A per-node granularity decentralized optimal power flow for radial distribution networks with PV and EV integration

Decentralized saddle-point dynamics solution for optimal power flow of distribution systems with multi-microgrids

The interline power flow controller (IPFC) is one of the most versatile integrated flexible alternating current transmission systems (FACTS) controllers and can realize power flow control for multiple transmission lines in modern power systems. However, control characteristics are ignored in conventional IPFC models, in which unreasonable assumptions about injected voltages may lead to security problems in realistic operation. Besides, preventive security constraints considering IPFC control modes are not included in optimal power flow (OPF) control of the system with IPFC, squandering IPFC control potential. To solve these problems, a preventive-security-constrained optimal power flow (PSCOPF) model considering IPFC control modes is proposed in this paper. IPFC control characteristics under different control modes are analyzed and employed as constraints of the optimization model. The iterative updates of converter output voltages for different control modes are derived respectively for power flow calculation, and the power and voltages required in the objective function and constraints of the proposed model can then be obtained. Through optimal selection of IPFC control modes and control parameters, the proposed model can better reconcile the economical and secure operation of the system. Numerical results demonstrate the efficient performance and superiority of the PSCOPF model considering IPFC control modes.

Objective: This work involves a convex-based mathematical reformulation for the optimal power flow problem in DC networks. The objective of the proposed optimization model corresponds to the minimization of the power losses through all the network branches considering a convex conic model that warranties finding the global optimal. Methodology: This is split into three stages: The first stage presents the mathematical model of optimal power flow for DC networks and all its geometric features that make it non-convex; the second stage presents the convex reformulation from a second order conic relaxation; the third stage shows the main characteristics of the DC system under study; and the fourth stage presents the optimal solution of the power flow problem and its comparisons with some methods reported in the specialized literature. Results: The numerical validations demonstrate that the model of proposed convex optimal power flow obtains the same solution as the exact model of the problem with an efficiency of 100%, which is in contrast with the variability of the results that are presented by the metaheuristic techniques reported as comparison methodologies. Conclusions: The proposed second-order conic relaxation warrantied the convexity of the solution space and therefore, the finding of the optimal solution at each execution; besides of this, demonstrated that for optimal power flow problems in DC networks, the numerical performance is better than most of the comparative metaheuristic methods; and the provided solution by the proposed relaxation is equivalent to that provided by the exact model. Keywords: Direct current networks, second-order conic relaxation, non-linear programming model, convex optimization.

This paper proposed the Lagrangian optimization model for Optimal Power Flow (OPF) problem. It is designed by relaxing the constraints from the Quadratic Programming (QP) problem. The objective of this model is to minimize the total cost of active power generation. The solution of QP is obtained by different optimization techniques like Particle Swarm Optimization (PSO) method, Genetic Algorithm (GA), Differential Evolution (DE) algorithm. In this paper, the optimum value of QP is obtained by the proposed model and it is compared with other methods PSO, GA, DE. The results of the methods have been tested through the standard IEEE 30 bus system. Based on numerical calculations and graphical representation, the optimal generation cost for OPF can be achieved.

Optimal power flow (OPF) is a crucial aspect of distribution network planning and operation. Conventional heuristic algorithms fail to meet the system requirements for speed and accuracy, while linearized OPF approaches are inadequate for distribution networks with high R/X ratios. To address these issues and cater to multi-period scenarios, this study proposes a dynamic linearized second-order cone programming-based (SOCP) OPF model. The model is built by first establishing a dynamic OPF model based on linearized second-order conic relaxation (LSOCR-DOPF). The components of the active distribution network, such as renewable energy power generation units, energy storage units, on-load-tap-changers, static var compensators, and capacitor banks, are then separately modeled. The model is implemented in MATLAB and solved by YALMIP and GUROBI. Finally, three representative scenarios are used to evaluate the model accuracy and effectiveness. The results show that the proposed LSOCR-DOPF model can ensure calculation time within 3 min, voltage stability, and error control within 10−6 for all three applications. This method has strong practical value in the fields of active distribution network day-ahead dispatch, accurate modeling of ZIP load, and real-time operation.

Modern power systems which integrate renewable energy sources (RESs), such as wind or solar energy sources and plug-in electric vehicles (PEVs), need to carry out the uncertainty due to the access of demanded or injected power. Therefore, it is necessary to consider uncertainty costs in optimal power flow problems. To develop the uncertainty cost functions, log-normal probability distribution function (PDF) for solar irradiance, normal PDF for unloading and loading behavior of PEVs, and Rayleigh PDF for wind speed are considered. In this work, a dynamic optimal power flow (DOPF) model is formulated by considering the uncertainties of RESs and PEVs. A newly hybrid metaheuristic algorithm named cross entropy (CE) covariance matrix adaption evolutionary strategy (CMAES) is proposed to evaluate the DOPF problem in a modified IEEE 118-bus system. The application of adaptive step length in the CMAES method improves the local exploitation capability, while the CE method is used in the initial stage for global exploration due to its fast convergence. Simulation results indicate that the proposed technique can solve the DOPF problems with RESs and PEVs effectively and can provide high-quality solutions compared to different techniques. The conventional statistical method called ANOVA test is performed for comparative analysis of different techniques. The results of this test show the validation of CE-CMAES compared to different optimization techniques. Therefore, the proposed method could be easily and efficiently applied by power system operators in real-time optimal power flow operations.

An optimal power flow (OPF) model is developed in this paper, which includes three highly volatile energy sources: wind energy, photovoltaic energy, and electric vehicle as a vehicle to grid energy source. An interpretable probabilistic approach is implemented to estimate the power generation from the mentioned energy sources using different probability distribution functions. A single static synchronous series compensator is optimally configured and positioned in the combined grid power system to achieve balanced operation. This significant uncertainty imposed OPF model is solved by blending (a) chaotic mapping technique, and (b) Nelder–mead simplex method with conventional moth swarm algorithm (MSA) and the modified version of MSA is called chaotic simplex MSA (CSMSA). Proposed CSMSA's performance is evaluated analytically using extensive simulation approaches that include six different power‐related simulation instances considering IEEE 30 and 118‐bus test grid systems. The strength of the proposed CSMSA is examined by comparing its performance to five outstanding metaheuristic techniques.

This is the second part (Part-II) of the companion paper (Part-I) on variable reverse power flow in active distribution networks with wind stations (WSs). In Part-I, the original model of active-reactive optimal power flow was further developed to explore the pure potential of the reactive power capability of WSs in the absence of battery storage systems. Here, we answer the questions raised in Part-I by investigating an electricity market model. The most interesting results from applying the extended model on a real medium-voltage network are presented. For instance, we demonstrate that the reactive power capability of WSs will be never utilized during days with zero wind power and varying limits on power factors (PFs). In contrast, more than 10% of active and 15% of reactive energy losses costs, respectively, and 100% of the cost of reactive energy to be imported from a transmission network can be saved if WSs are operated like capacitor banks with no limits on PFs.

Mae Hong Son (MHS) is a prototype city that developed a smart grid system to utilize renewable energy power plants and Battery Energy Storage System to the fullest. With many power plants being incorporated into the system, Energy Management System (EMS) is a significant factor in improving the efficiency of renewable energy usage. This paper presents the modified Optimal Power Flow (OPF) model that improves the operation condition. The objectives are to enhance the accuracy, capability, and realism of the OPF model. Furthermore, to introduce a Combined Economic and Emission Dispatch (CEED). In this work, the problem is formulated as second order one programming (SOCP) and use the mathematical model of the power system in MHS. Load data and power generation profile will be utilized as the input to Nonlinear Model Predictive Control (NMPC) of EMS to simulate the problem solving under different objective functions. The results illustrate that the NMPC with the modified OPF can significantly reduce Total Operating Cost (TOC) and Total CO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> Emission (TCOE). In addition, the improved OPF gives a broader range of feasible solutions when the transmission length is increased. When comparing the results in normal operation, the proposed NMPC with improved OPF can reduce the TOC by 0.49% and the TCOE by 1.39% in the rainy season.

A realistic and practicable modeling of unbalanced distribution networks (DNs) is the missing link in most studies undertaken in these networks, e.g., optimal power flow (OPF), energy markets, etc. To address the issue, this letter proposes an unbalanced linear three-phase four-wire power flow (PF) model based on current injection equations at nodes. Also, the ZIP representation is considered for loads. The model can be easily generalized for unbalanced three-wire networks with minor changes and assumptions. Hence, the scope of the proposed method can be extended to cover both low-voltage and medium-voltage DNs. The performance of the proposed model is verified through simulations on two IEEE test feeders.

Distribution networks typically have unbalanced loads; however, most works on Active Distribution Networks (ADNs) use single-phase representations. This paper proposes a linear alternate current (AC) three-phase optimal power flow (OPF) for a day-ahead operation planning of ADNs and microgrids. The proposed AC linear three-phase optimal power flow model is based on polar coordinate systems and considering some consistent approximations for linearization of power flow equations. The shunts admittances of the network and the mutual impedances between phases of the three-phase lines are considered in the model. In this paper, the proposed linear AC three-phase OPF model is used to define the optimal day-ahead operation planning of active distribution systems and microgrids with three-phase feeders and three-phase distributed generators (DG) and energy storage (ES). Since this model proposes a three-phase representation of the system, it provides more accurate results, making it an effective tool for optimal planning of the ADN operation. The proposed model is illustrated using the IEEE 34-bus test system and results show its effectiveness and excellent performance, presenting an error of less than 4% for the voltage magnitude of the buses and less than 2% for the apparent power flow of the lines, when compared with non-linear models.

Participation of adjustable loads in demand response can alleviate power supply and demand challenges. As a typical adjustable load, this paper gives an optimal scheduling method considering optimal power flow in distribution networks of air source heat pumps, and studies adjustable load power allocation schemes for multiple distribution network nodes. The scheme with the goal of the lowest network loss determines the scheduling amount of the corresponding node heat supply stations to achieve optimal power flow dispatch, and the genetic algorithm is used to solve the model. Specific examples analysis shows that the proposed decision-making method can reasonably allocate power adjustments, prevent node voltage overruns in distribution networks, and reduce active power losses.

Experimental investigation and optimal power flow modelling of the first renewable microgrid in Chocó, Colombia

The integration of renewable power can pose uncertainty to power system operation, causing operational risk like power imbalance or line congestion. To improve the operational security and economy of the system under uncertainties, this paper considers two potential directions. The first is to enhance the system capability for safely accommodating uncertainties using various network resources. Such capability is often termed as the operational flexibility. The second direction is to employ appropriate risk management methods. With these two directions, a conditional value-at-risk (CVaR)-constrained optimal power flow (OPF) model is developed in this paper for wind-integrated power systems. In this model, dynamic line rating (DLR) and flexible AC transmission system (FACTS) technologies are exploited to unlock transfer capacities of transmission lines and enable line reactance control. As a result, power system has capability to allow more flexible and cost-efficient power flow distributions. That is, additional operational flexibility is provided by the transmission-side DLR and FACTS technologies. Such flexibility is termed as the transmission-side flexibility. Meanwhile, CVaR is employed as the risk management tool to control the security level of each operational constraint. To address the non-linearity of CVaR and solve the proposed model, a novel solution method is developed by combining Gaussian mixture model for uncertainty modelling with cutting-planes for CVaR reformulation. Numerical experiments in MATLAB reveal the economic benefit of the proposed model: the inclusion of transmission-side flexibility in formula can reduce the operational cost by 6.10% on a 14-bus system. The simulation results also show that the proposed solution method overcomes the poor system security associated with the traditional Gaussian method and is more economical than the previous robust method (3.79% reduction in operational cost on a 14-bus system).

The optimal power flow (OPF) problem seeks to control the power generation/consumption to minimize the generation cost, and is becoming important for distribution networks. OPF is nonconvex and a second-order cone programming (SOCP) relaxation has been proposed to solve it. We prove that after a small modification to OPF, the SOCP relaxation is exact under a mild condition. Empirical studies demonstrate that the modification to OPF is small and that the mild condition holds for all test networks, including the IEEE 13-bus test network and practical networks with high penetration of distributed generation.