Publications
228 results found
Yu Y, Nduka O, Ul-Nazir F, et al., 2023, A three-stage stochastic framework for smart electric vehicle charging, IEEE Access, Vol: 11, Pages: 655-666, ISSN: 2169-3536
As one of the most significant part of carbon neutralisation, the rapid growth of electric vehicle (EV) market in past few years has greatly expedited the transport electrification, which, however, has brought in new challenges to power system including isolated distribution network for commercial and industrial set up. Stochastic and complex EV behaviours would violate network permissible operation region and increase costs for system operators. To address these problems, a chance-constrained smart EV charging strategy in a DC microgrid (DCMG) supporting large office complex is proposed to minimize system cost from distribution network and fleet battery degradation cost from EVs providing ancillary service to the DCMG. When dealing with uncertainties from EVs, a Markov Chain Monte Carlo (MCMC) model is built to couple different parameters in load profiles and characterize the time series of likelihood of charging and discharging. A state-of-charge (SOC) space random walk method is then proposed to solve the resultant massive recursive probabilistic charging requirements. Based on that, a three-stage optimization framework is established to illustrate the work flow in system level. Numerical results verifying the effectiveness of the proposed method are also presented.
Cheng Y, Fan L, Rose J, et al., 2023, Real-World Subsynchronous Oscillation Events in Power Grids With High Penetrations of Inverter-Based Resources, IEEE TRANSACTIONS ON POWER SYSTEMS, Vol: 38, Pages: 316-330, ISSN: 0885-8950
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- Citations: 6
Nazir FU, Pal B, Jabr R, 2023, Affinely adjustable robust Volt/VAr control without centralized computations, IEEE Transactions on Power Systems, Vol: 38, Pages: 656-667, ISSN: 0885-8950
This paper proposes a completely non-centralized Volt/VAr control (VVC) algorithm for active distribution networks which are faced with voltage magnitude violations due to the high penetration of solar photovoltaics (PVs). The proposed VVC algorithm employs a two-stage architecture where the settings of the classical voltage control devices (VCDs) are decided in the first stage through a distributed optimization engine powered by the alternating direction method of multipliers (ADMM). In contrast, the PV smart inverters are instructed in the second stage through linear Q(P) decision rules - which are computed in a decentralized manner by leveraging robust optimization theory. The key to this non-centralized VVC routine is a proposed network partition methodology (NPM) which uses an electrical distance metric based on node Q-V 2 sensitivities for computing an intermediate reduced graph of the network, which is subsequently divided into the final partitions using the spectral clustering technique. As a result, the final network partitions are connected, stable, close in cardinality, contain at least one PV inverter for zonal reactive power support, and are sufficiently decoupled from each other. Numerical results on the UKGDS-95 bus system show that the non-centralized solutions match closely with the centralized robust VVC schemes, thereby significantly reducing the voltage violations compared to the traditional deterministic VVC routines.
Pal B, Guo Y, Jabr R, 2022, Model-free optimal control of inverter for dynamic voltage support, IEEE Transactions on Power Systems, ISSN: 0885-8950
Inverter-based resources (IBRs) are required to provide dynamic voltage support (DVS) during voltage dips to enhance the low-voltage ride-through capability. In this paper, a model-free control method is developed to achieve the optimal DVS (ODVS) without relying on the knowledge of grid parameters. Delving into the optimum trajectory of the ODVS problem, it is found that the current constraint and the maximum active power constraint of IBRs are both binding, or one of them is binding. This inspires us to search for the optimum in a closed-loop way by a perturb-and-observe (P&O)-based optimum seeking (OS) controller with either the power factor angle or the reactive current being the manipulated (perturbed) variable. The system is guaranteed to converge asymptotically to the optimum provided the stepsize sequence is diminishing and non-summable. The proposed model-free optimal control is finally implemented within a single-stage photovoltaic (PV) system, where dynamic simulations demonstrate the optimal and fast DVS performance. Moreover, the implementation strategy for other types of IBRs that are not self-protected by nature is also discussed.
Fan L, Miao Z, Shah S, et al., 2022, Real-World 20-Hz IBR Subsynchronous Oscillations: Signatures and Mechanism Analysis, IEEE TRANSACTIONS ON ENERGY CONVERSION, Vol: 37, Pages: 2863-2873, ISSN: 0885-8969
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- Citations: 1
Kampitsis G, Batzelis E, Antonis K, et al., 2022, A generalized phase-shift PWM extension for improved natural and active balancing of flying capacitor multilevel inverters, IEEE Open Journal of Power Electronics, Vol: 3, Pages: 621-634, ISSN: 2644-1314
The emergence of wide bandgap power devices has brought the attention back to the flying capacitor (FC) multilevel inverters witha large number of stages, in an effort to increase the power density by minimizing the passive components. The main challenge that such systemsface, particularly the ones based on high-frequency Gallium-Nitride devices and small-value ceramic capacitors, relate to the stringentrequirements for precise and fast capacitor balancing. Conventional natural balancing techniques exhibit poor settling times, while most improvednatural balancing methods are not easily scalable to more than five levels. The alternative of active balancing normally requires one isolatedsensor per FC which increases the overall system cost and footprint, or a single ac-side sensor that is more compact but calls for sophisticatedPWMs that again are not available for multiple levels. In this paper we introduce a generalized pulse width modulation (PWM) strategy based onthe phase-shift and carrier swapping principles for an arbitrary number of levels. We provide an easy and intuitive method for the extraction ofthe PWM pattern, the switching states, and their sequence. Simulations were carried out in Matlab/Simulink and experimental tests were conductedon a single-phase 7-level GaN inverter prototype. Not only is the extended PWM advantageous in natural balancing, but it also provides the rightzero switching states for ac-side FC sensing in active balancing
Guo Y, Pal BC, Jabr RA, et al., 2022, Global optimality of inverter dynamic voltage support, IEEE Transactions on Power Systems, Vol: 37, Pages: 3947-3957, ISSN: 0885-8950
This paper investigates the dynamic voltage support (DVS) of inverter-based resources (IBRs) under voltage sags to enhance the low-voltage ride-through performance. The DVS problem is formulated as a nonconvex optimization program that maximizes the positive-sequence voltage magnitude at the point of common coupling (PCC) subject to the current, active power, and synchronization stability constraints. Then, we perform the optimality analysis to explore the global optimum analytically. It is found that the unique global optimum has three scenarios/stages (S1S3), which depends on the specific relationship among grid voltage, grid strength, and physical limits of IBRs. The explicit closed-form solutions in S1 and S3 are derived, and the optimality conditions (an implicit solution) of S2 are provided, which guarantees the global optimality and enables the compatibility with fast real-time control. Finally, we implement the optimum with a grid-connected single-stage photovoltaic (PV) power plant by integrating a DVS controller. Dynamic simulations are carried out under different scenarios to test our proposal. The robustness against model errors is also discussed. Dynamic simulations are carried out under different scenarios to test our proposal and compare it with other existing methods.
Dozein M, Pal BC, Mancarella P, 2022, Dynamics of inverter-based resources in weak distribution grids, IEEE Transactions on Power Systems, Vol: 37, Pages: 3682-3692, ISSN: 0885-8950
This work presents the modelling fundamentals to study the dynamics of inverter-based resources (IBRs) in weak distribution grids and derive disturbance performance characteristics describing how they should behave under different conditions. More specifically, with respect to small-signal disturbances we study the possible voltage violations following frequency response from IBRs due to low system strength and also propose specific design requirements for IBR d-q current control to guarantee a stable response. In the context of large-signal disturbances, we highlight how active power-voltage control may not be effective due to a delay imposed by the physical features of the distribution network. Further, we mathematically discuss how IBR reactive power control could enhance its phase-locked loop stability. The proposed disturbance performance characteristics are then integrated into the IBR converter control via a novel voltage-priority reference generation strategy. Simulation results on a real Australian network show the efficacy of the proposed operational and control design requirements, and highlight possible unexpected active/reactive power interactions in weak distribution grids.
Ortiz-Villalba D, Llanos J, Munoz-Jadan Y, et al., 2022, Optimizing system operation with nadir considerations via simulations of detailed system dynamic responses, ELECTRIC POWER SYSTEMS RESEARCH, Vol: 212, ISSN: 0378-7796
Cifuentes N, Sun M, Gupta R, et al., 2022, Black-Box Impedance-Based Stability Assessment of Dynamic Interactions Between Converters and Grid, IEEE TRANSACTIONS ON POWER SYSTEMS, Vol: 37, Pages: 2976-2987, ISSN: 0885-8950
Mir AS, Singh AK, Pal BC, et al., 2022, Adequacy of lyapunov control of power systems considering modelling details and control indices, IEEE Transactions on Power Systems, Pages: 1-12, ISSN: 0885-8950
Kampitsis G, Batzelis E, Mitcheson PD, et al., 2022, A clamping circuit based voltage measurement system for high frequency flying capacitor multilevel inverters, IEEE Transactions on Power Electronics, Vol: 37, Pages: 1-1, ISSN: 0885-8993
In an era where high-frequency flying capacitor (FC) multilevel inverters (MLI) are increasingly gaining attention in energy conversion systems that push the boundaries of power density, the need for a compact, fast, and accurate FC voltage monitoring is also increasing. In this paper we designed and developed a new FC measurement system, based on precise sampling of the inverter switching node voltage, through a bidirectional clamping circuit. The deviation of FC voltages from their nominal values are extracted by solving a set of linear equations. With a single sensor per phase and no isolation requirements, as opposed to dozens of sensors in traditional FC monitoring, our approach results in significantly lower cost, complexity, and circuit-size. Detailed device-level simulations in LTspice and system-scale simulations in Matlab, validate the accuracy and speed of the proposed measurement system and the balancing strategy in steady state, abrupt load change and imbalance conditions. Experiments carried out in a 3-phase Gallium-Nitride 5-level inverter prototype, reveal a gain in precision and bandwidth that is more than 30 times that of conventional methods, at a fraction of their cost and footprint. The recorded performance renders the developed sensor an ideal solution for fast MLIs based on wide-bandgap technology
Kazmi SHH, Viafora N, Sorensen TS, et al., 2022, Offshore Windfarm Design Optimization Using Dynamic Rating for Transmission Components, IEEE TRANSACTIONS ON POWER SYSTEMS, Vol: 37, Pages: 1820-1830, ISSN: 0885-8950
Guo Y, Pal BC, Jabr RA, 2022, On the optimality of voltage unbalance attenuation by inverters, IEEE Transactions on Sustainable Energy, Vol: 13, Pages: 1492-1506, ISSN: 1949-3029
In this paper, we investigate the control of inverterbased resources (IBRs) for optimal voltage unbalance attenuation(OVUA). This problem is formulated as an optimization program under a tailored dq-frame, which minimizes the negativesequence voltage at the point of common coupling (PCC) subjectto the current, active power, synchronization stability, and feasibility constraints. The program is inherently nonconvex andintractable. So, to guarantee the optimality, a rigorous optimality analysis is performed by leveraging analytical optimization.The analysis is divided into two cases: full mitigation of VU andpartial attenuation of VU. For the former case, we directly solvethe original program since the resultant VU is immediately deducible. For the latter one, directly solving the problem becomesvery hard. Thus, we reformulate the program into an equivalentbut more tractable form under certain conditions, by which theanalytical optimum can be derived. It is found that the optimumtrajectory has three stages (O1–O3), depending on two criticalboundary conditions (C1 and C2). We implement the optimumwith a photovoltaic (PV)-storage system by developing an OVUAcontroller. The proposed approach is demonstrated by dynamicsimulations under different VU conditions and is compared withseveral existing practices. Finally, we discuss the extension of theproposed solution in a multi-IBR system.
Chakravarthi K, Bhui P, Sharma NK, et al., 2022, Real Time Congestion Management Using Generation Re-dispatch: Modeling and Controller Design, IEEE Transactions on Power Systems, Pages: 1-14, ISSN: 0885-8950
Lekshmi DJ, Rather ZH, Pal BC, 2021, A new tool to assess maximum permissible solar pv penetration in a power system, Energies, Vol: 14, ISSN: 1996-1073
With diminishing fossil fuel resources and increasing environmental concerns, large-scale deployment of Renewable Energy Sources (RES) has accelerated the transition towards clean energy systems, leading to significant RES generation share in power systems worldwide. Among different RES, solar PV is receiving major focus as it is most abundant in nature compared to others, complimented by falling prices of PV technology. However, variable, intermittent and non-synchronous nature of PV power generation technology introduces several technical challenges, ranging from short-term issues, such as low inertia, frequency stability, voltage stability and small signal stability, to long-term issues, such as unit commitment and scheduling issues. Therefore, such technical issues often limit the amount of non-synchronous instantaneous power that can be securely accommodated by a grid. In this backdrop, this research work proposes a tool to estimate maximum PV penetration level that a given power system can securely accommodate for a given unit commitment interval. The proposed tool will consider voltage and frequency while estimating maximum PV power penetration of a system. The tool will be useful to a system operator in assessing grid stability and security under a given generation mix, network topology and PV penetration level. Besides estimating maximum PV penetration, the proposed tool provides useful inputs to the system operator which will allow the operator to take necessary actions to handle high PV penetration in a secure and stable manner.
Nsengiyaremye J, Pal BC, Begovic MM, 2021, Low-cost communication-assisted line protection for multi-inverter based microgrids, IEEE Transactions on Power Delivery, Vol: 36, Pages: 3371-3382, ISSN: 0885-8977
Multi-inverter microgrid systems, particularly those with loop topology, offer higher power supply reliability and robustness compared to conventional radial distribution systems. In meshed systems, communication-less protection schemes have proved to be ineffective for multi-inverter microgrids due to bidirectional power flow, and limited and controlled fault currents generated by the voltage source converters interfacing the energy source to the network. This makes communicationassisted line protection schemes preferable for such systems despite the necessity for communication means. While these protection schemes are effective, their reliability depends much on the communication availability. This requires a back-up communication path in case the main one fails bringing up the cost issue that hinders their uptake. This paper proposes a novel and low-cost line protection based on directional blocking strategy that can operate as a main as well as a back-up protection to any protection scheme using communication means between the line terminals. As the main, it requires low-bandwidth communication system. As a back-up, it would share the same communication means with the main one and use those of the healthy lines when the faulted lines fails. Thus saving the cost of back-up communication system.
Liu Y, Singh AK, Zhao J, et al., 2021, Dynamic state estimation for power system control and protection, IEEE Transactions on Power Systems, Vol: 36, Pages: 5909-5921, ISSN: 0885-8950
Dynamic state estimation (DSE) accurately tracks the dynamics of a power system and provides the evolution of the system state in real-time. This paper focuses on the control and protection applications of DSE, comprehensively presenting different facets of control and protection challenges arising in modern power systems. It is demonstrated how these challenges are effectively addressed with DSE-enabled solutions. As precursors to these solutions, reformulation of DSE considering both synchrophasor and sampled value measurements and comprehensive comparisons of DSE and observers have been presented. The usefulness and necessity of DSE based solutions in ensuring system stability, reliable protection and security, and resilience by revamping of control and protection methods are shown through examples, practical applications, and suggestions for further development.
Pawar B, Batzelis E, Chakrabarti S, et al., 2021, Grid-forming control for solar PV systems with power reserves, IEEE Transactions on Sustainable Energy, Vol: 12, Pages: 1947-1959, ISSN: 1949-3029
This paper presents a grid-forming control (GFC) scheme for two-stage photovoltaic (PV) systems that maintains power reserves by operating below the maximum power point (MPP). The PV plant in GFC mode behaves like a voltage source that supports the grid during disturbances in full or limited grid-forming mode as per the reserve availability. This is a model-free method that avoids the estimation of MPP power in real-time commonly done in the literature, which makes it simpler and more reliable. The proposed control also features an enhanced current limitation scheme that guarantees containment of the current overshoots during faults, which is not trivial in voltage-sourced GFC inverters. A thorough investigation is done, exploring various generation mixtures of synchronous machines (SM), GFC and grid-following (GFL) inverters, and all common disturbances, e.g., load change, faults and irradiance transients. The results show very favorable dynamic performance by the GFC inverters, far superior to GFL inverters and directly comparable to SMs. It is found that replacing SMs with GFC inverters may improve the frequency profile and terminal voltage during disturbances, despite losing out in the mechanical inertia and the strict inverter overcurrent limits.
Hatziargyriou N, Milanovic J, Rahmann C, et al., 2021, Definition and classification of power system stability - revisited & extended, IEEE Transactions on Power Systems, Vol: 36, Pages: 3271-3281, ISSN: 0885-8950
Since the publication of the original paper on power system stability definitions in 2004, the dynamic behavior of power systems has gradually changed due to the increasing penetration of converter interfaced generation technologies, loads, and transmission devices. In recognition of this change, a Task Force was established in 2016 to re-examine and extend, where appropriate, the classic definitions and classifications of the basic stability terms to incorporate the effects of fast-response power electronic devices. This paper based on an IEEE PES report summarizes the major results of the work of the Task Force and presents extended definitions and classification of power system stability.
Liu J, Singh R, Pal B, 2021, Distribution system state estimation with high penetration of demand response enabled loads, IEEE Transactions on Power Systems, Vol: 36, Pages: 3093-3104, ISSN: 0885-8950
Demand-side operations incentivize utility customers to take part in various grid services. A demand response enabled load (DREL) is a flexible grid asset that schedules electricity consumption in response to a time-of-use (TOU) energy price. Consequently, its energy profile differs from that of a conventional load that is insensitive to price. This difference may cause new challenges for distribution system state estimation (DSSE). It is well known that DSSE often needs to use pseudo-measurements based on historic load profiles to increase system observability. However, historic profiles of conventional loads are not representative of DREL behaviors. The inaccuracy impacts DSSE results and other DSSE-dependent operations. In this paper, we propose an online pseudo-measurement generation approach for DSSE with DRELs. We formulate an optimization model to represent DRELs self-adjusting actions. Sampling-based stochastic optimization techniques are proposed to account for uncertainties in DRELs. A set of representative DREL behavior data corresponding to the samples are used to characterize DREL pseudo-measurements. Case studies with modified IEEE 123-bus test system verify the validity of the proposed work.
Cifuentes N, Pal BC, 2021, A new approach to the fault location problem: using the fault’s transient intermediate frequency response, IEEE Open Access Journal of Power and Energy, Vol: 8, Pages: 510-521, ISSN: 2687-7910
The fault location problem has been tackled mainly through impedance-based techniques, the travelling wave principle and more recently machine learning algorithms. These techniques require both current and voltage measurement. In the case of impedance-based methods they can provide multiples solutions. In the case of the travelling wave approach it usually requires high sampling frequency measurements together with sophisticated identification algorithms. Machine learning techniques require training data and re-tuning for different grid topologies. This paper proposes a new fault location method based on the fault’s transient intermediate frequency response of the system immediately after a fault occurs. The transient response is characterized by the travelling wave phenomenon together with intermediate frequencies of oscillation, which are dependent on the faulted section and the fault location. In the proposed fault location solution, an offline methodology identifies these intermediate frequencies and their dependency on the fault location is fitted using a polynomial regression. The online fault location is performed using those polynomial regressions together with voltage measurements from the system and simple signal processing techniques. The full method is tested with an EMT simulation in PSCAD, using the exact frequency dependent model for underground cables.
Zhao J, Netto M, Huang Z, et al., 2021, Roles of dynamic state estimation in power system modeling, monitoring and operation, IEEE Transactions on Power Systems, Vol: 36, Pages: 2462-2472, ISSN: 0885-8950
Power system dynamic state estimation (DSE) remains an active research area. This is driven by the absence of accurate models, the increasing availability of fast-sampled, time-synchronized measurements, and the advances in the capability, scalability, and affordability of computing and communications. This paper discusses the advantages of DSE as compared to static state estimation, and the implementation differences between the two, including the measurement configuration, modeling framework and support software features. The important roles of DSE are discussed from modeling, monitoring and operation aspects for today's synchronous machine dominated systems and the future power electronics-interfaced generation systems. Several examples are presented to demonstrate the benefits of DSE on enhancing the operational robustness and resilience of 21st century power system through time critical applications. Future research directions are identified and discussed, paving the way for developing the next generation of energy management systems and novel system monitoring, control and protection tools to achieve better reliability and resiliency.
Karbouj H, Rather Z, Pal B, 2021, Adaptive voltage control for large scale solar PV power plant considering real life factors, IEEE Transactions on Sustainable Energy, Vol: 12, Pages: 990-998, ISSN: 1949-3029
This paper presents an accurate and realistic estimation of reactive power capability of solar photovoltaic (PV) inverters considering ambient temperature, solar irradiance, and terminal voltage. Based on the accurate estimation of reactive power capability, a self-adaptive voltage controller is proposed to enable solar PV power plant participation in voltage control ancillary service. The proposed accurate and realistic estimation has revealed the possibility of solar PV power plant failing to comply with grid code requirements under extreme weather conditions. On the other hand, the proposed control strategy has shown significantly better effectiveness to utilise solar PV inverter capability, and provide better voltage control support service to the grid.
Pawar B, Saikat C, Batzelis E, et al., 2021, Grid-Forming Control for Solar PV Systems with Real-Time MPP Estimation, IEEE PES GM
Ul Nazir F, Pal BC, Jabr RA, 2021, Approximate Load Models for Conic OPF Solvers, IEEE-Power-and-Energy-Society General Meeting (PESGM), Publisher: IEEE, ISSN: 1944-9925
Ali H, Pal B, 2021, Model order reduction of multi-terminal direct-current grid systems, IEEE Transactions on Power Systems, Vol: 36, Pages: 699-711, ISSN: 0885-8950
This paper proposes a methodology to develop a linear low-order model of a multi-terminal direct-current (MTDC) system connected to practically-sized offshore wind farm systems. The method individually linearizes the model of wind farm systems and subsequently performs model order reduction (MOR) using iterative rational Krylov algorithm (IRKA). This is, therefore, a modular approach and expandable to any number of wind farm connections. On the other hand, the model order and non-linearity of other components are retained. Effectiveness of the proposed method is demonstrated on an MTDC system connected to two large-scale wind farm models by comparing the responses obtained from the full order model (FOM) and reduced order model (ROM). From the simulation studies, it can be seen that the ROM obtained from proposed method is able to maintain high degree accuracy of FOM responses at a much faster simulation time, and hence this can help power system operation planning. Various control functionalities and strategies, different operating conditions and faults of the MTDC system are also considered to investigate robustness of the proposed method.
Yu Y, Nduka O, Pal B, 2020, Smart control of an electric vehicle for ancillary service in DC microgrid, IEEE Access, Vol: 8, Pages: 197222-197235, ISSN: 2169-3536
This article presents a two-stage framework for optimal Electric Vehicle (EV) charging/discharging strategy for DC Microgrid (MG) with Distributed Generators (DGs). A multi-objective optimisation task aimed at minimising system losses and EV battery degradation with Vehicle-to-Grid (V2G) peak shaving service has been realised. This coordinated EV integration into the DCMG was formulated as a directed weighted single source shortest path problem that was solved using a modified Dijkstra’s algorithm. The weights of the edges were obtained using primal-dual interior point method. The proposed framework has been experimentally verified using simulations with a test DCMG system with practical IEEE European low voltage test feeder load profiles. Results show realisation of peak demand shaving leveraging on EV discharge with minimal on-board battery degradation as well as reduced system losses. It is also shown that the proposed two-stage framework reduces the battery state of charge (SOC) sample space requirements in the analysis, thus, reducing the computational burden.
Chen Y, Mazhari SM, Chung CY, et al., 2020, Rotor angle stability prediction of power systems with high wind power penetration using a stability index vector, IEEE Transactions on Power Systems, Vol: 35, Pages: 4632-4643, ISSN: 0885-8950
This paper proposes a methodology for predicting online rotor angle stability in power system operation under significant contribution from wind generation. First, a novel algorithm is developed to extract a stability index (SI) that quantifies the margin of rotor angle stability of power systems reflecting the dynamics of wind power. An approach is proposed that takes advantage of the machine learning technique and the newly defined SI. In case of a contingency, the developed algorithm is employed in parallel to find SIs for all possible instability modes. The SIs are formed as a vector and then applied to a classifier algorithm for rotor angle stability prediction. Compared to other features used in state-of-the-art methods, SI vectors are highly rec-ognizable and thus can lead to a more accurate and reliable prediction. The proposed approach is validated on two IEEE test systems with various wind power penetration levels and compared to existing methods, followed by a discussion of results.
Ul Nazir F, Pal B, Jabr R, 2020, Approximate load models for conic OPF solvers, IEEE Transactions on Power Systems, Vol: 36, Pages: 549-552, ISSN: 0885-8950
The global optimum of the optimal power flow (OPF) problem can be sought in various practical settings by adopting the conic relaxations, such as the second order cone programs (SOCPs) and semi-definite programs (SDPs). However, the ZIP (constant impedance, constant current, constant power) and exponential load models are not directly amenable with these conic solvers. Thus, these are mostly treated as constant power loads in the literature. In this letter, we propose two simple methods to approximate these static loads with good accuracy. The proposed methods perform much better than the traditional constant power approximation.
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