Virtual Resistances Research Articles

VSG Sequence Impedance Modeling and Stability Analysis of Dead-Beat Control

Virtual Synchronous Generator uses dead-beat predictive control in the voltage and current loop to improve the dynamic response speed of the system, but the presence of zero-order hold and computation time can lead to system instability. To address this issue, this paper adopts an improved dead-beat predictive control strategy for VSG. This is achieved by linear interpolation to forward predict voltage-current reference values to reduce the impact of delay, while introducing error compensation coefficients to enhance the stability of the voltage-current inner loop of VSG. The selection of error compensation coefficients is based on closed-loop impulse response functions. A harmonic linearization method is used to construct a complete sequence impedance model of VSG, and it's stability is analyzed. The results indicate that VSG's negative sequence impedance exhibits instability in the low-frequency range. To address this, a method of introducing a virtual resistor into VSG is proposed to improve stability. By constructing a sequence impedance model of VSG that includes virtual resistance, the variations in system stability under different virtual resistances and grid impedances are analyzed. The effectiveness of the proposed method is verified by building a VSG model.

State-of-charge balancing strategy of battery energy storage units with a voltage balance function for a Bipolar DC mircrogrid

For an islanded bipolar DC microgrid, a special problem of making the better compromise between a state-of-charge (SOC) balance among multiple battery energy storage units (MBESUs) in positive and negative polar, and bus voltage balance, should be considered. In order to solve this problem, three kinds of the simplified load equivalent circuits on the different operation status of voltage balancer (VB) are established; based on these equivalent circuits, the SOC unbalance mechanism is analyzed and the rules of SOC deviation and voltage unbalance factor are summarized, which are influenced by micro-source and load changing; then a SOC automatic balancing strategy among MBESUs with a voltage balance function is proposed in this paper. The proposed controlling strategy takes into consideration the energy flow relationship under various working conditions; with the aim of controlling the equilibrium time and energy flow direction of SOC, creates a SOC balancing power bridge with the SOC deviation as the main control variable; adopts the adaptive virtual resistance algorithm for both positive and negative BESUs according to the variation rule of the SOC deviation. When the SOC deviation is significant, according to the net power difference of the system, the values of the virtual resistances can be adaptively adjusted to alter the operation mode of BESUs and the VB control strategy is also adjusted so as to ensure the stable running of the system and accelerate the SOC balancing speed via maximizing the balancing power by VB. In order to decrease the voltage unbalance on SOC balancing, apart from adding bus voltage recovery control to the positive and negative batteries, the virtual resistances are related to the SOC deviation when the SOC deviation is slight. The simulation results demonstrate that the control strategy proposed in this paper can quickly realize SOC balancing when the SOC deviation is significant, has superior equilibrium performance as load and micro-source power varying when the SOC deviation is slight, and is also feasible in decreasing the bus voltage unbalance.

Accurate power sharing for islanded DC microgrids considering mismatched feeder resistances

Accurate load power sharing and bus voltage regulation are two critical control objectives for ensuring power quality and reliable operation of DC microgrids. Although regulating the DC Bus voltage can be achieved by adopting an external secondary control loop, inaccurate load power/current sharing among converters is a prominent issue due to feeder resistances mismatch. This can lead to undesired overloading of converters, triggering over-current protection relays, and potentially resulting in cascading failure of the whole system. Existing literature uses virtual resistance techniques to improve the power sharing accuracy; however, so far, no explicit relation between the values of the virtual resistances and the feeder resistances mismatch has been formulated, opening the possibility to enhance power sharing even further. Therefore, this paper proposes an accurate power sharing strategy in which the virtual resistances are chosen to account for the feeder resistances mismatch. The proposed technique relies on the optimal tuning of the virtual resistance assigned to the local controller of each converter. An online estimation algorithm of the physical feeder resistances, required for virtual resistance tuning, is embedded into the control loop of each converter. Thus, prior information about the feeder resistances in the design stage is not required. The proposed approach is validated through simulation and experimental results from a Hardware-in-the-Loop setup of a typical islanded DC microgrid. The results demonstrate the approach merits, achieving accurate power sharing among converters and ensuring robust operation, even in scenarios involving communication failures.

A Decentralized Power and Bus Voltage Regulation Approach for DC Microgrids

In this paper a decentralized power regulation approach is presented for converters operating in DC microgrids. The method enables classical droop control to perform power regulation tasks by employing auto-adaptive virtual resistances for the controlled devices. Moreover, the auto-adaptive nature of the droop characteristic is employed to constraint, through a decentralized approach, the microgrid DC bus voltage within an admissible range of values, despite unpredictable changes in the operating conditions of the microgrid (i.e., sudden variations in load and/or in renewable production). The proposed approach is formalized as a multi-objective optimization problem whose solution is entrusted to a method based on dynamic system theory and Lyapunov theory. Simulations are carried out on test DC microgrids, in order to prove the approach effectiveness.

A Distributed Control Strategy for State-of-Charge Balance of Energy Storage Without Continuous Communication in AC Microgrids

With the high penetration of renewable energy sources (RES), the energy storage system (ESS) units have been employed as critical components to compensate for the power fluctuation generated by RESs in an ac microgrid. However, it's a major challenge to achieve the state-of-charge (SoC) balance of ESS units due to the difference of initial SoC values and varied capacities. To deal with this issue, a distributed event-triggered control strategy has been proposed to realize the SoC balance among ESS units by regulating the virtual resistances. Compared with existing methods, only the local SoC of each energy storage is exchanged with the neighboring ESS units. Furthermore, by employing the proposed event-triggered mechanism, the data sampling and signal transmission are only conducted when the predefined triggering condition is satisfied, which effectively saves the usage of communication resources. Moreover, the stability and inter-event interval with the proposed control strategy is analyzed in this paper. Finally, several case studies are presented in the experiment where the presented approach shows its robustness against dynamic load and unexpected single-point communication failure.

An Adaptive Fault Ride-Through Scheme for Grid-Forming Inverters Under Asymmetrical Grid Faults

Three-phase four-wire grid-forming (GFM) inverters are promising to interface distributed energy resources into low-voltage networks. However, these inverters are prone to overcurrent under grid faults. Physically increasing the inverter current capacity is not cost-effective to cope with complicated fault conditions. In this article, an adaptive fault ride-through (FRT) scheme based on instantaneous saturators and virtual negative- and zero-sequence resistances is proposed. It features not only overcurrent limitation by modifying voltage references, but also seamless transition between normal and grid fault conditions. The proposed FRT scheme is first analyzed from different aspects, including the virtual sequence resistances, grid short-circuit ratio, fault types, and fault levels. The virtual sequence resistances are then designed to be adaptive to ensure high voltage quality at the healthy phase. The proposed FRT scheme is verified by MATLAB/Simulink simulations under asymmetrical faults. A laboratory platform with a grid-connected 3kW GFM inverter is further constructed to demonstrate its effectiveness (a video of the experimental results under three asymmetrical faults is attached).

Advanced three-stage photovoltaic system phasor model for grid integration dynamic studies

As the penetration of photovoltaic (PV) generation increases at different system voltage levels, their impact on the power grid operation and control is more important to analyze. Hence, suitable PV models must be developed with which it is possible to carry out dynamic analysis for fair-sized electrical networks. This is a demanding task, computationally-wise, for detailed switching-based PV models using small numerical integration steps required by the associated power electronic devices. In this sense, an advanced three-stage PV system phasor model is proposed in this paper whose hallmark resides in the proper characterization of the PV arrays and DC/DC converter through a nonlinear potential regression technique in combination with the generatrix method. As a result, the PV operating surfaces, as function of irradiance and temperature, can be determined and used for the calculation of virtual resistances relating to the PV optimal operation and internal power losses. The virtual resistances are seamlessly combined with a developed AC/DC converter phasor model for efficient dynamic simulations of electrical networks.The new PV model has been thoroughly validated using Simscape Electrical of Simulink where an electrical network with one PV system is dynamically simulated. The outcomes of the developed model are compared to those obtained from switching-based PV models based on different maximum power tracking strategies, i.e., the incremental conductance (IC) and perturbation and observation (P&O) algorithms. The impact of the PV system on the power grid operation and the accuracy of results are assessed, demonstrating that the proposed model favorably agrees with the benchmark switching-based PV models as errors inferior to 2 % are obtained. Furthermore, it is confirmed that the new PV system model enables faster dynamic simulations than what it is possible to achieve with switching-based models since it is 28.82 times faster than the PV model based on the IC algorithm and 31.80 times faster than that using the P&O technique.

Robust Stabilization of Inverter-Based Resources Using Virtual Resistance-Based Control

This paper proposes a virtual resistance-based nonlinear control to stabilize and robustify the current layer of inverter-based resources, subject to the grid voltage disturbances, and the grid parameter uncertainties. A class of virtual resistances is proposed and analyzed using concepts from dissipative systems theory. Moreover, specific nonlinear virtual resistance-based controllers are derived, with their corresponding performance analytically bounded. The theoretical and simulation results show that the proposed nonlinear virtual resistance-based controllers significantly reduce the L2 gain of the closed-loop error system to grid voltage variation and parametric uncertainties. Significant improvements of the transient and steady-state current responses are also demonstrated over linear virtual resistance counterparts.

Droop K-Sharing Function for Energy Management of DC Microgrids

Slow dynamic response sources, such as fuel cells, are frequently used with faster units, such as batteries and ultracapacitors. In this context, this article gathers the advantages of two energy management techniques to propose the droop k-sharing function. In droop control, energy management is easily implemented using the virtual resistances concept, eliminating the need for fast communication links between the sources. The k-sharing function improves the performance of microgrids with slower sources assigning a preestablished dynamic behavior using a low-pass filter, while the storage unit absorbs the fast transients. Additionally, the k-sharing function also enables the storage unit to share power at a steady state. Therefore, the main advantage of the proposed energy management algorithm is that the control loops of each power source are not coupled to each other, which is accomplished by designing the k-sharing function similarly to the droop technique, eliminating the need for high-speed links of communication and improving the microgrid speed response during fast changes of load. The effectiveness of the proposed function and the theoretical analysis are evaluated using a dc microgrid composed of an H-1000 fuel cell manufactured by Horizon Fuel Cells and three Zippy Compact 5000 25 C Li-Ion batteries in series connection.

Coordinated control method of multiple hybrid energy storage systems based on distributed event-triggered mechanism

An islanded DC microgrid with multiple hybrid energy storage systems is the object of this research, and a hierarchical coordinated control method of hybrid energy storage systems based on an event-triggered mechanism is proposed. The local layer adopts a virtual-resistance droop control and conducts the power distribution of a battery and a supercapacitor using a low-pass filter. Control strategies based on the state of charge are proposed to achieve coordinated and safe operation between hybrid energy storage systems. The distributed control layer uses a sparse communication network to regulate the average voltage and the proportional current of each hybrid energy storage system to improve the problems arising from a large bus voltage deviation and poor power sharing accuracy caused by virtual and line resistances. Based on this research, a Zeno-free event-triggered control method is proposed. The detailed derivation and proof process of the method is introduced using Lyapunov stability theory. This method can achieve similar control performance as time-triggered, but with fewer communication traffic. By setting prejudgment thresholds of the triggering function, the communication traffic is further reduced during the steady state of the system. Finally, simulations studies are conducted to demonstrate the effectiveness and robustness of the proposed control method in an islanded DC microgrid.

Control strategy to improve load/power sharing, DC bus voltage restoration, and batteries SOC balancing in a DC microgrid

DC microgrids are well known as a proper solution to link different DC sources, such as photovoltaic panels and wind turbines, directly to DC loads. Along with their advantages, they suffer from an imbalance state of charge (SOC) in their energy storage units (ESUs), improper current-sharing between ESUs, and DC bus voltage deviation. This study proposes a novel control strategy for DC microgrids, which not only balances ESUs SOC and shares current between ESUs proportional to their capacity but also, reduces DC bus voltage deviation significantly. In this way, the same droop curve is defined. Then, three virtual resistances are considered. The first one is set based on the lines resistance and ESUs capacity to share current among the ESUs properly. As the lines resistance changes affect the proportional current-sharing, the second virtual resistance is intended to relieve this effect. The third one is suggested to balance the ESUs SOC. The small-signal stability analysis is performed, which demonstrates that the proposed method has stability in all operating conditions. Simulation results in MATLAB/Simulink confirm that with the aid of the proposed control method, not only proper current-sharing and ESUs SOC balancing are obtained, but also DC bus voltage deviation is effectively diminished.

Operating Cost Reduction of DC Microgrids Under Real-Time Pricing Using Adaptive Differential Evolution Algorithm

Virtual resistance-based droop control is widely adopted as secondary-layer control for grid-connected converters in DC microgrids. This paper presents an alternative usage of the virtual resistances to minimize the total operating cost of DC microgrids under real-time pricing. The total operating cost covers the running cost of utility grids, renewable energy sources (RES), energy storage systems (ESS), fuel cells, and power loss on the distribution lines. An adaptive Differential Evolution (ADE) algorithm is adopted in this paper to optimize the virtual resistances of the droop control for the grid-connected converters of dispatchable units, such that the power flow can be regulated. The performances of the proposed strategy are evaluated by the case studies of a 12-bus 380 V DC microgrid using Matlab and a 32-bus 380 V DC microgrid using a Real-Time Digital Simulator (RTDS). Both results validate that the ADE can significantly reduce the operating cost of DC microgrids and outperform the conventional Genetic Algorithm (GA) in terms of cost saving. Comparisons among the microgrids with different numbers of dispatchable units reveal that the cost saving is more prominent when the expansion of dispatchable units.

Analysis and hardware implementation of virtual resistance based PV inverters for harmonics suppression

Traditional PV inverter is designed for power generation and reducing harmonic distortion without capability of actively participating in harmonic elimination of power grid. This study proposes a virtual resistance based PV inverter to suppress the voltage harmonics at point of common coupling (PCC), in which PV inverters could simultaneously deliver power for fundamental and behave as a series of virtual resistances to absorb power harmonics and then convert them into fundamental power; as a result, voltage distortion of each node of power grid is significantly reduced. No additional sensors are required to measure the non-linear load current, such that a more flexible installation location of PV inverter can be achieved. Furthermore, current harmonics are controlled by PI controller to track the voltage harmonics multiplied by harmonic conductance, i.e. K h, such that the PV inverter can be equivalent to a virtual resistance. In particular, the absorbed power harmonics are used to evaluate the harmonic suppression, while harmonic conductance K h is regulated automatically to maximise the absorbed power harmonics. Both the simulation and experiment results demonstrate that the effectiveness of the propose method.

How Karen Tei Yamashita Literalizes Feminist
 Subversion: Extreme Domesticity, Space-Off
 Reversals, and Virtual Resistances in Tropic of Orange

In Tropic of Orange (1997), Karen Tei Yamashita builds an expansive narrative on the premise that the Tropic of Cancer shifts mysteriously from its actual latitude, barely north of Mazatlán, México, to that of L.A.’s latitude: from 23.43692° north of the Equator to 34.0522° N. By doing so, Yamashita literally takes that which is “south of the border” and repositions it in a hub of neoliberal hegemony; that is, she takes what is below (“sub-”) and puts it on top (“-vert”). I read such a literal and magically realistic move as an allegorical template that guides the novel in its entirety, but more specifically, in its repositioning of women from their spaces of relegation to spaces animated by their resistances to such relegation; from spaces of dependency to spaces characterized by feminine influence. This essay examines three strategies through which feminist subversions may be accomplished according to Yamashita’s textual template: The first follows Susan Fraiman’s theory of Extreme Domesticity (Fraiman 2017) as it tracks how subservient spaces of home and household can become sites of nonconformity; the second takes its cue from the cinematic strategies of “space-off” and “reversal” as examples of how marginal or negative spaces can be leveraged against the male gaze (c.f. José Rodríguez Herrera’s analysis of Sarah Polley’s film adaptation of Alice Munro’s “The Bear Came Over The Mountain,” Herrera 2013); and the third engages my own notion of a spatial virtuality (“that which is present without being local,” Munro 2014) as a mode of resistance that culminates, ultimately, in “a condition of literature,” that is to say, a condition in which Tropic of Orange refers to the conditions of its own making instead of referring to the conditions that create it (ibid.). My tripartite method thus highlights and celebrates the domestic, cinematic, and technological spaces of Yamashita’s writing, respectively, just as it articulates how these spaces might also be read as subversively feminist and feminizing. But it also meditates formally and contextually, as Tropic of Orange’s condition of literature implies, a sort of ablated feminist narratology, even as it works toward feminist narratological ends.

A Frequency-Dependent Virtual Impedance for Voltage-Regulating Converters Feeding Constant Power Loads in a DC Microgrid

The power oscillations at the input of constant power loads (CPLs) fed by LC filters is a well-known phenomenon in dc microgrids. The phenomenon happens because of the negative resistance characteristic exhibited by CPLs. The oscillations can be damped by inserting virtual resistances at the output of voltage-regulating converters to offset the negative resistance of the CPLs. However, large virtual resistances lead to a poor voltage regulation of the dc bus. This paper proposes a frequency-dependent virtual impedance comprising of a parallel RL branch, which solves the issue of poor voltage regulation. Further, the large signal stability of the system in the presence of the virtual impedance is also investigated through the Brayton–Moser mixed potential analysis. Detailed simulations and analysis of the frequency-domain interactions of the system are carried out and the effectiveness of the proposed technique is showcased. Experimental results from a 250 W prototype CPL are included to validate the proposed technique.

A Dynamic Consensus Algorithm to Adjust Virtual Impedance Loops for Discharge Rate Balancing of AC Microgrid Energy Storage Units

A dynamic consensus algorithm (DCA)-based coordinated secondary control with an autonomous currentsharing control strategy is proposed in this paper for balancing the discharge rate of energy storage systems (ESSs) in an islanded ac microgrid. The DCA is applied for information sharing between distributed generation (DG) units to regulate the output power of DGs according to the ESS capacities and state-of-charge (SoC). Power regulation is achieved by adjusting the virtual resistances of voltage-controlled inverters with an autonomous current-sharing controller. Compared with existing methods, the proposed approach can provide higher system reliability, expandability, and flexibility due to its distributed control architecture. The proposed controller can effectively prevent operation failure caused by over-current and unintentional outage of DGs by means of balanced discharge rate control. It can also provide fast response and accurate current sharing performance. A generalizable linearized state-space model for n-DG network in the z-domain is also derived and proposed in this paper; the model includes electrical, controller, and communication parts. The system stability and parameter sensitivity have been analyzed based on this model. To verify the effectiveness of the proposed control approach, this paper presents simulation results from a ten-node network and a comparison between experimental results obtained from the conventional power sharing control and the DCA-based SoC coordinated control in a setup with three 2.2 kW DG units.

Second Ripple Current Suppression by Two Bandpass Filters and Current Sharing Method for Energy Storage Converters in DC Microgrid

With the increase in ac loads injected into the dc microgrid (MG) through inverters, the second ripple current (SRC) in the front-end energy storage converter (ESC) and the circulating current among the ESCs in dc MG become more and more serious. In this paper, the SRC suppression method by introducing two bandpass filters (BPFs) into the output voltage and inductance current feedback of the ESC is proposed. Compared with the traditional dual-loop control method, the proposed method effectively reduces the SRC and improves the dynamic performance in case of a lower cutoff frequency in the outer voltage loop. Simultaneously, an adaptive droop control method by introducing the fine-tuning virtual resistances is adopted to reduce the output voltage deviation of parallel ESCs and improve the output current sharing among the ESCs. Considering the allowed range of deviation between the output voltage and the rated voltage for each ESC, the impacts of the line power loss and circulating current power loss caused by the introduced virtual resistances are analyzed in detail. While the sum of the line power loss and circulating current power loss reaches the minimum value, the appropriate control parameters are obtained. Simulation and experimental results verify the validity of the proposed method.

Coordinated Secondary Control for Balanced Discharge Rate of Energy Storage System in Islanded AC Microgrids

A coordinated secondary control approach based on an autonomous current-sharing control strategy for balancing the discharge rates of energy storage systems (ESSs) in islanded ac microgrids is proposed in this paper. The coordinated secondary controller can regulate the power outputs of distributed generation (DG) units according to their states-of-charge and ESS capacities by adjusting the virtual resistances of the paralleled voltage-controlled inverters. Compared with existing controllers, the proposed control strategy not only effectively prevents operation failure caused by overcurrent incidents and unintentional outages in DG units, but also aims to provide a fast transient response and an accurate output-current-sharing performance. A complete root locus analysis is given in order to achieve the system stability and parameter sensitivity. Experimental results are presented to show the performance of the whole system and to verify the effectiveness of the proposed controller.

Intelligent Distributed Generation and Storage Units for DC Microgrids—A New Concept on Cooperative Control Without Communications Beyond Droop Control

Low voltage dc microgrids have been widely used for supplying critical loads, such as data centers and remote communication stations. Consequently, it is important to ensure redundancy and enough energy capacity in order to support possible increments in load consumption. This is achieved by means of expansion of the energy storage system by adding extra distributed energy storage units. However, using distributed energy storage units adds more challenges in microgrids control, since stored energy should be balanced in order to avoid deep discharge or over-charge in one of the energy storage units. Typically, voltage droop loops are used for interconnecting several different units in parallel to a microgrid. This paper proposes a new decentralized strategy based on fuzzy logic that ensures stored energy balance for a low voltage dc microgrid with distributed battery energy storage systems by modifying the virtual resistances of the droop controllers in accordance with the state of charge of each energy storage unit. Additionally, the virtual resistance is adjusted in order to reduce the voltage deviation at the common dc bus. The units are self-controlled by using local variables only, hence, the microgrid can operate without relying on communication systems. Hardware in the loop results show the feasibility of the proposed method.

Supervisory Control of an Adaptive-Droop Regulated DC Microgrid With Battery Management Capability

DC power systems are gaining an increasing interest in renewable energy applications because of the good matching with dc output type sources such as photovoltaic (PV) systems and secondary batteries. In this paper, several distributed generators (DGs) have been merged together with a pair of batteries and loads to form an autonomous dc microgrid (MG). To overcome the control challenge associated with coordination of multiple batteries within one stand-alone MG, a double-layer hierarchical control strategy was proposed. 1) The unit-level primary control layer was established by an adaptive voltage-droop method aimed to regulate the common bus voltage and to sustain the states of charge (SOCs) of batteries close to each other during moderate replenishment. The control of every unit was expanded with unit-specific algorithm, i.e., finish-of-charging for batteries and maximum power-point tracking (MPPT) for renewable energy sources, with which a smooth online overlap was designed and 2) the supervisory control layer was designed to use the low-bandwidth communication interface between the central controller and sources in order to collect data needed for adaptive calculation of virtual resistances (VRs) as well as transit criteria for changing unit-level operating modes. A small-signal stability for the whole range of VRs. The performance of developed control was assessed through experimental results.