Energy Balance Constraints Research Articles

Optimal economic dispatch of combined cooling, heating and power‐type multi‐microgrids considering interaction power among microgrids

With the rapid growth of microgrids, many regional multi-microgrids systems emerge gradually with microgrids being integrated to the certain distribution network. By connecting each microgrid using cables and coordinating interaction power among microgrids, the total operation cost of multi-microgrids system can be decreased. On the basis of modeling a variety of energy supply and storage devices, this paper proposes an energy supply infrastructure for combined cooling, heating and power (CCHP) microgrid on centralized and interconnected energy exchange network, and energy loads are subdivided into cooling load, thermal load and power load. Then the optimal economic dispatch model considering interaction power among microgrids is proposed in this study for CCHP type multi-microgrids, and energy balance constraints are established according to load types. This model not only takes into account the power interaction between microgrid and the distribution network, but also considers the power interaction among microgrids. The objective is the minimal total operation cost of CCHP type multi-microgrids system. In case studies of Sino-Singapore district, Tianjin, China, the output power of pre-defined equipment and the total operation cost are compared under two different operation mode, coordination mode and independence mode, which verifies the effectiveness and economy of the proposed model.

Design optimization of a tri-lobed solar powered stratospheric airship

The increased interest over multi-lobed hybrid airships which have been recently identified as an ideal platform for high altitude long endurance applications urges to develop a methodology for conceptual design optimization. The sizing methodology estimates the area of solar array required to meet the constraints of energy balance and the weight/lift equilibrium. The methodology involves the coupling of four disciplines (viz., Environment, Geometry, Aerodynamics, and Energy) and accounts for their mutual interactions. Sizing of the airship is carried out in terms of five design variables corresponding to the geometry and layout of the envelope and the solar array. This methodology is coupled to an intelligence-based heuristic algorithm viz., Particle Swarm Optimization (PSO) to obtain the configuration corresponding to a minimum area of solar array for such an airship, meeting the user-specified operating requirements. The effect of wind speed, airship attitude and altitude, geographical location and day of operation on the optimum area are included in this study. The results show the effect of season and operating conditions of deployment on the optimal envelope shapes obtained for deployment on specific days of the year. This study helps in the preliminary design of solar array on an unconventional stratospheric airship.

Optimal design of distributed energy systems for industrial parks under gas shortage based on augmented ε-constraint method

Natural gas distributed energy systems have developed rapidly owing to their high efficiency, low environmental impact, high energy supply reliability, and good economic returns. As the main users of natural gas distributed energy, industrial parks account for 67.7% of the total installed capacity of the industry. Therefore, disrupted gas supply to industrial parks during gas shortage periods results in decreased production and consequently huge economic losses. This study addresses this issue by attempting to develop an optimized design for distributed energy systems and natural gas allocation in multiple industrial parks under gas shortage conditions. A multi-objective mathematical programming (MOMP) model is established to minimize the total construction investment and operation costs of each industrial park considering emission, energy balance and other technical constraints. Using the augmented ε-constraint method, optimal configurations of distributed energy systems, operation strategy, and economic and emission performance of each industrial park are determined. The distributed energy system design for three industrial parks in Jinan, China, is taken as an example to verify the model. Compared with the non-cooperation case, the annual total cost of full-cooperation can be reduced by 8.29%, and the annual total carbon emission of full-cooperation can be reduced by 427.55 t. Additionally, sensitivity analyses of energy price and total input natural gas are conducted to provide further insights into the optimization of distributed energy system for each industrial park. The results show that electricity price has the strongest impact on the economic performance of the industrial parks, followed by natural gas price and biomass price, but natural gas price does not affect the gas allocation ratio. Moreover, when the total input natural gas is increased by 10–90%, the total cost can be reduced by 0.69%–7.83%.

A mixed integer nonlinear programming approach for petroleum refinery topology optimisation

This work presents a mixed integer nonlinear programming (MINLP)-based superstructure optimisation approach to synthesize an optimal petroleum refinery topology or configuration for large-scale grassroots refinery systems. We develop a superstructure to include many possible prospective configurations and formulate rigorous models for the 32 commercial refinery processes that constitute the configurations, which gives rise to a convex MINLP model. The objective function is to maximize the total refinery profit for a given crude oil feed subject to material and energy balance constraints. We apply a two-level optimisation procedure: a master module to construct configurations from the superstructure and a submodule to optimize the process unit conversions and product temperatures of the configurations. A numerical example based on an actual operating refinery in Kuwait is illustrated to implement the approach with a resulting configuration that agrees with real-world practices.

A Bi-Level Capacity Optimization of an Isolated Microgrid With Load Demand Management Considering Load and Renewable Generation Uncertainties

Aiming at capacity optimization of an isolated microgrid, this paper establishes a bi-level capacity optimization model that considers load demand management (LDM) while comprehensively considering load and renewable generation uncertainties. The uncertainties in this paper are brought by the source and load on the same timescale, as well as by the different characteristics of uncertainty presented over different timescales. For long timescales, the problem of source/load random uncertainty is solved using the stochastic network calculus theory to meet the energy balance constraints. For short timescales, we primarily aim to resolve the problem of power balance at the operation level, considering the uncertainty of source/load prediction errors and the impact of LDM. Particularly, by controlling the interruptible and shiftable loads, the LDM can optimize load characteristics, reduce operation costs, and increase system stability. The bi-level optimization model established in this paper is analyzed with regard to energy and power balance constraints, and the proposed mixed integer linear programming (MILP) model is solved by utilizing the CPLEX solver to minimize the investment cost. A typical microgrid, comprising a wind turbine (WT), a photovoltaic panel (PV), a controllable micro generator (CMG), and an energy storage system (ESS), is taken as an example to study capacity optimization problems. The simulation results verify the rationality and effectiveness of the proposed model and method.

Adaptive Consensus Algorithm for Distributed Heat-Electricity Energy Management of an Islanded Microgrid

This paper proposes a novel adaptive consensus algorithm (ACA) for distributed heat-electricity energy management (HEEM) of an islanded microgrid. In order to simultaneously satisfy the heat-electricity energy balance constraints, ACA is implemented with a switch between unified consensus and independent consensus according to the dynamic energy mismatches. The feasible operation region of a combined heat and power (CHP) unit is decomposed into eight searching sub-regions, thus its electricity and heat energy outputs can simultaneously match the incremental cost consensus requirement and the heat-electricity energy balance constraints. Case studies are thoroughly carried out to verify the performance of ACA for distributed HEEM of an islanded microgrid.

Sustainable Design and Synthesis of Shale Gas Processing and Chemical Manufacturing Processes

In this work, we propose a superstructure of integrated shale gas processing and chemical manufacturing processes with 51,840 alternative possible process designs. The superstructure consists of eight sections, namely acid gas removal, dehydration, NGLs recovery, NGLs separation, hydrocarbons conversion, light olefins separation, C4 separation, and acid gas disposal. For the steam cracking reactions in the hydrocarbons conversion section, we optimize the product distributions of steam cracking of ethane, propane, n-butane, and i-butane. Extensive process simulations are performed for all the involved processes in the superstructure in order to collect high-fidelity process data and develop detailed process models for the technology/process alternatives in the superstructure. Next, we propose a multiobjective mixed-integer nonlinear programming (MINLP) superstructure optimization model with five groups of constraints, namely superstructure network configuration constraints, mass balance constraints, energy balance constraints, techno-economic evaluation constraints, environmental impact assessment constraints. Three objective functions are maximizing the net present value per GJ of raw shale gas, minimizing the global warming potential per GJ of raw shale gas, and minimizing the water footprint per GJ of raw shale gas, respectively. A tailored global optimization algorithm is applied to efficiently solve the resulting nonconvex MINLP problem. The application of the proposed framework is illustrated through a case study based on a Marcellus shale gas feed.

Assessment of bagasse and trash utilization for ethanol production: A case study in india

Retrofitting existing sugar mills to produce ethanol from sugarcane bagasse provides a significant opportunity in India to meet the nation's liquid transportation fuel demands. Utilization of sugarcane trash in the sugar mill can enhance the economic feasibility of this approach. This work developed an optimization model to determine the optimal distribution of bagasse and trash for ethanol production while simultaneously ensuring energy sufficiency of the sugar mill. A superstructure of sugar mill integrated with a second generation ethanol facility along with trash utilization and lignin valorization processes is developed. The model determines the break‐even selling price (BESP) of ethanol by optimizing the distribution of bagasse and trash subjected to the mass and energy balance constraints and cost functions. The application of the model for a sugar mill with a throughput of 150 Mg (Mega grams)/h of sugarcane showed the ethanol BESP to be Rs. 63/L when trash and lignin was available along with bagasse for heat production. Trash retention on farm increased the BESP to Rs. 117/L, indicating the economic value of trash utilization. However, on‐farm trash retention led to about 82% savings in GHG emissions due to reduced fertilizer use. Lignin valorization was found to be economically infeasible. © 2018 American Institute of Chemical Engineers Environ Prog, 37: 1901–1907, 2018

An MILP Method for Design of Distributed Energy Resource System Considering Stochastic Energy Supply and Demand

A distributed energy resource (DER) system, which can be defined as a medium or small energy conversion and utilization system with various functions for meeting multiple targets, is directly oriented towards users and achieves on-site production and energy supply according to users’ demands. Optimization research on system construction has recently become an important issue. In this paper, simple stochastic mathematical equations were used to interpret the optimal design problem of a DER system, and based on this, a novel method for solving the optimization problem, which has multi-dimensional stochastic uncertainties (involving the price of input-energy and energy supply and demand), was put forward. A mixed-integer linear programming (MILP) model was established for the optimal design of the DER system by combining the ideas of mean value and variance, aiming to minimize the total costs, including facility costs, energy purchase costs, and loss caused by energy supply shortage, and considering the energy balance and facility performance constraints. In the end, a DER system design for an office building district in Xuzhou, China, was taken as an example to verify the model. The influences of uncertainty on the selection of system facilities and the economic evaluation were analyzed. The result indicated that uncertainty of energy demand played a significant role in optimal design, whereas energy price played a negligible role. With respect to economy, if uncertainties are not considered in system design, it will result in a short supply, and therefore the total cost will increase considerably. The calculation convergence was compared with previous work. The implementation results showed the practicality and efficiency of the proposed method.

Fish Feeding Behavior in a Local Canada Goose (Branta canadensis) Population

ABSTRACT.— North American geese (Anserini) are largely herbivorous, yet exploration and exploitation of a variety of food sources is well known. Utilization of a novel food source can be limited by many factors, including, but not limited to, general morphology and physiology, availability in the landscape, and energy balance constraints. Canada Geese (Branta canadensis) are documented to be exclusively herbivorous, yet herein we report observations over a two-year period of at least 8 different individual Canada Geese catching and eating fish. We hypothesize that this behavior represents an opportunistic exploitation of a readily available food source during a time when weather conditions limit foraging activities on the surrounding landscape. Our observations suggest the possibility of fish as a potential food source not previously recognized for Canada Geese.

Possibility of hydrogen supply by shared residential fuel cell systems for fuel cell vehicles

Residential polymer electrolyte fuel cells cogeneration systems (residential PEFC systems) produce hydrogen from city gas by internal gas-reformer, and generate electricity, the hot water at the same time. From the viewpoint of the operation, it is known that residential PEFC systems do not continuously work but stop for long time, because the systems generate enough hot water for short operation time. In other words, currently residential PEFC systems are dominated by the amount of hot water demand. This study focuses on the idle time of residential PEFC systems. Since their gas-reformers are free, the systems have potential to produce hydrogen during the partial load operations. The authors expect that residential PEFC systems can take a role to supply hydrogen for fuel cell vehicles (FCVs) before hydrogen fueling stations are distributed enough. From this perspective, the objective of this study is to evaluate the hydrogen production potential of residential PEFC systems. A residential PEFC system was modeled by the mixed integer linear programming to optimize the operation including hydrogen supply for FCV. The objective function represents annual system cost to be minimized with the constraints of energy balance. It should be noted that the partial load characteristics of the gas-reformer and the fuel cell stack are taken into account to derive the optimal operation. The model was employed to estimate the possible amount of hydrogen supply by a residential PEFC system. The results indicated that the system could satisfy at least hydrogen demand for transportation of 8000 km which is as far as the average annual mileage of a passenger car in Japan. Furthermore, hydrogen production by sharing a residential PEFC system with two households is more effective to reduce primary energy consumption with hydrogen supply for FCV than the case of introducing PEFC in each household.

Dynamic Spatial Auction Market Models with General Cost Mappings

The deregulation of electricity markets in Europe has deeply changed the organization of this sector. Vertically integrated generating companies have been unbundled to create competition and to increase the competitiveness of electricity markets. Directive 96/92/EC was issued by the European Commission to liberalize electricity markets and to pave the way for the creation of the Internal Electricity Market. In particular, this Directive aimed at promoting the competition in the activities of electricity generation and wholesale through the creation of a “marketplace” and the maximization of transparency and efficiency. Competition in European day-ahead electricity markets has been established through auction markets where electricity producers and consumers offer/bid prices and volumes. This paper suggests a dynamic equilibrium model for a system of auction markets linked by transmission lines and subject to energy balance and transmission constraints, such as those characterizing restructured electricity markets. This model is treated as a system of variational inequalities with arbitrary monotone mappings. An inexact splitting type method is proposed to find its solution. Numerical experiments are conducted on the Italian day-ahead electricity market.

Evaluating the complementary relationship for estimating evapotranspiration using the multi-site data across north China

The ability to predict actual evapotranspiration flux (λEa) by physically based evaporanspiration (ET) model is limited globally due to the difficulty in validating the site-specific model parameters. Thus, the approaches for estimating λEa using only routine meteorological variables play a critical role in understanding and predicting hydrological cycle in the context of climate change. In this study, the performance of a complementary relationship (CR) method (Granger and Gray, 1989; GG model) on different timescales (daily and half-hourly) was evaluated using a high-quality dataset of selected 12 eddy covariance flux towers, which encompassed a number of cropland, grassland, evergreen needleleaf forest, desert shrub and wetland sites across northern China. The results indicated that the GG model is applicable in estimating daily λEa for most ecosystems across northern China. However, significant underestimations of daily λEa were found for the croplands (Daman and Dunhuang sites) and the desert shrub (Ejina) in the arid northwest China, which may be attributed to the enhanced λEa by horizontal advection and the deep root water-uptake, respectively. By using the Monin-Obukhov similarity theory with a surface energy balance constraint, the model performance on half-hourly timescale was satisfactory for the 12 tower sites with R2 ranging from 0.54 to 0.81 and the slopes of Deming regression line between measured and simulated λEa from 0.77 to 1.14. Indeed, the study highlights the need for further investigation of the timescale dependence of the CR-based ET models.

Data reconciliation with application to a natural gas processing plant

Data reconciliation is a mathematical technique that uses process information to fulfill material and energy conservation laws. This technique adjusts random errors in the measured data in weighted least squares to satisfy mass and energy balance constraints. In this paper, data reconciliation is applied to a natural gas processing plant. Based on the measured data, the mass flow of output streams is greater than the mass flow of the raw feed to the plant which leads to an imbalance of about 7%.The global test is employed to check the presence of systematic errors (gross errors) in the measured data. The results indicate that there is no gross error in the measurements.

The Observed State of the Energy Budget in the Early Twenty-First Century

Abstract New objectively balanced observation-based reconstructions of global and continental energy budgets and their seasonal variability are presented that span the golden decade of Earth-observing satellites at the start of the twenty-first century. In the absence of balance constraints, various combinations of modern flux datasets reveal that current estimates of net radiation into Earth’s surface exceed corresponding turbulent heat fluxes by 13–24 W m−2. The largest imbalances occur over oceanic regions where the component algorithms operate independent of closure constraints. Recent uncertainty assessments suggest that these imbalances fall within anticipated error bounds for each dataset, but the systematic nature of required adjustments across different regions confirm the existence of biases in the component fluxes. To reintroduce energy and water cycle closure information lost in the development of independent flux datasets, a variational method is introduced that explicitly accounts for the relative accuracies in all component fluxes. Applying the technique to a 10-yr record of satellite observations yields new energy budget estimates that simultaneously satisfy all energy and water cycle balance constraints. Globally, 180 W m−2 of atmospheric longwave cooling is balanced by 74 W m−2 of shortwave absorption and 106 W m−2 of latent and sensible heat release. At the surface, 106 W m−2 of downwelling radiation is balanced by turbulent heat transfer to within a residual heat flux into the oceans of 0.45 W m−2, consistent with recent observations of changes in ocean heat content. Annual mean energy budgets and their seasonal cycles for each of seven continents and nine ocean basins are also presented.

Effects of Mission Requirements on Primary Parameters of Wing-Sail Solar-Powered Aircraft

Solar-powered aircraft of wing-sail configuration employ sail tails mounted with photovoltaic (PV) modules, which could maximize solar energy absorption by rotation around individual roll axes or by yawing control of the aircraft. The guidelines of determining primary parameters for the wing-sail configuration differ significantly from solar-powered aircraft of conventional configuration. Effects of top-architecture mission requirements under the constraints of energy balance and mass balance are explored to investigate flight principles of the wing-sail configuration. The results show that the wing-sail has more potential for year-round operation at wide latitudes, equilibrium ceiling capacity of the wing-sail still differs significantly in a whole year: higher near summer and lower near winter and larger payload mass leads to higher payload-carrying capacity.

Hourly Demand Response in Day-Ahead Scheduling Considering Generating Unit Ramping Cost

This paper proposes a day-ahead scheduling model in which the hourly demand response (DR) is considered to reduce the system operation cost and incremental changes in generation dispatch when the ramping cost of thermal generating units is considered as penalty in day-ahead scheduling problem. The power output trajectory of a thermal generating unit is modeled as a piecewise linear function. The day-ahead scheduling is formulated as a mixed-integer quadratically constrained programming (MIQCP) problem with quadratic energy balance constraint, ramping cost, and DR constraints. A Lagrangian relaxation (LR) based method is applied to solve this problem. Numerical tests are conducted on a 6-bus system and the modified IEEE 118-bus system. The results demonstrate the merits of the proposed scheduling model as well as the impact of introducing ramping costs as penalty and DR as incentives in the day-ahead scheduling of power systems.

Interpretation of Diffusive and Nondiffusive Transport in Tokamak Edge Pedestal Measurements

A formalism, based on particle, momentum, and energy balance constraints, for the interpretation of diffusive and nondiffusive transport from plasma edge measurements is presented and applied to interpret transport differences between low-mode and high-mode DIII-D [J. Luxon, Nucl. Fusion, Vol. 42, p. 614 (2002)] plasmas. The experimental values of basic transport properties (thermal diffusivities and momentum transport frequencies) inferred for H-mode and L-mode are compared with each other and with “classical” predictions. Once the basic transport mechanisms are ascertained by such comparison of theoretical predictions with experimental inference, the presented formalism will provide a first-principles predictive model for density, temperature, velocity, and pressure profiles in the edge pedestal.

A mathematical programming approach for optimal design of distributed energy systems at the neighbourhood level

This paper presents a mixed-integer linear programming (MILP) super-structure model for the optimal design of distributed energy generation systems that satisfy the heating and power demand at the level of a small neighborhood. The objective is the optimal selection of the system components among several candidate technologies (micro combined heat and power units, photovoltaic arrays, boilers, central power grid), including the optimal design of a heating pipeline network, that allows heat exchange among the different nodes. The objective function to be minimised contains the annualised overall investment cost and the annual operating cost of the system. We show that besides the usual energy balance and unit operations constraints, additional equations must be included in the model to guarantee correctness of the produced heating pipeline designs. A special instance of the problem where a single centralised combined heat and power unit is installed in the neighborhood is also considered. The efficiency of the proposed model is evaluated through illustrating examples.

Model for Predicting the Mean Drop Size in Effervescent Sprays

This paper is focused on the development of a model for predicting the mean drop size in effervescent sprays. A combinatorial approach is followed in this modeling scheme, which is based on energy and entropy principles. The model is implemented in cascade in order to take primary breakup (due to exploding gas bubbles) and secondary breakup (due to shearing action of surrounding medium) into account. The approach in this methodology is to obtain the most probable drop size distribution by maximizing the entropy while satisfying the constraints of mass and energy balance. The comparison of the model predictions with the past experimental data is presented for validation. A careful experimental study is conducted over a wide range of gas-to-liquid ratios, which shows a good agreement with the model predictions: It is observed that the model gives accurate results in bubbly and annular flow regimes. However, discrepancies are observed in the transitional slug flow regime of the atomizer.