Constant Impedance Load Research Articles

Analysing a grid-forming storage hub for an offshore platform cluster supplied by wind energy

Abstract This paper performs an analysis of the electrification of an of-the-grid offshore oil and gas cluster of six platforms by means of a wind farm combined with a hydrogen energy hub. The latter, whose model is made publicly available, contains a grid-forming battery system and grid-following electrolysis and fuel cells units. State-of-the-art aerodynamic simulations are used for representing the wind farm power output, which encompasses wake losses and correlated wind fuctuations between turbines arising from farm-scale turbulence. One of the offshore platforms is represented by a detailed publicly available model named LEOGO. The other five platforms are represented as aggregated mixes of constant power and constant impedance loads. The computer simulations presented in the paper provide valuable insights into furthering the design and optimization of the hub concept. These insights include, among others, sizing of batteries depending on maximum ramp rates of fuel cells and electrolysers, identifying and mitigating instabilities induced by interactions among power electronic converters, and evaluating the consequences for the converters when those contribute with voltage support at the hub.

Integration of Distributed Generations and electric vehicles in the distribution system

Power quality challenges are a major problem these days because of the significant increase in load demand and the existence of various reasons for disruptions in the distribution system. A voltage sag or a decrease in the magnitude of the line voltage can be brought on by rapid fluctuations in load or distribution system issues. Enhancing the grid current profile, reducing grid voltage sag, and improving other performances can all be achieved through the combination of electric vehicles with distribution generation systems. In this paper, the integration of Distributed Generation with Electric Vehicles in the distribution system has been done to enhance system performances such as true power loss index, imaginary power loss index, voltage deviation index, short circuit current index, cost function, and environmental impact reduction index for 16 bus distribution system in constant impedance, constant current, and constant power load models, or ZIP load models through proper location, sizing, coordinated controlling, and types of Distributed Generation and Electric Vehicle pairs for both charging and discharging modes by adopting Hybrid Genetic Algorithm - Monte Carlo Simulation optimization methodologies. This study's primary goal is to determine the optimal distribution generation and electric vehicle pairing to improve the aforementioned parameters, which will assist researchers in their future planning. Researchers, industry professionals, scientists, and individuals working with Distributed Generation and Electric vehicles in the smart grid will find this statement to be of great use.

WITHDRAWN: Robust voltage regulation of DC-DC buck converter with ZIP load via an energy shaping control approach

ZIP loads (the parallel combination of constant impedance loads, constant current loads and constant power loads) exist widely in power system. In order to stabilize buck converter based DC distributed system with ZIP load, an adaptive energy shaping controller (AESC) is devised in this paper. Firstly, based on the assumption that the lumped disturbances are known, a full information controller is designed in the framework of the port Hamiltonian system via energy shaping technique. An obvious merit is that it is PI-type controller, which is easy to implement in practical application. Besides, using mathematical deductive method, an estimation of the domain of attraction is given to ensure the strict stability. Furthermore, to eliminate the influence of parameter perturbations on the system, a disturbance observer is proposed to reconstruct the lumped disturbances and then the estimated terms are introduced to above controller to form an adaptive control scheme. In addition, the strict stability analysis of the closed-loop system is given. Lastly, the simulation and experiment results are presented for assessing the designed controller.

Nodal price-based demand response management via orderly time-of-use strategy for an unbalanced isolated microgrid considering voltage stability constraints

This paper scrutinizes the compatibility of voltage stability criteria with price-based demand response management (DRM) for a large-scale isolated microgrid considering severe dependency of constant-impedance loads (CILs) on nodal voltage magnitude. Meanwhile, a hybrid nodal pricing (HNP) scheme is developed to determine clearing prices for resources and time-of-use (TOU) tariffs for price-responsive loads. The proposed framework is composed of three ingredients including two optimization molds with the objective of actual net profit and recast operation expense sequentially solved in an iterative process together with one pay-off module. The energy schedules, unbalanced voltages and nodal prices are determined considering intermittency of renewable resources, unbalances, circuit limitations, and reactive power requirements. Two bus and line voltage stability indices as well as voltage profile management criterion are used to prevent voltage instability. Thus, load profile is corrected such that voltage stability can be upheld as well. The proposed method is implemented via a modified CIGRE benchmark. The simulation results demonstrate that load factor improves at least 4.30% under desirable stability margins. Moreover, total energy loss and line voltage unbalance rate (LVUR) decrease at least 1.02% and 10.03% respectively.

Time domain modeling of constant power loads for electromagnetic transient simulations

This paper proposes a dynamic constant power load offering constant active and reactive power and constant power factor suitable for electromagnetic transient simulations. The proposed model is agnostic to the frequency components of the system because it is developed in the time domain. The proposed model returns current and voltage quantities imitating the behavior of either inductive or capacitive loads. The model is customized so that it can be solved using readily available numeric solvers, such as branch-and-bound algorithms. The bottleneck of the computational speed depends on the numeric solver that is employed to solve the proposed model and the hardware used to process the computations. Also, convergence to a solution (an issue associated with every solver) is more likely to occur if the optimum initial solution is provided, which is left for future research. The model is validated using constant impedance load data. In this work, 2500 data points were simulated, and the output shows that the proposed model is accurate, and any approximations can be attributed to the adopted numerical differentiation method. The model is computationally exhaustive; thus, its application is limited to small systems.

Design of Dynamic Voltage Restorer for Power Quality Improvement

Solutions for customers with delicate loads and quick voltage regulation are essential. Protect important loads from supply-side voltage disturbances with a power electronic converter-based Dynamic Voltage Restorer (DVR). In the case of severe sag and swell, DVR is a well-known, low-cost therapy option. On the basis of its maximum voltage injection and active power contribution, a DVR's mitigation ability is determined. Standard DVRs use batteries as their DC input, but batteries are cumbersome, expensive, and hazardous to dispose of after they've been used. This limits compensation for DVRs. It is recommended to increase the DVR's VA rating by 1.5 times by increasing the DC connection voltage to 1.5 times the micro grid voltage regulation and quality improvement methods are proposed in this study. As a series voltage compensator, these solutions incorporate a Dynamic Voltage Restorer (DVR) for regulation, quality improvement, and reduction of harmonic distortion. Continuous adjustment of the DVR output voltage is proposed to reduce harmonic distortions while minimizing network bus voltage changes. As a result of this strategy, the peak demand voltage loss is compensated for. In constant impedance loads, voltage rise reduces network demand, resulting in lower branch currents and losses

Microgrids control: AC or DC, that is not the question

In these lecture notes, we delve into the models of the most commonly used DC-DC power converters: namely, the buck converter and the boost converter. Furthermore, we derive models for a DC microgrid consisiting of multiple buck and/or boost converters interconnected via (dynamic) resistive-inductive power lines and supplying the so-called ZIP loads, which are characterized by the parallel combination of constant impedance (Z), current (I), and power (P) load components. Furthermore, we introduce the primary control objectives in DC microgrids, focusing on voltage regulation and current sharing. Finally, we explore the most advanced control techniques to achieve these objectives. Importantly, these lecture notes are not intended to advocate total replacement of Alternating Current (AC) power systems with their Direct Current (DC) counterparts, but rather aim to offer a balanced perspective between them, acknowledging the historical dominance of AC power systems while underscoring the contemporary relevance of DC microgrids, which, with their inherent advantages, represent a viable complement to the existing infrastructure, fostering innovation and resilience in modern power networks.

Network dynamics in hybrid microgrid and its implications on stability analysis

Abstract Dynamic load is one of the significant factor affecting the stability of hybrid microgrid (MG), owing to their frequency and voltage dependency. As compared with the static load, a small variation in voltage or frequency significantly influences the stability of MG having dynamic load. Therefore, it necessitates considering the dynamics of load for stability analysis of an MG. Moreover, the stability issues become more critical for the islanded operation. This paper investigates the small signal (SS) stability of a hybrid MG utilizing composite load model (CLM) to include the load dynamics. This paper also investigates the critical universal droop control parameters and other internal controller parameters that influence MG stability. Eigenvalue analysis is used to identify the respective stability domain of different control parameters. The effectiveness of the proposed approach is tested by comparing the dynamics of CLM with constant power and impedance load. In addition, a memetic algorithm and SQP-GS is used to find the optimal values of different key parameters. The simulation results confirmed the effectiveness of the proposed SS dynamic model of hybrid MG and the efficacy of the optimization algorithm for tuning control parameters, which improved the dynamic performance of the hybrid MG.

“Adaptive virtual synchronous generator control using optimized bang-bang for Islanded microgrid stability improvement”

In this paper, a virtual synchronous generator (VSG) controller is applied to a hybrid energy storage system (HESS) containing a battery energy storage system and supercapacitor storage system for maintaining the frequency stability of an isolated microgrid. The microgrid contains a photovoltaic generation system and a diesel generator in addition to the HESS and two constant impedance loads that are fed through a medium voltage radial feeding system. The adaptive virtual inertia constant (H) with constant virtual damping coefficient (D) based on ‘ bang-bang’ control for the microgrid’s frequency stability enhancement is investigated and compared with the constant parameter VSG. In addition, the bang-bang control is modified to adapt the D beside the adaptive H, and the system response is investigated and compared with the conventional adaptive H technique. The VSG parameters are evaluated based on two different methods. The first is a computational method based on the simplified small signal stability analysis, while the other is based on an optimization method using two different objective functions and the particle swarm optimization technique. This paper also investigates the superiority of the proposed technique compared to other techniques in enhancing frequency stability, accelerating steady-state frequency restoration, and reducing the energy requirement of the HESS. The required power from the HESS is shared between the two energy storages using the low pass filter technique so as to reduce battery peak current.

Investigating effect of various time varying load models in grid connected microgrid system integrated with renewables and cogeneration units

ABSTRACT The optimal allocation of sources considering voltage-dependent load models is essential as the power consumption of the loads is sensitive to voltage magnitude. In this paper, optimal allocation of microgrid system with cogeneration units, renewable energy sources (RES), shunt capacitors and heat boiler are determined for constant, residential, industrial, commercial and mixed load models. The cost, emission, energy loss, voltage deviation and voltage stability values for each load model is determined using particle swarm optimisation (PSO) integrated fuzzy max–min approach while the uncertainties in RES are taken into account. Results demonstrate that the cost, energy loss and voltage deviation values are maximum for constant power (CP) load model compared with other load models. Furthermore, the system with constant impedance (CZ) load achieves maximum loading capability than with other types of constant loads. The proposed method is validated on 33-bus grid-connected microgrid system with all the load models.

Measurement-based ZIP load modelling using opposition based differential evolution optimization

With the large integration of distributed generations, power grids are on the verge of instability if the generation and load side is not synchronized properly. To predict the load, a proper load model should be developed for the purpose of power system monitoring. The ZIP load model is considered in this work due to its simplicity. The parameter of the ZIP load corresponding to constant power, constant impedance, and constant current load must be estimated accurately for predicting the load behavior. In this paper, the measurements are being compared with the estimated value for estimating the load parameters using a suitable parameter tuning method. For ZIP load modeling Measurement-based parameter estimation is applied. In this paper, measurements are simulated by statistically infusing the Gaussian noise into the true value (obtained from the load flow study). The parameter-tuning algorithm iteratively feeds the error discovered from the comparison to determine the optimal solution. In this paper, Opposition-based differential evolution optimization (ODEO) is being proposed as a parameter tuning method for estimating the load parameters from the measurements collected at a given load bus. Measurement of the ZIP load is collected at bus 30 of the NE 39 Bus system after applying step disturbance of voltage at generator 4. The proposed ODEO method is validated and compared with the other tuning methods, like Particle Swarm optimization (PSO) and Grey Wolf optimization (GWO). The proposed ODEO method has a better performance as compared to PSO and GWO.

On the stability of distributed secondary control for DC microgrids with grid-forming and grid-feeding converters

This paper investigates the stability problem of a single-bus DC microgrid with mixed grid-forming/grid-feeding converters and the constant impedance, constant current, and constant power (ZIP) loads. Considering the different output properties of grid-forming and grid-feeding converters, distributed secondary controllers with mixed V–I droop and I–V droop controllers are designed to achieve accurate bidirectional current sharing and voltage regulation. As few converters have access to the information of the common bus, an observer is designed for each local controller to estimate the bus voltage. Then, the observer state is used to generate voltage correction term in the feedback loop, which gets potential faster regulation compared with the existing approaches that use pinning gains. Based on the rank-one perturbation analysis, a stability criterion of DC microgrid is given for the case of ZI load, where global voltage regulation and current sharing are guaranteed. Then, the stability criterion is extended to the case of ZIP load, where local stability of the DC microgrid is guaranteed. Both numerical examples and experimental tests are given to verify the effectiveness of the theoretical results.

A Power Flow Calculation Method Considering High-order Load Models

Given the popularity of new energy and the connection between large power electronic equipment and power system, the operation of power system becomes more complex and requires higher accuracy of power flow calculation. Therefore, a power flow calculation method considering high-order load model is proposed. On the basis of the Newton-Raphson method, when considering the load voltage characteristics, it is necessary to change the variables in the Newton-Raphson method power flow. Therefore, the established polynomial load model is introduced into the Newton-Raphson method, and the effect becomes more obvious with the increase of the order. Finally, constant power, constant current, constant impedance load and fifth order load models are tested in IEEE14-bus system respectively to verify the good accuracy and robustness of the proposed method.

Optimal Adaptive Droop Design via a Modified Relaxation of the OPF

The ever-increasing penetration of renewable energy resources (RESs) in power distribution networks has brought, among others, the challenge of maintaining the grid voltages within the secure region. Employing droop voltage regulators on the RES’s inverters is an efficient and low-cost solution to reach this objective. However, fixing droop parameters or optimizing them only for overvoltage conditions does not provide the required robustness and optimality under changing operating conditions. In this article, a convex optimization approach is proposed for reconfiguring <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V$ </tex-math></inline-formula> droop regulators during online operation. The objective is to minimize power curtailment, power losses, and voltage deviation subject to electrical security constraints. This enables to optimally operate the grid with high RES penetration under variable conditions while preserving electrical security constraints (e.g., current and voltage limits). As a first contribution, a mixed-integer linear model of the droop characteristics is developed. According to this model, a droop-regulated generation unit is represented as a constant-power generator in parallel with a constant-impedance load. As a second contribution, a modified augmented relaxed optimal power flow (MAR-OPF) formulation is proposed to guarantee that the electrical security constraints are respected in the presence of constant-impedance loads in the network. Sufficient conditions for the feasibility of the MAR-OPF solution are provided. Those conditions can be checked a priori and are valid for several real distribution networks. Furthermore, an iterative approach is proposed to derive an approximate solution to the MAR-OPF that is close to the global optimal one. The performance of the MAR-OPF approach and the accuracy of the proposed model are evaluated on standard 34- and 85-bus test networks.

Increasing the region of attraction in DC microgrids

Based on the port-Hamiltonian framework, this paper proposes a novel control scheme for stabilising the voltage in DC networks affected by (i) unknown ZIP-loads, i.e., nonlinear loads consisting of the parallel combination of constant impedance (Z), current (I) and power (P) load types, and (ii) unknown (but bounded) time-varying disturbances. Differently from the results existing in the literature, where restrictive (sufficient) conditions on the load parameters, voltage trajectory and voltage reference are assumed to be satisfied, this is the first paper (to the best of our knowledge) proposing a controller that relaxes such conditions and guarantees the exponential stability of the desired equilibrium point, whose region of attraction can be increased by simply tuning the control gains. In the case the network is affected by unknown time-varying disturbances, local input-to-state stability (l-ISS) is ensured. Furthermore, if non-ideal P-loads are considered, excluding the unrealistic possibility that the load absorbs infinite current when the voltage approaches zero, the aforementioned stability results hold globally.

Analytic solution to swing equations in power grids with ZIP load models.

This research pioneers a novel approach to obtain a closed-form analytic solution to the nonlinear second order differential swing equation that models power system dynamics. The distinctive element of this study is the integration of a generalized load model known as a ZIP load model (constant impedance Z, constant current I, and constant power P loads). Building on previous work where an analytic solution for the swing equation was derived in a linear system with limited load types, this study introduces two fundamental novelties: 1) the innovative examination and modeling of the ZIP load model, successfully integrating constant current loads to augment constant impedance and constant power loads; 2) the unique derivation of voltage variables in relation to rotor angles employing the holomorphic embedding (HE) method and the Padé approximation. These innovations are incorporated into the swing equations to achieve an unprecedented analytical solution, thereby enhancing system dynamics. Simulations on a model system were performed to evaluate transient stability. The ZIP load model is ingeniously utilized to generate a linear model. A comparison of the developed load model and analytical solution with those obtained through time-domain simulation demonstrated the remarkable precision and efficacy of the proposed model across a range of IEEE model systems. The study addresses the key challenges in power system dynamics, namely the diverse load characteristics and the time-consuming nature of time-domain simulation. Breaking new ground, this research proposes an analytical solution to the swing equation using a comprehensive ZIP model, without resorting to unphysical assumptions. The close-form solution not only assures computational efficiency but also preserves accuracy. This solution effectively estimates system dynamics following a disturbance, representing a significant advancement in the field.

Optimal charging of electric vehicles for cost minimization in re-configurable active distribution network considering conservation voltage reduction

ABSTRACT This paper presents a coordinated plug-in electric vehicle (PEV) charging scheme in the presence of conservation voltage reduction (CVR) with a possibility of network re-configuration in a half-hourly based tariff environment. The information of the arrived PEVs in time slot “t” are gathered in a centralized manner, including initial and desired state of charge (SOC), rating of PEV charger, and arrival and departure times. In addition, the load forecasted data of all the nodes are also collected. A linear programming (LP) based intelligent charging framework is developed whereby an optimal global solution for EV charging is obtained that tends to minimize the charging cost, and the schedule is dispatched to all the PEVs. At first, PEV charging cost is minimized using the existing time of use (TOU) based tariff structure. After that, the charging schedule is carried out under the same TOU tariff structure but on a re-configured network with and without CVR deployment. The proposed charging strategy through re-configuration of the distribution network under CVR is implemented on a modified IEEE-33 bus test system. The results obtained from the simulation show that the proposed PEV charging scheme through network re-configuration under a TOU-based tariff structure considerably reduces the charging cost by 55.8% compared to uncoordinated charging. However, a 50.2% cost reduction is achieved in the absence of network re-configuration. Therefore, the proposed PEV charging through network re-configuration under a TOU-based tariff is more effective in cost reduction. Further, investigations were carried out on EV charging through network re-configuration under TOU-based tariff and CVR deployment. It was observed that the PEV charging cost was reduced by 51.3% compared to uncoordinated charging, where higher cost benefits were obtained through the reduction in energy consumed by constant impedance loads. It has been further observed that the proposed scheme effectively flattens the load profile by clipping the peak and filling the valley load.

A Unified Passivity-Based Framework for Control of Modular Islanded AC Microgrids

Voltage and frequency control in an islanded ac microgrid (ImG) amounts to stabilizing an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> unknown ImG equilibrium induced by loads and changes in topology. This article puts forth a unified control framework, which, while guaranteeing such stability, allows for modular ImGs interconnecting multiple subsystems, that is, dynamic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$RLC$ </tex-math></inline-formula> lines, nonlinear constant impedance, current, power (ZIP) and exponential (EXP) loads, and inverter-based distributed generation units (DGUs) controlled with different types of primary controllers. The underlying idea of the framework is based on the equilibrium-independent passivity (EIP) of the ImG subsystems, which enables stability certificates of ImG equilibria without explicit knowledge of these equilibria. In order to render DGUs EIP, we propose a decentralized controller synthesis algorithm based on port-Hamiltonian systems (PHSs). We also show that EIP, being the key to stability, provides a general framework, which can embrace other solutions available in the literature. Furthermore, we provide a novel argument based on LaSalle’s theorem for proving asymptotic voltage and frequency stability. Finally, we analyze the impact of actuator saturation on the stability results by exploiting the inherent EIP properties of the PHS DGU model. Theoretical findings are backed up by realistic simulations based on the medium-voltage CIGRE benchmark network.

Impact of Passive-Components’ Models on the Stability Assessment of Inverter-Dominated Power Grids

Power systems are experiencing some profound changes, which are posing new challenges in many different ways. One of the most significant of such challenges is the increasing presence of inverter-based resources (ibrs), both as loads and generators. This calls for new approaches and a wide reconsideration of the most commonly established practices in almost all the levels of power systems’ analysis, operation, and planning. This paper focuses specifically on the impacts on stability analyses of the numerical models of power system passive components (e.g., lines, transformers, along with their on-load tap changers). Traditionally, loads have been modelled as constant power loads, being this both a conservative option for what concerns stability results and a computationally convenient simplification. However, compared to their counterparts above, in some operating conditions ibrs can effectively be considered real constant power loads, whose behaviour is much more complex in terms of the equivalent impedance seen by the network. This has an impact on the way passive network components should be modelled to attain results and conclusions consistent with the real power system behaviour. In this paper, we investigate these issues on the ieee14 bus test network. To begin with, we assess the effects of constant-power and constant-impedance load models. Then, we replace a transmission line with a dc line connected to the network through two modular multilevel converters (mmcs), which account for the presence of ibrs in modern grids. Lastly, we analyse how and to which extent inaccurate modelling of mmcs and other passive components can lead to wrong stability analyses and transient simulations.

Consensus-Based Current Sharing and Voltage Balancing in DC Microgrids With Exponential Loads

In this work, we present a novel consensus-based secondary control scheme for current sharing and voltage balancing in dc microgrids (DCmGs), composed of distributed generation units (DGUs), dynamic RLC lines, and nonlinear ZIE (constant impedance, constant current, and exponential) loads. Situated atop a primary voltage control layer, our secondary controllers have a distributed structure and utilize information exchanged over a communication network to compute necessary control actions. Besides showing that the desired objectives are always attained in steady state, we deduce sufficient conditions for the existence and uniqueness of an equilibrium point for constant power loads--E loads with zero exponent. Our control design hinges only on the local parameters of the generation units, facilitating plug-and-play operations. We provide a voltage stability analysis and illustrate the performance and robustness of our designs via simulations. All results hold for arbitrary, albeit connected, mG and communication network topologies.