Security-constrained Optimal Power Flow Research Articles

Security constrained economic dispatch with VSC-HVDC connected wind farms

The rise in wind power in electrical networks creates complex challenges for transmission system operators (TSOs), particularly regarding real-time operation. TSOs rely on grid codes to enforce wind farm (WF) participation in primary frequency control (PFC), like conventional plants. This paper addresses this need by proposing a security constrained economic dispatch (SCED) model with VSC-HVDC connected WFs based on variable speed wind generators. A key differentiator from existing models is the explicit calculation of the spinning reserve and the droop parameter of the WFs. This method uses the deloading schemes related to blade pitch angle and mechanical rotor speed to ensure compliance with grid codes related to PFC. We show that the wind speed and these deloading schemes significantly impact the WF droop parameter. For efficient studies, linear shift factors are used to model the transmission grid and the VSC-HVDC connected WFs. The performance of the SCED model was assessed using two standard test systems that incorporate WFs connected by VSC-HVDC lines. Its effectiveness was confirmed by comparing it with the security constrained optimal power flow (SCOPF). The results showed agreement between both models, with differences less than 3 % and with the SCED saving about 70 % of the computing time.

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.

Formal analytics for stealthy attacks against Contingency Analysis in power grids

Contingency Analysis (CA) is a critical part of the Energy Management System of a power grid, ensuring the optimal operating set-points without violating constraints, even in the face of contingency events. CA relies on State Estimation (SE) to perform its analysis, paving the way for Security Constrained Optimal Power Flow (SCOPF) that ensures optimal economic generator dispatches, even in scenarios like n−1 contingencies, such as a single line failure. This integrated approach enhances the grid’s resilience and efficiency under diverse conditions. However, it is shown that an adversary can alter specific power measurements to corrupt the SE without being detected. Such a corrupted estimation will provide CA with a fake model to deal with, which can further lead the grid to an even more vulnerable state. This research formally models and analyzes these attacks on CA, particularly on SCOPF, which are routed from SE. We formally model these complex attacks as a set of constraints and solve them using Satisfiability Modulo Theories (SMT) to synthesize potential attack vectors. Each of these vectors specifies a set of measurements that an adversary can alter to cause one or more transmission lines to be overloaded when some specific contingencies happen. We apply various sensitivity factors to make the solution to this complex synthesis problem tractable. We demonstrate our formal analytics on IEEE bus systems and verify the results using OPAL-RT, a standard virtual power grid testbed. We finally evaluate the tool with respect to various attack and grid characteristics.

Transferability-Oriented Adversarial Robust Security-Constrained Optimal Power Flow

Transferability-Oriented Adversarial Robust Security-Constrained Optimal Power Flow

Improved Proximal Policy Optimization Algorithm for Sequential Security-constrained Optimal Power Flow Based on Expert Knowledge and Safety Layer

Improved Proximal Policy Optimization Algorithm for Sequential Security-constrained Optimal Power Flow Based on Expert Knowledge and Safety Layer

On the robustness of machine-learnt proxies for security constrained optimal power flow solvers

In this paper, we focus on the robustness of machine learning based proxies used to speed up, alone or jointly with state-of-the-art mathematical optimization methods, optimal power flow and security-constrained optimal power flow calculations. On data sets for the Nordic32 alternative current security-constrained optimal power flow benchmark, we evaluate the robustness of proxies with respect to load distribution, power factors, on-line generators and network topology, and generator costs. We show that simplified random load sampling procedures that are used in most published academic studies, are insufficient to yield robust machine learnt proxies, and consequently limit their usefulness in the real world. Based on these results, we formulate recommendations for future research.

SECURITY CONSTRAINED OPTIMAL POWER FLOW BASED ON AN ARTIFICIAL INTELLIGENCE TECHNIQUE

In the past, artificial intelligence techniques were successfully adopted for obtaining optimal power flow in a power system. However, this optimality is limited to the economic aspects of the system's operating conditions. The other aspects of the operation, like security conditions, have been given limited attention. Hence, this paper presents an attempt to dispatch the power generation in electrical power systems optimally by taking into consideration both economic and secure operations, so that modern power systems can operate reliably and effectively. Security-constrained optimal power flow is addressed in this paper as a multi-objective optimization problem, consisting of four objective functions: minimizing power generation costs; minimizing voltage deviation; minimizing power losses; and alleviating the overloading on transmission lines. A detailed steady-state generator model is adopted in the present formulation. A metaheuristic optimization technique, namely, differential evolution, is used to obtain the security constraint optimal power dispatch. Additionally, the operating states of a power system have been addressed in this paper. The identification of the operating states is vital to the assessment of the security of the EPS. Improvements and appropriate security assessments have been made in some cases. The proposed algorithm is applied to a typical power system with different operating strategies. The obtained results are compared to those obtained from previous studies in the literature to demonstrate the suggested method's validity and effectiveness.

A Tractable Linearization-Based Approximated Solution Methodology to Stochastic Multi-Period AC Security-Constrained Optimal Power Flow

The growing presence of renewable energy sources (RES), energy storage systems (ESSs) and flexible loads (FLs) in power systems necessitates a new approach to N-1 security in day-ahead operation planning considering stochasticity and time coupling. To this end, a comprehensive approach based on stochastic multi-period AC security-constrained optimal power flow (S-MP-AC-SCOPF) was proposed recently in a form of a large-scale non-linear programming problem, which is not scalable. This paper proposes the first-time new tractable solution methodology for the most complete AC-SCOPF problem to date: S-MP-AC-SCOPF. As other main novelty, the proposed methodology achieves tractability by solving sequentially a limited number of different linear approximations of the full S-MP-AC-SCOPF problem. These linear approximations differ in terms of: state dependency regarding losses approximation, carefully reduced sets of constraints or tightening of critical constraints. The performance of the methodology is demonstrated in power system models of Sweden and Portugal. Extensive numerical experiments have shown that the methodology is able to reduce progressively until complete removal the number of violated thermal or voltage constraints. It leads to reasonably accurate solution with small optimality gap within few iterations and is at least 85% faster than the competitor IPOPT solver.

Security‐constrained active power curtailment considering line temperature and thermal inertia

AbstractA novel method is introduced to determine cost‐optimized active power curtailment (APC) of renewable energy sources (RES) considering weather‐dependent dynamic line rating (DLR). A new formulation of the security‐constrained optimal power flow (SC‐OPF) is developed and applied in a case study. The reduction of the required preventive APC in the case for secure grid operation due to the consideration of thermal inertia of overhead power lines is demonstrated. Considering thermal inertia allows relying on curative APC that is activated only after an situation occurs. The overhead power line temperature, calculated with the temperature‐dependent power flow (TDPF), acts as a new limit for line loading and releases unused transmission reserves. The TDPF algorithm is integrated in the open‐source Python library pandapower, providing access to it to the broader community. The power system can be utilized to a greater extent, with a reduced demand for congestion management.

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.

SCOPF considering voltage and power fluctuation under renewable energy integration

Security-Constrained Optimal Power Flow (SCOPF) method could generate system optimal operation point, which guarantee system security by avoiding any overload whenever expected N-1 contingencies occurred. However, renewable power integration increases uncertainty of system security, which is not well treated in conventional SCOPF model. Then this study proposes an improved SCOPF model, which aims at optimizing outputs of generators to increasing security of system facing challenges by N-1 contingencies accompanied by renewable power fluctuations. Semi-invariant is employed to express the stochastic behavior of wind and photovoltaic power generation. Considering the influence of transformer transformation ratio on admittance matrix, the uncertainty of injected renewable power is combined with the adjustable characteristics of network parameters to obtain the fluctuation model of branch power and bus voltage. Therefore, the constraints for SCOPF are restated to treat the problem that expected value based traditional model makes errors to confirm overload. The probability analysis for branch overload allows this study to present a potential reduced contingency set, in which small-probability events are rationally excluded. Thus, the constraint quantities as well as the complexity of the optimization problem are effectively reduced to decrease the computation burden. A Benders decomposition method based interior point approach is used to solve the improved SCOPF optimization model. Case studies based on IEEE39 bus system demonstrate the efficiency of proposed method.

Physics-Constrained Vulnerability Assessment of Deep Reinforcement Learning-Based SCOPF

The decarbonization of energy systems has posed unprecedented challenges in system complexity and operational uncertainty that render it imperative to exploit cutting-edge artificial intelligence (AI) technologies to realize real-time, autonomous power system operation and control. In particular, deep reinforcement learning (DRL)-based approaches in power systems are extensively studied and implemented in several trials worldwide. Nevertheless, the vulnerability of DRL brings new security threats to power systems that have not been well identified and investigated in the literature. To this end, this paper proposes a physics-constrained vulnerability assessment methodological framework for the DRL-based power system operation and control, with a special focus on the problem of security-constrained optimal power flow (SCOPF). In particular, we develop a novel adversarial example generation method, defined as a false data injection attack against the DRL-based SCOPF (FDIAI), to realize a targeted adversarial attack considering the nonlinear physical constraints in power systems via two main stages of constructor function design and unconstrained optimization problem transformation. In this way, the proposed FDIAI can significantly influence the decision-making procedure of DRL while successfully evading the bad data detection mechanism in power systems. Case studies are conducted to explore the stealthiness and effectiveness of FDIAI and then show its severe impacts on system operation and control on the winners&#x0027; models of the Learning to Run a Power Network (L2RPN) competitions, including L2RPN IJCNN 2019 (IJCNN), L2RPN WCCI 2020 (WCCI), and L2RPN NeurIPS 2020 (NeurIPS).

Revealing Vulnerability of N-1 Secure Power Systems to Coordinated Cyber-Physical Attacks

Coordinated cyber-physical (CCP) attacks have attracted wide attention in power systems because of their potential to cause severe disturbance including cascading failures. However, as realistic power systems operate within the N-1 security criterion, existing CCP attacks may be in part mitigated. As such, this paper analyzes impacts of CCP attacks on the vulnerability of the power systems that employ the N-1 security constrained optimal power flow (SCOPF). Specifically, a tri-level model is proposed to analyze the CCP attack impacts, whereby the adversary coordinates a physical attack with cyber attacks to initiate and propagate post-contingency overload based on N-1 SCOPF. A methodology utilizing semidefinite programming (SDP) relaxation and primal-dual formulation is proposed to transform the tri-level model into a conic optimization, such that the model can be easily solved by SDP solvers. Case studies on the IEEE 14, 57, and 118 bus test systems demonstrate that the CCP attacks in power systems with N-1 security criterion are able to cause N-1-1 contingency and even trigger cascading failures.

A generalised approach for efficient computation of look ahead security constrained optimal power flow

We consider a generalised comprehensive Look-ahead Security-constrained Optimal Power Flow (LASCOPF) formulation under the N−1 contingency criterion over multiple dispatch intervals. We observe that the number of decision variables varies quadratically with the number of intervals. To improve scalability, we propose a reduced LASCOPF formulation for which the number of decision variables varies only linearly. We extend these formulations to the N−k contingency criterion. For reduced LASCOPF we observe that the number of decision variables varies with the number of k-permutations of contingencies. To improve scalability, we propose a formulation that is further reduced to vary only with the number of k-combinations. Also, we show that our formulations can be extended simply to model recovery from the corresponding outages. Furthermore, we present LASCOPF under the N−1 contingency criterion using DC and AC power flow under generator contingencies. We prove that, barring borderline cases, solving the reduced formulation is equivalent to solving the comprehensive formulation. We extend these results to the N−k contingency criterion. Finally, we present numerical results on the IEEE 14 bus, IEEE 30 bus and IEEE 300 bus test cases, and the 1354 bus part of the European power system using AC power flow to demonstrate the computational advantage of the reduced formulations under the N−1 and N−2 contingency criteria.

Parallel computing for reducing time in security constrained optimal power flow analysis

This paper presents a novel approach for solving the security-constrained optimal power flow (SCOPF) optimization problem using parallel Computing. In this approach, switched shunt capacitors, generation power ramp, and demand response are considered in the SCOPF by maximizing the market surplus during regular operation and for a set of contingencies of branches and generators. The optimization problem is solved using the Nonlinear Interior Point Method. The contingency assessment is paralleled in multiple CPU cores to decrease the computation time. Additionally, the test systems used in ARPA-GO competition were used and compared with the ARPA benchmark results to assess the proposed algorithm. The numerical results show this method is suitable for fast SCOPF using paralleling Computing.

Decentralized risk‐based security‐constrained optimal power flow in interconnected multi‐carrier microgrids

The security of energy systems has always been one of the most important issues of energy systems operation. The multi-carrier multi-microgrid (MCMMG) is one of the novel structures in the power system. High penetration of renewable resources and their uncertainty, their ability to operate in isolation mode, and the presence of energy hubs in MCMMG systems increase the importance of security assessment in this type of system. This paper presents a decentralized risk-based security-constrained optimal power flow model for an MCMMG system. The stochastic nature of wind energy, photovoltaic generation, and electrical and heating loads are considered in the proposed model. In the model, the risk level of the system is determined by considering both the electrical and natural gas (NG) networks’ contingencies. The proposed model is decomposed into three types of subproblems with the augmented Lagrangian relaxation (ALR) method: The subproblem related to the multi-microgrid operator level, the NG network subproblem, and the individual microgrid level subproblem. The decomposed problem is solved using MATLAB software. According to the results, the proposed model can secure the system from high costs that may impose on the system due to the contingency occurrence.

A novel two-stage TSO–DSO coordination approach for managing congestion and voltages

This paper proposes a novel approach to TSO–DSO coordination in day-ahead operation planning for the procurement of ancillary services (AS) such as congestion management and voltage control. The approach overcomes two major issues hindering practical applicability of existing TSO–DSO coordination mechanisms, namely the computational complexity due to the large number of times the TSO and DSO problems are resolved as well as the inability to map analytically the cost and amount of flexibility at DSO level into TSO problem. To this end, a two-fold novelty of our approach consists of the decomposition of the overall AS problem into two sequential stages, which seek the procurement of: (i) “active power related” AS (i.e., for congestion management) and then (ii) the “reactive power related” AS (i.e., for voltage support), respectively as well as a fast approximation of the cost of aggregated active and reactive power flexibilities of active distribution systems (ADSs). Unlike existing mechanisms, the proposed approach considers real-world challenging aspects such as the N-1 security at TSO level and operation uncertainties at both TSO and DSO levels. Accordingly, the approach relies on tailored versions of stochastic multi-period AC security-constrained optimal power flow (S-MP-SCOPF) at TSO level and stochastic multi-period AC optimal power flow (S-MP-OPF) at DSO level, which are formulated as non-linear programming (NLP) problems. The importance and performance of the proposed approach are illustrated on a power system connecting a 60-bus transmission system (under 33 N-1 contingencies) with five 34-bus ADSs.

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.