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The promise of improved system efficiency, reliability, and higher renewable energy hosting capability of the Integrated Energy System concept has driven the development of innovative network coupling technologies and energy system integration methods. Co-ordinated design and operation of the traditionally separate energy systems, including electric power, gas, and heat will lead to the optimal use of synergies between energy networks and bring forth numerous benefits to the energy sector. To fully understand the potential and quantitatively assess the operation performance of the combined energy networks, a unified modeling and simulation framework using an extended MANA formulation is proposed in this paper, which is capable of incorporating arbitrary gas network configurations and unbalanced power networks in a systematic manner needed. A case study with combined power and gas networks via EnergyHubs is implemented to demonstrate the application of the proposed method.

The application of synchronized phasor measurement technology at distribution networks provides new options for voltage-to-power sensitivity estimation and voltage regulation. An augmented sensitivity estimation-based voltage control strategy with a phasor measurement unit (PMU) measurement is proposed for active distribution networks (ADNs). The voltage control records are extracted from historical synchronized phasor measurements. The voltage-to-power sensitivities reflecting the relationship of voltage change and power fluctuation are estimated with the obtained voltage control records. In addition to the linear parameter, parameters to match the nonlinearity between voltage and power variation and to track the operation conditions are introduced in the fitting model to improve the accuracy of the voltage control strategy. Rule-based and sensitivity-based optimization voltage control methods are proposed using the sensitivities estimated in which the measurements of partial nodes at the distribution network are the only needed data. The voltage control is also realized with faster computation speed. Case studies and analysis on the IEEE 33-node test feeder verify the correctness and effectiveness of the proposed method.

Real-time simulation of large-scale active distribution networks exhibiting a wide range of time-scales puts forward higher requirements for simulation accuracy and efficiency. This paper presents an extendable method and design for the real-time simulation of active distribution networks utilising high-performance hardware field programmable gate arrays. In the aspect of numerical algorithm, a high-accuracy and stable multirate simulation algorithm is proposed. The entire active distribution network is decoupled into different subsystems by their inherent time-scales and distinct time steps are used to solve the subsystems. Then root-matching method is adopted to form the exponential difference equations that represent the behaviours of the electric distribution network being modelled, which eliminates the truncation errors and thus provides a highly accurate time-domain solution. To handle the interface between the subsystems, a multirate interfacing method is proposed. The hardware design of the multirate interfaces is presented as well. With the multirate algorithm, a fully functional extendable real-time simulator based on field programmable gate arrays is designed and implemented. Two modified IEEE 33-node systems with photovoltaics and energy storage are simulated on the 4-field-programmable-gate-arrays-based real-time simulator. Simulation results are compared with the commercial simulation tool PSCAD/EMTDC to validate the correctness and effectiveness of the proposed method and design.

This letter presents the latest improvements of a previously proposed parallel and multistep approach based on the functional mock-up interface standard for the simulation of electromagnetic transients. The improved approach extends the capacity of the original parallel asynchronous mode into accommodating the use of different time-steps in different decoupled subsystems. It also introduces a signal correction procedure using linear extrapolation in multistep simulations, greatly enhancing simulation flexibility, efficiency, and accuracy. Numerical examples are provided to demonstrate the computational advantages of the improved approach.

This paper is related to research on parallelization techniques for the simulation of electromagnetic transients (EMTs). It presents a new approach based on a parallel-in-time equation grouping and reordering (PEGR) technique whose original theoretical formulation is modified, extended and generalized from state-space to the modified-augmented-nodal analysis (MANA) formulation method. The highly efficient sparse linear solver KLU is incorporated in the approach for power system network matrix solution. The proposed approach is implemented with OpenMP Multithreading for CPU-based parallelization. Test results show that EMT simulations can be accelerated by exploiting the intrinsic independency of certain solution procedures using the PEGR technique.

Real-time simulation of a microgrid involving massive high-frequency power electronic converters, various distributed generators and energy storage systems is computationally demanding. Due to the prominent computing resources and high speed communication, field programmable gate arrays (FPGAs) can be used together to realise the real-time simulation of a microgrid. For a complete multi-FPGA-based real-time simulator, interfaces are essential to communicate with each other and with different types of apparatus. The internal interfaces between FPGAs make it possible to operate in parallel, sharing the computational burden. External interfaces between an FPGA and physical devices contribute to the implementation of hardware-in-the-loop simulation. In this study, interfacing techniques including multi-FPGA system topology determination, time-step synchronisation mechanism and precise communication are proposed in detail. An analogue-to-digital and digital-to-analogue interface is designed to facilitate physical connections to external devices. A modified microgrid benchmark with photovoltaics and a battery is simulated with a time-step of 3 μs on a 4-FPGA-based real-time simulator. Simulation results are compared with PSCAD/EMTDC to validate the interface design.

Power system electro-magnetic transient programs (EMTP) have been popular among researchers and practitioners due to their detailed component modeling and high simulation accuracy for complex system operations. Despite broad applications in simulations with wide range of timescales, the small discretization step of these programs makes their use very time-consuming for system studies with long time span. Facing the increasingly complex power system transient characteristics and simulation demands, a multiscale algorithm that integrates the simulations of the electromagnetic and slower electromechanical transients is desirable. The multiscale simulation algorithm preserves the high fidelity of the EMTP and attains higher efficiency for the overall transient simulation. In this paper, we achieve this goal by exploiting the unique properties of the matrix exponential function. The proposed algorithm is capable of utilizing large step sizes to speed up the simulation of slow dynamics, whereas the fast transients are accurately reconstructed through efficient dense output mechanism, which is built upon the matrix exponential function computation. Numerical studies including a large-scale wind farm simulation are conducted to demonstrate the effectiveness of the proposed multiscale algorithm.

This paper presents two variable time-step algorithms for time-domain simulation of electromagnetic transients. The first one has been created to simulate basic switching transients and the second one is intended to simulate power-electronic systems. Each algorithm is tested in a dedicated circuit. Simulation results yield excellent accuracy and significant improvements in computation time when compared to fixed time-step algorithm.

Reconfigurable computing is that the logical resources in the system can be reconfigured according to the real-time changing data flow to achieve different calculation functions. The reconfigurable computing system has both high efficiency on hardware and universality of software. The field programmable gate array (FPGA)-based real-time simulator for active distribution networks (ADNs) requires a long compilation time for case modification, with low efficiency and low versatility, making it inconvenient and difficult for users. To solve the problem of long compile time with a new case, a universal design of the FPGA-based real-time simulator for ADNs based on reconfigurable computing is proposed in this paper. It includes the universal design of the simulation parameter configuration, the simulation initial value setting, the linear equations solving module and the simulation result output module. The proposed universal design of the simulator makes the modification and change of the cases and parameters without recompiling and further improves the simulation efficiency. Simulation results are conducted and compared with PSCAD/EMTDC to validate the correctness and effectiveness of the universal design.

Modern power electronic circuits contain numerous switches driven by high frequency controllers and can cause discontinuities in time-domain simulation methods. This paper presents numerical problems resulting from discontinuities when simulating power electronic circuits. Limitations in existing methods are analyzed. Three new methods are proposed to improve accuracy and computational performance.

With a high penetration of power electronic equipment, transient simulation for power electronic circuit has been a main challenge for performance improvement of the electromagnetic transient simulation tools. In this paper, two new solvers for the matrix exponential-based simulation method are proposed based on the dense output formula and Pade approximation of different orders. The proposed solvers are implemented with the optimal combination of numerical integration method and interpolation method. Both solvers are L-stable. One has 3rd-order accuracy which is more accurate than existing simulation tools in power electronic simulation. The other solver achieves 1st-order accuracy with a lower precision numerical integration method than the same-order algorithms and is appealing from computation speed perspective. Numerical studies including TCR circuit and two types of VSC-HVDC systems are conducted to demonstrate the effectiveness of the proposed solvers.

With the extensive application of power electronic equipment in power systems, electromagnetic transient (EMT) simulation involving power converters becomes more challenging. Due to its multithreads and high throughput architecture, the graphics processing unit (GPU) can be used to accelerate those EMT simulations. A GPU-based matrix exponential method and its memory management for power converter transient simulation are proposed in this paper. A parallel exponential integration algorithm is established from two aspects to fully utilize the GPU multithreads capability. The matrix exponentials which are recomputed with the on/off state changes of power electronic switches are cached in GPU memory. The simulation efficiency is improved by reusing the cached data and reducing heterogeneous data transmission between CPU and GPU. Several strategies are experimented to manage the cache memory considering the EMT simulation workflow. The proposed memory management expands the simulation capability by substantially reducing the memory requirement and maintains the speed advantage of the GPU-based simulator. The proposed method is tested on wind power plants of different scales with power electronic interfaced wind generators. Simulation results indicate that the proposed method and its memory management expand the simulation capability and achieve speedups.

A variety of numerical integration methods are currently being used for simulating electromagnetic transients in commercial software and experimental codes. This paper intends to provide a review and comparison of these methods for time-domain integration, including 2S-DIRK, ARTEMiS art5 solver, and a semi-analytical matrix exponential-based method. The possibility of utilizing these methods is explored for reliable and efficient treatment of discontinuity, which is known to give rise to numerical oscillations for the widely used trapezoidal method. Case studies are conducted to show the strengths and limitations of these methods and their combinations.

The field-programmable gate array (FPGA)-based real-time simulator takes advantage of many merits of FPGA, such as small time-step, high simulation precision, rich I/O interface resources, and low cost. The sparse linear equations formed by the node conductance matrix need to be solved repeatedly within each time-step, which introduces great challenges to the performance of the real-time simulator. In this paper, a fine-grained solver of the FPGA-based real-time simulator for active distribution networks is designed to meet the computational demand. The framework of the solver, offline process design on PC and online process design on FPGA are proposed in detail. The modified IEEE 33-node system with photovoltaics is simulated on a 4-FPGA-based real-time simulator. Simulation results are compared with PSCAD/EMTDC under the same conditions to validate the solver design.

Facing the increasingly complex power system transient characteristics, the electromagnetic transient simulation tools are gaining popularity, thanks to their detailed modeling of power system equipment and high fidelity simulation results. Consequently, the Electro-Magnetic Transient Programs are increasingly used in simulation studies of higher dimensions and wider range of scales, which challenges the circuit-based algorithmic design of these programs. This paper proposes to use explicit integration formulas based on the matrix exponential function in the transient simulations of large-scale wind farms, which possess both high efficiency of explicit methods and numerical stability of implicit methods. A Krylov subspace-based order reduction technique embedded into the integration formulas was developed to specifically address the simulation needs of high dimensional EMT model of detailed wind farms. Numerical studies are conducted based on a realistic large-scale wind farm, where the proposed state space modeling framework is established, and the matrix exponential-based algorithm is implemented and compared against a set of classical stiff ODE solvers. Simulation tests with different fault types and fault locations are presented, showing a superior computation speed for studies with both equivalent and detailed wind farm modeling. On the other hand, numerical errors of the new algorithm are shown to be at least one order of magnitude smaller than other solvers in the range of typical step sizes, under the same simulation setting. These properties ensure an efficient, reliable and highly scalable simulation capability for the computation challenges in the studies of large-scale wind farms.

In order to meet the demand of fast electromagnetic transient simulation for large-scale interconnected power systems, a new method of GPU based parallel matrix exponential algorithm for power system electromagnetic transient simulation is presented in this paper. Firstly, the hardware structure and programming model of GPU are introduced. Then the high data parallelism based on matrix exponential integration algorithm is proposed. Then, a simulation test is carried out for a wind farm system including 17 WTGs. The accuracy and efficiency of the proposed method are verified. The results show that the speed of parallel computing based on GPU is about 2 times faster than that of CPU and Matlab/SimPowerSystems.

The ever-increasing scale of system interconnection and diverse dynamic time constants of power equipment pose challenges to power system transient simulation algorithms. In this paper, an adaptive numerical integration method for DAE systems based on matrix exponential operator is presented. Krylov subspace technique is utilized to effectively reduce the problem dimension. A novel step adaption scheme is established to enable the method adjusting the computation step size according to error budget while maintaining the output step size unchanged. Acceleration is accomplished without perceived degradation in the simulation results. Numerical performance and computation efficiency is demonstrated through numerical case studies.