Optimal Power Flow Constraints Research Articles

The Calibrated Safety Constraints Optimal Power Flow for the Operation of Wind-Integrated Power Systems

As the penetration of renewable energy sources (RESs), particularly wind power, continues to rise, the uncertainty in power systems increases. This challenges traditional optimal power flow (OPF) methods. This paper proposes a Calibrated Safety Constraints Optimal Power Flow (CSCOPF) model that uses the Improved Acceleration Coefficient-Based Bee Swarm algorithm (IACBS) in combination with the equivalent current injection (ECI) model. The proposed method addresses key challenges in wind-integrated power systems by ensuring preventive safety scheduling and enabling effective power incident safety analysis (PISA). This improves system reliability and stability. This method incorporates mixed-integer programming, with continuous and discrete variables representing power outputs and control mechanisms. Detailed numerical simulations were conducted on the IEEE 30-bus test system, and the feasibility of the proposed method was further validated on the IEEE 118-bus test system. The results show that the IACBS algorithm outperforms the existing methods in both computational efficiency and robustness. It achieves lower generation costs and faster convergence times. Additionally, the CSCOPF model effectively prevents power grid disruptions during critical incidents, ensuring that wind farms remain operational within predefined safety limits, even in fault scenarios. These findings suggest that the CSCOPF model provides a reliable solution for optimizing power flow in renewable energy-integrated systems, significantly contributing to grid stability and operational safety.

Cooperative energy interaction for neighboring multiple distribution substation areas considering demand response

With the growing integration of renewable energy into medium- and low-voltage distribution networks, the distribution substation area (DSA) has emerged, encompassing energy storage and loads. This paper introduces an energy interaction framework for multiple DSAs aimed at enhancing local renewable energy consumption. The energy interaction issue among various DSAs is modeled as a Nash bargaining problem to encourage energy exchanges. However, the variability in pricing and internal demand response may influence scheduling decisions, necessitating further investigation. To address price forecast errors, scenarios are developed using a stochastic programming approach to represent price uncertainties while adjusting the DSA’s load accordingly. Optimal power flow constraints are integrated into the model to bolster power system operation security. Additionally, the transmission capacity can impact scheduling outcomes and operational costs. The influence of transmission limitations on operational strategies is examined within the allowable capacity. To solve this issue, the bargaining model is divided into two subproblems, and an enhanced alternating direction multiplier method (ADMM) is used to maintain the privacy of DSAs. The simulation results obtained using the IEEE-33 bus system indicate that energy interaction among multiple DSAs significantly lowers operating costs and facilitates the integration of renewable energy.

Risk-averse and flexi-intelligent scheduling of microgrids based on hybrid Boltzmann machines and cascade neural network forecasting

The future of energy flexibility in microgrids (MGs) is steering towards a highly granular control of the end-user customers. This calls for more highly accurate uncertainty forecasting and optimal management of risk and flexibility options. This paper presents a novel data-driven model to optimize the operation of MGs based on a risk-averse flexi-intelligent energy management system (RFEMS), considering the rising challenge of global climate change. It considers the presence of renewables, a diesel generator, and flexibility resources (FRs) containing a demand response program (DRP), distributed electric vehicles (EVs), and electric springs (ESs). In the first phase, the proposed model, by means of a novel hybrid deep-learning (DL) model, forecasts uncertain parameters associated with wind and solar generations, load demand, and day-ahead energy market price. The architecture of the proposed hybrid forecasting model is composed of several stacked restricted Boltzmann machines and a cascade neural network. In the second phase, the MG operator (MGO), based on the obtained uncertainty forecasting results, in the context of a hybrid risk-controlling model, optimizes the MG operation using the provided demand-side flexibility. The proposed optimization problem is linearized stochastic programming with robust concepts, subject to AC optimal power flow constraints, MG flexibility restrictions, and operating limits of local resources. Finally, the efficiency of the proposed RFEMS by using real German datasets on a 33-bus test MG is analyzed. Numerical results demonstrate the superior performance of the proposed forecasting model over several hybrid DL models. In particular, the root mean square error (RMSE) index for wind, solar, load, and price forecasting is improved by 53.35%, 73.24%, 80.24%, and 58.1%, respectively. Further analysis of the proposed RFEMS reveals that operating indices in two 33-bus and 69-bus test networks are significantly improved. It paves pathways to risk-averse, flexible, and economic operation of smart active distribution networks.

Stochastic Coordinated Management of Electrical–Gas–Thermal Networks in Flexible Energy Hubs Considering Day-Ahead Energy and Ancillary Markets

This paper presents an optimal operation framework for electrical, gas, and thermal networks in the presence of energy hubs (EHs), so that EHs can benefit from day-ahead ancillary and energy markets. Therefore, to consider the goals of network operators (optimal operation of networks) and EHs (optimal operation in markets), the proposed model is developed in the form of a bi-level optimization. Its upper-level formulation minimizes the expected energy loss in the proposed networks based on the optimal power flow constraints and technical limits. At the lower-level problem, maximizing the expected profit of EHs in day-ahead energy and ancillary markets (including reactive and reserve regulation) is formulated based on the operational model of resources, storage devices, and responsive load in the EH framework, and the flexible constraints of EHs. This scheme includes the uncertainties of load, market price, renewable energy resources, and mobile storage energy demand, which uses the point estimation method to model them. Karush–Kuhn–Tucker is then used to extract the single-level model. Finally, by implementing the proposed scheme on a standard system, the obtained numerical results confirm the capability of the proposed model in improving the network’s operation and economic status of EHs. As a result, the proposed scheme is able to decrease operation indices such as energy losses, voltage drop, and temperature drop by approximately 28.5%, 39%, and 27.8%, respectively, compared to load flow analysis. This scheme can improve the flexibility of EHs, including non-controllable sources such as renewable resources, by nearly 100% and it obtains considerable profits for hubs.

Bi-level fuzzy stochastic-robust model for flexibility valorizing of renewable networked microgrids

This paper presents a new bi-level multi-objective model to valorize the microgrid (MG) flexibility based on flexible power management system. It considers the presence of renewable and flexibility resources including demand response program (DRP), energy storage system and integrated unit of electric spring with electric vehicles (EVs) parking (IUEE). The proposed bi-level model in the upper-level maximizes expected flexibility resources profit subject to flexibility constraints. Also, in the lower level, minimizing MG energy cost and voltage deviation function based on the Pareto optimization technique is considered as the objective functions; it is bounded by the linearized AC optimal power flow constraints, renewable and flexibility resources limits, and the MG flexibility restrictions. In the following, the proposed bi-level model using Karush–Kuhn–Tucker (KKT) technique is converted to a single-level counterpart, and the fuzzy decision-making method is employed to achieve the best compromise solution. Further, hybrid stochastic-robust programming models uncertain parameters of the proposed model, so that stochastic programming models uncertainties associated with demand, energy price, and the maximum renewables active generation. Also, to capture the flexible potential capabilities of the IUEE, robust optimization models the EVs’ parameters uncertainty. Finally, numerical results confirm the proposed model could jointly improve operation, economic and flexibility conditions of the MG and turned it to a flexi-optimized-renewable MG. • Bi-level model to value the microgrid flexibility is presented. • Integrated unit of electric spring with electric vehicles is modeled. • The paper deals with maximizing flexibility value in renewable microgrids. • Fuzzy stochastic/robust optimization is proposed to handle uncertainty.

Active and Reactive Power Management in the Smart Distribution Network Enriched with Wind Turbines and Photovoltaic Systems

The penetration of renewable energy sources has been intensified during the last decade to tackle the climate crisis by providing clean energy. Among various renewable energy technologies, wind turbines and photovoltaic systems have received increasing attention from investors. Generally, electronic power converters are used to control renewable generations. The present study discusses the power management of smart distribution networks enriched with wind and photovoltaic units. The model aims to minimize the expected network operating cost of the system formulated as an objective function regarding AC optimal power flow constraints. In addition, stochastic programming based on unscented transformation is adopted to model the probable behavior of loads, renewable generations, and energy market prices. The model employs a linear approximation model to burden the complexity of the problem and achieve the optimum solution. The problem is tested to a 33-bus system using the General Algebraic Modeling System (GAMS). The obtained results confirm the proposed model’s potential in reducing energy costs, power losses, and voltage deviations compared to conventional power flow studies. In the proposed scheme compared to network load distribution studies, the active and reactive power losses, network energy costs, and voltage deviations are improved by about 40.7%, 33%, 36%, and 74.7%, respectively.

BESS based voltage stability improvement enhancing the optimal control of real and reactive power compensation

<abstract> <p>With the increase in the integration of renewable energy resources in the grid and ongoing growth in load demand worldwide, existing transmission lines are operating near their loading limits which may experience voltage collapse in a small disturbance. System stability and security can be improved when the closeness of the system to collapse is known. In this research, voltage stability of IEEE 30 bus test network is analyzed and assessed under continuously increasing load condition, utilizing the Critical Boundary Index (CBI); and improved with continuous integration of battery energy storage system (BESS). BESS is considered to be a hybrid combination of storage units and voltage source converter to have a controllable real and reactive power output. Security constraint optimal power flow is utilized for optimally sizing the installed BESS. It is evident from the outcome of the research that the voltage stability of the system is controlled to be above the acceptable range of 0.3 pu CBI in all lines and the system voltage is kept within the acceptable and constrained range of 0.9–1.1 pu.</p> </abstract>

A Convexification Approach for Small-Signal Stability Constrained Optimal Power Flow

In this article, a novel convexification approach for small-signal stability constraint optimal power flow has been presented that does not rely on eigenvalue analysis. The proposed methodology is based on the sufficient condition for the small-signal stability, developed as a bilinear matrix inequality (BMI), and uses network structure-preserving differential algebraic equation modeling of the power system. The proposed formulation is based on semidefinite programming and objective penalization that has been proposed for feasible solution recovery, making the method computationally efficient for large-scale systems. A vector-norm based objective penalty function has also been proposed for feasible solution recovery while working over large and dense BMIs with matrix variables. An effectiveness study carried out on WECC 9-bus, New England 39-bus, and IEEE 118-bus test systems shows that the proposed method is capable of achieving a stable equilibrium point without inflicting a high stability-induced additional cost.

A Two-Level ADMM Algorithm for AC OPF With Global Convergence Guarantees

This paper proposes a two-level distributed algorithmic framework for solving the AC optimal power flow (OPF) problem with convergence guarantees. The presence of highly nonconvex constraints in OPF poses significant challenges to distributed algorithms based on the alternating direction method of multipliers (ADMM). In particular, convergence is not provably guaranteed for nonconvex network optimization problems like AC OPF. In order to overcome this difficulty, we propose a new distributed reformulation for AC OPF and a two-level ADMM algorithm that goes beyond the standard framework of ADMM. We establish the global convergence and iteration complexity of the proposed algorithm under mild assumptions. Extensive numerical experiments over some largest test cases from NESTA and PGLib-OPF (up to 30 000-bus systems) demonstrate advantages of the proposed algorithm over existing ADMM variants in terms of convergence, scalability, and robustness. Moreover, under appropriate parallel implementation, the proposed algorithm exhibits fast convergence comparable to or even better than the state-of-the-art centralized solver.

Coordinated expansion planning problem considering wind farms, energy storage systems and demand response

During the recent years, the power system has entered a new technological era. The trends associated with increased commitment to wind farms (WFs) and energy storage systems (ESSs) as well demand side flexibility require disruptive changes in the existing power system structures and procedures. Being at the heart of a paradigm shift from passive users of the grid to active prosumers, storage owners and demand responsive actors, this paper expresses a flexible coordinated power system expansion planning (CPSEP) while considering local WFs, ESSs and incentive-based demand response programs (DRPs). This model minimizes the summation of the expansion planning, operation and reliability costs while taking the network model based on AC optimal power flow constraints, and the reliability and flexibility considerations into account. The proposed framework is firstly formulated by mixed integer non-linear programming (MINLP), then to have a well-handed optimization model it is converted to mixed-integer linear programming (MILP). Additionally, the uncertainties of load, energy price, maximum WF generation and availability/unavailability of the network equipment are included in the proposed model where the first three parameters are modeled based on the bounded uncertainty-based robust optimization (BURO), and the scenario-based stochastic programming (SBSP) is used to model the last uncertain parameter. Finally, the proposed method is examined on several test networks to assess the performance of the proposed framework for flexi-reliable transmission network operation and planning.

Technical and economic analysis of curative actions in distribution networks utilizing battery energy storage systems

Renewable energy generation curtailment increases due to more frequently occurring congestions in power system operation. Post-contingency curative congestion management actions can reduce the necessity of renewable energy curtailment by enabling a more efficient utilization of transmission capacities. In this research, the potential of curative actions to substitute renewable energy curtailment is studied considering technical and economic criteria. Therefore, a novel pricing methodology for the market-based provision of curative actions is introduced. The method is based on the security constraint optimal power flow technique. Simulations are carried out on a modified version of the IEEE 14-bus network and a real-world 110 kV distribution network. Battery energy storage systems are implemented as an exemplary technology to provide curative actions. The developed method achieves a positive power system impact by reducing operational costs and maximizing renewable energy integration. Also, novel business models for merchant-owned battery energy storage systems are unveiled. The provision of curative actions further proves to be competitive to established battery storage applications. Additionally, results of different grid expansion scenarios of the 110 kV network reveal the need to coordinate power system planning and operation more extensively in the future.

Multi objective functions of constraint optimal power flow based on modified ant colony system optimization technique

This article presents the development of Ant Colony System algorithm for solving the constrained Optimal Power Flow (OPF) problem. In this modification of ant colony, a local and global update of pheromone has been used. This optimization technique is used to adjust an optimal control variables of the system while satisfying the constraint of the state variables in their limits. The proposed algorithm tested on the IEEE-30 bus with different cases of single and multiple OPF objectives. The obtained results are analysed and compared with other previous studies. This comparison illustrates the efficiency of the ACS technique for solving different OPF problems of complex objective functions where the propose algorithm of ACS has been reduce the single objective function of total fuel cost, power losses, voltage profile improvement and the total generation emission to minimum value of 800.83 $/h, 3.2723 MW, 0.1194 pu and 0.2066 ton/h respectively with reduction of these objective function of 11.216%, 43.991%, 89.660%, 13.952% respectively. The authors have been used the MATLAB software for programming the propose technique without using any simulators. The Ant Colony System has the facility of simplicity in analysis, easy in program, faster in execution, less iteration with accurate result over the other optimization techniques.

Adaptive robust operation of the active distribution network including renewable and flexible sources

This paper presents the optimal scheduling model of the active distribution network (ADN) containing renewable energy sources (RESs) and flexible sources (FSs) such as non-RESs (NRESs) and electric vehicles (EVs) parking lot based on the adaptive robust optimization (ARO). In the deterministic programming, a two-objective optimization model is expressed. It minimizes the difference between the network and NRES operation cost and the revenue of the RES, NRES and FS due to the sale of active and reactive power in the first objective function, and the second objective function considers the minimizing of the voltage deviation. Also, this problem considers AC optimal power flow constraints for the ADN in the presence of the RES, NRES and EVs parking lot. This method is as the non-linear programming (NLP). It is converted to the linear programming (LP) model based on the conventional linearization approaches to achieve the optimal solution at a short computational time. Then, the proposed approach is modeled as a single-objective optimization formulation using ε-constraint-based Pareto optimization. This problem contains uncertainty of load, market price, EVs and RES characteristics; therefore, the ARO is used in this paper to model/obtain these uncertain parameters/robust capabilities of renewable and flexible sources to improve the network operation indices. The proposed scheme is implemented on the IEEE 33-bus ADN to improve the network indices such as voltage profile with determining optimal and robust scheduling of RES and FS according to numerical results.

Artificial intelligence and optimization: a way to speed up the security constraint optimal power flow

Abstract Optimal power flow is a widely used tool in power system planning and management. Due to the complexity of the power system both in terms of number of variables, degrees of freedom and uncertainty, there is a continuous effort to find more efficient computational methods to solve optimal power flow problems. This article presents a novel method to speed-up the solution of a security constraint optimal power flow problem. An unconventional warm start based on the training of a neural network is investigated as an option to improve the computational efficiency of the optimization problem. The principle of the method and the validity of the approach is demonstrated by different analysis performed on the IEEE14 test grid and based on a linearized mathematical formulation of the problem. The results show the effectiveness of the method in reducing the number of iterations needed to converge to global optimum.

Hybrid stochastic/robust scheduling of the grid-connected microgrid based on the linear coordinated power management strategy

It can be predicted that the future power system, especially microgrids (MGs) will consist of many different sources and storages. In this regard, many researches have been conducted on different energy management strategies to improve power system adequacy indices. This paper presents a hybrid stochastic/robust coordinated power management strategy (CPMS) to simultaneously improve the flexibility, reliability and security indices of MG in the presence of electric vehicles (EVs), energy storage system (ESS), distributed generation (DG) and demand response programming (DRP). At first, this paper models the original problem which minimizes the difference between MG operation and reliability costs and its flexibility and security benefits considering MG optimal power flow constraints. This problem is non-linear programming (NLP) that is generally resulted in the local optimal, hence, this formulation is converted into linear programming (LP) using the first-order expansion of Taylor’s series for linearization of power flow equations and a polygon for linearization of circular inequalities. In addition, the active and reactive load demand, energy price, active power of renewable energy source (RES), different parameters of EVs, and availability/unavailability of MG equipment are considered as uncertain parameters. Hence, the hybrid stochastic/robust optimization with coupling the bounded uncertainty-based robust optimization (BURO) and scenario-based stochastic programming (SBSP) is used for the presented problem for modeling of uncertain parameters. Finally, the proposed method is applied to 32-bus MG using GAMS software. The numerical results show the capabilities of the proposed strategy to improve power system adequacy indices determining the optimal power scheduling for MG devices.

Modified Artificial Bee Colony Optimization Technique with Different Objective Function of Constraints Optimal Power Flow

Modified Artificial Bee Colony Optimization Technique with Different Objective Function of Constraints Optimal Power Flow

Robust linear model for multi‐period AC optimal power flow

In the near future power systems, efficient management of uncertainties with considering the system constraints without any simplification will be a challenge for system operators. Considering AC constraints leads to providing more accurate schedule of generating units, which can have a significant impact on the reduction of operating costs. Although numerous studies have been done to convexify AC optimal power flow constraints, most of the models are non-linear, which can be intractable for large-scale systems. In this study, a novel linear robust AC model is introduced using a combination of the quadratic convex relaxation (QCR) and the Frank–Wolfe algorithm for linearising the AC constraints. The uncertainties are modelled by applying the robust optimisation with recourse to obtain an optimal schedule for the conventional units in multi-period real-time markets. The Benders-dual algorithm is implemented to solve the optimisation problem. The proposed model was applied to the IEEE 3-bus, 118-bus, and 300-bus systems. The results indicate that the proposed algorithm obtains more precise approximation than the QCR method. In addition, the costs and losses of the proposed model are less than those of the conventional robust DC and stochastic models. Furthermore, because the proposed model is linear, its runtime is rational.

Adaptive Technique for Transient Stability Constraints Optimal Power Flow

This document explains about an adaptive method for optimal power flow (OPF) of the power system, which is depending on the transient constancy restraints. The adaptive method is the mixture of both Cuckoo Search (CS) algorithm and artificial neural network (ANN). The innovative anticipated adaptive method is extremely flexible in nonlinear loads, suitable for user interface and logical reasoning, and allowing controlling formats. In the predefined generator, the CS algorithm optimises the generator arrangements by the load demand. The foremost intention of the CS algorithm is to reduce the fuel cost and emission cost. The obtainable ANN method is mainly used to develop the levy flight searching activities of the CS algorithm. The levy flight parameters are generally used to meet of the requirements the ANN, which envisage the precise consequences at the testing time. The anticipated adaptive method is executed in the MATLAB/Simulink platform and the efficiency of the anticipated procedure is investigated by the comparison analysis.

Adaptive technique for transient stability constraints optimal power flow

Adaptive technique for transient stability constraints optimal power flow

Optimize globally, control locally: Coordinated optimal local voltage control in hybrid AC/DC microgrid

The increasing penetration of photovoltaic (PV) generation leads to voltage violations in hybrid AC/DC microgrids. Due to the uncertainty and volatility of PV outputs, fast-responding voltage control devices are obliged to coordinate with each other and regulate nodal voltages in real time. This paper follows the concept of optimizing globally and controlling locally to propose a combined central and local voltage control strategy based on a two-stage voltage control framework. In the first stage, minutely optimal power flow based on predicted PV outputs within one hour is performed in microgrid central controller (MGCC) to calculate voltage and optimal power settings for each controllable device. The uncertainty of PV is considered using chance constraint optimal power flow (CCOPF) method. In the second stage, according to minutely voltage and power settings, local controller (LC) generates improved voltage control curves based on curve fitting method. With minutely measurements of nodal voltages, power outputs of PVs, smart loads (SLs) energy storage systems (ESSs) and VSC are cooperated based on improved local control curves to minimize power losses without communication requirements. In order to coordinate the active and reactive power of SLs ESSs, and VSC, a combined P(V) and Q(V) curve is proposed. The piecewise linear curve fitting method is used to generate optimal voltage control curves due to its higher fitting accuracy compared with other fitting methods. Simulations are performed to verify the effectiveness of the proposed voltage control strategy in mitigating voltage rise problems and reducing power losses.