Tools for handling steady‐state under‐frequency regulation in isolated microgrids

Linear power flow formulations and optimal operation of three-phase autonomous droop-controlled Microgrids

The complexity and computational burden of nonlinear power flow (PF) models have motivated the introduction of various approximations. While these approximations provide tractability and reduced computational burden in PF, for optimal power flow (OPF) and control purpose, the accuracy of these models becomes a major concern in the presence of high renewable energy penetration/increased demand in distribution feeders. This paper compares and analyzes, for the first time to our knowledge, the performance of commonly used PF models in OPF formulations for single-phase and unbalanced three-phase distribution systems. Simulations performed on the phase-coupled and phase-decoupled versions of the IEEE 123-node and a reduced model extracted from the IEEE 8500-node feeder with varying levels of negative and positive net loads show that, ignoring mutual coupling impedances, as in the phase-decoupled PF models, is the largest source of error on the voltage profiles. Also, the performance of the linear PF models is acceptable only for a small range around the nominal operating point; hence, they can lead to large errors if used in OPF/control framework that seeks solutions on wider operating range.

Distributed generators (DGs) are nowadays most commonly used in distribution networks to meet the rising demand. The distribution network power flow is altered as more distributed generations are integrated with the distribution network. Analyzing and researching the network's power flow with distributed generation is an essential element of analyzing the distributed generation's influence on the networks. This study proposed new sites in the test network for the purpose of connecting DGs. Good results were obtained in improving the necessary network elements. Firstly, applying a Newton-Raphson method to measure the distribution network's power flow without distributed generations. Then the optimal power flow approach with DGs is set up based on many goals such as minimizing fuel cost, minimizing losses, voltage deviation, increasing efficiency, and the incremental fuel cost in the network appeared. Eventually, applying Particle Swarm to overcome the optimization problems. In MATLAB software environment and programing MATPOWER version 6.0, the simulation is evaluated and validated using the IEEE30 node method. The test results indicate that optimal power flow analysis with distributed generation will accomplish many networks aims and boost system economy.

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.

This paper focuses on distribution systems featuring renewable energy sources and energy storage devices, and develops an optimal power flow (OPF) approach to optimize the system operation in spite of forecasting errors. The proposed method builds on a chance-constrained multi-period AC OPF formulation, where probabilistic constraints are utilized to enforce voltage regulation with a prescribed probability. To enable a computationally affordable solution approach, a convex reformulation of the OPF task is obtained by resorting to i) suitable linear approximations of the power flow equations, and ii) convex approximations of the chance constraints. Particularly, the approximate chance constraints provide conservative bounds that hold for arbitrary distributions of the forecasting errors. An adaptive optimization strategy is then obtained by embedding the proposed OPF task into a model predictive control framework.

Base on the power flow formulations, a new power flow model that allows for power exchanges among subareas of network and automation generation control in each subarea, is established. The proposed power flow model is rendering by unified newton iteration formulation. Parameters representing the level or allocation of the unbalancing power are introduced to indicate the performance of the generators that participate in the automation generation control. The power exchange formulations for subareas are derived from the power flow equations of the interconnected branches. The Newton iteration method is used to solve the equations that consist of node power injection equations and interconnected power equations. Because of the consideration of the power balance in each subarea and the order of power exchange, the presented method is applicable for power flow problems of interconnected power networks, and is in particular applicable for the system analysis and calculation that based on the uniform iteration formulation. Case studies of IEEE 5 bus test system and IEEE RTS96 system illustrate the efficiency and the convergence of the proposed method.

The study of power system planning, security and control is crucial for determining optimal power flow (OPF), a highly non-linear complicated issue. The functioning of the power system remains complex when Renewable energy sources are connected to the grid along traditional generators. This review paper describes various techniques applicable to the power system networks accessible in the literature. The conventional optimisation algorithms have been reintroduced, while the power systems have been heavily predisposed over the last few years. The most crucial technical, adaptive and economic tool in this context is OPF. In this paper, we compare OPF approaches related to objective functions. Aside from computational power, the case study network and publication dates for these algorithms are described. Finally, we will address some of the basic challenges that arise from the new OPF approach to the modern grid. Mainly, optimisation techniques are compared in terms of reliability, accurateness, faster convergence and applicability for single and multiple objective functions. Initially, the paper discusses types of networks such as AC or DC, constraints and their objectives on OPF, mathematical and different optimisation techniques reviewed. The heuristic and meta-heuristic algorithms, like genetic algorithm and Jaya algorithm, were compared for various operational parameters. In this work, OPF with single- or multi-objective functions such as voltage stability, voltage deviation, emission, cost and losses, consisting of conventional and renewable energy resources were considered. Additionally, Pseudo-code algorithms were presented for some recently evolved algorithms to ease the understanding of the readers.

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 proposes an approach for optimal power flow considering several contingency states. Initially, contingency selection is conducted to measure how much a specific contingency may affect the operation cost. Then, some severe contingencies are incorporated into optimal power flow problem. All considered states, normal and contingency states, are simulated simultaneously. Thus, if contingency occurs, it can be ensured that all constraints such as generation limit, transmission limit and ramp rate will be satisfied. To solve the problem, quadratic programming is applied. IEEE 30 bus system is used as test system to show the ability of the proposed approach.

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.

Proliferation of Distributed Energy Resources (DERs) and Phasor Measurement Units (PMUs) into electric power distribution grids presents new opportunities for utility operators to manage distribution systems more effectively. In this work we formulate an Optimal Power Flow (OPF) approach that manages DER power injections to minimize the voltage phasor difference between two nodes on a distribution network with the goal of enabling efficient network reconfiguration. To accomplish this, we develop a linear model that relates voltage phase angles to active and reactive power flows in unbalanced distribution systems. Used in conjunction with existing linearizations relating voltage magnitudes to power flows, we formulate an OPF capable of minimizing the voltage phasor difference between two points in a network. In simulations, we explore the use of the developed approach to minimize the phasor difference across switches to be closed, thereby providing an opportunity to automate and increase the speed of reconfiguration in unbalanced distribution grids.

Volt-VAR control (VVC) in distribution networks is typically performed by autonomously operating voltage regulation devices. In modern distribution systems, most of the control and coordination functions are being carried out by Distribution Management System (DMS), which is a highly digitalized and automated platform. Even though the grid equipment and infrastructure are being modernized, there still exist legacy devices that operate based on local control rules. Integration of such legacy device models into the modern DMS is essential to ensure effective VVC. Hence, this paper proposes optimal coordination of onload tap changers by solving a mixed integer linear programming (MILP)-based mathematical program such that the tap switching operations can be reduced. Unlike existing works, which often ignore the local controller mechanism of LTCs, this work models and integrates the local control rule of the bang-bang controllers of LTCs in the optimal coordination procedure. To this end, the operational principle of the controller is interpreted as a set of mixed-integer linear constraints, enabling the formation of an efficient optimal power flow (OPF) formulation based on a linearized power flow model. Extensive numerical tests on the proposed formulation suggest satisfactory and promising performance.

The paper reviews the formulation of optimal power flow (OPF) and its role in dispatch. It then outlines possible uses of OPF market structures and describe the major drawbacks. The use of OPF for market players with a portfolio of generating units, however, is an appropriate and useful application of OPF in competitive markets. The OPF in such cases is a useful tool to determine the most cost-effective approach to discharge certain contracted market obligations since there is a centrally controlled single ownership situation. The application of OPF in such cases is reviewed. The paper emphasizes the limitations and capabilities of applying the OPF tool in market structures.

The increasing penetration of wind generation in electric power systems has made evident the necessity of a unified energy infrastructure interdependency analysis, in order to explore the optimal use of fossil fuel-based generation and the security constraints associated with different energy infrastructures. In this context, the optimal generation dispatch of online generating units is important in the daily operation planning. This paper proposes a multi-energy day-ahead optimal power flow (OPF) approach in order to assess the wind energy penetration in an electric power system and its impact on the fossil fuel-based generation management. The applicability of the proposed approach is demonstrated by integrating a 15-node natural gas network and a 4-node coal distribution system with the IEEE 118-bus power system.

Transformer models are important components of power systems. Under certain configurations, incorporating transformer models with the nodal admittance matrix of the power flow (PF) formulation makes it singular, rendering the resultant PF algorithm unfeasible. This paper addresses these issues by modelling special transformer configurations (center-tap, three winding, voltage regulators) into a unique Augmented Jacobian based multiphase PF formulation. In this formulation, power system components can be modelled with PF constraints independently and accurately resolving associated singularities in classical nodal admittance matrix. The proposed method is evaluated on two IEEE feeders (modified IEEE-9 bus and IEEE-8500 node). Results are validated with benchmark published results and IPSA software. Numerical examples confirm the effectiveness of the proposed models and algorithm in successfully resolving matrix singularity.