Accurate Power Flow Research Articles

A Newton–Raphson-Based Sequential Power Flow Algorithm for Hybrid AC/DC Microgrids

A hybrid ac/dc microgrid (MG) has the advantages of both ac and dc subgrids, and the operator should perform an accurate power flow analysis to ensure the MG's operational economy and reliability. This article proposes a Newton—Raphson (NR)-based sequential power flow algorithm for the hybrid ac/dc MG. First, the MG's islanded operation mode and the three-phase unbalance feature of ac subgrids are considered, and the droop control for distributed generations participating in the voltage and frequency regulation is modeled. Then, a sequential algorithmic framework is proposed to handle the coupling between ac and dc subgrids. Within this framework, the power flow of ac and dc subgrids is solved separately and iteratively with modified NR subalgorithms. The accuracy of the proposed sequential algorithm is validated in comparison with the results from MATLAB/Simulink, and the advantage of employing this algorithm is confirmed compared with an equivalence approach. The case studies demonstrated that the proposed algorithm can significantly improve the result accuracy with acceptable computational time. Finally, the convergence performance of the proposed algorithm is verified in the cases of varying ac and dc subgrid loading.

An Advanced Power Flow Control in Small Scale DC Power Structure by Using Multilevel Converter

Because they combine outstanding harmonic performance with low switching frequencies, multilevel transforms are attractive options in Small-Scale DC Power Ne2rks. High dependability can also be obtained by including redundant submodules into the cascaded transform chain. DC microgrids are developing as the next generation of smallscale electric power structures, with very low line impedance. This phenomena creates high currents in microgrids even with little voltage changes; hence, a power flow controller must have quick transient reaction and accurate power flow management. Multi-level transforms are used as power flow controllers in this work to provide high speed and high accuracy power flow management in a dc microgrid. Because a multi-level transform is employed, the output filter can be tiny. The linear controller, such as PI or PID, is established and widely used in the power electronics sector, but its performance degrades as system parameters change. In this paper, a neural structure (NN) based voltage management technique for a DC-DC transform is developed. This project also shows how to construct the output LC filter of a multi-level transform to meet a current ripple requirement. In comparison to typical 2-level transforms, we can demonstrate that a multilevel transform with a smaller filter may provide high-speed and high-precision power flow management for low line impedance situations. MATLAB/Simulink Simulation results are used to evaluate the control performance of each output current in the step response while accounting for transient variations in the power flow.

Accurate and Efficient Derivative-Free Three-Phase Power Flow Method for Unbalanced Distribution Networks

The power flow problem in three-phase unbalanced distribution networks is addressed in this research using a derivative-free numerical method based on the upper-triangular matrix. The upper-triangular matrix is obtained from the topological connection among nodes of the network (i.e., through a graph-based method). The main advantage of the proposed three-phase power flow method is the possibility of working with single-, two-, and three-phase loads, including Δ- and Y-connections. The Banach fixed-point theorem for loads with Y-connection helps ensure the convergence of the upper-triangular power flow method based an impedance-like equivalent matrix. Numerical results in three-phase systems with 8, 25, and 37 nodes demonstrate the effectiveness and computational efficiency of the proposed three-phase power flow formulation compared to the classical three-phase backward/forward method and the implementation of the power flow problem in the DigSILENT software. Comparisons with the backward/forward method demonstrate that the proposed approach is 47.01%, 47.98%, and 36.96% faster in terms of processing times by employing the same number of iterations as when evaluated in the 8-, 25-, and 37-bus systems, respectively. An application of the Chu-Beasley genetic algorithm using a leader–follower optimization approach is applied to the phase-balancing problem utilizing the proposed power flow in the follower stage. Numerical results present optimal solutions with processing times lower than 5 s, which confirms its applicability in large-scale optimization problems employing embedding master–slave optimization structures.

An Efficient Backward/Forward Sweep Algorithm for Power Flow Analysis through a Novel Tree-Like Structure for Unbalanced Distribution Networks

The increase of distributed energy resources (DERs) in low voltage (LV) distribution networks requires the ability to perform an accurate power flow analysis (PFA) in unbalanced systems. The characteristics of a well performing power flow algorithm are the production of accurate results, robustness and quick convergence. The current study proposes an improvement to an already used backward-forward sweep (BFS) power flow algorithm for unbalanced three-phase distribution networks. The proposed power flow algorithm can be implemented in large systems producing accurate results in a small amount of time using as little computational resources as possible. In this version of the algorithm, the network is represented in a tree-like structure, instead of an incidence matrix, avoiding the use of redundant computations and the storing of unnecessary data. An implementation of the method was developed in Python programming language and tested for 3 IEEE feeder test cases (the 4 bus feeder, the 13 bus feeder and the European Low Voltage test feeder), ranging from a low (4) to a very high (907) buses number, while including a wide variety of components witnessed in LV distribution networks.

Non‐linear switched model for accurate voltage estimation and power flow analysis of DC railway systems

Non‐linear switched model for accurate voltage estimation and power flow analysis of DC railway systems

Real-Time Validation of Power Flow Control Method for Enhanced Operation of Microgrids

This paper describes a control methodology for electronic power converters distributed in low-voltage microgrids and its implementation criteria in general microgrid structures. In addition, a real-time simulation setup is devised, implemented, and discussed to validate the control operation in a benchmark network. Considering these key aspects, it is shown that operational constraints regarding the power delivered by sources, flowing through network branches, and exchanged at the point of connection with the main grid can generally be fulfilled by the presented control approach. The control is performed considering a cost function aiming at optimizing various operation indexes, including distribution losses, current stresses on feeders, voltage deviations. The control system allows an enhanced operation of the microgrid, specifically, it allows dynamic and accurate power flow control enabling the provision of ancillary services to the upstream grid, like the demand–response, by exploiting the available infrastructure and the energy resources. Then, the validation of the approach is reported by using a real-time simulation setup with accurate models of the power electronic converters and related local controllers, of the grid infrastructure, of the power flow controller, and of the communication network used for data exchange. It is also shown that the implemented platform allows to fully reproduce, analyze, and finally validate all the relevant steady-state and dynamic behaviors related in the considered scenario.

An MPC-Based Dual-Solver Optimization Method for DC Microgrids With Simultaneous Consideration of Operation Cost and Power Loss

In this paper, a dual-solver framework based on model predictive control (MPC) is proposed, $E-$ solver and $L-$ solver. The economic scheduling problem is formulated using mixed-integer linear programming (MILP), which can be solved in an efficient way by using commercial solver ( $E-$ solver). While the transmission loss problem is formulated using non-linear programming (NLP), which can be solved in the interior point method, namely $L-$ solver. The $E-$ solver provides an economic priority power scheduling plan for the $L-$ solver, and the $L-$ solver solves the entire microgrid accurate power flow scheduling plan. The proposed planning model decomposition technique aims to solve the planning model in a time-sharing manner and combines the characteristics of the two optimizers with a reasonable matching algorithm to achieve economic, efficient, and fast real-time control. A case study of a DC microgrid is employed to assess the performance of the online optimization-based control strategy. Simulations based on eight-node DC microgrid show that the method reduces the operating cost by $12.10\%$ and increases the calculation speed by $80.18\%$ compared with the traditional interior point method. With a shorter delay, the proposed optimization method will facilitate the implementation of real-time control and optimization.

Deep Reinforcement Learning Based Volt-VAR Optimization in Smart Distribution Systems

This paper develops a model-free volt-VAR optimization (VVO) algorithm via multi-agent deep reinforcement learning (DRL) in unbalanced distribution systems. This method is novel since we cast the VVO problem in distribution networks to an intelligent deep Q-network (DQN) framework, which avoids solving a specific optimization model directly when facing time-varying operating conditions in the systems. We consider statuses/ratios of switchable capacitors, voltage regulators, and smart inverters installed at distributed generators as the action variables of the agents. A delicately designed reward function guides these agents to interact with the distribution system, in the direction of reinforcing voltage regulation and power loss reduction simultaneously. The forward-backward sweep method for radial three-phase distribution systems provides accurate power flow results within a few iterations to the DRL environment. The proposed method realizes the dual goals for VVO. We test this algorithm on the unbalanced IEEE 13-bus and 123-bus systems. Numerical simulations validate the excellent performance of this method in voltage regulation and power loss reduction.

Universal Power Flow Algorithm for Bipolar Multi-Terminal VSC-HVDC

An effective and accurate power flow algorithm provides control references for active power dispatch and initial steady state operating points, used for stability analysis, short-circuit calculations, and electromagnetic transient simulations, which is not only a fundamental precondition to analyze the system operating conditions, but also the basis to improve the accuracy of power flow and DC voltage control of the multi-terminal voltage source converter-based high voltage direct current (VSC-HVDC). This paper proposes a nodal voltage-based universal steady-state power flow algorithm for the newly-developed bipolar multi-terminal VSC-HVDC (VSC-MTDC). Firstly, as the positive-pole and negative-pole DC network of the bipolar VSC-MTDC can be operated individually, a bipolar power flow alternating iterative method is proposed here to obtain the positive/negative-pole DC network power flow. Secondly, a series of nodal equivalent methods involving various control strategies are proposed for the universal power flow algorithm. Then the detailed calculation procedure and a general MATLAB(TM) program for the universal power flow algorithm is presented. A typical 4-terminal bipolar VSC-MTDC system was built in the PSCAD/EMTDC to verify the validity of the proposed algorithm, and the results are discussed here. Moreover, the calculation results of more complex bipolar VSC-MTDC systems under different operating conditions, employing the proposed universal power flow algorithm, are presented to illustrate its universality and efficiency.

Accurate active power flow diagrams of Brushless doubly-fed induction machine in motoring and generating modes

The brushless doubly-fed induction machine (BDFIM) shows interesting features for incorporating as wind generator or variable speed drive. The BDFIM operation is based on magnetic flow modulation of two stator winding fields through a special squirrel cage rotor. Hence, the power flow is very different from that of a regular induction machine. Taking into account, accurate analysis of the power flow is very valuable for the comprehension and design of BDFIM as well as the selection of converter capacity. In this paper, the power balance for BDFIM is discussed in the motoring and the generating modes and for both super- and sub-synchronous speed intervals. For this purpose, the power flow equations are extracted and power flow diagrams taking into account all the power loss components are presented. The accuracy of the proposed power flow diagrams is verified by comparing the obtained results with the experimental and finite element ones.

Fast Probabilistic Voltage Control for Distribution Networks With Distributed Generation Using Polynomial Surrogates

Renewable distributed generation will be a key component of future power distribution networks. In order to control the voltage conditions for distribution networks integrated with distributed generation (DG) units, it is vital to quantify the impacts of control variables on voltage magnitudes under consumption and generation uncertainties. To do so, we need to run, for each control action, several power flow simulations for various consumption and generation realizations. This is computationally infeasible for systems with many uncertain inputs. In this work, we address this challenge by developing surrogates, or metamodels, that analytically estimate the random voltage as a function of input variables which include random parameters (consumption and generation levels) and control actions (power factors). Specifically, we propose a model reduction method for building these surrogates, which reduces the number of simulations needed for training. This method identifies and includes only the consumption and generation variables that are influential on the voltage at a given bus. Using this `reduced' surrogate, we then develop a sensitivity-based approach for probabilistic voltage control. We demonstrate the computational efficacy of the control approach on a IEEE 69-bus system with a large number of correlated input parameters. The highlights of computational efficiency in this case study include (1) accurate probabilistic power flow analysis using surrogates constructed by only 500 training simulations for a system with more than 150 random parameters, and (2) successful surrogate-based voltage control approach which only requires 150 additional simulation samples, as opposed to the conventional perturb-and-observe voltage control which needs more than 500,000 samples.

Linear three-phase power flow model for autonomous microgrid systems

In this work, the authors propose a linear three-phase power flow model for droop-controlled autonomous microgrids. The proposed linear power flow model adopts a set of linear algebraic equations and can, with small errors, be compared to the detailed nonlinear model, account for the lack of a slack bus, the variability of autonomous microgrid frequency and the operation of distributed generation units in droop control mode. The proposed linear model can as such provide a fast and accurate power flow solution and has great potential in the stochastic planning and online operational applications of autonomous microgrids, as well as in linear or convex optimal power flow and probabilistic load flow analysis. The accuracy and effectiveness of the proposed linear power flow model are validated through different case studies considering balanced and unbalanced test systems.

A Comprehensive Power Flow Approach for Multi-terminal VSC-HVDC System Considering Cross-regional Primary Frequency Responses

For the planning, operation and control of multiterminal voltage source converter (VSC) based high-voltage direct current (HVDC) (VSC-MTDC) systems, an accurate power flow formulation is a key starting point. Conventional power flow formulations assume the constant frequencies for all asynchronous AC systems. Therefore, a new feature about the complex coupling relations between AC frequencies, DC voltages and the exchanged power via VSC stations cannot be characterized if VSC-MTDC systems are required to provide cross-regional frequency responses. To address this issue, this paper proposes a comprehensive frequency-dependent power flow formulation. The proposed approach takes the frequencies of asynchronous AC systems as explicit variables, and investigates the novel bus models of the interlinking buses of VSC stations. The proposed approach accommodates different operation modes and frequency droop strategies of VSC stations, and considers the power losses of VSC stations. The effectiveness and generality of the developed approach are validated by a 6-terminal VSC-HVDC test system. The test system presents the characteristics of the coexistence of numerous VSC operation modes, the absence of slack buses in both AC and DC subsystems, and diversified grid configurations such as point-to-point integration of renewable energy sources and one AC system integrated with multiple VSC stations.

Static and dynamic evaluation of different architectures for an actual HVDC link project

The employment of High-Voltage Direct Current (HVDC) transmission in modern power systems is mainly driven by requirements of increasing power transfer over high distances in a cost-efficient and controllable way. HVDC control can ensure fast and accurate power flow control to improve the whole system performance as well as increased flexibility to manage power flows from remote renewable generation to load centers, especially in a zonal market configuration. However, in the network planning phase the implications of a new HVDC connection, both on the steady-state and on the dynamic operation of a power system, must be carefully evaluated with particular reference to possible outage events, depending on the operating conditions and on the exploited control schemes. In this paper, a real HVDC project within the Italian transmission network is considered in both the Voltage Source Converter (VSC) and Line Commutated Converter (LCC) technologies. The study implies a methodology to analyze the impact on steady-state and dynamic performances in the presence of faults, with a focus on grid security and market efficiency aspects. The behavior of the interconnected Italian power system is simulated in a development planning viewpoint by means of software tools exploited by the System Operator.

An Improved Mixed AC/DC Power Flow Algorithm in Hybrid AC/DC Grids with MT-HVDC Systems

One of the major challenges on large-scale Multi-Terminal High Voltage Direct Current (MT-HVDC) systems is the steady-state interaction of the hybrid AC/DC grids to achieve an accurate Power Flow (PF) solution. In PF control of MT-HVDC systems, different operational constraints, such as the voltage range, voltage operating region, Total Transfer Capability (TTC), transmission reliability margin, converter station power rating, etc. should be considered. Moreover, due to the nonlinear behavior of MT-HVDC systems, any changes (contingencies and/or faults) in the operating conditions lead to a significant change in the stability margin of the entire or several areas of the hybrid AC/DC grids. As a result, the system should continue operating within the acceptable limits and deliver power to the non-faulted sections. In order to analyze the steady-state interaction of the large-scale MT-HVDC systems, an improved mixed AC/DC PF algorithm for hybrid AC/DC grids with MT-HVDC systems considering the operational constraints is developed in this paper. To demonstrate the performance of the mixed AC/DC PF algorithm, a five-bus AC grid with a three-bus MT-HVDC system and the modified IEEE 39-bus test system with two four-bus MT-HVDC systems (in two different areas) are simulated in MATLAB software and different cases are investigated. The obtained results show the accuracy, robustness, and effectiveness of the improved mixed AC/DC PF algorithm for operation and planning studies of the hybrid A/DC grids.

Weather-Dependent Power Flow Algorithm for Accurate Power System Analysis Under Variable Weather Conditions

Accurate power flow analysis is essential to system operators for planning, design, analysis, and control of power networks. The accuracy of power flow analysis can be increased significantly by including the weather-dependent characteristics of the system. In this paper, a novel weather-dependent power flow algorithm is proposed and studied in comparison to the very well-known conventional power flow. The weather-dependent power flow algorithm is novel in the sense that it is explicitly parameterized in terms of typically available measured weather parameters (ambient temperature, solar irradiance, wind speed, and wind angle) to perform a fully coupled weather-dependent power flow analysis. Using this algorithm, the IEEE 30-bus power network was studied utilizing real weather data by performing three year-long steady-state time-series power flow analyses. The study demonstrates that the proposed weather-dependent power flow algorithm accurately estimates the branch resistances, the system states (current and voltages), the power losses, the branch flows, and the branch loadings. These are made possible because the proposed algorithm accurately estimates branch conductor temperature due to the coupling of power flow with the nonlinear heat balance model. An analysis of the computational complexity of the proposed algorithm is also presented.

Combined decentralized and local voltage control strategy of soft open points in active distribution networks

With the integration of high shares of distributed generators (DGs), it is increasingly difficult to cope with the voltage violations and puts forward a higher requirement for the operational flexibility in active distribution networks (ADNs). Soft open point (SOP) can realize accurate power flow control and continuous voltage regulation, which is usually operated by the centralized control strategy. However, the heavy burden of communication and complex global optimization process hinder its application on fast voltage control. This paper proposes a combined decentralized and local voltage control strategy of SOPs to rapidly cope with the frequent voltage fluctuations. Based on the dynamic network partition results, the decentralized optimization is applied to regulate active power transmission of SOPs among the connected areas. The Q-V control curve is optimally tuned to locally regulate the reactive power outputs of SOPs by using the intra-area information. Compared to the widely-used centralized strategy, the proposed combined control strategy of SOPs can effectively reduce the communication and computational burden with acceptable voltage control performance. Finally, the effectiveness of the proposed control strategy of SOPs is validated on the modified PG&E 69-node distribution system and modified IEEE 123-node distribution system.

Modeling and Optimization of Dual Active Bridge DC-DC Converter with Dead-Time Effect under Triple-Phase-Shift Control

Dead-time effect has become an apparent issue in high-switching-frequency high-power dual active bridge (DAB) DC-DC converter. This paper gives a detailed analysis of phase-shift errors effect caused by dead time, including output voltage offset, soft-switching failure, optimal scheme failure, etc. Phase-shift errors effect will invalidate traditional analyses of optimal control and mislead the design of DAB converter. To overcome these drawbacks, various operating modes and an accurate transmission power model incorporating dead time under triple-phase-shift (TPS) control are developed. On this basis, an optimal TPS incorporating dead time (TPSiDT) scheme is further proposed to minimize the current stress, while guaranteeing soft-switching operation by using Lagrange multiplier method (LMM) and Genetic Algorithm (GA). The novel transmission power model can provide accurate power flow computation to avoid phase-shift errors. Therefore, in practical applications, the minimum current stress and soft-switching operation can be guaranteed, and the efficiency of DAB converter can be improved. Finally, the experimental results verify the feasibility of the proposed TPSiDT scheme.

An efficient graph-based power flow algorithm for electrical distribution systems with a comprehensive modeling of distributed generations

Real-time operation, analysis and control of active distribution systems (DSs) mainly rely on accurate power flow (PF) results. Almost all decisions are made considering PF calculations. On the other hand, efficiency of PF algorithm should be updated to comply with new smart grid paradigms which affect traditional management methods of DSs. A new graph theory based PF algorithm is proposed in this paper for active electrical DSs including various distributed generation (DG) models, three phase equipment and meshed topologies. At first, two incidence matrices are proposed for modeling of DSs. These matrices could successfully handle meshed topologies and unbalanced networks. They could also be modified to consider various three phase equipment such as transformers and voltage regulators. Moreover, a comprehensive study of various modeling methods of DGs in PF studies is presented. In order to handle DG models, a new sensitivity matrix is proposed for in-algorithm calculation of reactive power injection of PV buses. Since, the proposed incidence matrices provide a decoupled model of the network, any topology and characteristic change could be simply applied in this PF algorithm. The proposed PF algorithm was tested in several simulations in various test systems. The results of accuracy test, performance test, and robustness test show capability of the proposed PF algorithm for handling various situations in different PF calculations.

A Decentralized Voltage Control Strategy of Soft Open Points in Active Distribution Networks

With the integration of high shares of distributed generators (DGs), it is increasingly difficult to cope with the risk of voltage violations and puts forward a higher requirement for the operational flexibility in active distribution networks (ADNs). Soft open point (SOP) is a novel power electronic device which can realize accurate power flow control and continuous voltage regulation. Currently, the centralized control strategy is mainly used to operate SOPs. However, the heavy burden of communication and complex global optimization processing will hinder its fast response to the frequent voltage fluctuations. This paper proposes a decentralized voltage control strategy of SOPs in ADNs. Based on the results of network partition, the alternating direction method of multipliers (ADMM) algorithm is applied to realize the decentralized optimization of the transmission power of SOPs among connected areas. The near-global optimal solution can be obtained without the huge calculation burden. The potential benefits of SOPs are fully explored to reduce power losses and improve the voltage profile of ADNs. Finally, the effectiveness of the decentralized voltage control strategy of SOPs is validated on the PG&E 69-node distribution system.