Droop Equation Research Articles

Centralised Control and Energy Management of Multiple Interconnected Standalone AC Microgrids

When microgrids operate autonomously, they must curtail the surplus of renewable energy sources (RES) while minimising reliance on gas. However, when interconnected, microgrids can collaboratively minimise RES curtailment and gas consumption due to the ability of exchanging power. This paper presents a centralised controller and energy management of multiple standalone AC microgrids interconnected to a common AC bus using back-to-back converters. Each microgrid consists of RES, a battery, a gas-powered auxiliary unit, and a load. The battery’s state of charge (SOC) is controlled and is used in the AC bus frequency to indicate whether the microgrid has a surplus or shortage of power. High-level global droop control exchanges power between the microgrids. The optimisation problem for this interconnected system is modelled cooperatively to determine the optimal dispatch solution that minimises the energy cost from the auxiliary unit. The optimal dispatch is solved in three cases using the Nelder–Mead simplex algorithm under different settings: one-variable optimisation, three-variable optimisation with the standard droop equation, and three-variable optimisation with a modified droop equation. The optimised performance results are compared with those of the non-optimised benchmark to determine the percentage of optimal performance. The simulation results show that the total energy cost from the auxiliary unit is minimised by 8.98%.

Static state estimation of islanded AC/DC Hybrid microgrids

In this work, a static state estimation (SSE) approach for the hybrid AC/DC microgrid (MG)s operating in islanded mode is studied. In the islanded mode, the Interlinking Converter (IC) is critical for maintaining equal or normalized power between the AC and DC parts of the Microgrid (MG). Since the power exchange between AC and DC parts of the MG is determined from AC MG frequency and DC bus voltage, these also need to be considered as system variables along with bus voltages. Hence, in the proposed approach, the Weighted Least Squares (WLS) method is used to estimate the steady-state frequency (ω), along with AC bus voltages (magnitude and phase) of AC MG and DC bus voltages of DC MG simultaneously. Further, to incorporate frequency and droop equation of IC measurement, the Jacobian matrix of WLS is revised. The developed WLS-based Static SE is tested on two test systems: i) 12 bus system (6 bus AC and 6 bus DC) and ii) 71 bus system (38 bus AC and 33 bus DC). Moreover, the impact of accuracy classes of measurements is studied on a large Hybrid AC/DC MG (906 nodes AC MG and 118 node DC MG). All the SE results have been validated by comparing the obtained results with the corresponding true values (calculated from load ow analysis).

The concept of intracellular regulation of phytoplankton growth – 55 years of the Droop equation

The concept of intracellular regulation of phytoplankton growth – 55 years of the Droop equation

Luenberger Observer-Based Microgrid Control Strategy for Mixed Load Conditions

In this paper, a Luenberger observer-based microgrid control strategy is proposed to enhance the power quality of microgrids, when the grid loads are mixed and strongly non-linear. To improve performance under this condition, a Luenberger observer is designed for three phase power grids. On the basis of the observer, the components of different frequencies and sequences of voltages and currents are obtained accurately. The virtual impedance of different frequencies and sequences is designed, which makes the equivalent line impedance meet the power-sharing condition, reducing the fundamental negative sequence voltages and harmonic voltages. The active power droop equation, meanwhile, is proposed, where the bus voltage is modified. The value range of virtual impedance is discussed in the complex frequency domain. The proposed control strategy does not require any communication lines, so the hardware structure is simplified. The simulations and experiments are provided to verify the effectiveness of the proposed method.

Distributed Supervisory Secondary Control for a DC Microgrid

This article investigates the current sharing and voltage regulation problem of a DC microgrid by a distributed supervisory control method. In the existing secondary control methods, current sharing feedback control loop and voltage regulation feedback control loop are linearly integrated to shift the droop equation. However, the linear combination of two loops may easily offset the control effect of each other, as the control dimension is less than the objective dimension. This fact motivates us to design a distributed supervisory secondary control (DSSC) scheme to achieve a more flexible configuring of each converter. The DSSC consists of two candidate controllers and a supervisor. The two controllers refer to current sharing configuring and DC bus voltage regulation respectively, and the supervisor is to orchestrate the switching between candidate controllers based on the system environment of DC microgrid. Under the proposed DSSC, each converter selects to configure the current sharing or regulates the DC bus voltage according to its need. Theoretical stability analysis is rigorously conducted. Finally, both simulation and experiment results are presented to demonstrate the effectiveness of DSSC.

A Virtual Complex Impedance based P — V Droop Method for Parallel-connected Inverters in Low-voltage AC Microgrids

Due to the high R/X ratio and mismatched feeder impedance of low-voltage microgrids, conventional droop method is no longer able to decouple the active and reactive power of distributed generators and the powersharing accuracy is degraded. In this article, a virtual complex impedance based P - V̇ droop method is proposed to decouple the powers and improve the power-sharing accuracy among DGs. With the virtual impedance method, the equivalent impedance between virtual power source and point of common coupling is shaped to be purely resistive. Then, a P - V̇ strategy is adopted to alleviate the effect of mismatched line impedance, where the virtual powers rather than the ordinary P/Q are used in the droop equation. In case the output voltage violates the operation code, a restoration mechanism is proposed to reset V̇ to zero. Compared with existing virtual impedance and Q - V̇ droop methods, the proposed method combines the advantages of both. Besides, a modified P - V̇ strategy is also presented to accelerate the restoration process and improve the active power-sharing accuracy at the same time. Simulation results validate the effectiveness of the proposed method.

Properties of main phytoplankton species of the Black Sea, determining the change in their dominance in annual dynamics

Using mathematical model, we tested three hypotheses of bloom regulation mechanisms for dominant phytoplankton species in the northeastern Black Sea. The model is based on the concept of intracellular regulation using the Droop equation, and values of the model constants that satisfy the conditions of domination are found. The bloom of the small-cell diatom Pseudo-nitzschia pseudodelicatissima is due to higher specific growth rates than other species in early spring. The half-saturation constants and minimum quotas for mineral nutrition elements (nitrogen and phosphorus) are also relatively high. In late spring and early summer, the bloom of coccolithophore Emiliania huxleyi is usually recorded. Prerequisites are a low half-saturation constant for nitrogen uptake and minimum quota for this nutrient. The third mechanism gains strength in the summer with the deepening of seasonal thermocline and the dominance of large-cell diatoms. It was shown that for the supremacy of large diatom Proboscia alata, it is necessary to have low half-saturation constants for the phosphorus uptake and minimum quotas for this nutrient.

Distributed control of multiple-bus microgrid with paralleled distributed generators

A microgrid is hard to control due to its reduced inertia and increased uncertainties. To overcome the challenges of microgrid control, advanced controllers need to be developed. In this paper, a distributed, two-level,communication-economic control scheme is presented for multiple-bus microgrids with each bus having multiple distributed generators &#x0028 DGs &#x0029 connected in parallel. The control objective of the upper level is to calculate the voltage references for one-bus subsystems. The objectives of the lower control level are to make the subsystems &#x02BC bus voltages track the voltage references and to enhance load current sharing accuracy among the local DGs. Firstly, a distributed consensus-based power sharing algorithm is introduced to determine the power generations of the subsystems. Secondly, a discrete-time droop equation is used to adjust subsystem frequencies for voltage reference calculations. Finally, a Lyapunov-based decentralized control algorithm is designed for bus voltage regulation and proportional load current sharing. Extensive simulation studies with microgrid models of different levels of detail are performed to demonstrate the merits of the proposed control scheme.

A Physiologically Structured Equation to Consider Quota Heterogeneity in the Droop Model

The Droop model allows to represent microalgae growth limited by a nutrient, using a cell quota (also referred to as variable-yield) approach. Single-cell measurements have revealed quota heterogeneity in phytoplankton collected from field studies. Such heterogeneity can be due, among other factors, to spatial structure (e.g. in biogeochemical cycles in the ocean, or for photobioreactors connected in series). Nonetheless, quota heterogeneity is generally omitted in modelling studies, using an average quota approach, or included in size-structured or individual-based models. Here, we propose a distributed Droop equation to tackle this problem, considering subpopulation growth -in line with Droop macroscopic view- rather than cell division dynamics. We provide analytical solutions for two case studies. First, we consider a constant substrate concentration without biomass input, which leads to a monomorphic population. The second case, considering a biomass input without substrate, leads to quota heterogeneity. Simulations are then carried out for the two case studies (showing good agreements with the analytical solutions) and for a more general case. Finally, we show that the error induced by the average quota approach increases considerably with microalgae plasticity (i.e. the maximal over minimal quota ratio), which points out the benefit of considering quota heterogeneity in these cases.

독립운전 모드에서 가상 인덕터를 활용한 대용량 인버터 병렬운전을 위한 드룹제어

This paper investigates the droop control-based real and reactive power load sharing with a virtual inductor when the line impedance between inverter and Point of Common Coupling (PCC) is partly and unequally resistive in high-capacity systems. In this paper, the virtual inductor method is applied to parallel inverter systems with resistive and inductive line impedance. Reactive power sharing error has been improved by applying droop control after considering each line impedance voltage drop. However, in high capacity parallel systems with large output current, the reference output voltage, which is the output of droop controller, becomes lower than the rated value because of the high voltage drop from virtual inductance. Hence, line impedance voltage drop has been added to the droop equation so that parallel inverters operate within the range of rated output voltage. Additionally, the virtual inductor value has been selected via small signal modeling to analyze stability in transient conditions. Finally, the proposed droop method has been verified by MATLAB and PSIM simulation.

A numerical model study on multi-species harmful algal blooms coupled with background ecological fields

Based on systematized physical, chemical, and biological modules, a multi-species harmful algal bloom (HAB) model coupled with background ecological fields was established. This model schematically embodied that HAB causative algal species and the background ecological system, quantified as total biomass, were significantly different in terms of the chemical and biological processes during a HAB while the interaction between the two was present. The model also included a competition and interaction mechanism between the HAB algal species or populations. The Droop equation was optimized by considering temperature, salinity, and suspended material impact factors in the parameterization of algal growth rate with the nutrient threshold. Two HAB processes in the springs of 2004 and 2005 were simulated using this model. Both simulation results showed consistent trends with corresponding HAB processes observed in the East China Sea, which indicated the rationality of the model. This study made certain progress in modeling HABs, which has great application potential for HAB diagnosis, prediction, and prevention.

Phosphate-limited growth of the marine diatom Thalassiosira weissflogii (Bacillariophyceae): evidence of non-monod growth kinetics(1).

The marine diatom Thalassiosira weissflogii (Grunow) G. A. Fryxell & Hasle was grown in a chemostat over a series of phosphate-limited growth rates. Ambient substrate concentrations were determined from bioassays involving picomolar spikes of (33) P-labeled phosphate, and maximum uptake rates were determined from analogous bioassays that included the addition of micromolar concentrations of unlabeled phosphate and tracer concentrations of (33) P. The relationship between cell phosphorus quotas and growth rates was well described by the Droop equation. Maximum uptake rates of phosphate spikes were several orders of magnitude higher than steady state uptake rates. Despite the large size of the T. weissflogii cells, diffusion of phosphate through the boundary layer around the cells had little effect on growth kinetics, in part because the cellular N:P ratios exceeded the Redfield ratio at all growth rates. Fitting the Monod equation to the experimental data produced an estimate of the nutrient-saturated growth rate that was ~50% greater than the maximum growth rate observed in batch culture. A modified hyperbolic equation with a curvature that is a maximum in magnitude at positive growth rates gave a better fit to the data and an estimate of the maximum growth rate that was consistent with observations. The failure of the Monod equation to describe the data may reflect a transition from substrate to co-substrate limitation and/or the presence of an inducible uptake system.

PHOSPHATE-LIMITED GROWTH OF PAVLOVA LUTHERI (PRYMNESIOPHYCEAE) IN CONTINUOUS CULTURE: DETERMINATION OF GROWTH-RATE-LIMITING SUBSTRATE CONCENTRATIONS WITH A SENSITIVE BIOASSAY PROCEDURE(1).

The relationship between steady-state growth rate and phosphate concentration was studied for the marine prymnesiophyte Pavlova lutheri (Droop) J. C. Green grown in a chemostat at 22°C under continuous irradiance. A bioassay procedure involving short-term uptake of 10 picomolar spikes of (33) P-labeled phosphate was used to estimate the concentration of phosphate in the growth chamber. The relationship between growth rate and phosphate was well described by a simple rectangular hyperbola with a half-saturation constant of 2.6 nM. The cells were able to take up micromolar spikes of phosphate at rates two to three orders of magnitude higher than steady-state uptake rates. The kinetics of short-term uptake displayed Holling type III behavior, suggesting that P. lutheri may have multiple uptake systems with different half-saturation constants. Chl a:C ratios were linearly related to growth rate and similar to values previously reported for P. lutheri under nitrate-limited conditions. C:N ratios, also linearly related to growth rate, were consistently lower than values reported for P. lutheri under nitrate-limited conditions, a result presumably reflecting luxury assimilation of nitrogen under phosphate-limited conditions. C:P ratios were linearly related to growth rate in a manner consistent with the Droop equation for growth rate versus cellular P:C ratio.

Hemolytic toxicity and nutritional status of Prymnesium parvum during population growth

The haptophyte flagellate Prymnesium parvum forms blooms in brackish waters and produces toxins that harm aquatic organisms. Batch cultures of P. parvum were grown in phospho- rus-limited artificial seawater medium with 3 treatments: no aeration or buffering, continuous aera- tion, and buffering to a high, basic pH. Over a period of 32 d, frequent samples were taken to deter- mine: cell abundance; cellular composition of carbon (C), nitrogen (N), and phosphorus (P); culture pH; and hemolytic activity. Only pH differed significantly among media treatments: it was basic in all treatments after 10 d of culture, but consistently highest in the buffered medium treatment. In all treatments, exponential population growth was observed during the first 10 d of culture, at rates of about 0.4 to 0.6 d -1 . The cell quota for P declined rapidly over the first 8 d of culture and more slowly thereafter. A transition from exponential growth to stationary phase occurred over 10 to 21 d of cul- ture. Population growth rate was related to cell quota for P according to Droop's equation, with an estimated quota for zero growth of about 5 fmol cell -1 . In all cultures, high hemolytic activity was seen on Days 8 and 12. All but one culture displayed oscillations of hemolytic activity thereafter. At times of high hemolytic activity, the cell quota for P was <100 fmol cell -1 and the cellular C:P ratio was at or above the Redfield ratio of 106.

GROWTH DYNAMICS OF ULVA ROTUNDATA (CHLOROPHYTA) IN A FISH FARM: IMPLICATIONS FOR BIOMITIGATION AT A LARGE SCALE(1).

Changes in biomass of several macroalgae [Ulva rotundata Bliding; Gracilariopsis longissima (S. G. Gmel.) Steentoft, L. M. Irvine et Farnham; Ulva intestinalis L.; and Cladophora sp.] and marine plants (Zostera noltii and Ruppia cirrhosa) growing naturally in earthen ponds of a fish farm (Acuinova, San Fernando, Southern Spain) were recorded during a year. The farm is mainly devoted to the culture of gilthered seabream (Sparus aurata). The most conspicuous algal species thriving in the ponds was U.rotundata, which reached densities up to 600 g dry mass · m(-2) and produced up to 20.45 g C · m(-2) · d(-1) . Dissolved nutrients (phosphate and ammonium), tissue nutrient content, and growth rates of this species were estimated during 2001 and 2002. Evidence of natural biomitigation by U.rotundata when water circulates throughout the fish farm is presented. Due to the fish cultivation, both phosphate and ammonium increased as water circulated from the preculture ponds to the postculture ponds. As a consequence, U.rotundata tissue nitrogen (N) and phosphorus (P) increased from algae growing in preculture ponds to algae growing in the outflow channel, so that mean C:N:P ratio varied from 773:57:1 in preculture ponds to 567:64:1 in the outflow channel. Phosphorus limited growth of U.rotundata during the spring. As growth rates increased as a function of tissue P, data were fitted to the Droop equation. From this equation, the estimated maximal growth rate was 0.295 ± 0.041 d(-1) , the subsistence quota was 0.05 ± 0.01% P of dry mass, and the critical quota was 0.215% P of dry mass. The results suggest that management of the fish farm based on a large-scale integrated mariculture system of fish and macroalgae may increase the total ecological and economic benefits, both for the farm and for the environment.

Nutrition and growth kinetics in nitrogen- and phosphorus-limited cultures of the novel red tide flagellate Chattonella ovata (Raphidophyceae)

In the summer of 2004, a harmful bloom caused by Chattonella ovata (Raphidophyceae) occurred over almost the entire area of the Seto Inland Sea and caused fishery damages. This incident was the first record of a bloom and damage to the fisheries caused by this species in Japanese waters. In order to elucidate the mechanism of the bloom outbreak, we examined the nutrition and the growth kinetics in nitrogen (N)- and phosphorus (P)-limited semi-continuous cultures of this species. Inorganic N compounds, such as nitrate, nitrite, and ammonium, were found to be good nitrogen sources for the growth of C. ovata, while organic nitrogen (urea and uric acid) was not utilized. This species was capable of using ATP, ADP and inorganic phosphorus compounds, but did not utilize phosphate monoesters as a sole P source. Under both N-limited and P-limited steady state conditions, the growth rate as a function of cell nitrogen and phosphorus quota, respectively, followed the Droop equation. Kinetic parameters μ m (maximum growth rate) and k q (minimum cell quota) obtained for N- and P-limited cultures were 0.79 day −1 and 5.5 pmol N cell −1 and 0.86 day −1 and 0.48 pmol P cell −1, respectively. The minimum cell quotas were 23–30% lower than those of C. antiqua. The nutrient availability and kinetic parameters of C. ovata are compared with other harmful algae and the ecological implications of these characteristics discussed.

The ‘Droop Equation’–Michael Droop and the Legacy of the ‘Cell-Quota Model’ of Phytoplankton Growth

The ‘Droop Equation’–Michael Droop and the Legacy of the ‘Cell-Quota Model’ of Phytoplankton Growth

Nitrogen load and irradiance affect morphology, photosynthesis and growth of Caulerpa prolifera (Bryopsidales: Chlorophyta)

MEPS Marine Ecology Progress Series Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsTheme Sections MEPS 298:101-114 (2005) - doi:10.3354/meps298101 Nitrogen load and irradiance affect morphology, photosynthesis and growth of Caulerpa prolifera (Bryopsidales: Chlorophyta) Erik-jan Malta1,2,*, Daniela G. Ferreira1,3, Juan J. Vergara1, J. Lucas Pérez-Lloréns1 1Departamento de Biología, Área de Ecología, Facultad de Ciencias del Mar y Ambientales, Universidad de Cádiz, 11510 Puerto Real (Cádiz), Spain2Present address: ALGAE-Marine Plant Ecology Research group, Centre of Marine Sciences, Universidade do Algarve,Campus de Gambelas, 8005-139 Faro, Portugal3Present address: Department of Biology, University of the Azores, Rua São Gonçalo, 9504-539 Ponta Delgada, Portugal *Email: emalta@ualg.pt ABSTRACT: The effect of nitrogen (N) load and irradiance on morphology, growth and photosynthetic performance was studied in the green macroalga Caulerpa prolifera (Forsskål) J.V. Lamouroux from the Gulf of Cádiz (south Spain). Constant growth rates were obtained for thalli growing at different N loads, which could be fitted to tissue N using the Droop equation, rendering a maximum growth rate of 0.09 d–1, a minimum tissue N level of 1.71% dry weight (DW) and a critical tissue N of 5.2% DW. N limitation had no effects on Fv/Fm (maximum quantum yield of chlorophyll a fluorescence). Stolon production was significantly highest at low N loads; a reverse trend was observed for assimilator production. In a second experiment, algae were subjected to combinations of high and low N loads (HN and LN) and irradiance (HL and LL) levels. Highest growth rates were observed in the HNLL treatment, whereas the reverse combination rendered the lowest growth rate. High irradiance and high N load both led to increased biomass allocation to assimilators; at low N, the bulk of the biomass (>75% in the HLLN treatment) was allocated to the stolons. HN had a positive effect on Fv/Fm, and HL had a negative effect. HL algae had a higher capacity for non-photochemical quenching. Despite its prolific nature, C. prolifera should be characterised as a slow-growing, but highly nitrophilic alga which has the capacity to forage for nutrients by allocating biomass to the stolons. KEY WORDS: Caulerpa prolifera · Clonal growth · Morphology · Nitrogen foraging · Growth rate · Photosynthesis Full text in pdf format PreviousNextExport citation RSS - Facebook - Tweet - linkedIn Cited by Published in MEPS Vol. 298. Online publication date: August 15, 2005 Print ISSN: 0171-8630; Online ISSN: 1616-1599 Copyright © 2005 Inter-Research.

Stoichiometric Plant-Herbivore Models and Their Interpretation

The purpose of this note is to mechanistically formulate a mathematically tractable model that specifically deals with the dynamics of plant- herbivore interaction in a closed phosphorus (P)-limiting environment. The key to our approach is the employment of the plant cell P quota and the Droop equation for its growth. Our model takes the simple form of a system of two autonomous ordinary differential equations. It can be shown that our model includes the LKE model (Loladze, Kuang and Elser (2000)) as a special case. Our study reveals that the details of ecological stoichiometry models really matter for quantitative predictions of plant-herbivore dynamics, especially at intermediate ranges of the carrying capacity.

DIEL RHYTHM OF ALGAL PHOSPHATE UPTAKE RATES IN P‐LIMITED CYCLOSTATS AND SIMULATION OF ITS EFFECT ON GROWTH AND COMPETITION1

Oscillations in the phosphate (Pi) uptake rates for three species of green algae were examined in a P‐limited cyclostat. For Ankistrodesmus convolutus Corda and Chlorella vulgaris Beyerinck, the Pi uptake rates increased during the daytime and decreased at night. In contrast, Chlamydomonas sp. exhibited the opposite uptake pattern. Cell densities also oscillated under a light:dark cycle, dividing at a species‐specific timing rather than continuously. In general, the cell densities exhibited an inverse relationship with the Pi uptake rates. A competition experiment between A. convolutus and C. vulgaris in a P‐limited cyclostat resulted in the dominance of C. vulgaris, regardless of the relative initial cell concentrations. Chlorella vulgaris also dominated in a mixed culture with Chlamydomonas sp., irrespective of the initial seeding ratio and dilution rate. However, Chlamydomonas sp. and A. convolutus coexisted in the competition experiment with gradual decrease of Chlamydomonas sp. when equally inoculated. Mathematical expressions of the oscillations in the Pi uptake rate and species‐specific cell division gate were used to develop a simulation model based on the Droop equation. The simulation results for each of the species conformed reasonably well to the experimental data. The results of the competition experiments also matched the competition simulation predictions quite well, although the experimental competition was generally more delayed than the simulations. In conclusion, the model simulation that incorporated the effect of diel rhythms in nutrient uptake clearly demonstrated that species diversity could be enhanced by different oscillation patterns in resource uptake, even under the condition of limitation by the same resource.