Power Flow Algorithm Research Articles

The Effect of Unbalanced Impedance Loads on the Short-Circuit Current

Conventional short-circuit studies often neglect the load current because the short-circuit current (SCC) flowing from generators is much greater than the SCC that is affected by various loading conditions. As distributed or clustered loads that are unbalanced in phases are connected to the grid, they can also change the magnitude and phase angle of the SCC, despite their small capacities. Thus, the objective of this study is to present algorithms that are able to analyze such an impedance unbalanced load. For this purpose, this study initially derives an SCC model of the unbalanced impedance load in phases. Since the proposed SCC model requires the pre-fault voltage, it uses a power-flow analysis algorithm that iteratively calculates the current that is to be injected and the pre-fault voltage, using the bus impedance matrix. Then, the proposed SCC calculation algorithm transforms the unbalanced loads into equivalent impedances, using the pre-fault voltage, and adds them to sequence networks as input data, using the proposed SCC model. The proposed algorithms are verified in various case studies. As a result, the proposed SCC calculation algorithms are more accurate, because they do not neglect unbalanced loads.

A Holomorphic embedding approach for finding the Type-1 power-flow solutions

A holomorphic embedding method (HEM)-based algorithm for finding Type-1 power-flow solutions is introduced whose complexity is the same as that of the HEM power-flow algorithm for calculating the high voltage (operable) power-flow solution. The algorithm is tailored to finding Type-1 solutions by using a modified embedded system and a numerical mapping from a set of integer-based boundary conditions to a floating-point-number-based reference state. The modified system can also be viewed as a homotopy whose initial point (no-load reference state) is consistent with the Type-1 solution homotopy path of the modified system, with an embedding parameter that functions simultaneously as the homotopy parameter. By using analytic continuation, starting from the initial point/reference state, the solution obtained for the modified system matches the one obtained from the original system model at the load of interest. Numerical results for three-/five-/seven-/14- and 118-bus systems are presented to demonstrate the numerical robustness.

Probabilistic Voltage Sensitivity Analysis (PVSA)—A Novel Approach to Quantify Impact of Active Consumers

Active consumers will be integral to the future smart grid, scheduling their load and managing renewable generation in accordance with real-time pricing. The impact of spatially distributed renewable generation and active consumers on the distribution system must be quantified for operational planning. Most of the current studies are scenario-based and derived results are scenario specific. Determining the impact of spatially distributed active consumers with temporally variable behavior requires investigation of a large number of scenarios, which is computationally intractable using current iterative power flow algorithms. The objective of this work is to provide a new analytical method of voltage sensitivity analysis that allows for stochastic analysis of change in grid voltage due to change in consumer behavior (load and generation choices). This paper first derives an upper bound for change in voltage at a particular bus due to change in complex power at other buses in a radial distribution network. This bound is verified via simulations. Next, this bound is used to derive the probability distribution of voltage change at a bus due to random behavior of spatially distributed multiple active consumers. Results from the proposed probabilistic voltage sensitivity analysis is validated via traditional-scenario-based simulation of the IEEE 69 bus test system.

A Distributed Transmission-Distribution-Coupled Static Voltage Stability Assessment Method Considering Distributed Generation

The recent rapid development of distributed generation (DG) necessitates the consideration of transmission–distribution interactions in voltage stability assessment (VSA), and how to perform a transmission–distribution-coupled static VSA (TDVSA) has become a pressing problem. To resolve this urgent issue, this paper first theoretically analyzes the impacts of the voltage-maintaining capacity and low-voltage tripping of DG units on the static voltage stability of an integrated transmission–distribution system and then proposes a distributed TDVSA method that fully considers these impacts when assessing the voltage stability of the integrated system. As the core of the method, a distributed continuation power flow algorithm is designed that includes a distribution-equivalencing-based predictor, a distributed transmission–distribution corrector, and a step-length regulator and requires only a limited amount of data to be exchanged between the transmission system operator (TSO) and the distribution system operator (DSO). Numerical simulations show that even in the case of low DG penetration, a cascading low-voltage tripping event can significantly degrade an integrated system's voltage stability, and only the proposed distributed TDVSA method can produce an accurate assessment. In addition, the number of iterations between the TSO and DSO is shown to be limited, indicating the potential of applying the proposed method to future grids.

A comprehensive power-flow model of multi-terminal PWM based VSC-HVDC systems with DC voltage droop control

This paper presents power-flow models of AC power systems integrated with voltage-sourced converter (VSC) based multi-terminal high voltage direct current (MTDC) grids. Pulse-width modulation (PWM) control is employed for the VSCs. In the proposed approach, the VSC modulation indices are considered as unknowns. For control of the MTDC grid, DC voltage droop control has been implemented. The proposed method includes both linear and nonlinear voltage droop characteristics. Converter losses are included in the proposed model. Depending upon the terminal end line active power specifications of the VSCs, two different voltage droop control models have been developed. The convergence properties in the proposed approach are found to be independent of the MTDC grid location, its topology, the MTDC control strategy employed and the operating point specification. Numerous case studies are carried out by applying different control modes to multiple topologies of MTDC grids embedded in the IEEE-300 bus test system. For all the case studies, the power-flow algorithms were implemented with MATLAB. In all occurrences, a mismatch error tolerance of 10−10 p.u. was selected. The results validate the proposed work.

A Distributed Multi-Control-Center Dynamic Power Flow Algorithm Based on Asynchronous Iteration Scheme

From the study of dispatcher power flow in a distributed energy management system (DEMS) among multiple control centers, a fixed-point iteration scheme for boundary bus states is constructed to modify the exterior network equivalent through data exchange. Implementation details such as determination of combination parameters, independent choice of reference bus, and distribution of unbalanced power are analyzed. Using this method, each subsystem involved in distributed computing can maintain its method of modeling the exterior network. Adverse effects of communication interference on computing can also be eliminated. Results consistent with integrated power flow are obtained with little loss of accuracy. Thus, the proposed algorithm is especially suitable for application in DEMS, in which control centers can only communicate by WAN. Tests are conducted on the IEEE 118-bus system partitioned into five subsystems, the IEEE 300-bus system, and an actual power system, which verifies the favorable convergence and effectiveness of the method.

On the Convergence of the Sequential Power Flow for Multiterminal VSC AC/DC Systems

Following the vision of future Supergrids, the existing power systems are expected to evolve into AC/DC systems containing voltage source converters with multiterminal configurations. This paper presents a new sequential power flow algorithm for such power systems. The algorithm can be applied to systems with multiple AC and DC grids of any grid topology. Because of its pure AC/DC network decomposition, the simplification of elements within the converter stations is not required, as is the case with other proposals in the literature. The paper also addresses the convergence properties of the proposed algorithm. A convergence factor has been designed that allows controlling the exit criterion within each inner loop of the sequential AC/DC load flow problem. It is shown that by modulating the convergence factor, the number of inner loop iterations needed to achieve a solution can be diminished.

CONTINUATION POWER FLOW OF AN UNBALANCED THREE-PHASE FOUR-WIRE DISTRIBUTION SYSTEM


 A continuation power flow algorithm for an unbalanced three phase four wire distribution system is presented. The proposed algorithm is used to trace the loci of the voltage of the different phases of an unbalanced three-phase distribution system. The locus of the neutral voltage for a wide range of loading conditions is also obtained. The proposed technique is applied on a typical unbalance three phase radial Iraqi distribution system. The results obtained reveal the effectiveness of the continuation technique for exploring all the possible solutions and the determination of maximum loadability of the distribution feeder.
 

A Novel Direct Power Flow for Distribution Systems with Voltage-Controlled Buses

Large-scale distribution systems (DSs) require an efficient power flow algorithm which can explicitly exploit their characteristics. This paper presents a novel power flow algorithm for radial and weakly meshed distribution systems (WMDSs) using a direct method (DM). The paper also develops a novel approach to simulate the voltage-controlled buses which is becoming increasingly important due to the introduction of distributed generations in DSs. The proposed power flow algorithm is constructed based on simple electrical circuit rules so that only a Z matrix expressing common impedances between loads is required for simulation. For WMDSs, only modification is to use the current divider rule to solve meshes. The simulation of PV-buses is presented using the Newton–Raphson solution algorithm. The validation and comparison of results in different systems show the simplicity and low computations of the proposed method which make it time-saving and very efficient for large-scale DSs.

Integration of voltage dependent power injections of distributed generators into the power flow by using a damped Newton method

Voltage dependent active and reactive power injections are used to improve the grid integration of distributed generators, such as photovoltaic systems. In state-of-the-art literature these power injections are considered during power flow calculations via an external loop, which requires to perform multiple (up to ten or more) power flow calculations in order to obtain one static operation point. In this paper it is shown how to integrate voltage dependent power injections into the nonlinear grid equations in order to solve for a static working point by means of performing one Newton power flow calculation. That makes the external loop unnecessary and save computational time. Furthermore, it is shown for a two-bus system that the integration of voltage dependent power injections into the nonlinear grid equations can exhibit ill-conditioned power mismatch functions. Therefore, a damped Newton method is used in order to avoid numerical oscillations. Simulations of the IEEE 118-bus test system and a real German 234-bus test system show that the damped method converges faster and is computationally more efficient than the external approach currently used in literature and state-of-the-art simulation tools in power systems. In addition, the implemented power flow algorithm is validated in the laboratory for a two-bus system and a numerical example of a low-voltage feeder is given.

Assessment of overvoltage mitigation techniques in low‐voltage distribution networks with high penetration of photovoltaic microgeneration

Nowadays, a strong concern to decrease greenhouse gas emissions is encouraging the implementation of renewable energy sources closer to end-users, in low-voltage (LV) distribution networks. Due to the expected high microgeneration (μG) penetration level, several problems are likely to arise, such as overvoltages and reverse power flow. This study presents a review of the several techniques used to deal with these problems. These are compared in terms of their capacity to smooth the voltage profile and avoid reverse power flow. An unbalanced three-phase power flow algorithm, based on current summation method for radial distribution networks, is proposed. A study based on a highly unbalanced test radial LV distribution network for a typical summer day, with a high μG penetration, is performed. The voltage profile, active power flow in the service transformer, and power losses on the network are the monitored electrical quantities. The obtained results indicate that self-consumption with storage is the recommended solution to eliminate overvoltages, to avoid reverse power flow and allow for a decreasing in the power losses. Nevertheless, the economic viability of this solution must be carefully assessed, because the profitability of the project is not straightforward at the current time.

Hybrid AC/DC Post-Contingency Power-Flow Algorithm Considering Control Interaction of Asynchronous Area

This paper presents an approach for the calculation and estimation of control interactions between asynchronous power systems coupled via multi-terminal high-voltage direct current grids using static analysis methods. This aims at possible application within online security assessment where, as of today, static analysis methods are still a common practice. Therefore, the postcontingency power flow is evaluated using an integrated approach for the solution of AC and DC systems in the power-flow algorithm. Thereby, equations for DC voltage control and AC frequency control of converter stations, generators, loads as well as wind turbines with frequency support are embedded into the extended system Jacobian. The results show that by using the proposed approach, the post-contingency power-flow situation can be accurately determined and the frequency changes in each subsystem can be sufficiently tracked. Using an application example of an offshore power system with frequency support by offshore wind turbines, all results have been validated against dynamic simulation, while simulation models and controllers are provided. It is shown that active power balancing controls of AC and DC systems could have a high impact on line loadings and need to be respected for security analyses.

Linear optimal power flow using cycle flows

Linear optimal power flow (LOPF) algorithms use a linearization of the alternating current (AC) load flow equations to optimize generator dispatch in a network subject to the loading constraints of the network branches. Common algorithms use the voltage angles at the buses as optimization variables, but alternatives can be computationally advantageous. In this article we provide a review of existing methods and describe a new formulation that expresses the loading constraints directly in terms of the flows themselves, using a decomposition of the network graph into a spanning tree and closed cycles. We provide a comprehensive study of the computational performance of the various formulations, in settings that include computationally challenging applications such as multi-period LOPF with storage dispatch and generation capacity expansion. We show that the new formulation of the LOPF solves up to 7 times faster than the angle formulation using a commercial linear programming solver, while another existing cycle-base formulation solves up to 20 times faster, with an average speed-up of factor 3 for the standard networks considered here. If generation capacities are also optimized, the average speed-up rises to a factor of 12, reaching up to factor 213 in a particular instance. The speed-up is largest for networks with many buses and decentral generators throughout the network, which is highly relevant given the rise of distributed renewable generation and the computational challenge of operation and planning in such networks.

A Novel Power Flow Algorithm for Traction Power Supply Systems Based on the Thévenin Equivalent

With the rapid development of high-speed and heavy-haul railways throughout China, modern large power locomotives and electric multiple units (EMUs) have been applied in main railway lines. The high power requirements have brought about the problem of insufficient power supply capacity (PSC) of traction power supply systems (TPSSs). Thus, a convenient method of PSC assessment is meaningful and urgently needed. In this paper, a novel algorithm is proposed based on the Thévenin equivalent in order to calculate the PSC. In this algorithm, node voltage equations are converted into port characteristic equations, and the Newton-Raphson method is exploited to solve them. Based on this algorithm, the PSC of a typical high-speed railway is calculated through the repeated power flow (RPF). Subsequently, the effects of an optimized organization of train operations are analyzed. Compared to conventional algorithms, the proposed one has the advantages of fast convergence and an easy approach to multiple solutions and PV curves, which show vivid and visual information to TPSS designers and operators. A numerical analysis and case studies validate the effectiveness and feasibility of the proposed method, which can help to optimize the organization of train operations and design lines and enhance the reliability and safety of TPSSs.

Analysis and Assessment of Operation Risk for Hybrid AC/DC Power System based on the Monte Carlo Method

Based on the Monte Carlo method, an improved risk assessment method for hybrid AC/DC power system with VSC station considering the operation status of generators, converter stations, AC lines and DC lines is proposed. According to the sequential AC/DC power flow algorithm, node voltage and line active power are solved, and then the operation risk indices of node voltage over-limit and line active power over-limit are calculated. Finally, an improved two-area IEEE RTS-96 system is taken as a case to analyze and assessment its operation risk. The results show that the proposed model and method can intuitively and directly reflect the weak nodes and weak lines of the system, which can provide some reference for the dispatching department.

Optimal capacity of storage systems and photovoltaic systems able to control reactive power using the sensitivity analysis method

As weather-dependent distributed renewable energy resources (RERs) such as photovoltaic (PV) systems and wind farms have increasingly been connected to distribution networks, energy storage systems able to compensate intermittency in their power generation may be required. Moreover, such RERs can participate in reactive power control upon voltage regulation. Thus, the problem of optimizing the capacity of storage systems for RERs with the capability of reactive power control is necessary for planning, maintaining, or upgrading a distribution network. The objective of this study is to optimize the capacity of storage systems for RERs, particularly PV inverters with the capability of reactive power control in this study. For this purpose, this study proposes the power-flow algorithm able to optimize reactive power amount to be either consumed or injected by PV systems and a hybrid multi-objective sensitivity analysis algorithm that optimizes the capacity of PV and storage systems. The proposed algorithm includes an objective function that minimizes voltage variations and capital costs of PV and storage as well as maximizes energy savings and peak load reduction. Then, it successfully optimizes the capacity of PV and storage systems in the well-known IEEE test feeders.

Advances in Distribution System Analysis with Distributed Resources: Survey with a Case Study

Distribution System Analysis (DSA) is witnessing a renewed interest in the presence of distributed energy resources along with the Smart Grid initiatives in the form of setting up of new information and communication layer for management and control of energy resources and network components in recent times. The centralized generation, dispatch and control philosophy is giving way to new decentralized approaches in power grids where penetration of intermittent sources of energy is increasing. It has necessitated the modeling of distribution network components even up to and including secondaries of distribution transformers. In this context, the present article reviews recent advances in (a) modeling of distribution network components including distributed generators, (b) distribution power flow algorithms and (c) simulation tools for planning and operations of Active Distribution Networks (ADNs). It also includes a case study of an actual ADN operating in India with sequential time simulations over the period of one year. The article is aimed at providing a holistic view – with a demonstration of a case study – of advancements in DSA as a part of Smart Grid developments that reflects the significant shift from the way it has been perceived for long.

An Efficient Method of Determining Operating Points of Droop-Controlled Microgrids

Traditional methods of determining steady-state power system operating points are not applicable to droop-controlled microgrids. The conditions of an islanded microgrid, including the absence of a slack bus and inherent coupling of complex power, frequency, and bus voltage, require new tools to properly analyze. In this study, a method of determining the operating points of droop-controlled microgrids is proposed. The procedure is similar in form and function to a traditional power flow analysis, but is performed in the synchronous reference frame to ensure compatibility with conventional inverter models. A quasi-Newton iterative process is used to solve the nonlinear equations pertaining to each generation unit and load bus. The method provides a structured approach to determining the consistent system-level linearization points required for large-scale microgrid studies. Grid-forming, grid-feeding, and grid-supporting generation units are supported, along with both constant impedance and constant power loads. The method is validated in hardware experiments, simulations, and comparisons to results of existing power flow algorithms. As an example of the method's potential applications, a procedure for determining droop constants that ensure equal Q sharing between generation units is constructed around the proposed method's basic functionality.

Novel approach to reconfiguration power loss reduction problem by simulated annealing technique

Summary The network reconfiguration is done by changing the status of the switches, mainly for 2 reasons: an active power loss reduction and load balancing attracting the attention of distribution engineers for quite a long period of time. In this article, solving method for the active power loss reduction is given. Searching for the relevant radial configurations is done by a simulated annealing technique. To aid the search, a program for checking the connectivity of the power system, with imposed radiality constraint, is enhanced by a new approximate power flow method. The applied power flow program is very efficient and fast but can be used only as an indication for the loss estimation because of the insufficient method accuracy. At the end of the algorithm, it is necessary to run an efficient power flow program to determine the real situation concerning loss reduction. A numerical example for Baran and Wu network is analyzed. The developed method converges to the global optimum given in a numerical example. The time duration of the used method is of an hour order and does not depend on the fast manipulation of incoming data files. This advantage makes the method interesting in the planning stage as well as the application in real time. Main contribution of this paper is a novel approach that exploits mostly the following mechanisms: network connectivity checking matrix, Lavorato et al criterion for imposing radiality constraint, and efficient power flow algorithm combined with precise power flow for exact loss calculation.

An Affine Arithmetic-Based Power Flow Algorithm Considering the Regional Control of Unscheduled Power Fluctuation

With consideration of the intermittency of renewable generation and uncertain load, a regional control strategy is presented to smooth the unscheduled power fluctuation in this letter. Then, an affine arithmetic-based modeling method is proposed to describe the unscheduled power tracking characteristic of dispatchable generation resources (DGRs), based on which interval power flow solutions with narrower ranges can be obtained. Finally, the proposed algorithm is applied to a modified IEEE 33-bus distribution system to demonstrate its effectiveness.