Direct Current Grids Research Articles

Fault identification in HVDC grids using a transient parametric model

This paper presents a novel single-ended fault identification algorithm for meshed High Voltage Direct Current grids. This algorithm can be used in the context of fully-selective fault-clearing strategies. Once a fault is suspected, using a parametric model describing the voltage and current evolution just after the fault occurrence, a maximum-likelihood estimate of the fault distance and impedance is evaluated. The presence of the fault is then confirmed depending on the size of the confidence region of the obtained estimate. The approach is evaluated on a simulated three-node meshed grid. The current and voltage need to be observed during less than 0.2 ms to get an accurate estimate of the fault characteristics and to identify consistently the faulty line.

Optimal allocation of fault current limiter in MMC-HVDC grid based on transient energy flow

Economical and reliable protection of dc-side short-circuit faults has become a key technology for promoting the development of module multilevel converter based high voltage direct current grid (MMC-HVDC-Grid). The fault current limiter (FCL) can effectively suppress the rapid development of fault current and reduce the current breaking capacity of the circuit breaker. In this paper, a method based on transient energy flow (TEF) analysis is proposed to optimize the allocation of resistive and inductive FCL in MMC-HVDC-Grid. In the proposed method, the electromagnetic TEF is measured firstly, and then, the TEF suppression rate and suppression efficiency are defined as optimization objectives, and the installation place of the FCL and its impedance parameters as optimization variables. To test the proposed method, a two-terminal and four-terminal bipolar MMC-HVDC-Grids with single-pole-to-ground dc fault are modelled in the PSCAD/EMTDC so that the TEF data can be acquired. The optimal FCLs' location and parameter values are determined through investigating the evolution paradigm of TEF along with changes of FCL position and parameters. The results prove that the selected parameters can effectively slow down the dc fault current rising rate, thus reducing the requirements on tripping current of the dc breaker.

Solution of the optimal power flow problem in direct current grids applying the hurricane optimization algorithm

The Colombian electrical power system is being transformed by the large-scale integration of energy storage systems and renewable energy resources to the power system. These technologies can be integrated using alternating current or direct current technologies via power electronic converters. Here we analyze the direct current paradigm by proposing a master-slave optimizer for solving the problem of optimal power flow considering nonlinear loads. The master stage covers the dispatch of all distributed generators using the hurricane optimization algorithm. In the slave stage, a power flow method based on successive approximations is used to determine the voltage variables and evaluate the objective function of the problem, which is the minimization of power loss. A 69-nodes direct current network is used as a test case to compare the numerical performance of the hurricane optimization algorithm with a nonlinear optimization package and a metaheuristic approach called black hole optimizer. All simulations are performed using MATLAB software version 2017a licensed by Universidad Tecnológica de Bolívar, Colombia.

Application of the backward/forward sweep method for solving the power flow problem in DC networks with radial structure

This paper presents the application of the backward/forward sweep iterative method for solving the power flow problem in direct current networks with radial structure, considering resistive and constant power loads. The validation of the effectiveness and robustness of the proposed method is made by using six comparative methods proposed in literature for power flow analysis in radial direct current networks: Gauss-Jacobi, Gauss-Seidel, Newton-Raphson, linear approximation based on Taylor series, successive approximations, and the triangular matrix formulation. Those methods are evaluated using four test systems formed by 10, 21, 33 and 69 nodes. Simulation results, obtained in MATLAB, show that the proposed approach is efficient for radial direct current grids in terms of solution quality and processing time, increasing the efficiency for larger number of nodes increases.

Application of the Nested Convex Programming to the Optimal Power Flow in MT-HVDC Grids.

This paper deals with an application of the nested convex programming to the optimal power flow (OPF) in multi-terminal high-voltage direct-current grids (MT-HVDC). The real-world optimization problem under consideration is non-convex. This fact implies some possible inconsistencies of the conventional numerical minimization algorithms (such as interior point method). Moreover, the constructive numerical treatment of this problem is usually based on some approximative approaches, namely, on the suitable linearizations and problem relaxations. The resulting convex programming model constitutes an approximated model and can naturally involve the significant (approximation) errors. In difference to the strongly approximate computational approaches mentioned above, the numerical scheme we propose takes into account the specific bi-linear structure of the problem and operates with the originally given non-convex formulation of the problem. We implement the proposed nested optimization approach and study the numerical consistency of the resulting optimal design. The Python based numerical experiments demonstrate the imlementability of the proposed methodology. Optimization problem of the modified version of the CIGRE MT-HVDC is next used as a benchmark test for the approach we developed.

Impacts of MT-HVDC Systems on Enhancing the Power Transmission Capability

In this paper, improvement in the power transfer capacity of transmission lines (TLs) by utilizing a multi-terminal high voltage direct current (MT-HVDC) grid is discussed. A multi-terminal HVDC grid designed for wind power can be used as an extra transmission path in interconnected systems during low wind conditions, and provides extra dynamic stability and security. This paper deals with the power transfer capacity as well as the small signal (SS) stability assessments in less damped oscillations accompanying inter area modes. Computation of the maximum allowable power transfer capability is assessed via DC optimal power flow-based control architecture, permitting more power transfer with a definite security margin. The test system is assessed with and without the exploitation of MT-HVDC grid. Simulation work is done using a generic computational framework i.e., international council on large electric systems (CIGRE) B4 test bench with a Kundur’s two area system, shows that voltage source converters (VSCs) provide excellent control and flexibility, improving the power transfer capability keeping the system stable.

ANN‐based robust DC fault protection algorithm for MMC high‐voltage direct current grids

Fast and reliable protection is a significant technical challenge in the modular multilevel converter (MMC)-based DC grids. The existing fault detection methods suffer from the difficulty in setting protective thresholds, incomplete function, insensitivity to high-resistance faults and vulnerable to noise. This study proposes an artificial neural network (ANN)-based method to enable DC bus protection and DC line protection for DC grids. The transient characteristics of DC voltages are analysed during DC faults. On the basis of the analysis, the discrete wavelet transform is used as an extractor of distinctive features at the input of the ANN. Both frequency-domain and time-domain components are selected as input vectors. A large number of offline data considering the impact of noise is employed to train the ANN. The outputs of the ANN are used to trigger the DC line and DC bus protections and select the faulted poles. The proposed method is tested in a four-terminal MMC-based DC grid under PSCAD/EMTDC. The simulation results verify the effectiveness of the proposed method in fault identification and the selection of the faulty pole. The intelligent algorithm-based protection scheme has good performance concerning selectivity, reliability, robustness to noise and fast action.

Analysis of Local Measurement-Based Algorithms for Fault Detection in a Multi-Terminal HVDC Grid

One of the most important challenges of developing multi-terminal (MT) high voltage direct current (HVDC) grids is the system performance under fault conditions. It must be highlighted that the operating time of the protection system needs to be shorter than a few milliseconds. Due to this restrictive requirement of speed, local measurement based algorithms are mostly used as primary protection since they present an appropriate operation speed. This paper focuses on the analysis of local measurement based algorithms, specifically overcurrent, undervoltage, rate-of-change-of-current, and rate-of-change-of-voltage algorithms. A review of these fault detection algorithms is presented. Furthermore, these algorithms are applied to a multi-terminal grid, where the influence of fault location and fault resistance is assessed. Then, their performances are compared in terms of detection speed and maximum current interrupted by the HVDC circuit breakers. This analysis aims to enhance the protection systems by facilitating the selection of the most suitable algorithm for primary or backup protection systems. In addition, two new fault type identification algorithms based on the rate-of-change-of-voltage and rate-of-change-of-current are proposed and analyzed. The paper finally includes a comparison between the previously reviewed local measurement based algorithms found in the literature and the simulation results of the present work.

Faulty feeder selection and segment location method for SPTG fault in radial MMC‐MVDC distribution grid

As a modular multilevel converter-based medium-voltage direct current (MMC-MVDC) distribution grid mostly utilises small current grounding modes, the weak fault current for single-pole-to-ground (SPTG) fault is very difficult to detect especially in the case of noises and fault resistance. Therefore, this study proposes a fast and accurate faulty feeder selection and segment location method. For SPTG fault, the transient current fault component is the charge-discharge current of distributed capacitance on the DC feeder. Analysis indicates that the waveforms of current fault component of positive and negative poles are negatively correlated for a faulty feeder; while they are positively correlated for a non-faulty feeder. According to these characteristics, a faulty feeder selection criterion using Pearson correlation coefficient (PCC) is constructed. Then, utilising the energies difference between the current fault components of two poles, the faulty pole can be verified. In addition, the faulty segment is located by the PCC of the current fault component on both sides of each segment. Finally, simulation results confirm the validity of the proposed faulty feeder selection and segment location method.

Optimal power flow solution in direct current grids using Sine-Cosine algorithm

In the next years, Colombian power system will have the connection of distributed generators and constant power loads; Therefore, it is necessary to propose the analysis methods that allow establishing the minimum requirements that have to be satisfied for the power system to guarantee an optimal power flow in order to preserve safe and reliable operation of it. For this purpose, in this paper presents an optimal power flow in direct current resistive grids with constant power loads and distributed generators. The optimal power flow problem is formulated as a master-slave optimization algorithm. The master stage covers the dispatching of all the distributed generators by using the Sine-Cosine algorithm. In the slave stage an efficient power flow method based on successive approximations is employed to determine the voltage variables and evaluate the objective function of the problem, which corresponds to the power loss minimization. A direct current distribution network composed by 21 nodes is used as test case by comparing its numerical performance with nonlinear optimization packages and two metaheuristic approaches named black-hole optimization and continuous genetic algorithm. All the simulations are conducted via MATLAB software.

Optimal power flow studies in direct current grids: An application of the bio-inspired elephant swarm water search algorithm

Colombian power system is experienced important changes due to the large scale integration of renewable power generation based on solar and wind power; added to the fact that direct current networks have taken important attention, since they are efficient in terms of power loss and voltage profile at distribution or transmission levels For addressing this problem, this paper presents the application of an emerging bio-inspired metaheuristic optimization technique known as elephant swarm water search algorithm to the optimal power flow problem in direct current networks. A master-slave hybrid optimization strategy for optimal power flow analysis is addressed in this paper by decoupling this problem in two optimizing issues. The first problem corresponds to the selection of the power generated by all non-voltage controlled distributed generators; While the second problem lies in the solution of the classical power flow equations in direct current networks. The solution of the master problem (first problem) is made by applying the elephant swarm water search algorithm, while the second problem (slave problem) is solved by a conventional Gauss-Seidel numerical method. The proposed hybrid methodology allows solving the power flow problem by using any basic programming language with minimum computational effort and well-precision when is compared with optimizing packages such as general algebraic modeling system/CONOPT solver and conventional metaheuristic techniques such as genetic algorithms.

Alternative power flow method for direct current resistive grids with constant power loads: A truncated Taylor-based method

The power flow in electrical system permits analyzing and studying the steady-state behavior of any grid. Additionally, the power flow helps with the proper planning and management of the system. Therefore, it is increasingly necessary to propose power flows with fast convergence and high efficiency in their results. For this reason, this paper presents an alternative power flow approach for direct current networks with constant power loads based on a truncated Taylor-based approximation. This approach is based on a first-order linear approximation reformulated as a recursive, iterative method. It works with a slope variable concept based on derivatives, which allow few iterations and low processing times. Numerical simulations permit identifying the best power flow approaches reported in the specialized literature for radial and mesh dc grids, including the proposed approach. All the simulations were conducted in MATLAB 2015a.

Accurate and Efficient Estimation of Short-Circuit Current for MTDC Grids Considering MMC Control

DC short-circuit current calculation for the modular multilevel converter based multi-terminal direct current (MMC-MTDC) grid is critical and fundamental in equipment selection and protection setting. The existing MTDC grid short-circuit current calculation methods suffer from low efficiency, poor adaptability, and inflexibility. To address these issues, this paper proposes an efficient and general companion circuit-based method to estimate the short-circuit currents of asymmetric bipolar MTDC grids. First, an MMC is equivalent to an RLC series circuit in parallel with a time-dependent controlled current source. The equivalent model considers not only the discharge currents of the sub-module capacitors but also the ac in-feed current determined by MMC controllers. Then, the equivalent model for a bipolar MTDC grid with the dedicated metallic return is established by combing the equivalent MMC model with the lumped model of the dc transmission lines. Next, the companion circuit method is employed to efficiently and readily solve the equivalent model of the dc grid to obtain post-fault branch currents and node voltages. Both theoretical analyses and intensive tests on the CIGRE benchmark MTDC grid and Zhangbei bipolar MTDC grid verify the improved accuracy, efficiency, adaptability, and flexibility of the presented method.

Modeling and simulation of large power system with inclusion of bipolar MTDC grid

This paper presents an electromechanical transient modeling and simulation method for large power system with inclusion of bipolar multi-terminal direct current (MTDC) grid. First, the dynamic model of a modular multilevel converter (MMC) is presented. The dynamic model of the bipolar DC grid is then established by using the companion circuit method. In particular, the inductances of DC lines are carefully modeled to ensure the simulation accuracy when a DC fault occurs. Second, the electromechanical transient simulation procedure for a power system with inclusion of an MTDC grid is presented. The AC and DC grids are solved alternately. Due to the difference between time constants of AC and DC grids, the multi-rate scheme is used to ensure the simulation efficiency. Third, the proposed method is employed to simulate a real-life large power system with inclusion of a bipolar MTDC grid. The simulation results validate the correctness and the effectiveness of the proposed method. Unique interaction characteristics between AC and DC grids are also revealed by the results.

A Generalized Power-Flow Model of VSC-Based Hybrid AC–DC Systems Integrated With Offshore Wind Farms

This paper presents a unified power-flow model of ac power systems incorporating voltage-sourced converter (VSC) based multi-terminal high voltage direct current (MTDC) grids. Offshore wind farms (OWFs) are appropriately interfaced with the MTDC grid(s). Pulsewidth modulation control is employed for the VSCs. In the proposed model, the VSC modulation indices are considered as unknowns. The proposed model employs realistic grid control strategies like nonlinear distributed dc voltage control. The power-flow solution is carried out using the Newton–Raphson method. The convergence properties of the proposed algorithm are investigated vis-a-vis varying terminal end active and reactive power specifications of the VSCs and the rectifying power injections of the OWFs, in light of different MTDC control strategies employed. Corresponding to nonlinear dc voltage droop control, five different operating points are considered to observe the sharing of power among the dc terminals with changes in the operating point specifications. The results validate the model.

Toward Flexible Risk-Limiting Operation of Multi-Terminal HVDC Grids With Vast Wind Generation

Contingencies occurring in multi-terminal high voltage direct current (MT-HVDC) grids can result in DC voltage/flow violations and also affect the frequency stability of the connected multiple asynchronous grids. To recognize and control such notable operating risks, a novel flexible risk-limiting optimal power flow (FROPF) for the MT-HVDC grid with vast wind generation is proposed in this paper. Within the two-stage FROPF structure, the pre-contingency operation of grid-side voltage-source converters (GVSCs) is optimized to minimize MT-HVDC grid power losses. Immediately following an outage occurring in the MT-HVDC grid, various fast-acting corrective actions of GVSCs are utilized to hedge against the overall risk exposure, including the wind power curtailment risk of the MT-HVDC grid and the rate-of-change-of-frequency (RoCoF) violation risk imposed on associated asynchronous grids. Reformulation techniques are introduced to ease the computational complexity of the optimization model. Case studies of two MT-HVDC grids demonstrate the effectiveness of the proposed FROPF.

A non-unit boundary protection of DC line for MMC-MTDC grids

Due to the low-impedance characteristic, the multi-terminal high voltage direct current (MTDC) grid based on modular multilevel converter (MMC) requires protection to detect and discriminate line faults within several milliseconds, which is a serious challenge for protection. Therefore, this paper proposes a non-unit line protection scheme based on the initial line-mode voltage traveling waves (ILVTWs). Based on the analysis of the traveling wave (TW) propagation characteristics, the transfer functions of ILVTWs under typical internal and external faults are derived. By comparing the differences of the transfer functions in frequency domain, the corresponding protection principles are developed. Besides, a method to determine the protection threshold is elaborated, which is independent of simulation. Extensive simulations show that the proposed protection scheme can accurately operate with high sensitivity and reliability.

Single‐ended line protection for MMC‐MTDC grids

This study proposes a novel non-unit line protection for modular multilevel converter-based (MMC) multi-terminal high-voltage direct current (MTDC) grids. On the basis of the symmetrical component analysis, the initial values of positive-sequence voltage travelling waves (PSVTWs) generated by the fault are first investigated. Then, according to the TW theory and the inherent composition of the primary equipment of MMC-MTDC grids, the initial values of PSVTWs on both sides of the series inductor are obtained in Laplace domain. Moreover, a fast fault line protection based on the positive-sequence voltage on the series inductor at the line terminal is proposed. Besides, the method of the protection threshold determination is elaborated and is independent of simulation. Finally, extensive simulation studies are carried out in a four-terminal MMC-MTDC grid. Simulation results show the effectiveness of the proposed line protection method.

Control Method for Avoiding Transformer Saturation in High-Power Three-Phase Dual-Active Bridge DC–DC Converters

The classic top to down structure of electrical infrastructure is changing due to the extensive spread of renewable energy sources which are connected to medium-voltage and low-voltage grids. Especially for medium-voltage direct-current grids, the three-phase dual-active bridge (DAB) dc–dc converter is one of the most promising converter topologies, as it features bidirectional power flow and galvanic isolation at highest efficiency. Unwanted saturation of the transformer of this converter can occur, particularly for multimegawatt converters with highly efficient, low-loss transformers. The saturation leads to additional core losses, elevated voltage stress at the windings, and increased magnetostriction of the transformer core, which can result in undesired acoustic emissions. The following article presents a feedback control and modulation method that controls the DAB converter such that saturation of the transformer is avoided. The chosen approach evaluates the star-point voltage of the transformer to determine the dc component of the magnetizing current, thereby avoiding the need for expensive high-precision current sensors. The control method is analytically derived and verified by simulation. Experiments carried out using a 5 MW medium-voltage three-phase DAB converter prototype verify the presented modulation method.

Reducing the Fault-Transient Magnitudes in Multiterminal HVdc Grids by Sequential Tripping of Hybrid Circuit Breaker Modules

A sequential switching strategy for hybrid dc circuit breaker (CB) is proposed to improve transients during dc fault interruption in multiterminal high voltage direct current (HVdc) grids. Compared to the conventionally tripped dc CB, the proposed switching strategy, which sequentially trips the breaking modules within the CB, reduces the peak fault current and overvoltage as well as fault clearance time. These metrics are analytically computed through a time-domain calculation approach considering the traveling wave phenomena in dc transmission systems. By rescheduling the tripping sequence and optimal rating and number of individual modules of the CB, the energy distributed among the modules is well balanced. Finally, an analytic evaluation of the proposed sequential tripping is performed and, subsequently, the best practice and the optimal design process are provided. Performance of the sequential switching strategy as well as the optimal design process are verified through simulation studies in the PSCAD/EMTdc software environment.