Variable Electricity Prices Research Articles

Nonconvex model predictive control for commercial refrigeration

We consider the control of a commercial multi-zone refrigeration system, consisting of several cooling units that share a common compressor, and is used to cool multiple areas or rooms. In each time period we choose cooling capacity to each unit and a common evaporation temperature. The goal is to minimise the total energy cost, using real-time electricity prices, while obeying temperature constraints on the zones. We propose a variation on model predictive control to achieve this goal. When the right variables are used, the dynamics of the system are linear, and the constraints are convex. The cost function, however, is nonconvex due to the temperature dependence of thermodynamic efficiency. To handle this nonconvexity we propose a sequential convex optimisation method, which typically converges in fewer than 5 or so iterations. We employ a fast convex quadratic programming solver to carry out the iterations, which is more than fast enough to run in real time. We demonstrate our method on a realistic model, with a full year simulation and 15-minute time periods, using historical electricity prices and weather data, as well as random variations in thermal load. These simulations show substantial cost savings, on the order of 30%, compared to a standard thermostat-based control system. Perhaps more important, we see that the method exhibits sophisticated response to real-time variations in electricity prices. This demand response is critical to help balance real-time uncertainties in generation capacity associated with large penetration of intermittent renewable energy sources in a future smart grid.

Two-Stage Mathematical Programming Approach for Steelmaking Process Scheduling Under Variable Electricity Price

The steelmaking process scheduling problem by considering variable electricity price (SMSPVEP) was investigated. A decomposition approach was proposed for the SMSPVEP. At the first stage, mathematical programming was utilized to minimize the maximum completion time for each cast without considering variable electricity price. At the second stage, based on obtained relative schedules of all casts, a mathematical model was formulated with an objective of minimizing the energy cost for all casts scheduling problem. The two-stage models were tested on randomly generated instances based on the practical process in a Chinese steelmaking plant. Computational results demonstrate the effectiveness of the proposed approach.

Do local energy prices and regulation affect the geographic concentration of employment?

Manufacturing industries differ with respect to their energy intensity, labor-to-capital ratio and their pollution intensity. Across the United States, there is significant variation in electricity prices and labor and environmental regulation. This paper examines whether the basic logic of comparative advantage can explain the geographical clustering of U.S. manufacturing. We document that energy-intensive industries concentrate in low electricity price counties and labor-intensive industries avoid pro-union counties. We find mixed evidence that pollution-intensive industries locate in counties featuring relatively lax Clean Air Act regulation.

A Communication-Based Appliance Scheduling Scheme for Consumer-Premise Energy Management Systems

In this paper, a communication-based load scheduling protocol is proposed for in-home appliances connected over a home area network. Specifically, a joint access and scheduling approach for appliances is developed to enable in-home appliances to coordinate power usage so that the total energy demand for the home is kept below a target value. The proposed protocol considers both “schedulable” appliances which have delay flexibility, and “critical” appliances which consume power as they desire. An optimization problem is formulated for the energy management controller to decide the target values for each time slot, by incorporating the variation of electricity prices and distributed wind power uncertainty. We model the evolution of the protocol as a two-dimensional Markov chain, and derive the steady-state distribution, by which the average delay of an appliance is then obtained. Simulation results verify the analysis and show cost saving to customers using the proposed scheme.

Cycling Coal and Natural Gas-fired Power Plants with CCS

The profitability impacts of solvent storage are modeled for new coal and natural gas-fired power plants with amine and ammonia-based post-combustion CCS facing variable electricity prices. With perfect information of future prices, up to 3hours of solvent storage was valuable due to price volatility at carbon prices up to $40/tonne CO2 and no regenerator undersize. With imperfect information with relaxed constraints on regenerator undersizing, up to 8hours of solvent storage was valuable when coupled with an undersized CO2 capture system at carbon prices up to $60/tonne CO2. The results indicate that storage does not have value above the breakeven CO2 price for these plants.

Economic implications of thermal energy storage for concentrated solar thermal power

Solar energy is an attractive renewable energy source because the sun's energy is plentiful and carbon-free. However, solar energy is intermittent and not suitable for base load electricity generation without an energy backup system. Concentrated solar power (CSP) is unique among other renewable energy options because it can approach base load generation with molten salt thermal energy storage (TES). This paper describes the development of an engineering economic model that directly compares the performance, cost, and profit of a 110-MW parabolic trough CSP plant operating with a TES system, natural gas-fired backup system, and no backup system. Model results are presented for 0–12 h backup capacities with and without current U.S. subsidies. TES increased the annual capacity factor from around 30% with no backup to up to 55% with 12 h of storage when the solar field area was selected to provide the lowest levelized cost of energy (LCOE). Using TES instead of a natural gas-fired heat transfer fluid heater (NG) increased total plant capital costs but decreased annual operation and maintenance costs. These three effects led to an increase in the LCOE for PT plants with TES and NG backup compared with no backup. LCOE increased with increasing backup capacity for plants with TES and NG backup. For small backup capacities (1–4 h), plants with TES had slightly lower LCOE values than plants with NG backup. For larger backup capacities (5–12 h), plants with TES had slightly higher LCOE values than plants with NG backup. At these costs, current U.S. federal tax incentives were not sufficient to make PT profitable in a market with variable electricity pricing. Current U.S. incentives combined with a fixed electricity price of $200/MWh made PT plants with larger backup capacities more profitable than PT plants with no backup or with smaller backup capacities. In the absence of incentives, a carbon price of $100–$160/tonne CO2eq would be required for these PT plants to compete with new coal-fired power plants in the U.S. If the long-term goal is to increase renewable base load electricity generation, additional incentives are needed to encourage new CSP plants to use thermal energy storage in the U.S.

Simultaneous optimization of size and short-term operation for an RO plant

The single day operation and size of a seawater reverse osmosis (RO) plant subject to a half-hourly varying electricity price is optimized. The study herein is an extension of Ghobeity and Mitsos, 2010 Desalination. Their model is modified to have a variable plant size controlled by the number of modules. The operating and capital costs are calculated as a function of size and operation. The objective of the optimization is to minimize the total annualized cost of the plant. The number of modules and the half-hourly varying operating frequency constitute the decision variables. The operation and size are optimized for four different electricity price functions: constant, moderately fluctuating, highly fluctuating, and actual electricity prices from a given day in Spain. The results show that variable operation and oversizing can produce savings of up to 7% for a highly fluctuating electricity price. The plant has a higher operating frequency when electricity is cheap and shuts off during periods of high electricity price when oversized. The size and day-by-day operation are also optimized for one year subject to Spain's electricity price. Little savings via oversizing are obtainable for the day-by-day optimization due to low fluctuations in the electricity price during the year.

Decarbonization scenarios for the EU and MENA power system: Considering spatial distribution and short term dynamics of renewable generation

We use the multi-scale power system model LIMES-EU+ to explore coordinated long term expansion pathways for Renewable Energy (RE) generation, long distance transmission and storage capacities for the power sector of the Europe and Middle East/North Africa (MENA) regions that lead to a low emission power system. We show that ambitious emission reduction targets can be achieved at moderate costs by a nearly complete switch to RE sources until 2050, if transmission and storage capacities are expanded adequately. Limiting transmission capacities to current levels leads to higher storage requirements, higher curtailments, and to an increase in temporal and spatial electricity price variations. Results show an escalation of electricity prices if emission reductions exceed a critical value. Adequate expansion of transmission and storage capacities shift this threshold from 70% to 90% emission reductions in 2050 relative to 2010.

Optimal Generation Mix With Short-Term Demand Response and Wind Penetration

Demand response, defined as the ability of load to respond to short-term variations in electricity prices, plays an increasingly important role in balancing short-term supply and demand, especially during peak periods and in dealing with fluctuations in renewable energy supplies. However, demand response has not been included in standard models for defining the optimal generation technology mix. Three different methodologies are proposed to integrate short-term responsiveness into a generation technology mix optimization model considering operational constraints. Elasticities are included to adjust the demand profile in response to price changes, including cross-price elasticities that account for load shifts among hours. As energy efficiency programs also influence the load profile, interactions of efficiency investments and demand response are also modeled. Comparison of model results for a single year optimization with and without demand response shows peak reduction and valley filling effects, impacting the optimal amounts and mix of generation capacity. Increasing demand elasticity also increases the installed amount of wind capacity, suggesting that demand response yields environmental benefits by facilitating integration of renewable energy.

Sensitivity of district heating system operation to heat demand reductions and electricity price variations: A Swedish example

In the future, district heating companies in Sweden must adapt to energy efficiency measures in buildings and variable fuel and electricity prices. Swedish district heating demands are expected to decrease by 1–2% per year and electricity price variations seem to be more unpredictable in the future. A cost-optimisation model of a Swedish local district heating system is constructed using the optimisation modelling tool MODEST. A scenario for heat demand changes due to increased energy efficiency in buildings, combined with the addition of new buildings, is studied along with a sensitivity analysis for electricity price variations. Despite fears that heat demand reductions will decrease co-generation of clean electricity and cause increased global emissions, the results show that anticipated heat demand changes do not increase the studied system's primary energy use or global CO2 emissions. The results further indicate that the heat production plants and the fuels used within the system have crucial importance for the environmental impact of district heat use. Results also show that low seasonal variations in electricity price levels with relatively low winter prices promote the use of electric heat pumps. High winter prices on the other hand promote co-generation of heat and electricity in CHP plants.

Multi-objective optimal control of an air-to-water heat pump for residential heating

The current study investigates the optimal operation of an air-to-water heat pump system. To this end, the control problem is formulated as a classic optimal control or dynamic optimization problem. As conflicting objectives arise, namely, minimizing energy cost while maximizing thermal comfort, the optimization problem is tackled from a multi-objective optimization perspective. The adopted system model incorporates the building dynamics and the heat pump characteristics. Because of the state-dependency of the coefficient of performance (COP), the optimal control problem (OCP) is nonlinear. If the COP is approximated by a constant value, the OCP becomes convex, which is easier to solve. The current study investigates how this approximation affects the control performance. The optimal control problems are solved using the freely available Automatic Control And Dynamic Optimization toolkit ACADO. It is found that the lower the weighting factor for thermal discomfort is, the higher the discrepancy is between the nonlinear and convex OCP formulations. For a weighting factor resulting in a quadratic mean difference of 0.5°C between the zone temperature and its reference temperature, the difference in electricity cost amounts to 4% for a first scenario with fixed electricity price, and up to 6% for a second scenario with a day and night variation in electricity price.

Model predictive control technologies for efficient and flexible power consumption in refrigeration systems

Considerable amounts of energy are consumed in supermarket refrigeration systems worldwide. Due to the thermal capacity of refrigerated goods and the rather simplistic control most commonly applied, there is a potential for distributing the system load over time in a more cost-optimal way. In this paper we describe a novel economic-optimizing Model Predictive Control (MPC) scheme that reduces operating costs by utilizing the thermal storage capabilities. A nonlinear optimization tool to handle a non-convex cost function is utilized for simulations with validated scenarios. In this way we explicitly address advantages from daily variations in outdoor temperature and electricity prices. Secondly, we formulate a new cost function that enables the refrigeration system to contribute with ancillary services to the balancing power market. This involvement can be economically beneficial for the system itself, while crucial services can be delivered to a future flexible and intelligent power grid (Smart Grid). Furthermore, we discuss a novel incorporation of probabilistic constraints and Second Order Cone Programming (SOCP) with economic MPC. A Finite Impulse Response (FIR) formulation of the system models allows us to describe and handle model as well as prediction uncertainties in this framework. This means we can demonstrate means for robustifying the performance of the controller.

Fast Nonconvex Model Predictive Control for Commercial Refrigeration

We consider the control of a commercial multi-zone refrigeration system, consisting of several cooling units that share a common compressor. The goal is to minimize the total energy cost, using real-time electricity prices, while obeying temperature constraints on the zones. We propose a variation on model predictive control to achieve this goal. When the right variables are used, the dynamics of the system are linear, and the constraints are convex. The cost function, however, is nonconvex. To handle this nonconvexity we propose a sequential convex optimization method, which typically converges in fewer than 5 or so iterations. We employ a fast convex quadratic programming solver to carry out the iterations, which is more than fast enough to run in real-time. We demonstrate our method on a realistic model, with a full year simulation, using real historical data. These simulations show substantial cost savings, and reveal how the method exhibits sophisticated response to real-time variations in electricity prices. This demand response is critical to help balance real-time uncertainties associated with large penetration of intermittent renewable energy sources in a future smart grid.

Simultanous emergency demand response programming and unit commitment programming in comparison with interruptible load contracts

Different reasons such as power system restructuring, electricity price variation in some hours of a day and growth in the fuel price, have led to more attention to demand response (DR) programmes for consumers. Two important issues in DR programmes are emergency demand response programming (EDRP) and Interruptible/Curtail able (I/C) programme that is utilised as interruptible load contracts (ILC). The EDDR is utilised to decrease the consumption in peak load or critical hours of the day. This occurs by means of customer's behaviour in response to the incentives. However, the curtailment of voluntarily loads in the critical hours considering the consumer requirements is an action that can be performed in DR. A model has been proposed for EDRP and ILC implementation in the unit commitment (UC) programme. Then, the effect of these two DR programmes have been compared in long-term UC problem with fuel constraints. The proposed methodology has been formulated as a mixed integer linear problem and implemented in GAMS environment. The proposed model is applied to a 6-bus test system and a modified IEEE 118-bus system to demonstrate its effectiveness.

Optimal operation of an integrated energy system including fossil fuel power generation, CO 2 capture and wind

This study considers the optimization of operations for an integrated fossil-renewable energy system with CO 2 capture. The system treated consists of a coal-fired power station, a temperature-swing absorption CO 2 capture facility powered by a natural gas combustion turbine, and wind generation. System components are represented in a modular fashion using energy and mass balances. Optimization is applied to determine hourly system dispatch to maximize operating profit given energy prices and wind generation data. A CO 2 emission constraint, modeled after a California law, is enforced. Idealized and realistic scenarios are considered, along with several different system specifications. For a year of operation, simulated using available wind and energy price data, operating profit for optimized operation is shown to be approximately 20% greater than profit using a heuristic procedure. The benefit from optimization is positively correlated with electricity price variability and mean wind generation. The impact of different component specifications and different CO 2 absorption solvents on the optimal operation of the energy system is also assessed. In total, this study demonstrates that the effective operating cost of an integrated energy system operating under a CO 2 emission constraint can be substantially reduced via optimal flexible operation.

Lyapunov stability of economically oriented NMPC for cyclic processes

Abstract Several applications in process industries, such as simulated moving bed (SMB) separation and pressure swing adsorption (PSA), exhibit cyclic steady state behavior. Moreover, it is of economic interest to require energy intensive applications to take advantage of the periodically varying electricity price by changing the operating point frequently. Because traditional two-layer optimization methods are difficult to apply to these systems, we consider instead an economically oriented nonlinear model predictive control (NMPC) that directly considers system’s economic performance subject to the dynamic model. On the other hand, the commonly used Lyapunov framework to analyze the stability for the economically oriented NMPC cannot be applied directly. This work proposes two economically oriented NMPC formulations and proves nominal stability for both. We introduce transformed systems by subtracting the optimal cyclic steady state from the original system, for which the Lyapunov function can easily be established. Moreover, we show that the asymptotical stability of the transformed system is equivalent to that of the original system. Hence, the original systems are also nominally stable at the cyclic optimal solution. Finally, an industrial size air separation unit case study with periodic electricity cost is presented.

Optimal charging of electric drive vehicles in a market environment

With a potential to facilitate the integration of renewable energy into the electricity system, electric drive vehicles may offer a considerable flexibility by allowing for charging and discharging when desired. This paper takes the perspective of an aggregator that manages the electricity market participation of a vehicle fleet and presents a framework for optimizing charging and discharging of the electric drive vehicles, given the driving patterns of the fleet and the variations in market prices of electricity. When the aggregator is a price-taker the optimization can be stated in terms of linear programming whereas a quadratic programming formulation is required when he/she has market power. A Danish case study illustrates the construction of representative driving patterns through clustering of survey data from Western Denmark and the prediction of electricity price variations through regression on prices from the Nordic market. The results show that electric vehicles provide flexibility almost exclusively through charging. Moreover, the vehicles provide flexibility within the day but only limited flexibility from day to day when driving patterns are fixed.

A multiperiod nonlinear programming approach for operation of air separation plants with variable power pricing

AbstractCryogenic air separation processes consume a large amount of electricity producing significant quantities of high purity gases. Rather than operating at a fixed steady state, it may be profitable to switch among different operating conditions because of variability of electrical prices and product demands. This article addresses the problem of determining the optimal daily multiperiod operating conditions for an air separation process under variable electricity pricing and uncertain product demands. The multiperiod nonlinear programming formulation includes a rigorous nonlinear model of the highly‐coupled process, and decision variables include the operating conditions within each period, as well as the transition times. Demand uncertainty is treated using the loss function included in the objective function and constraints on customer satisfaction levels. Solutions are obtained with high computational efficiency, allowing management to make informed decisions regarding operating strategies while considering the trade off between profitability and customer satisfaction levels. © 2010 American Institute of Chemical Engineers AIChE J, 2011

A comparative analysis of the value of pure and hybrid electricity storage

Significant natural gas and electricity price variation and volatility, especially during the past few years, raise questions about understanding the value drivers behind electricity storage. The impact of these drivers for pure storage (such as pumped hydroelectric storage) and compressed air energy storage (CAES) are different and in this paper we explore these differences in operation and net revenue over a variety of timescales. We also consider the arbitrage value that is attainable in practice and explain why simple forecasting techniques based on historical data will generally be less successful for CAES. The breakeven cost of storage and how this can depend on regulatory treatment of storage and market structure is also considered.

EABOT – Energetic analysis as a basis for robust optimization of trigeneration systems by linear programming

The optimization of synthesis, design and operation in trigeneration systems for building applications is a quite complex task, due to the high number of decision variables, the presence of irregular heat, cooling and electric load profiles and the variable electricity price. Consequently, computer-aided techniques are usually adopted to achieve the optimal solution, based either on iterative techniques, linear or non-linear programming or evolutionary search. Large efforts have been made in improving algorithm efficiency, which have resulted in an increasingly rapid convergence to the optimal solution and in reduced calculation time; robust algorithm have also been formulated, assuming stochastic behaviour for energy loads and prices. This paper is based on the assumption that margins for improvements in the optimization of trigeneration systems still exist, which require an in-depth understanding of plant’s energetic behaviour. Robustness in the optimization of trigeneration systems has more to do with a “correct and comprehensive” than with an “efficient” modelling, being larger efforts required to energy specialists rather than to experts in efficient algorithms. With reference to a mixed integer linear programming model implemented in MatLab for a trigeneration system including a pressurized (medium temperature) heat storage, the relevant contribute of thermoeconomics and energo-environmental analysis in the phase of mathematical modelling and code testing are shown.