Time Of Use Electricity Pricing Research Articles

Joint capacity configuration and demand response optimization of integrated energy system considering economic and dynamic control performance

This paper proposes a joint optimization framework for the demand response-capacity configuration design of the integrated energy system (IES), in which both the economic cost and closed-loop dynamic regulation performance under source-load fluctuations are considered. The joint optimization consists of two layers. The upper layer optimizes the time of use electricity price to adjust the demand response of electric load; while the lower layer optimizes the capacity configuration, scheduling instructions and incentive-based thermal load demand response under typical scenarios. To fairly evaluate the impact of equipment capacity and demand response on the dynamic control performance of the IES, multi-parameter programming-based predictive control approach is applied to develop an offline design and scheduling-perceptive control system. A closed-loop dynamic scheduler is then developed based on the control system, which can optimize the operating instruction of each equipment considering their dynamic operating practice. Simulation studies on a typical off-grid combined heat and power IES show that the proposed approach can effectively match the demand response to the capacity configuration of the IES, helping the system achieve a dynamically flexible and economic energy supply.

An Effective Method of Equivalent Load-Based Time of Use Electricity Pricing to Promote Renewable Energy Consumption

The variability and intermittency inherent in renewable energy sources poses significant challenges to balancing power supply and demand, often leading to wind and solar energy curtailment. To address these challenges, this paper focuses on enhancing Time of Use (TOU) electricity pricing strategies. We propose a novel method based on equivalent load, which leverages typical power grid load and incorporates a responsibility weight for renewable energy consumption. The responsibility weight acts as an equivalent coefficient that accurately reflects renewable energy output, which facilitates the division of time periods and the development of a demand response model. Subsequently, we formulate an optimized TOU electricity pricing model to increase the utilization rate of renewable energy and reduce the peak–valley load difference of the power grid. To solve the TOU pricing optimization model, we employ the Social Network Search (SNS) algorithm, a metaheuristic algorithm simulating users’ social network interactions to gain popularity. By incorporating the users’ mood when expressing opinions, this algorithm efficiently identifies optimal pricing solutions. Our results demonstrate that the equivalent load-based method not only encourages renewable energy consumption but also reduces power generation costs, stabilizes the power grid load, and benefits power generators, suppliers, and consumers without increasing end users’ electricity charges.

Optimization method of time-of-use electricity price for the cost savings of power grid investment

The concept of time-of-use (TOU) electricity pricing is widely recognized as a key strategy to bridge the gap between electricity availability and consumption, enhance the efficiency of electricity, and refine the patterns of electricity usage. Nonetheless, the existing policy on pricing electricity based on TOU electricity pricing is missing a theoretical approach that evaluates the load properties and the advantages of investing in the power grid. Consequently, the article suggests a method for optimizing electricity prices based on TOU electricity pricing to reduce the costs associated with investing in power grids. Initially, a model for optimizing electricity prices based on TOU electricity pricing is developed, offering support for the pricing strategy of the power grid; Subsequently, a method for dividing TOU electricity pricing using the Gaussian Mixture Module (GMM) clustering algorithm is introduced, offering theoretical backing for the creation of such pricing strategies; Following this, a detailed optimization approach for electricity pricing of electricity TOU electricity pricing is suggested, along with taking into account the benefits of grid investments and the power grid’s load properties, the formulation of the electricity pricing strategy for TOU electricity pricing; Ultimately, this approach is corroborated by the Chongqing power system in China, aiming to minimize disparities in peak load valleys and enhance the advantages of grid investments, thereby offering technical assistance for the scientific determination of TOU electricity pricing.

On the role of time‐of‐use electricity price in charge scheduling for electric bus fleets

AbstractAs electric buses become increasingly popular, it is imperative to optimize the schedules of electric buses with explicit consideration of their charging requirements. Unfortunately, existing studies failed to properly model the impacts of essential operating factors, including the time‐of‐use (TOU) electricity price, partial charging, and limited chargers. Our paper proposes a mixed‐integer nonlinear program to minimize the total operating cost of an electric bus fleet for fulfilling a group of timetabled trips, considering the above realistic features simultaneously. To effectively solve the problem of global optimality, we convert this model to an equivalent set partitioning model and develop a specialized branch‐and‐price approach subsequently. Our approach's computational efficiency is verified via extensive numerical experiments. The model is applied to a real‐world case study in Nanjing, China. Results show that incorporating the TOU electricity price into the electric bus scheduling problem can produce a sizeable cost saving of up to 22%. Managerial insights unveiled by the numerical results are discussed. These insights inform the practitioners of how the operations of electric buses can be both cost‐effective and grid‐friendly.

Multi-objective optimization of intermittent operation schemes of thermally activated building systems using grey relational analysis: A case study

The thermal storage of thermally activated building systems (TABS) demonstrates the advantages of intermittent operation, however, the existing studies rarely compared different intermittent schemes to determine the optimal one. Therefore, this study presented a case study on the multi-objective optimization of intermittent operation schemes of a TABS system equipped in a typical residential building in Xi'an. Three objectives including thermal comfort, energy conservation and economic efficiency were balanced. The comparison of the 6-h, 8-h, 12-h, and 24-h cooling durations were presented. The optimal cooling duration was determined, which further optimized the cooling time distribution, and the effects of different time-of-use (TOU) electricity prices were analyzed. The results show the 8-h cooling duration is the optimal one. When the 8-h duration is designed such that to include five cooling time distributions (i.e., 8-h daytime cooling, 8-h nighttime cooling, 2-h cooling + 1-h intermittence, 1-h cooling + 1-h intermittence, and 30-min cooling + 30-min intermittence), it is found that the optimal cooling time distribution under the TOU electricity price of Xi'an is the 1-h cooling + 1-h intermittence. In addition, the TOU electricity price greatly affect determining the optimal scheme. The results can provide references for the operation of TABS.

A pricing strategy for electric vehicle charging in residential areas considering the uncertainty of charging time and demand

In residential areas, the hours when commuters charge their electric vehicles (EVs) after work often coincide highly with the peak residential electricity consumption hours, which will create security risks to the power system and affect the normal operation of the power grid. In contrast to the inevitability and immutability of the use of household appliances, the duration and time period of charging electric vehicles can be changed. This paper addresses the aforementioned problem by time-of-use (TOU) electricity price, which can guide residents to stagger hours to charge, achieving the objective of peak load shifting. Taking residential areas as the research scope, considering the uncertainty of EV users’ homecoming time, departure time and charging demand, the article proposes a bi-level planning model for pricing electric vehicle charging. The lower level is a minimization model of charging costs for individual users, which can acquire the charging load of all vehicles for multiple days. The upper level is a robust optimization model of TOU electricity price considering uncertain factors, which obtains the fast and slow charging prices. It has been demonstrated that the model increases grid stability by 43.46%.

A novel algorithm for optimal equipment scheduling and dispatch of chilled water systems with ice thermal storage

Using thermal energy storage in chilled water systems can reduce electricity bill charges and required chiller cooling capacity through load shifting and peak demand shavings. As opposed to simple heuristic strategies, optimal storage dispatch maximizes savings by considering the time of use tariffs and system efficiency. In this paper, we propose a solution to the optimal equipment scheduling and storage dispatch problem of multi-chiller chilled water systems with ice thermal storage. We model the system in a bi-level optimization formulation that is solved using the genetic algorithm. The upper level minimizes daily operation costs and decides the storage dispatch amount over the next 24 h. The decided upon dispatch amount is fed to the lower-level optimizer to solve the equipment scheduling problem sequentially and return the corresponding system power consumption over the next 24 h. Flowrate and energy balancing constraints are handled using the penalty function method. Tuning of the penalty factors and genetic algorithm parameters significantly diminished and eliminated the problem of premature convergence. While the genetic algorithm is computationally taxing, we reduced the run time to 1–2 min by pre-solving the lower-level problem under various input conditions and tri-linearly interpolating between them. We compared the developed optimal control strategy to two commonly used heuristic storage dispatch strategies: chiller priority control and storage priority control in three scenarios of cooling demand under a time of use electricity pricing. Our model suggests optimal control reduces cost and energy by 11–14% and 10–12%, respectively, relative to storage priority control, and 16–33% and 1–9%, respectively, relative to chiller priority control. In a scenario with a demand charge, optimized control reduces demand charges by 17% relative to storage priority and 26% relative to chiller priority control. The gains from the proposed approach are augmented when a more sophisticated tariff structure is present.

Minimizing pricing policies based on user load profiles and residential demand responses in smart grids

This paper considers the time of use (TOU) pricing scheme to propose a consumer aware pricing policy (CAPP), where each customer receives a separate electricity pricing signal. These pricing signals are obtained based on individualized load demand patterns to optimally manage the flexible load demand. The main objective of CAPP is to reduce the peaks in overall system demand in such a way that the pricing signals remain non-discriminatory. To achieve this goal, firstly the mathematical model of CAPP comprising TOU electricity price, and its variation based on consumption patterns is formulated. Secondly, the proposed CAPP model is further extended by integrating renewable energy and storage sources to overcome the possible creation of rebound peaks due to scheduling. This objective is achieved by implementing a control variable modeling the upper bound of the low tariff area. Thirdly, the cost minimization optimization problem is solved by using a Genetic Algorithm (GA) with the objective of the fair price distribution. Numerical and simulation results are obtained to validate the proposed model in terms of convergence, optimality, and cost reduction objective function. Results reveal that each customer receives a separate electricity price signal based on his demand pattern without affecting the utility/retailer revenue. Furthermore, the total cost results are also compared with and without TOU & CAPP schemes to further validate the nondiscrimination in electricity price.

Time of use electricity pricing in power system planning and operation: Case study of Nepalese power system

The difference between load demand in the off-peak and peak period is usually high in the context of Nepal, and the high peak load for a short time is the main reason for insufficiency in electricity, frequent electricity outage, and poor power quality. This paper investigates the effectiveness of the time of use (TOU) strategy to reduce peak demand and to improve power quality. TOU electricity price is one of the electric demand response (DR) strategies, which may motivate the customers to reduce their consumption in peak periods and shift load in the off-peak period, which propel the electricity industry towards a higher efficiency compared to that of common flat prices. In this paper, a process based on an equal step length iteration algorithm is used to obtain an optimal period partition. Using the particle swarm optimization (PSO) algorithm, a TOU-based optimization model is proposed to find the optimal electricity price. Then, its impact on peak demand reduction and voltage fluctuation is analyzed. The impact of TOU price on peak demand reduction is investigated in the hourly load profile of Nepal, which indicates the significant reduction in peak demand. Similarly, the impact on voltage fluctuation is analyzed through a case study of the IEEE 33-bus radial distribution test system, which shows voltage profile is improved.

Hierarchical framework for maintenance and production scheduling of continuous ball mills in tile industries under TOU electricity pricing

In this paper, the interaction among Time-of-Use (TOU) electricity prices, production scheduling, and preventive maintenance of continuous slurry ball mills is addressed via a hierarchical mathematical modelling framework. Slurry ball mills are considered as the main consumer of electrical energy so that they impose high energy costs on tile factories. However, rarely energy expenses have been taken into consideration in the scheduling. In this study, a mixed-integer energy-cost-aware hierarchical formulation (ECA-H) is proposed and its superiority in terms of various indicators compared to its four possible counterparts is shown. The main contribution of the proposed model in reducing energy costs is obtained by reducing the peak load, and a small share is related to the energy saving. Based on the average of the numerical results, the proposed model compared to its classic counterpart leads to 26% reduction in energy costs, 73% reduction in the peak load, and 3% reduction in the energy consumption. Finally, several easy-yet-effective managerial insights are extracted for mangers to benefit from the findings of our study when they face practical limitations to implement the proposed mathematical model.

Optimal Time-of-Use Electricity Price for a Microgrid System Considering Profit of Power Company and Demand Users

With high proportions of renewable energy generation in power systems, the power system dispatch with renewable energy generation has currently become a popular research direction. In our study, we propose a multi-objective dispatch model for a hybrid microgrid comprising a wind generator, photovoltaic (PV) generator, and an energy storage system to optimize the time-of-use (TOU) electricity price. The objective of the proposed multi-objective dispatch model is to maximize the profit of the power company and demand users, and minimize the proportion of users abandoning PV power and wind power. The elastic price of the load demand with a linear function is employed to optimize the TOU electricity price. Finally, we applied five test cases to validate the practicability of the multi-objective dispatch model.

Collaborative optimization method and operation performances for a novel integrated energy system containing adiabatic compressed air energy storage and organic Rankine cycle

Integrated energy system (IES) coupled with advanced adiabatic compressed air energy storage (AA-CAES) and organic Rankine cycle (ORC) has the superiority to peak-load regulation and improve system performance. Therefore, a novel IES-ORC-CAES system, which includes AA-CAES, ORC and ICE, is proposed in this paper. In this system, the user return water is used to recover the compression heat generated by AA-CAES. The ICE exhaust smoke flows through three parts successively, the heat exchangers of AA-CAES energy release side, the ORC and absorption heat pump arranged in parallel and the tail heat exchanger, realizing the cascade utilization of energy and meeting the diversified energy demand of users. Considering the time of use electricity price and aiming at economy, environmental protection and energy efficiency, a collaborative optimization method that can dynamically adjust the energy output of the system is proposed. The results indicate that compared with the IES-ORC system (without AA-CAES), the annual operation cost, CO2 emission and primary energy consumption of the IES ORC-CAES system can be reduced by 14.84%, 13.06% and 11.69% under the economic, environmental and energy efficiency objectives. Furthermore, by coordinating the regulation of ICE, AA-CAES and ORC, the flexibility of the system energy supply is realized, and the matching of the electric-heat ratio on the source and load side is improved. Finally, the thermodynamic analysis of the IES-ORC-CAES system is carried out through parameter analysis. The research results can provide the reference for the operation optimization of the complex IES.

Demand Response for Industrial Micro-Grid Considering Photovoltaic Power Uncertainty and Battery Operational Cost

An intelligent demand response (DR) program is developed for multi-energy industrial micro-grid consisting of manufacturing facilities, photovoltaic (PV) panels, and battery energy storage system (BESS). The proposed DR program tackles the practical challenges of components in the micro-grid including industrial process represented by a discrete manufacturing production model, uncertainty of PV generation, and operational cost of the BESS. The proposed DR program optimizes day-ahead production scheduling for manufacturing facilities and operation regime for the BESS in response to time of use electricity price and probabilistic forecasting of PV power. To capture the uncertainty of PV power, a data-driven PV power probabilistic forecasting model is developed and a copula-based approach is deployed for the sampling of temporally correlated scenarios of PV power over the scheduling horizon from probabilistic forecasts. The multi-energy management optimization problem is formulated as a scenario-based stochastic nonconvex mixed integer nonlinear programming (MINLP). A hybrid optimization method integrating the evolutionary algorithm and the branch-and-bound algorithm for mixed integer liner programming is proposed to solve the nonconvex MINLP. Simulation studies illustrate that the proposed DR program efficiently reduces the operational cost for manufacturing production and releases the stress of the main grid by making full use of flexibility of all the components in the micro-grid.

Research on Capacity Configuration and Optimal Operation of Microgrid Energy Storage under Demand Management

In order to reduce the energy consumption cost, considering the influence of the correlation of photovoltaic output, load demand and peak valley TOU price in different periods on the optical storage capacity configuration, the system operation strategy and capacity configuration principle are determined based on the peak valley TOU price and energy storage charge state information and the actual size of photovoltaic output and load.Integrated with the historical load, time of use electricity price, state of charge, charge discharge power and other constraints of the energy storage system, the minimum objective function is utilized to optimize the output power of energy storage.The effectiveness of the model is verified by an example. The sensitivity analysis shows that different demand tariff rules affect the user demand declaration strategy. The energy storage system planning selects the light storage combination with appropriate capacity according to the demand tariff rules and the change of energy storage investment cost, which has practical engineering value.

An Approximation Algorithm for Unrelated Parallel Machine Scheduling Under TOU Electricity Tariffs

In an era of sustainable development, considerable emphasis has been put onto energy saving, environment friendly, and social welfare as well as productivity in the manufacturing sector. In this work, an unrelated parallel manufacturing setting with time-of-use (TOU) electricity price is explored, with an aim to reduce the electricity cost and increase productivity simultaneously. A nonlinear mathematical programming model is formulated to exploit the special structure of the scheduling problem, where the quadratic constraints are reformulated as second-order-cone (SOC) constraints, and several tailored cutting planes are introduced to further tighten the feasible region of the problem. Then, the original scheduling problem is transformed into several single-machine scheduling problems with TOU electricity price, which could be relaxed as a single-objective programming problem, and it could be solved rapidly via commercial solvers, such as CPLEX. Based on the optimal solution of the relaxed problem, an approximate algorithm is proposed, where a special rounding technique is employed to assign jobs to the unrelated parallel machines in a local search manner. Furthermore, a lower bound model is constructed by eliminating the nonpreemption constraint, and an iteration-based algorithm is devised to obtain the optimal solution of the lower bound problem. Meanwhile, a dispatch rule-based approach is proposed to provide an upper bound of the scheduling problem with TOU constraint. In the numerical analysis section, the proposed approximate algorithm is validated through extensive testing on various scales of instances, different emphasis on productivity and electricity price, and under two typical TOU electricity pricing policies. It is observed that the gap between the proposed approximate algorithm and CPLEX is mostly within 4%, and the lower/upper bound methods could obtain a relaxed/feasible solution within 0.01 s.

Model and Algorithm for Planning Hot-Rolled Batch Processing under Time-of-Use Electricity Pricing

Batch-type hot rolling planning highly affects electricity costs in a steel plant, but previous research models seldom considered time-of-use (TOU) electricity pricing. Based on an analysis of the hot-rolling process and TOU electricity pricing, a batch-processing plan optimization model for hot rolling was established, using an objective function with the goal of minimizing the total penalty incurred by the differences in width, thickness, and hardness among adjacent slabs, as well as the electricity cost of the rolling process. A method was provided to solve the model through improved genetic algorithm. An analysis of the batch processing of the hot rolling of 240 slabs of different sizes at a steel plant proved the effectiveness of the proposed model. Compared to the man–machine interaction model and the model in which TOU electricity pricing was not considered, the batch-processing model that included TOU electricity pricing produced significantly better results with respect to both product quality and power consumption.

Dynamic Electricity Price Guidance Analysis of Urban Electric Vehicle Based on Actual Data Drive

Establishing a dynamic electricity price to guide the charging behavior of car owners can better help electric vehicles (EV) to participate in peak shaving and valley filling of the grid. On the basis of this, a dynamic electricity price mechanism for electric vehicle charging stations in city was proposed in this paper.It was aimed at the distribution network where residential areas are located and mean to improve the ability of EV to cut peaks and fill valleys. Firstly, the load characteristics of residential areas were analyzed, in addition, the load status of the distribution network in the area before and after the EV charging station connected in were compared. Secondly, according to the proposed dynamic electricity price calculation process and related function based on the TOU (time-of-use) electricity price for electric vehicle charging station, the dynamic price of the day was established, then in order to predict the power load after the dynamic electricity price is implemented, the corresponding model based on the residential load elastic demand matrix was established. Finally, taking the actual data of a certain district near residential area in Anhui province and an electric vehicle charging station as an example, formulated the targeted dynamic electricity price and further verified the feasibility and effectiveness of the study.

A MINLP model for multi-period optimization considering couple of gas-steam-electricity and time of use electricity price in steel plant

This paper presents an optimization model for multi-period scheduling of an energy system in a steel plant. The objective function is constructed by the gasholder penalty cost (GPC), energy purchase cost (EPC) and carbon emission cost (CEC), which are used to evaluate the model. The model divides the gasholder into four operating intervals and the corresponding penalty of each interval is set. The couple of gas-steam-electricity is introduced into the model. The fitting curves are conducted to describe the operating characteristic of boilers and turbines in the self-power plants (SPPPs). The carbon emission factors supported by IPCC are used for the carbon calculation. The Optimal results showed that total cost is decreased by 2.97%, when the GPC is decreased by 52.37%, the EPC is decreased by 1.92% and the CEC is increased by 21.54%. The couple of gas-steam-electricity allows the optimization model to redistribute the energy sources to minimum the total cost. The efficiency of different type of boilers has different operation characteristics. The sensitivity analysis of the model on electricity trade price and coal purchase price are conducted. The analysis results show that the variation of those parameters would influence the electricity generation under different situation.

Reliability Evaluation of Power System Considering Time of Use Electricity Pricing

This paper proposes an analytical method that incorporates the time of use (TOU) strategy into the reliability evaluation of power system. The TOU electricity price strategy enables the savings of electricity cost, but its impact on power system reliability has not been thoroughly studied. The proposed method constructs a peak-flat-valley period partition model and develops an equal step length iteration algorithm to obtain the optimal period partition. A price-based demand response is modeled to calculate the hourly load using an apportionment method. Using the particle swarm optimization algorithm, a TOU-based optimization model with a penalty is constructed to find the optimal electricity price. Then, an analytical “electricity price–reliability” model is developed to evaluate the reliability of the power system considering TOU. The effectiveness of the proposed method is investigated through the case study on the Roy Billinton test system and reliability test system.

Optimal Time of Use Electricity Pricing Model and Its Application to Electrical Distribution System

Because the time of use (TOU) strategies can directly affect the power flow distribution of electrical distribution system, this paper investigates the optimal TOU electricity pricing model and its functions for improving the power quality and reducing the power loss of electrical distribution system. Firstly, an optimal period partitioning algorithm based on a moving boundary technique is proposed for dividing an entire day to the different periods. Secondly, an optimal TOU electricity pricing model is proposed through minimizing the peak-valley difference, the voltage fluctuation, and the power loss. The particle swarm optimization (PSO) algorithm is adopted to solve the proposed optimization problem, and the multi-objective constrained optimization problem is transformed into a single objective unconstrained optimization problem. Thirdly, two novel indices of describing the voltage variation and the power loss are defined for considering the impact of TOU strategies and improving the power quality and reducing the power loss. Finally, an IEEE 14-bus system is applied to verifying the correctness and effectiveness of the proposed method. The results prove that the algorithm which proposed in this paper has a great significance in improving the power quality and the economic benefits of electrical distribution system.