An Adaptive Robust Optimization Model for Power Systems Planning With Operational Uncertainty

There is an increasing necessity for new long-term planning models to adequately assess the flexibility requirements of significant levels of short-term operational uncertainty in power systems with large shares of variable renewable energy. In this context, this paper proposes an adaptive robust optimization model for the generation and transmission expansion planning problem. The proposed model has a two-stage structure that separates investment and operational decisions, over a given planning horizon. The key attribute of this model is the representation of daily operational uncertainty through the concept of representative days and the design of uncertainty sets that determine load and renewable power over such days. This setup allows an effective representation of the flexibility requirements of a system with large shares of variable renewable energy, and the consideration of a broad range of operational conditions. To efficiently solve the problem, the column and constraint generation method is employed. Extensive computational experiments on a 20-bus and a 149-bus representation of the Chilean power system over a 20-year horizon show the computational efficiency of the proposed approach, and the advantages as compared to a deterministic model with representative days, due to an effective spatial placement of both variable resources and flexible resources.

The increasing high penetration of wind power will further increase the uncertainty in power systems, and three key issues should be addressed: 1) determining the maximum accommodation level of wind power without sacrificing system reliability; 2) quantifying the potential risk when the wind generation realization is beyond the prescribed uncertainty sets; and 3) how to reduce the risk loss. Motivated by these, a risk-based two-stage robust unit commitment (RUC) model is proposed to analyze the admissibility of wind power. In this model, the electricity storage system (ESS) is utilized for managing the wind power uncertainty to reduce the risk loss. Different from a determined uncertainty set in the previous RUC, the proposed method can flexibly adjust the uncertainty set by optimizing the operational risks including the wind spillage risk and load shedding risk. Conditional Value-at Risk (CVaR) is adopted to describe the risk loss when the real wind power output is beyond the predefined uncertainty set. Meanwhile, the low-probability, high-influence events are taken into the account based on CVaR to determine the optimal acceptable wind generation considering the tradeoff between reliability and economics. The proposed model is solved effectively by the modified column and constraint generation method. Case studies on two benchmark systems illustrate that the ESS can reduce the risk loss of power system and improve the ability to accommodate the uncertainty of wind generation.

A comprehensive review of uncertainties in power systems, covering modeling, impact, and mitigation, is essential to understand and manage the challenges faced by the electric grid. Uncertainties in power systems can arise from various sources and can have significant implications for grid reliability, stability, and economic efficiency. Australia, susceptible to extreme weather such as wildfires and heavy rainfall, faces vulnerabilities in its power network assets. The decentralized distribution of population centers poses economic challenges in supplying power to remote areas, which is a crucial consideration for the emerging technologies emphasized in this paper. In addition, the evolution of modern power grids, facilitated by deploying the advanced metering infrastructure (AMI), has also brought new challenges to the system due to the risk of cyber-attacks via communication links. However, the existing literature lacks a comprehensive review and analysis of uncertainties in modern power systems, encompassing uncertainties related to weather events, cyber-attacks, and asset management, as well as the advantages and limitations of various mitigation approaches. To fill this void, this review covers a broad spectrum of uncertainties considering their impacts on the power system and explores conventional robust control as well as modern probabilistic and data-driven approaches for modeling and correlating the uncertainty events to the state of the grid for optimal decision making. This article also investigates the development of robust and scenario-based operations, control technologies for microgrids (MGs) and energy storage systems (ESSs), and demand-side frequency control ancillary service (D-FCAS) and reserve provision for frequency regulation to ensure a design of uncertainty-tolerance power system. This review delves into the trade-offs linked with the implementation of mitigation strategies, such as reliability, computational speed, and economic efficiency. It also explores how these strategies may influence the planning and operation of future power grids.

This paper presents an AC optimal power flow (AC-OPF) model including flexible resources (FRs) to handle uncertain wind power generation (WPG). The FRs considered are thermal units with up/down re-dispatching capability, corrective topology control (CTC), and thyristor-controlled series capacitors (TCSC). WPG uncertainty has been modeled through a proposed interval-based robust approach, the goal of which is to maximize the variation range of WPG uncertainty in power systems while maintaining an adequate reliability level at a reasonable cost with the aid of FRs. However, utilization of FRs (especially CTC and TCSC devices) is limited due to the difficulty of their incorporation in the AC-OPF. The optimization framework of the full FR-augmented AC-OPF problem is a mixed-integer nonlinear programming (MINLP) in which the solution for large-scale systems is very hard to obtain. To solve this issue, this paper uses a two-stage decomposition algorithm to decompose the MINLP representation into a mixed-integer linear program (MILP) and a nonlinear program (NLP). Finally, the robust AC-OPF model with FRs is implemented and tested on a 6-bus and the IEEE 118-bus test systems to evaluate its efficiency and performance.

How to deal with uncertainties in electric power systems? A review

Renewable energy brings uncertainty in power system. In recent years, the proportion of renewable energy has gradually increased, which reduces traditional thermal reserve and flexibility in power system. Flexible resources are high-quality reserve resources, but it takes cost to transform general load resources into flexible resources. In this paper, a flexibility resources allocation method is proposed based on stochastic programming. Firstly, stochastic programming method based on multi-scenarios modelling is introduced. Then, a flexible resource allocation model based on stochastic programming is built to improve the reserve in power system. Finally, the effectiveness is verified by IEEE 30 bus system.

This paper proposes a robust scheduling model for microgrids considering the stochastic unintentional islanding conditions. The proposed model minimizes the total operating cost of the microgrid by efficiently coordinating the supply of power from local distributed energy resources and the main grid. To capture the prevailing uncertainties in renewable generation and demand as well as unintentional islanding conditions, a two-stage adaptive robust optimization model is formulated to minimize the total operating cost under the worst realization of the modeled uncertainties. The column and constraint generation (C&CG) method is used to solve the problem in an iterative manner. The solution of the proposed scheduling model ensures robust microgrid operation in consideration of all possible realization of renewable generation, demand and unintentional islanding condition. Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, two micro-turbines, a diesel generator and a battery demonstrate the effectiveness of the proposed approach.

Uncertainty handling techniques in power systems: A critical review

Summary form only given. This discussion is deliberated regarding the presentations of the session on “managing uncertainty in power systems” in 9th IREP Symposium 2013. The power grids are continuously exposed to numerous sources of uncertainties which threaten the reliable and secure supply of electricity. These uncertainties are mainly due to the occurrence of contingencies and more recently the high penetration of intermittent renewables. Managing uncertainties in power systems regarding the system security has received many attentions from power engineering communities using deterministic (e.g. N-1 criteria) and probabilistic (e.g. stochastic and robust) optimization approaches. These optimization methods aim to obtain a balance between the economy and security. In this respect, the value of security can be assessed in terms of risk. The risk is defined as the sum of the product of the consequence and probability of a given set of events. The evaluation of risk should be performed carefully in order to consider the high-probability/low-impact scenarios as well as the low-probability/high-impact ones. It is worth noting that the evaluation of the risk of low probable scenarios, with a certain accuracy level, is computationally much more difficult and time consuming. In order to elucidate the issue of risk evaluation more in depth, we would like to refer to the definitions of robustness and resilience in power systems. The robustness is defined as the ability of a system to maintain its function when it is subjected to a given class of perturbations, whereas the resilience is defined as the ability of a system to gracefully degrade its function in an agile way when it is subjected to a class of unexpected extreme perturbations. Therefore, the solution of an optimization problem should provide a tradeoff between the robustness and resilience. So far in the planning and operation optimizations, the resilience related events are not considered since the obtained solution becomes more expensive from the economical point of view and also its computational complexity increases. But it should be noted that when a power system is designed to be robust to a specific class of perturbations, it becomes more vulnerable to another class of failures. Similarly, a power system that is resilient to a certain type of failure may be fragile to another one. Furthermore, the analysis of the times series of blackouts size measures worldwide has shown a power law region in distributions of different quantities. It implies that the blackouts of different scales may take place and the extreme events cannot be overlooked. The system may experience large blackouts with certain probabilities and the occurrences of small/large blackouts are not independent but correlated each other. In the proposed optimizations of the literatures for the management of uncertainties in power systems, the effectiveness of the obtained solutions is usually evaluated using Monte Carlo Simulation for which the dependent and cascading outages are disregarded. Since the cascading events which can result into large blackouts are neglected, the risk of the rare but large blackouts is not evaluated properly. Thus, these significant perturbations are not taken into consideration in the optimizations neither their effects are evaluated appropriately. As a result, the value of risk is not assessed effectively in the proposed optimizations for the management of uncertainties. The consideration of the extreme perturbations in the optimizations may not be a plausible approach to solve the above-mentioned problem. However, the response of the solutions of proposed optimizations to both robust and resilient perturbations can be assessed using a variant of Monte Carlo Simulation which considers the model of dependent and cascading outages.

Robust optimization is an essential tool for addressing the uncertainties in power systems. Most existing algorithms, such as Benders decomposition and column‐and‐constraint generation (C&CG), focus on robust optimization with decision‐independent uncertainty (DIU). However, increasingly common decision‐dependent uncertainties (DDUs) in power systems are frequently overlooked. When DDUs are considered, traditional algorithms for robust optimization with DIUs become inapplicable. This is because the previously selected worst‐case scenarios may fall outside the uncertainty set when the first‐stage decision changes, causing traditional algorithms to fail to converge. This study provides a general solution algorithm for robust optimization with DDU, which is called dual C&CG. Its convergence and optimality are proven theoretically. To demonstrate the effectiveness of the dual C&CG algorithm, we used the do‐not‐exceed limit (DNEL) problem as an example. The results show that the proposed algorithm can not only solve the simple DNEL model studied in the literature but also provide a more practical DNEL model considering the correlations among renewable generators.

Facing stochastic variations of the loads due to an increasing penetration of renewable energy generation, online decision making under uncertainty in modern power systems is capturing power researchers' attention in recent years. To address this issue while achieving a good balance between system security and economic objectives, we propose a surrogate-enhanced scheme under a joint chance-constrained (JCC) optimal power-flow (OPF) framework. Starting from a stochastic-sampling procedure, we first utilize the copula theory to simulate the dependence among multivariate uncertain inputs. Then, to reduce the prohibitive computational time required in the traditional Monte-Carlo (MC) method, we propose to use a polynomial-chaos-based surrogate that allows us to efficiently evaluate the power-system model at non-Gaussian distributed sampled values with a negligible computing cost. Learning from the MC simulated samples, we further proposed a hybrid adaptive approach to overcome the conservativeness of the JCC-OPF by utilizing correlation of the system states, which is ignored in the traditional Boole's inequality. The simulations conducted on the modified Illinois test system demonstrate the excellent performance of the proposed method.

Uncertainty parameters of battery energy storage integrated grid and their modeling approaches: A review and future research directions

Stochastic programming is a competitive tool in power system uncertainty management. Traditionally, stochastic programming assumes uncertainties to be exogenous and independent of decisions. However, there are situations where statistical features of uncertain parameters are not constant but dependent on decisions, classifying such uncertainties as decision‐dependent uncertainty (DDU). This is particularly the case with future power systems highly penetrated by multi‐source uncertainties, where planning or operation decisions might exert unneglectable impacts on uncertainty features. This paper reviews the stochastic programming with DDU, especially those applied in the field of power systems. Mathematical properties of diversified types of DDU in stochastic programming are introduced, and a comprehensive review on sources and applications of DDU in power systems is presented. Then, focusing on a specific type of DDU, that is, decision‐dependent probability distributions, a taxonomy of available modelling techniques and solution approaches for stochastic programming with this type of DDU and different structural features are presented and discussed. Eventually, the outlook of two‐stage stochastic programming with DDU for future power system uncertainty management is explored, including both exploring the applications and developing efficient modelling and solution tools.

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.

Multiscale design for system-wide peer-to-peer energy trading