current magnitude over the nonlinear SOSM, based on a conic generalization of the Chebyshev bound. The resulting constraint handles the joint violation considering the correlation among individual constraints and also relaxes the nonconvex minimum voltage constraint. With the inclusion of BESS in the distribution networks, the SOPF problem has to deal with energy horizon constraints, which turns the problem into a multistage OPF problem under uncertainties. Tackling this problem at the distribution level implies dealing with load voltage dependence, which complicates the models. Furthermore, the load behavior at the distribution level changes over time, which leads to a changing PDF. To obtain a good balance between handling the risk of the highly changing load and optimality, the distributionally robust (DR) approach is applied. A distributionally robust multistage OPF (DR-MOPF) is proposed to deal with data-based formulations which rapidly grow in size with the amount of information available. The proposed new paradigm for DR-OPF leverages the optimality advantages of the DR methods and the speed advantages of a conic ambiguity set made around the first two moments of the load and stochastic generation. The optimization minimizes the multistage loss risk which is conic-representable based on the nested property of the expectation. Constraint risk violations being expressed as a distributionally robust CVaR are also conic representable. It is a data-driven approach that learns from data without growing with them

Optimization models for electricity networks and renewable energy under uncertainity

This work focuses on developing optimization models and algorithms to solve problems in electricity networks and renewable energy. The steady rise of electricity demand in the world, along with the deployment of volatile renewable energy resources in greater quantities, will require many researchers, policymakers, and other stakeholders in the field of power management to understand these challenges and use new methods, approaches and technologies to modernize the electric grid. We study reliable and efficient electricity dispatch with minimum costs in power networks and efficient and economic harvesting of ocean wave energy by optimizing wave farm configuration

Decision-making under uncertainty in short-term electricity markets

In the course of the energy transition, the share of electricity generation from renewable energy sources in Germany has increased significantly in recent years and will continue to rise. Particularly fluctuating renewables like wind and solar bring more uncertainty and volatility to the electricity system. As markets determine the unit commitment in systems with self-dispatch, many changes have been made to the design of electricity markets to meet the new challenges. Thereby, a trend towards real-time can be observed. Short-term electricity markets are becoming more important and are seen as suitable for efficient resource allocation. Therefore, it is inevitable for market participants to develop strategies for trading electricity and flexibility in these segments. The research conducted in this thesis aims to enable better decisions in short-term electricity markets. To achieve this, a multitude of quantitative methods is developed and applied: (a) forecasting methods based on econometrics and machine learning, (b) methods for stochastic modeling of time series, (c) scenario generation and reduction methods, as well as (d) stochastic programming methods. Most significantly, two- and three-stage stochastic optimization problems are formulated to derive optimal trading decisions and unit commitment in the context of short-term electricity markets. The problem formulations adequately account for the sequential structure, the characteristics and the technical requirements of the different market segments, as well as the available information regarding uncertain generation volumes and prices. The thesis contains three case studies focusing on the German electricity markets. Results confirm that, based on appropriate representations of the uncertainty of market prices and renewable generation, the optimization approaches allow to derive sound trading strategies across multiple revenue streams, with which market participants can effectively balance the inevitable trade-off between expected profit and associated risk. By considering coherent risk metrics and flexibly adaptable risk attitudes, the trading strategies allow to substantially reduce risk with only moderate expected profit losses. These results are significant, as improving trading decisions that determine the allocation of resources in the electricity system plays a key role in coping with the uncertainty from renewables and hence contributes to the ultimate success of the energy transition

Uncertainty Quantification via Polynomial Chaos Expansion – Methods and Applications for Optimization of Power Systems

Fossil fuels paved the way to prosperity for modern societies, yet alarmingly, we can exploit our planet’s soil only so much. Renewable energy sources inherit the burden to quench our thirst for energy, and to reduce the impact on our environment simultaneously. However, renewables are inherently volatile; they introduce uncertainties. What is the effect of uncertainties on the operation and planning of power systems? What is a rigorous mathematical formulation of the problems at hand? What is a coherent methodology to approaching power system problems under uncertainty? These are among the questions that motivate the present thesis that provides a collection of methods for uncertainty quantification for (optimization of) power systems. We cover power flow (PF) and optimal power flow (OPF) under uncertainty (as well as specific derivative problems). Under uncertainty---we view "uncertainty" as continuous random variables of finite variance---the state of the power system is no longer certain, but a random variable. We formulate PF and OPF problems in terms of random variables, thusly exposing the infinite-dimensional nature in terms of L2-functions. For each problem formulation we discuss a solution methodology that renders the problem tractable: we view the problem as a mapping under uncertainty; uncertainties are propagated through a known mapping. The method we employ to propagate uncertainties is called polynomial chaos expansion (PCE), a Hilbert space technique that allows to represent random variables of finite variance in terms of real-valued coefficients. The main contribution of this thesis is to provide a rigorous formulation of several PF and OPF problems under uncertainty in terms of infinite-dimensional problems of random variables, and to provide a coherent methodology to tackle these problems via PCE. As numerical methods are moot without numerical software another contribution of this thesis is to provide PolyChaos.jl: an open source software package for orthogonal polynomials, quadrature rules, and PCE written in the Julia programming language

Scenario generation and reduction for long-term and short-term power system generation planning under uncertainties

This dissertation focuses on computational issues of applying two-stage stochastic programming for long-term and short-term generation planning problems from the perspective of scenario generation and reduction. It follows a three-paper format, in which each paper discusses approaches to generating probabilistic scenarios and then reducing the substantial computational burden caused by a huge number of scenarios for different applications in power systems. The first paper investigates a long-term generation expansion planning model with uncertain annual load and natural gas price. A two-stage stochastic program is formulated to minimize the total expected expansion cost, generation cost and penalties on unserved energy while satisfying aggregated operational constraints. A statistical property matching technique is applied to simulate plausible future realizations of annual load and natural gas price over the whole planning horizon. To mitigate the computational complexity of a widely used classic scenario reduction method in this context, we firstly cluster scenarios according to the wait-and-see solution for each scenario and then apply the fast forward selection (FFS) method. The second paper prepares a basis for load scenario generation for the day-ahead reliability unit commitment problem. For the purpose of creating practical load scenarios, epi-splines, based on approximation theory, are employed to approximate the relationship between load and weather forecasts. The epi-spline based short-term load model starts by classifying similar days according to daily forecast temperature as well as monthly and daily load patterns. Parameters of the epi-spline based short-term load model are then estimated by minimizing the fitted errors. The method is tested using day-ahead weather forecast and hourly load data obtained from an Independent System Operator in the U.S. By considering the non-weather dependent load pattern in the short-term load model, the model not only provides accurate load predictions and smaller prediction variances in the validated days, but also preserves similar intraday serial correlations among hourly forecast loads to those from actual load. The last paper in this dissertation proposes a solution-sensitivity based heuristic scenario reduction method, called forward selection in recourse clusters (FSRC), for a two-stage stochastic day-ahead reliability unit commitment model. FSRC alleviates the computational burden of solving the stochastic program by selecting scenarios based on their cost and reliability impacts. In addition, the variant of pre-categorizing scenarios improves the computational efficiency of FSRC by simplifying the clustering procedure. In a case study down-sampled from an Independent System Operator in the U.S., FSRC is shown to provide reliable commitment strategies and preserve solution quality even when the reduction is substantial

Analysis of market incentives on power system planning and operations in liberalised electricity markets

The design of liberalised electricity markets (e.g., the energy, capacity and ancillary service markets) is a topic of much debate, regarding their ability to trigger adequate investment in generation capacities and to incentivize flexible power system operation. Long-term generation investment (LTGI) models have been widely used as a decision-support tool for generation investments and design of energy policy. Of particular interest is quantification of uncertainty in model outputs (e.g., generation projections or system reliability) given a particular market design while accounting for uncertainties in input data as well as the discrepancies between the model and the reality. Unfortunately, the standard Monte Carlo based techniques for uncertainty quantification require a very large number of model runs which may be impractical to achieve for a complex LTGI model. In order to enable efficient and fully systematic analysis, it is therefore necessary to create an emulator of the full model, which may be evaluated quickly for any input and which quantifies uncertainty in the output of the full model at inputs where it has not been run. The case study shows results from the Great Britain power system exemplar which is representative of LTGI models used in real policy processes. In particular, it demonstrates the application of Bayesian emulation to a complex LTGI model that requires a formal calibration, uncertainty analysis, and sensitivity analysis. In power systems with large amounts of variable generation, it is important to provide sufficient incentives for operating reserves as a main source of generation flexibility. In the traditional unit commitment (UC) model, the demand for operating reserves is fixed and inelastic, which does not reflect the marginal value of operating reserves in avoiding the events of load shedding and wind curtailment. Besides, the system-wide reserve constraint assumes that the operating reserve can be delivered to any location freely, which is not true in real-world power system operations. To recognize the value and deliverability of operating reserves, dynamic zonal operating reserve demand curves are introduced to an enhanced deterministic UC model for co-optimizing the day-ahead schedules for energy and operating reserves. In the case study on the RTS-73 test system, comparisons are made between the choices of reserve policies (e.g., single, seasonal or dynamic zones) and of different reserve zonal partitioning methods. Results suggest that the enhanced deterministic UC model produces on average lower operational cost, higher system reliability and higher energy and reserve revenues than the traditional one. Finally, we discuss future directions of methodological research arising from current energy system challenges and the computer models developed for better understanding of the impacts of market incentives on power system planning and operations