Security-constrained Optimal Power Flow Problem Research Articles

Multi-objective Snow Ablation Optimization Algorithm: An Elementary Vision for Security-Constrained Optimal Power Flow Problem Incorporating Wind Energy Source with FACTS Devices

This study delves into the exploration of a novel Multi-objective Snow Ablation Optimizer (MOSAO) algorithm, tailored for addressing expansive Optimal Power Flow (OPF) challenges inherent in intricate power systems. These systems are often complemented with the integration of renewable energy modalities and the state-of-the-art Flexible AC Transmission Systems (FACTS). Building upon the foundational framework of a previously documented single-objective Snow Ablation Optimizer, we have evolved it into the MOSAO paradigm. This transformation is achieved by harnessing the potency of non-dominated sorting coupled with the crowding distance strategy. The task of OPF magnifies in complexity when integrating renewable energy resources due to their inherent unpredictability and intermittent nature. As the modern power landscape evolves, FACTS devices are witnessing an increasing deployment to mitigate network demand and alleviate congestion issues. Within the ambit of this research, we've incorporated a stochastic wind energy source, working synergistically with an array of FACTS instruments. These encompass the static VAR compensator, thyristor-controlled series compensator and thyristor-driven phase shifter, all operating within the confines of an IEEE-30 bus framework. Strategic placement and calibration of these FACTS devices aim to optimize the system by minimizing the cumulative fuel expenditure. The capricious essence of wind as an energy source is elegantly depicted through the lens of Weibull probability density graphs. To distil the optimal middle-ground solutions, we've employed a fuzzy decision-making matrix. When benchmarking our findings against those derived from other esteemed optimization algorithms, we observe a notable distinction. The results from the modified IEEE-30 bus system accentuate the superior convergence, diversity and distribution attributes of MOSAO, especially when scrutinizing power flows. The MOSAO source code is available at: https://github.com/kanak02/MOSAO.

A Methodology to Evaluate Reactive Power Reserves Scarcity During the Energy Transition

The lack of reserves for reactive power production and absorption is an envisioned, still basically unexplored, threat to the voltage profile adequacy and thereby secure operation of transmission grids during the energy transition toward renewable-dominated power production. This paper proposes a novel, generic, comprehensive, and realistic methodology to identify when this issue of reactive power reserves (RPRs) scarcity during plausible scenarios of the energy transition would become severe. The computational core of the proposed methodology comprises four different AC security-constrained optimal power flow (SCOPF) problems: one conventional, two tailored ones that assess the RPRs scarcity in production and absorption modes, respectively, and an optimal reactive power dispatch. The methodology is versatile, offering the possibility to assess RPRs in different timescales, ranging from day-ahead short-term operation to years-ahead long-term operation, and considering appropriate renewable energy production forecasts and day-dependent load profiles. The proposed methodology can serve as a decision support tool for the transmission system operator (TSO), allowing to plug and play different plausible energy transition scenarios (e.g., differing in terms of sequence and timing of: phased out power plants as well as location, type, and size of renewable energy sources deployed) and ultimately informing the TSO about the timing where RPRs become insufficient to maintain security. Without loss of generality, the value of the proposed methodology is extensively demonstrated in a 60-bus Nordic32 system, considering 52 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N-1$</tex-math></inline-formula> line and generator contingencies, while the tractability of AC SCOPF problems is assessed in a 1,203-bus system.

Optimization with Neural Network Feasibility Surrogates: Formulations and Application to Security-Constrained Optimal Power Flow

In many areas of constrained optimization, representing all possible constraints that give rise to an accurate feasible region can be difficult and computationally prohibitive for online use. Satisfying feasibility constraints becomes more challenging in high-dimensional, non-convex regimes which are common in engineering applications. A prominent example that is explored in the manuscript is the security-constrained optimal power flow (SCOPF) problem, which minimizes power generation costs, while enforcing system feasibility under contingency failures in the transmission network. In its full form, this problem has been modeled as a nonlinear two-stage stochastic programming problem. In this work, we propose a hybrid structure that incorporates and takes advantage of both a high-fidelity physical model and fast machine learning surrogates. Neural network (NN) models have been shown to classify highly non-linear functions and can be trained offline but require large training sets. In this work, we present how model-guided sampling can efficiently create datasets that are highly informative to a NN classifier for non-convex functions. We show how the resultant NN surrogates can be integrated into a non-linear program as smooth, continuous functions to simultaneously optimize the objective function and enforce feasibility using existing non-linear solvers. Overall, this allows us to optimize instances of the SCOPF problem with an order of magnitude CPU improvement over existing methods.

A Surrogate-Based Asynchronous Decomposition Technique for Realistic Security-Constrained Optimal Power Flow Problems

Solving realistic security-constrained optimal power flow problems In “A surrogate-based asynchronous decomposition technique for realistic security-constrained optimal power flow problems,” we propose a new algorithm for solving a classical problem in power grid operations: the security-constrained optimal power flow, considering its nonlinearities and realistic transitions between nominal and emergency post-contingency operations. Solving security-constrained optimal power flow problems accurately is a critical function, upon which depends the reliability, security, and efficiency of power systems as well as the correct functioning of other critical infrastructure dependent on electricity. The proposed algorithm was extensively tested against many state-of-the-art approaches using realistic and real instances in the ARPA-E Grid Optimization Competition Challenge 1, where it found the best-known solution for 58% of the instances, attained an average gap of less than 0.2%, and obtained the best overall scores, thereby winning all divisions of Challenge 1 with a very strong first place.

A Novel MOGNDO Algorithm for Security-Constrained Optimal Power Flow Problems

The current research investigates a new and unique Multi-Objective Generalized Normal Distribution Optimization (MOGNDO) algorithm for solving large-scale Optimal Power Flow (OPF) problems of complex power systems, including renewable energy sources and Flexible AC Transmission Systems (FACTS). A recently reported single-objective generalized normal distribution optimization algorithm is transformed into the MOGNDO algorithm using the nondominated sorting and crowding distancing mechanisms. The OPF problem gets even more challenging when sources of renewable energy are integrated into the grid system, which are unreliable and fluctuating. FACTS devices are also being used more frequently in contemporary power networks to assist in reducing network demand and congestion. In this study, a stochastic wind power source was used with different FACTS devices, including a static VAR compensator, a thyristor- driven series compensator, and a thyristor—driven phase shifter, together with an IEEE-30 bus system. Positions and ratings of the FACTS devices can be intended to reduce the system’s overall fuel cost. Weibull probability density curves were used to highlight the stochastic character of the wind energy source. The best compromise solutions were obtained using a fuzzy decision-making approach. The results obtained on a modified IEEE-30 bus system were compared with other well-known optimization algorithms, and the obtained results proved that MOGNDO has improved convergence, diversity, and spread behavior across PFs.

A Hybrid Data-Driven Method for Fast Solution of Security-Constrained Optimal Power Flow

This paper proposes a hybrid data-driven method for fast solutions of preventive security-constrained optimal power flow (SCOPF) of power systems. The proposed method formulates the SCOPF problem as constraints-satisfying training of a deep reinforcement learning (DRL) agent, where the action-value function of DRL is augmented by contingency security constraints. In the training process, the proposed method hybridizes the primal-dual deep deterministic policy gradient (PD-DDPG) and the classic SCOPF model. Instead of building reward critic networks and cost critic networks via interacting with the environment (i.e., power flow equations), the actor gradients are approximated by solving KKT conditions of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Lagrangian</i> . Finally, with the formulated sparse Jacobians of constraints and sparse Hessians of Lagrangians, the interior point method is incorporated in PD-DDPG to derive the parameters updating rule of the DRL agent. Numerical tests are carried out on a modified IEEE 57-bus system and a modified IEEE 300-bus system for critical contingencies. The results show that the well-trained DRL agent can rapidly (real-time) obtain high-quality SCOPF solutions that satisfy the security constraints.

Fitness–Distance Balance based adaptive guided differential evolution algorithm for security-constrained optimal power flow problem incorporating renewable energy sources

One of the most difficult types of problems computationally is the security-constrained optimal power flow (SCOPF), a non-convex, nonlinear, large-scale, nondeterministic polynomial time optimization problem. With the use of renewable energy sources in the SCOPF process, the uncertainties of operating conditions and stress on power systems have increased even more. Thus, finding a feasible solution for the problem has become a still greater challenge. Even modern powerful optimization algorithms have been unable to find realistic solutions for the problem. In order to solve this kind of difficult problem, an optimization algorithm needs to have an unusual exploration ability as well as exploitation–exploration balance. In this study, we have presented an optimization model of the SCOPF problem involving wind and solar energy systems. This model has one problem space and innumerable local solution traps, plus a high level of complexity and discrete and continuous variables. To enable the optimization model to find the solution effectively, the adaptive guided differential evolution (AGDE) algorithm was improved by using the Fitness–Distance Balance (FDB) method with its balanced searching and high-powered diversity abilities. By using the FDB method, solution candidates guiding the search process in the AGDE algorithm could be selected more effectively as in nature. In this way, AGDE’s exploration and balanced search capabilities were improved. To solve the SCOPF problem involving wind and solar energy systems, the developed algorithm was tested on an IEEE 30-bus test system under different operational conditionals. The simulation results obtained from the proposed algorithm were effective in finding the optimal solution compared to the results of the metaheuristics algorithms and reported in the literature.

An exact and scalable problem decomposition for security-constrained optimal power flow

In this paper, we present decomposition techniques for solving large-scale instances of the security-constrained optimal power flow (SCOPF) problem with primary response. Specifically, under each contingency state, we require that the nodal demands are met and that the synchronized units generating below their limits follow a linear model for primary response. The resulting formulation is a mixed-integer linear program since the primary response model introduces disjunctions to the SCOPF problem. Unfortunately, exact methods relying on traditional Benders decomposition do not scale well. As an alternative, we propose a decomposition scheme based on the column-and-constraint-generation algorithm where we iteratively add disjunctions and cuts. We provide procedures for preprocessing dedicated cuts and for numerically determining the post-contingency responses based on the master problem solutions. We also discuss heuristics to generate high-quality primal solutions and upper bounds for the method. Finally, we demonstrate the efficiency of the proposed method on large-scale systems.

Combining Deep Learning and Optimization for Preventive Security-Constrained DC Optimal Power Flow

The security-constrained optimal power flow (SCOPF) is fundamental in power systems and connects the automatic primary response (APR) of synchronized generators with the short-term schedule. Every day, the SCOPF problem is repeatedly solved for various inputs to determine robust schedules given a set of contingencies. Unfortunately, the modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs, which are hard to solve. To address this challenge, leveraging the wealth of available historical data, this paper proposes a novel approach that combines deep learning and robust optimization techniques. Unlike recent machine-learning applications where the aim is to mitigate the computational burden of exact solvers, the proposed method predicts directly the SCOPF implementable solution. Feasibility is enforced in two steps. First, during training, a Lagrangian dual method penalizes violations of physical and operations constraints, which are iteratively added as necessary to the machine-learning model by a Column-and-Constraint-Generation Algorithm (CCGA). Second, another different CCGA restores feasibility by finding the closest feasible solution to the prediction. Experiments on large test cases show that the method results in significant time reduction for obtaining feasible solutions with an optimality gap below 0.1%.

Privacy-Preserving Computation for Large-Scale Security-Constrained Optimal Power Flow Problem in Smart Grid

In this paper, we present a distributed privacy-preserving quadratic optimization algorithm to solve the Security Constrained Optimal Power Flow (SCOPF) problem in the smart grid. The SCOPF problem seeks the optimal dispatch subject to a set of postulated constraints under the normal and contingency conditions. However, due to the large problem size and real-time requirement, a fast and robust technique is required to solve this problem. Moreover, due to privacy concerns, it is important that the data remains confidential and processed on local computers. Therefore, a fully privacy-preserving algorithm is proposed which performs computation directly over the encrypted SCOPF problem. The SCOPF is decomposed into smaller subproblems corresponding to individual pre-contingency and post-contingency cases using the Alternating Direction Method of Multipliers (ADMM) and gradient projection algorithms. Both algorithms are presented for solving the SCOPF problem in a privacy-preserving and distributed manner. Security analysis shows that our algorithm can preserve both system confidentiality and data privacy. Performance evaluations validate the correctness and effectiveness of the proposed algorithm.

A Fast Decomposition Method to Solve a Security-Constrained Optimal Power Flow (SCOPF) Problem Through Constraint Handling

This paper presents a decomposition methodology using constraint handling rules to improve the computation time of a security-constrained optimal power flow (SCOPF) problem. In order to evaluate methodology performance, tests over small (500 buses), medium (4,918 buses), and large scale (11,615 buses) transmission networks were carried out. The methodology consisted in the decomposition of the SCOPF problem into a base case problem and contingency sub-problems using constraint handling rules to solve the complete problem in an iterative fashion. The first stage involved solving an OPF problem using a base case network. The second stage dealt with the modification of the initial base case by updating some of the constraint limits according to the evaluation of potentially relevant contingencies. The entire algorithm resorted to parallel computing tools. The methodology, along with active power re-dispatch through droop control and PV/PQ switching in post-contingency scenarios, successfully solved the tested networks with the set of proposed constraints.

An Efficient Hybrid Method for Solving Security-Constrained Optimal Power Flow Problem

The optimal operation for different states such as normal and contingency cases of a power system has a very important role in the operation. Therefore, it is necessary to analyze contingencies in the system so as the most severe cases should be considered for integrating into the optimal power flow (OPF) problem and the security-constrained optimal power flow (SCOPF) becomes an important problem for considering in the power system operation. This paper proposes a combined pseudo-gradient based particle swarm optimization with constriction factor (PGPSO) and the differential evolution (DE) method for solving the SCOPF problem. The PGPSO-DE method is a newly developed method for utilizing the advantages of the pseudogradient guided PSO method with a constriction factor and the DE method. The proposed PGPSO-DE has been tested on the IEEE 30 bus system for the normal case and the contingency case with two types of the objective function. The results yielded from the proposed method have been validated via comparing to those from the conventional PSO, DE, and other methods reported in the literature. The comparisons for the results obtained from the proposed PGPSODE method have shown that it is very effective to solve the large-scale and complex SCOPF problem.

A Convex Three-Stage SCOPF Approach to Power System Flexibility With Unified Power Flow Controllers

This paper proposes a methodology for enhancing the power system flexibility, which can respond properly to contingencies in real-time operations. The proposed approach introduces a unified power flow controller (UPFC) in a three-stage security-constrained optimal power flow (SCOPF). The pre- and post-contingency system operation states are divided into three stages including the base case, post-contingency short-term, and post-contingency long-term periods. The UPFC applications re-route active power flow and provide reactive power to mitigate overloads and voltage violations when line outages occur in power systems. UPFC is adopted as a fast-response corrective control device during the post-contingency short-term period, which is coordinated with the conventional slow-response corrective control system during the post-contingency long-term period. A convex approach is applied to reformulate the original nonlinear nonconvex SCOPF problem into a second-order cone programming (SOCP) problem. A two-level algorithm using Benders decomposition and sequential cone programming (SCP) is applied to solve the large-scale SOCP problem. An improved covering cut bundle (CCB) strategy is proposed to accelerate the convergence of the Benders decomposition algorithm. Numerical results show the effectiveness of the proposed model and its solution technique for enhancing the power system flexibility.

An Improved Artificial Physics Optimization Algorithm Approach for Static Power System Security Analysis

The major functions involved in power system security analysis are security assessment and security enhancement. The contingency analysis plays a vital role in the security assessment which has been carried out based on the performance index. Security enhancement incorporates security constrained optimal power flow (SCOPF) which ensures that system is operating at normal state by taking preventive and control actions. An improved artificial physics optimization (APO) evolutionary algorithm is presented in this paper for solving SCOPF problem. The trial and error approach is used for selection of gravitational constant (G) in standard APO method. In order to circumvent this problem, a fuzzy approach is used to tune the gravitational constant (G). Simulations are done on IEEE 30-bus system, Indian 75-bus system, and IEEE 118-bus test system. To evaluate the robustness, results obtained using the proposed method are compared with results obtained using standard conventional algorithms, namely APO, Bat algorithm, and genetic algorithm. The obtained results indicate that the proposed fuzzy adaptive artificial physics optimization (FAAPO) method is efficient as well as robust for solving SCOPF problem to get near global optimization solution compared to standard APO algorithm and other heuristic methods reported in the literature.

Application of Sunflower Optimization Algorithm for Solving the Security Constrained Optimal Power Flow Problem

Finding the Optimal Power Flow (OPF) which minimizes total generator cost is the answer to one of the most important problems in the electricity market operation. Independent System Operators (ISO) face many challenges while operating the system in order to obtain economic benefits and security. The solution to this problem is known as Security Constrained Optimal Power Flow (SCOPF). SCOPF is a very large-scale and nonlinear optimization problem with many complex constraints. This paper proposes the Sunflower Optimization (SFO) algorithm for solving the SCOPF problem. The proposed method is tested on the IEEE 30-bus and the IEEE 118-bus systems for both normal and outage cases. The result comparison with other known methods showed that the proposed SFO algorithm is an effective method for solving the SCOPF problem in the electricity market.

A heuristic benders-decomposition-based algorithm for transient stability constrained optimal power flow

Security Constrained Optimal Power Flow (SCOPF) is traditionally performed to obtain the optimal generation levels to achieve the minimum generation cost under operational constraints in normal and contingency conditions. In this paper the SCOPF problem with DC load flow equations is extended to consider the transient stability margin of the generating units as a heuristic decomposition algorithm. However, the proposed algorithm is compatible with any SCOPF formulation. Due to computational complexities of security constraints and transient stability assessment, Benders decomposition algorithm is utilized to handle the transient stability margin of generating units as separate sub-problems. A transient energy function is developed to assess the transient stability of generating units under credible faults using the cut-set energy function criterion. In case of violation of the required transient stability margin, Benders cuts are constructed and added to the master problem. The proposed decomposed Transient Stability Constrained OPF (TSCOPF) is converged in few iterations. The developed TSCOPF algorithm is implemented on the IEEE 39-bus dynamic test system to validate its accuracy and efficiency.

LP based solution for Security Constrained Optimal Power Flow including Power Routers

Power Routers offers many benefits to the power system, it helps in improving the existing transmission asset utilization. Security Constrained Optimal Power Flow (SCOPF) is becoming more important in the electrical power system especially in the present deregulated environment. This paper focuses on completely linearizing the complex non-linear SCOPF problem. The objective function is linearized using Piecewise linearization technique and the constraints are framed using linear sensitivity factors. A formal extension is made to the traditional SCOPF by including power router control in the post contingency time frame. DC power flow analysis is used to calculate the real power flow in the lines.Thus, in this paper, further minimization of cost is achieved by using Power Router control and it is compared with the conventional SCOPF.

Two-Level Parallel Augmented Schur Complement Interior-Point Algorithms for the Solution of Security Constrained Optimal Power Flow Problems

Modern power grids incorporate renewable energy at an increased pace, placing greater stress on the power grid equipment and shifting their operational conditions towards their limits. As a result, failures of any network component, such as a transmission line or power generator, can be critical to the overall grid operation. The security constrained optimal power flow (SCOPF) aims for the long term precontingency operating state, such that in the event of any contingency, the power grid will remain secure. For a realistic power network, however, with numerous contingencies considered, the overall problem size becomes intractable for single-core optimization tools in short time frames established by real-time industrial operations. We propose a parallel distributed memory structure exploiting framework, BELTISTOS-SC, which accelerates the solution of SCOPF problems over state of the art techniques. The acceleration on single-core execution is achieved by a structure-exploiting interior point method, employing successive Schur complement evaluations to further reduce the size of the systems solved at each iteration while maintaining sparsity, resulting in lower computational resources for the linear system solution. Additionally the parallel, distributed memory implementation of the proposed framework is also presented in detail and validated through several large-scale examples, demonstrating its efficiency for large-scale SCOPF problems.

Worst-Case Probabilistic Network Outage Identification Under Physical Disturbances

This letter presents a mathematical optimization model to identify the worst-case probabilistic network outage scenario induced by physical disturbances. That is, we seek to find the outage scenario with the maximum combined likelihood and impact on the network. This is a challenging combinatorial problem, as the search domain exponentially grows with the size of the network and the impact of outages on the network is not usually explicitly quantifiable. In this letter, we develop an iterative algorithm to tackle these challenging issues by formulating it as a mixed-integer programming problem and tightening the search domain by bounding upper and lower bounds of the solution using the upper bound estimates of outage scenario probabilities. We also apply the proposed model to identify the worst-case outage scenarios in power networks, where the impacts of outage scenarios are calculated using the security-constrained optimal power flow problem. The numerical studies, conducted on two test power networks, demonstrate the efficiency and proven convergence of the proposed model in identifying the worst-case probabilistic outage scenario.

Enhanced goal attainment method for solving multi-objective security-constrained optimal power flow considering dynamic thermal rating of lines

Security-constrained optimal power flow (SCOPF) is an important problem in power system operation. Dynamic thermal rating (DTR), as an effective method to increase transmission capacity of power systems, has been recently considered in some optimal power flow (OPF) and SCOPF models. Additionally, in today power systems, OPF problem involves various objectives leading to multi-objective OPF models. In this paper, a new multi-objective SCOPF model considering DTR of transmission lines is presented. In addition, a new multi-objective solution method is proposed to solve the multi-objective SCOPF problem. The proposed method is an enhanced version of goal attainment technique in which the search capability of this technique to cover borders of the Pareto frontier is enhanced. The proposed multi-objective DTR-included SCOPF model as well as the proposed multi-objective solution method are tested on the IEEE 118-bus test system and the obtained results are compared with the results of other alternatives.