In this paper, a new decomposing strategy is proposed to solve the power flow problem in the large-scale multienergy carrier (MEC) systems, including gas, electrical, and heating subnetworks. This strategy has been equipped with a novel noniterative method named holomorphic embedding (HE) to solve the energy flow of the electrical subnetwork. Moreover, it benefits from the less-computational graph method for solving the energy flows of the heating subnetwork. The HE method unlike initial-guess iterative methods guarantees to find the power flow solution, if there is a solution. In addition, it finds only the operational power flow solution without concern about the convergence of the solution. In the proposed strategy, the decomposing method decouples various energy flows of subnetworks without losing the major benefits of the simultaneous analysis of the subnetworks and losing accuracy. Moreover, the proposed decomposing strategy has more reliability and faster computation time than the Newton–Raphson technique. In order to demonstrate the efficiency and superiority of the proposed decomposing strategy on solving large-scale MEC systems, the strategy is tested on three large-scale case studies.

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Fast Decomposed Energy Flow in Large-Scale Integrated Electricity–Gas–Heat Energy Systems

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

A multiperiod network reconfiguration to meet the requirement of hourly hosting capacity under a minimal required number of switching operations, taking into consideration the uncertainty of renewable generation, is formulated as a nonlinear, nondifferentiable integer optimization problem with nonlinear equality and inequality constraints. A four-stage solution methodology, including an assessment stage, a time-partitioning stage, an optimization stage, and an evaluation stage, is developed to solve the constrained large-scale nonlinear integer optimization problem. A fuzzy C-means clustering algorithm is applied to partition the time period to facilitate the design of a minimum-number switching solution. A hybrid particle swarm optimization algorithm is developed to find an optimal network topology for each partitioned time period. The IEEE 123-bus case and a 1001-node system, three-phase and unbalanced, are used to evaluate the proposed method with promising results.

Toward Optimal Multiperiod Network Reconfiguration for Increasing the Hosting Capacity of Distribution Networks

For decades high voltage alternating current (HVAC) was considered as most economical solution to transmit and deliver electric power. With the recent developments in power electronic devices, high voltage direct current (HVDC) system becomes most prominent technology. Multi-terminal direct current (MTDC) based system as a promising technology for future power system is the major focus area for researchers and industries these days. A number of MTDC systems have been implemented physically. The major motivation to construct such MTDC systems is the integration of large-scale offshore power sources such as wind turbines and solar systems. This article discusses the most critical challenges and issues related to operation, control and protection schemes for integration of modular multi-level converter (MMC) based MTDC systems. At first detailed literature survey has been presented to show the challenges for MMC based MTDC systems, then an analysis related to those challenges for operation, control and protection schemes for existing MMC based MTDC systems has been provided. Finally, a road map to tackle such challenges has been suggested.

MMC Based MTDC Grids: A Detailed Review on Issues and Challenges for Operation, Control and Protection Schemes

Load characteristics have substantial influence on the voltage stability of power systems. The self-restorative characteristic and stalling of induction motor loads can deteriorate the voltage stability, so it is necessary to develop accurate and efficient dynamic analysis methods for voltage stability analysis of systems with induction motor loads. In this paper, a set of methods based on holomorphic embedding is proposed, which is able to solve steady states and dynamics of a power system with induction motors. The paper is the first work that applies holomorphic embedding to dynamic problems of power systems. The test cases on the IEEE 14-bus system, the NPCC 140-bus system, and the Polish 2383-bus system verify both accuracy and efficiency of the proposed methods.

Voltage Stability Analysis of Power Systems With Induction Motors Based on Holomorphic Embedding

A novel, fast, and flexible holomorphic embedding (FFHE) method is proposed for solving power flow problems with Q-limits. New embedded systems are developed for power flow equations at the PV and PQ buses for flexibility that allows us taking any state, instead of accepting only some certain point (e.g., a flat start and a zero-current injection point), as the initial guess. This flexibility allows us a warm start, a dc power flow solution, or other starts, leading to the reduced runtime and a decreased number of needed steps, as compared with existing embedded systems that only accept several particular points as the initial guess. However, the proposed method may not be globally convergent in the sense that such flexibility and flexible embedded systems do not ensure convergence or a superior rate of convergence for an arbitrary start. To implement the proposed FFHE, a new numerical scheme is devised to compute the numerical solution without explicitly calculating the rational approximant. To evaluate its effectiveness and practicability, the proposed novel FFHE method is applied to a series of power flow test cases ranging from 3 to 13659 buses. It is found that the proposed FFHE method requires less runtime than Newton's method for most test cases. By using Newton's method as a reference, FFHE is shown to be more effective than the holomorphic embedding methods that had been documented in the literature; partly due to its flexibility and the new scheme for computing numerical solutions.

A Novel Fast and Flexible Holomorphic Embedding Power Flow Method

The widespread use of distributed generations (DGs) in utility distribution feeders is a trend, and it brings about several challenges to the operation, planning, and design of general distribution networks. In this paper, a comprehensive tool, Continuation Distribution Power Flow (CDFLOW), is presented and evaluated. CDFLOW can be used for tracing steady-state stationary behaviors of general unbalanced distribution systems due to various types of power injection variations, including high penetration of DGs. The major computation engine behind CDFLOW is the continuation method. Major components, either balanced or unbalanced, grounded or ungrounded, are well modeled in CDFLOW. A detailed description of CDFLOW and its implementation regarding the predictor, corrector, adaptive step-size control and parameterizations are presented. For illustrative purposes, CDFLOW was applied to the IEEE 8500-node test system and a practical 1103-node distribution networks with promising results.

CDFLOW: A Practical Tool for Tracing Stationary Behaviors of General Distribution Networks

In this paper, a novel non-intrusive probabilistic power flow (PPF) analysis method based on the low-rank approximation (LRA) is proposed, which can accurately and efficiently estimate the probabilistic characteristics (e.g., mean, variance, and probability density function) of the PPF solutions. This method aims at building up a statistically-equivalent surrogate for the PPF solutions through a small number of power flow evaluations. By exploiting the retained tensor-product form of the univariate polynomial basis, a sequential correction-updating scheme is applied, making the total number of unknowns to be linear rather than exponential to the number of random inputs. Consequently, the LRA method is particularly promising for dealing with high-dimensional problems with a large number of random inputs. Numerical studies on the IEEE 39-bus, 118-bus, and 1354-bus systems show that the proposed method can achieve accurate probabilistic characteristics of the PPF solutions with much less computational effort compared to the Monte Carlo simulations. Even compared to the polynomial chaos expansion method, the LRA method can achieve comparable accuracy, while the LRA method is more capable of handling higher-dimensional problems. Moreover, numerical results reveal that the randomness brought about by the renewable energy resources and loads may inevitably affect the feasibility of dispatch/planning schemes.

Probabilistic Power Flow Calculation Using Non-Intrusive Low-Rank Approximation Method

Considering the increasing penetration of renewable energy sources and electrical vehicles in utility distribution feeders, it is imperative to study the impacts of the resulting increasing uncertainty on the delivery capability of a distribution network. In this paper, probabilistic available delivery capability (ADC) is formulated for a general distribution network integrating various renewable energy sources (RES) and load variations. To reduce the computational efforts by using conventional Monte Carlo simulations, we develop and employ a computationally efficient method to assess the probabilistic ADC, which combines the up-to-date sparse polynomial chaos expansion (PCE) and the continuation method. Particularly, the proposed method is able to handle a large number of correlated random inputs with different marginal distributions. Numerical examples in the IEEE 13 and IEEE 123 node test feeders are presented, showing that the proposed method can achieve accuracy and efficiency simultaneously. Numerical results also demonstrate that the randomness brought about by the RES and loads indeed leads to a reduction in the delivery capability of a distribution network.

Applying Polynomial Chaos Expansion to Assess Probabilistic Available Delivery Capability for Distribution Networks With Renewables

The widespread use of distributed generators (DGs) in utility distribution feeders brings about several challenges to the operation, planning, and design of general distribution networks. In this paper, the task of accurate determination of available delivery capability (ADC) subject to thermal limits, voltage limits, and voltage stability limit is formulated. A rigorous numerical method to calculate the ADC of large-scale distribution networks with renewables is presented. This numerical method computes three critical points which are the saddle-node bifurcation point or structure-induced bifurcation point, voltage violation point, and thermal-limit violation point. To gain the speed and robustness for the proposed method, the continuation method is integrated into the proposed numerical method. For illustrative purposes, the proposed method is applied to the IEEE 14-bus test feeder and the IEEE 8500-node test system.

Hao Sheng

Papers

A Novel Fast and Flexible Holomorphic Embedding Power Flow Method

CDFLOW: A Practical Tool for Tracing Stationary Behaviors of General Distribution Networks

Probabilistic Power Flow Calculation Using Non-Intrusive Low-Rank Approximation Method

Applying Polynomial Chaos Expansion to Assess Probabilistic Available Delivery Capability for Distribution Networks With Renewables

Available Delivery Capability of General Distribution Networks With Renewables: Formulations and Solutions