Security-constrained Optimal Power Flow Model Research Articles

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.

Security constrained OPF model for AC/DC grids with unbalanced DC systems

The role of HVDC in power transmission systems continues to grow. The number of HVDC installations worldwide is increasing, and first, multi-terminal and meshed HVDC grids are being built. Large meshed HVDC grids with many terminals are expected to be operational in the near future. Bipolar HVDC grids can be operated in an asymmetrical configuration with converter stations connected between single poles. This paper presents a reliability assessment model for unbalanced AC/DC grids. The DC grid is modeled using a multi-conductor representation. A security-constrained optimal power flow model is developed allowing the representation of single-pole contingencies and single-line conductor outages. The model is implemented in the Julia/JuMP framework as an extension of the open-source package PowerModelsACDC.jl. The model is applied to a 67-bus test case considering several N-1 contingencies. Results show that unbalanced operation of HVDC grids in contingency situations can decrease operational costs by higher utilization of HVDC grid flexibility.

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 SCOPF model for congestion management considering power flow controlling devices

With an increase in the share of distributed renewable generation, the power flow patterns are changing, and there is an increasing probability of internal congestion. There is also an increase in the number of power flow controlling devices in the transmission system to provide greater flexibility to the system operator. Thus, there is a need to include these devices and intra-zonal transmission lines for the congestion management analysis. This paper presents a probabilistic security-constrained optimal power flow (SCOPF) model for congestion management based on the non-linear ac formulation. To ensure computational efficiency, a second-order cone (soc) relaxation for power flow controlling devices is proposed. A comparison between the ac and soc formulations has been carried out on the modified IEEE 118-bus AC/DC system. It is observed that with the soc formulation, the computational efficiency of the model is increased while ensuring a minimal gap between the ac and soc results.

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.

VSC-HVDC Incorporated Corrective Security-Constrained Optimal Power Flow

With the rapid development and diverse engineering applications of VSC-HVDC technology, development in power industry has put forward higher economic and security requirements for the security-constrained optimal power flow. Under these circumstances, this paper proposes a security-constrained optimal power flow model for hybrid AC/DC power grids that incorporates the VSC-HVDC corrective control. The linear relationship between the pre-contingency state power flow and post-contingency state power flow is established based on the shift factor and the reliability constraints are described as the linear inequality constraints of the post-contingency state active power flow which is expressed by the pre-contingency state branch power flow. With the inherent ability of the VSC-HVDC converter station (short as VSC station) to rapidly regulate active power taken into account, this paper utilizes the linear relationship between the active power adjustment of the VSC station and the power flows of transmission lines and electrical equipment and corrects the reliability constraints with the sensitivity coefficient. Hence the correction of the post-contingency state power flow is reflected in the constraints. By solving the proposed model with the primal-dual interior-point method, the pre-contingency state optimal security operating point that considers the corrective capability of the VSC stations is obtained. Finally, the correctness and validity of the proposed model is verified based on a VSC-HVDC modified IEEE 14-bus system.

Demand response programs in power systems with energy storage system-coordinated wind energy sources: A security-constrained problem

This study seeks to provide a secure operation for wind-integrated transmission networks by proposing a computationally efficient daily DC security-constrained optimal power flow model. The proposed model determines the active power initial set-points of the energy resources. Moreover, energy storage systems and demand response programs are contributed to the system to yield a flexible model. In this regard, a practical formulation for the energy storage system is included in the proposed model to cope with the undesired output power fluctuations of wind energy sources. To assure the scalability of the proposed model, a contingency filtering scheme is developed to filter the unnecessary contingencies from the optimization process for reducing the computational burden and solution time. Furthermore, the side-effects of wind energy fluctuations and the component outages are techno-economically explored and measured. The measures are the operational cost of the transmission network, the number of critical contingencies, peak-to-valley ratio, and load shedding. The numerical simulations on the New England 39-bus and IEEE 118-bus testbeds confirm the proper performance and good scalability of the proposed model. A priority list of the time-based demand response programs is also presented in each case of the study. The added value of the demand response programs on the security and economic performance of the proposed model is also tailored.

A Bayesian Learning Based Scheme for Online Dynamic Security Assessment and Preventive Control

In this paper, a two-stage Bayesian learning-based approach is proposed to enable online dynamic security assessment (DSA) and preventive control in power systems. To develop a reliable data mining-based model for DSA, the Bayesian neural network is learned by Bayes by Backprop to detect the security status in real-time and to inform the system operators with the confidence of the prediction. For dynamic insecurity prevention, the security-constrained optimal power flow (SCOPF) model incorporating the Bayesian neural network based security constraints is proposed, which is solved by the derivation-free Bayesian optimization. Case studies on the IEEE 39-bus system show that the Bayesian neural network is able to detect the security status of the power system correctly and reliably and is able to avoid the over-fitting problem compared with the traditional point estimation neural network. Also, Bayesian optimization is able to solve the non-analytical SCOPF model efficiently to mitigate the dynamic insecurity by preventive generation rescheduling.

An ISO-based security constrained generation maintenance coordination considering long-term SCOPF

Generation maintenance scheduling plays a crucial role in power system operation and planning; as it makes a significant effect on the outage time of generating units, and subsequently, to have a more secure and reliable power system with an optimal maintenance plan. Conventional maintenance scheduling methods are no longer applicable when the restructured power systems introduced. It is thus essential to develop novel approaches for the maintenance coordination. In this paper, an ISO-based security-constrained generation maintenance coordination approach is proposed. The approach comprises two main phases, the security-based maintenance scheduling, and the bidding based maintenance coordination. Moreover, the N−1 contingency analysis is considered in this study. The network security constraints are also incorporated in the investigation, using the security-constrained optimal power flow model. The model is solved by a binary-coded genetic algorithm which is combined with a primal-dual interior-point method. For systematic analysis, the IEEE 30-Bus and the IEEE-118 test systems are employed. The presented results emphasize the effectiveness and applicability of the proposed approach.

Preventive Security-Constrained Optimal Power Flow with Probabilistic Guarantees

The traditional security-constrained optimal power flow (SCOPF) model under the classical N-1 criterion is implemented in the power industry to ensure the secure operation of a power system. However, with increasing uncertainties from renewable energy sources (RES) and loads, the existing SCOPF model has difficulty meeting the practical requirements of the industry. This paper proposed a novel chance-constrained preventive SCOPF model that considers the uncertainty of power injections, including RES and load, and contingency probability. The chance constraint is used to constrain the overall line flow within the limits with high probabilistic guarantees and to significantly reduce the constraint scales. The cumulant and Johnson systems were combined to accurately approximate the cumulative distribution functions, which is important in solving chance-constrained optimization problems. The simulation results show that the model proposed in this paper can achieve better performance than traditional SCOPF.

Using the Thermal Inertia of Transmission Lines for Coping with Post-Contingency Overflows

For the corrective security-constrained optimal power flow (OPF) model, there exists a post-contingency stage due to the time delay of corrective measures. Line overflows in this stage may cause cascading failures. This paper proposes that the thermal inertia of transmission lines can be used to cope with post-contingency overflows. An enhanced security-constrained OPF model is established and line dynamic thermal behaviors are quantified. The post-contingency stage is divided into a response substage and a ramping substage and the highest temperatures are limited by thermal rating constraints. A solving strategy based on Benders decomposition is proposed to solve the established model. The original problem is decomposed into a master problem for preventive control and two subproblems for corrective control feasibility check and line thermal rating check. In each iteration, Benders cuts are generated for infeasible contingencies and returned into the master problem for adjusting the generation plan. Because the highest temperature function is implicit, an equivalent time method is presented to calculate its partial derivative in Benders cuts. The proposed model and approaches are validated on three test systems. Results show that the operation security is improved with a slight increase in total generation cost.

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.

A Robustness-Oriented Power Grid Operation Strategy Considering Attacks

Power system operation is facing increasing cyber and physical attack risks, so it becomes pressing to develop effective methods to improve the robustness of electric power infrastructure in the presence of significant attacks. As it is not guaranteed that attacks can always be detected and thwarted before they cause disturbances and damages to the power systems, increased robustness can contribute to reducing the consequence of attacks. In this paper, a holistic robustness framework is proposed by extending the conventional security-constrained optimal power flow (SCOPF) analysis to incorporate the risk caused by attacks. The corresponding solution methodology is proposed by combining particle swarm optimization and primal-dual interior point methods. Case studies conducted based on several test systems demonstrate that the proposed SCOPF model is able to reduce the consequence of attacks. This paper can provide some insight into improving the power system operation robustness in the face of significant attacks.

A parallel method for solving the DC security constrained optimal power flow with demand uncertainties

The security constrained optimal power flow (SCOPF) is a fundamental tool to analyze the security and economy of a power system. To ensure the safe and economic operation of a system considering demand uncertainties and to acquire economic and reliable solutions, in this paper, a parallel method for solving the interval DC SCOPF with demand uncertainties is presented. By using the interval optimization method, the uncertain nodal load can be expressed as interval variables and integrated into the DC SCOPF model, which is then formed as a large scale nonlinear interval optimization formulation. According to the theory of interval matching and selection of the extreme value intervals, the interval DC SCOPF problem can be transformed into two deterministic nonlinear programming problems and solved by alternating direction method of multipliers (ADMM) to obtain the range information of interval formulation variables. Using ADMM, the above two deterministic problems, which are large in scale because of the large number of preconceived contingencies, all can be split into independent sub-problems corresponding to pre-contingency status and each individual post-contingency cases. These small-scale sub-problems can be solved in parallel to improve the computing speed. Compared with the Monte Carlo (MC) method, the simulation results of the IEEE 30-, 57- and 118-bus systems validate the effectiveness of the proposed method.

Solution of security constrained optimal power flow for large‐scale power systems by convex transformation techniques and Taylor series

Security constrained optimal power flow (SCOPF) is a key operation function for today's power systems, extensively used, for example, in the dispatching centres. However, SCOPF is a complex optimisation problem for large practical power systems, mostly due to its highly non-convex nature. This study aims at changing highly non-convex SCOPF problem to a convex one. In this way, SCOPF can be solved with much less computation burden and more optimal solutions can be obtained for it by means of commercial solvers. For this purpose, the non-convex terms of SCOPF model (for instance, the terms associated with the valve loading effects of units and AC network modelling) are first reformulated using Signomial functions based on Taylor series. Then, the Signomial SCOPF formulation becomes convex by means of power transformation techniques. The constructed convex SCOPF formulation can be easily solved to obtain its optimal solution. The proposed solution approach is tested on well-known IEEE 30-bus, 118-bus, 300-bus and the polish 2746-bus test systems and its obtained results are compared with the results of several other SCOPF solution methods and published literature figures.

A contingency partitioning approach for preventive-corrective security-constrained optimal power flow computation

Security-constrained optimal power flow (SCOPF) is an important tool to optimize power system's operating state while satisfying security requirements with respect to credible contingencies. As a necessary extension to conventional SCOPFs, the recently proposed preventive–corrective SCOPF (PCSCOPF) aims to achieve the best coordination between the preventive control (PC) and corrective control (CC) considering the probabilistic nature of the contingencies and the cost of CC as well as other binding constraints. However, PCSCOPF renders a large-scale, multi-stage, non-linear programming problem which is difficult to directly solve. This paper proposes a novel and improved approach to the PCSCOPF problem. We aim to partition the contingencies into two exclusive sets: one is secured in the PC stage and the other in the corrective control CC stage. The PC corresponds to an ordinary SCOPF model and solved by the Benders decomposition method; the CC corresponds to an ordinary OPF model. The optimal partitioning of the contingencies is determined using an evolutionary algorithm (EA). Compared with the existing methods, the proposed approach is advantageous in that its searching dimension only depends on the number of insecure contingencies, hence tends to lead to a much higher solution speed. The proposed method is verified on the IEEE 118-bus system and compared with other two existing methods. Simulation results show that the proposed method can provide high-quality solutions with much higher computation speed.

Security constrained multi-period optimal power flow by a new enhanced artificial bee colony

Security constrained optimal power flow (SCOPF) is an important operation function for dispatching centers of current power systems. It optimizes operating conditions of the system, while saves its security. However, SCOPF in its present form focuses on a single time interval, which is known as static SCOPF. A multi-period SCOPF model, referred to as dynamic SCOPF (DSCOPF) in this paper, is presented. It extends static SCOPF to multi-period frameworks considering the inter-temporal constraints. The proposed DSCOPF is a more practical operation function and can optimize operating conditions of the system more realistically compared to traditional SCOPF. Moreover, to solve this DSCOPF model, considering its nonlinear and non-convex behavior, a new stochastic search method is presented, which is an enhanced version of artificial bee colony (ABC) algorithm. The proposed enhanced ABC (EABC) has high exploration capability and can discover different areas of the solution space. Also, it is a robust algorithm and has low sensitivity with respect to the initial population. Effectiveness of the proposed EABC is extensively illustrated on various test cases.

Minimal Impact Corrective Actions in Security-Constrained Optimal Power Flow Via Sparsity Regularization

This paper proposes a new formulation for the corrective security-constrained optimal power flow (SCOPF) problem with DC power flow constraints. The goal is to produce a generation schedule which has a minimal number of post-contingency corrections as well as a minimal amount of total MW rescheduled. In other words, the new SCOPF model effectively clears contingencies with corrective actions that have a minimal impact on system operations. The proposed SCOPF model utilizes sparse optimization techniques to achieve computational tractability for large-scale power systems. We also propose two efficient decomposition algorithms. Extensive computational experiments show the advantage of the proposed model and algorithms on several standard IEEE test systems and large-scale real-world power systems.

Discussion on “Solving Preventive-Corrective SCOPF by a Hybrid Computational Strategy”

Preventive control (PC) and corrective control (CC) are complementary actions in protecting large power systems against the risk of blackout. This paper addresses the optimal coordination between PC and CC via a preventive-corrective security-constrained optimal power flow model. The objective is to minimize the total expected-security-control cost which is the sum of the costs of PC and CC considering the probability of the contingencies. The constraints include system operating limits in pre- and post-contingency states, the existence of the post-contingency short-term equilibrium, and the coupling constraints on the CC actions. To solve the model, a hybrid computational strategy combining evolutionary algorithm and interior-point method is developed. The solution process consists of globally searching the critical feasible region and locally optimizing the operating variables in the found region, the two procedures interact iteratively to progressively tighten the solution region leading to the final solution. The proposed model and computational strategy are demonstrated on the IEEE 14-bus and 118-bus test systems. To speed up the computation, parallel processing of the approach is implemented.

Closure to Discussion on “Solving Preventive-Corrective SCOPF by a Hybrid Computational Strategy”

Preventive control (PC) and corrective control (CC) are complementary actions in protecting large power systems against the risk of blackout. This paper addresses the optimal coordination between PC and CC via a preventive-corrective security-constrained optimal power flow model. The objective is to minimize the total expected-security-control cost which is the sum of the costs of PC and CC considering the probability of the contingencies. The constraints include system operating limits in pre- and post-contingency states, the existence of the post-contingency short-term equilibrium, and the coupling constraints on the CC actions. To solve the model, a hybrid computational strategy combining evolutionary algorithm and interior-point method is developed. The solution process consists of globally searching the critical feasible region and locally optimizing the operating variables in the found region, the two procedures interact iteratively to progressively tighten the solution region leading to the final solution. The proposed model and computational strategy are demonstrated on the IEEE 14-bus and 118-bus test systems. To speed up the computation, parallel processing of the approach is implemented.