46 results about "Energy sharing" patented technology

The invention provides a distributed scheduling method for railway traction stations and peripheral micro-energy grids, and belongs to the technical field of energy supply of micro-energy grid groups containing the railway traction stations, and the method comprises the steps: building a micro-energy grid sharing mutual aid grid structure containing the railway traction stations, obtaining a power model of each railway traction station, and optimally configuring energy storage equipment, obtaining operation constraints of the energy storage equipment; constructing an energy sharing benefit function by taking each micro-energy network agent as a game main body and taking individual benefit maximization as a target, setting constraint conditions, and establishing an energy sharing non-cooperative game model; and solving the energy sharing non-cooperative game model by adopting an alternating direction multiplier algorithm to obtain a distributed energy transaction behavior result and a price result. According to the method, distributed solution is carried out on the micro-energy network energy sharing non-cooperative game model based on the alternating direction multiplier method, original centralized optimization is converted into coupling optimization among a plurality of micro-energy network agents through interactive variables, the efficiency of the whole iteration process is guaranteed, and the privacy of each energy network is protected.

The invention discloses a hydrogen production and hydrogenation integrated station electric energy-peak regulation combined market transaction method considering hydrogen load demand response. The method comprises the following steps: 1) constructing a hydrogen production and hydrogenation integrated station day-ahead electric energy-peak regulation combined market transaction mechanism and framework; 2) constructing a cost model of the hydrogen production and hydrogenation integrated station for regulating and controlling multi-type hydrogen load demand response; 3) considering uncertainty factors such as hydrogenation load of the hydrogen fuel cell vehicle, and proposing a hydrogen production and hydrogenation integrated station market transaction model with maximum operation income as a target based on distribution robustness; 4) constructing a day-ahead electric energy-peak regulation combined market clearing model containing the hydrogen production and hydrogenation integrated station by taking social welfare maximization as a target; and 5) proposing a market transaction strategy solving method based on a differential privacy-consistent alternating direction multiplier method (DP-C-ADMM). According to the invention, a cooperative transaction mechanism in which the hydrogen production and hydrogenation integrated station participates in multiple markets is constructed, and a transaction model based on distributed robustness and a transaction strategy solving method considering privacy protection are proposing.

The invention discloses an energy sharing mutual aid benefit balanced distribution mechanism among multiple micro-energy networks, which belongs to the field of multi-micro-energy network system operation scheduling, and comprises the following steps: S1, dividing micro-energy network groups and combined pairing according to a matching index of a comprehensive curve form and a distance of micro-energy network source and load data, and constructing a micro-energy network benefit objective function; s2, introducing contribution, cost and risk factors into a traditional Shapley value method model, and constructing an improved Shapley value method model; and S3, performing distributed optimization solution on the micro-energy network cooperation alliance based on an ADMM algorithm, and realizing benefit balanced distribution by adopting a cooperation game strategy of an improved Shapley value method model. According to the method, the interaction efficiency is improved by dividing the group through source load matching, the information privacy is protected by using the ADMM algorithm, fair distribution is realized by improving the Shapley value method model, and the method is suitable for collaborative optimization operation of a multi-micro energy network system.

The application provides a multi-output DC-DC converter based on shared DC capacitor, comprising a power conversion unit, an energy sharing regulation unit and an output unit; the power conversion unit is arranged between a power supply end and the output unit, and comprises a plurality of flying capacitors and a plurality of power switching tubes, thereby forming a flying capacitor switching network; the energy sharing regulation unit is connected with the power conversion unit, and comprises a DC capacitor and a plurality of power switching tubes, thereby forming a DC capacitor switching network; the output unit comprises a plurality of inductors and a plurality of output capacitors, thereby forming an inductor-capacitor output network, and the output unit has a plurality of output ends; the charging and discharging of the flying capacitor and the charging and discharging of the inductor are controlled by controlling the on-off of the power switching tubes in the power conversion unit and the energy sharing regulation unit, so that the output ends provide energy for loads, the DC capacitor is charged and discharged to store energy and provide energy for the output ends, and independent regulation of the output ends is realized.

The present invention relates to the technical field of photovoltaic energy storage, and in particular relates to a green energy sharing system and management method based on a photovoltaic energy storage system. The green energy sharing system comprises: a photovoltaic energy storage system; customer power generation systems, which are configured at all or some customers and are configured to connect to customer load circuits; an energy router, which is configured at each customer; and a system cloud platform, which is used for generating a scheduling instruction on the basis of the power generation of the photovoltaic energy storage system, the power generation of each customer power generation system and the power consumption of each customer load circuit. The management method is used for realizing energy scheduling on the basis of the green energy sharing system. The present invention provides a new solution for the application of new energy in different environments.

The invention discloses a park centralized and decentralized regulation and control method suitable for high-proportion photovoltaic consumption, and the method comprises the steps: building interactive energy sharing transaction mechanism mathematical models between market operators and parks and between a plurality of parks, building a non-cooperative game power distribution network and a target function of a plurality of park optimization regulation and control models, the market electricity price constraint, the electric quantity balance constraint and the electric energy supply and demand balance of the park are used as constraints; and solving a game model based on a Kriging meta-model algorithm. According to the method, a clear mathematical optimization model is adopted, a scheduling decision is determined by a clear objective function and constraint conditions, the whole scheduling process is transparent and traceable, and the interpretability is greatly enhanced. According to the method, electricity purchase and sale prices formulated by the power distribution network, all cost coefficients and a small number of parameters of the PSO algorithm are mainly adjusted, the structure enables the parameter space to be greatly reduced, parameter adjustment has more physical significance, and debugging is easy.

The invention provides a multi-output direct current-direct current converter based on a shared direct current capacitor. The multi-output direct current-direct current converter comprises a power conversion unit, an energy sharing adjusting unit and an output unit, the power conversion unit is arranged between the power supply end and the output unit, the power conversion unit comprises a plurality of flying capacitors and a plurality of power switch tubes, and a flying capacitor switch network is formed; the energy sharing adjusting unit is connected with the power conversion unit and comprises a direct-current capacitor and a plurality of power switch tubes to form a direct-current capacitor switch network; the output unit comprises a plurality of inductors and a plurality of output capacitors to form an inductor-capacitor output network, and the output unit is provided with a plurality of output ends; charging and discharging of a flying capacitor and magnetizing and demagnetizing of an inductor are controlled by controlling on-off of power switch tubes in the power conversion unit and the energy sharing adjusting unit, so that each output end provides energy for a load, energy is stored and provided for each output end through charging and discharging of a direct current capacitor, and independent adjustment of each output end is achieved.

The invention relates to a long-time scale energy efficiency optimization method and system for a direct-current nano-grid cluster, and belongs to the technical field of energy efficiency optimization of a power system. The method comprises the following steps: establishing a cluster equivalent circuit model considering interconnection converter loss, and accurately describing a cluster power flow relationship; based on an equivalent circuit model, constructing a cluster global loss model, and quantifying three types of core losses of a line, a battery and a converter; establishing a cluster energy sharing model, classifying nano-networks according to net power characteristics of the nano-networks, and defining an energy interaction rule; based on the three types of models, an energy optimization management strategy is adopted, on the premise that safe operation is guaranteed, energy flow is optimized through a particle swarm optimization algorithm, and the self-sufficiency rate and energy efficiency of the cluster under the long-time scale are improved. According to the method, the cluster energy flow mechanism is optimized by establishing the cluster analysis model considering the characteristics of the interconnection converter, and the energy transmission efficiency and the self-sufficiency rate of the cluster under the long-time scale are remarkably improved on the premise of ensuring safe and stable operation.

The application provides a power transaction method and system for a joint VPP in an energy blockchain environment, and relates to the technical field of virtual power plants. The application classifies producers and consumers and determines energy preferences when conducting a producer-consumer P2P transaction for a joint VPP, better meets the actual transaction demand, improves the satisfaction of the producers and consumers participating in the transaction, thereby improving the enthusiasm of the producers and consumers participating in the transaction and improving the activity of energy sharing for the VPP.

The utility model discloses an energy storage power supply. The energy storage power supply comprises a battery management system, a battery module, an electric energy management module and a first interface, the battery management system is connected with the battery module, the electric energy management module and the first interface, the first interface is connected with the electric energy management module, and the first interface is used for being connected with a first energy storage power supply. And when the energy storage power supply is a second energy storage power supply for charging the first energy storage power supply, the battery management system is used for controlling the electric energy management module to output the electric energy of the battery module, and the electric energy output by the battery module is matched with the parameters of the first energy storage power supply. And when the energy storage power supply is a third energy storage power supply charged by the first energy storage power supply, the battery management system is used for controlling the electric energy management module to charge the battery module by using the electric energy output by the first energy storage power supply, and the electric energy output by the first energy storage power supply is matched with the parameters of the third energy storage power supply. According to the energy storage power supply, energy sharing of the two energy storage power supplies can be realized, and the long-time and multi-device power utilization requirements of the energy storage power supply are met.

The invention relates to the technical field of electric power and electric quantity balancing, and particularly provides an electric power and electric quantity balancing method and device considering photovoltaic output uncertainty, and the method comprises the steps: solving a shared energy storage power station planning model which is corresponding to a to-be-optimized interconnected power grid and considers the photovoltaic output uncertainty, and obtaining an optimization result; based on the optimization result, obtaining an electric power and electric quantity balance optimization scheme of the to-be-optimized interconnected power grid, and planning the to-be-optimized interconnected power grid by using the electric power and electric quantity balance optimization scheme; wherein the optimization result comprises at least one of the charging power, the discharging power, the rated power to be planned and the rated capacity to be planned of the shared energy storage power station. According to the technical scheme provided by the invention, the uncertainty of photovoltaic output is considered, and the electric power and electric quantity balance of the interconnected power grid is ensured by utilizing the energy sharing of the shared energy storage power station, so that the capacity optimization and production simulation modeling in medium and long term planning are realized.

The application provides an optical storage and charging random optimization method based on a multi-port flexible interconnection device, comprising: obtaining community storage system parameter information; constructing a two-stage random energy sharing optimization model, and constructing a benefit distribution model based on cooperative game by using the optimization result of the model; constructing a two-stage robust optimization model according to the two-stage energy sharing optimization model, and constructing an uncertainty probability confidence constraint set by using 1-norm and inf-norm; dividing the two-stage robust optimization model into a main problem and a sub-problem for solving, and outputting a set of optimal scheduling strategies. The application improves the optimal result obtained, and calculates the profit obtained by each community through the energy sharing optimization system by using the benefit distribution model based on game, so that the optimal profit of each community is reasonably and effectively distributed.

The system comprises an energy sharing end which is provided with a plurality of energy sharing units which perform Internet of Things with an energy sharing scheduling platform; the energy sharing scheduling platform gives the control right to the energy sharing unit to the registered user; the energy digital display platform is used for visualizing the energy supply requests and the energy consumption requests of the registered users and publicizing the allocation among the registered users; the decentralized allocation module is used for providing an allocation environment for registered users; the allocation bookkeeping module is used for recording allocation; the registered user side is provided with a plurality of registered users and provides registration and login environments; the energy digital display platform, the registered user side, the decentralized allocation module and the allocation bookkeeping module serve as nodes to be added into the alliance chain for data encryption; according to the invention, reasonable energy scheduling is carried out on different user main bodies and different energy supply units, and the energy utilization efficiency is improved.

The invention provides a multi-scene adaptive solar unmanned aerial vehicle autonomous charging and discharging control system, and relates to the technical field of unmanned aerial vehicle charging and discharging control. The regulation and control system comprises a multi-mode energy collection module, a bionic heat energy management module, a group cooperation energy sharing module, an intelligent scheduling module driven by a neural network and an edge calculation and self-adaptive optimization module. The multi-modal energy acquisition module, the bionic heat energy management module, the group collaborative energy sharing module, the intelligent scheduling module driven by the neural network and the edge calculation and adaptive optimization module form a closed-loop energy ecological system through a high-speed serial bus and a wireless communication interface so as to realize autonomous charging and discharging adjustment and dynamic optimization under multiple scenes; by integrating the multi-mode energy collection module, solar energy, wind energy and temperature difference heat energy are collected in real time, and environment energy can be efficiently obtained in various scenes (such as high altitude, ocean and polar region).

The application discloses a kind of integrated energy supply system reliability detection method, device and computer equipment considering transmission and sharing dynamic optimization, comprising the following steps: first, the state of each multi-energy coupling element and each transmission device in integrated energy supply system is sampled, the state of all multi-energy coupling elements corresponding to several sampling operation scenarios and the state of transmission device are obtained;Then, the energy sharing amount between multi-energy coupling elements is optimized, and the optimal energy sharing amount between different multi-energy coupling elements under the current sampling operation scenario is obtained;Iterative calculation of the remaining sampling operation scenario, obtain the optimal energy sharing amount between different multi-energy coupling elements under all sampling operation scenarios;Finally, the reliability of the current integrated energy supply system is generated according to the optimal energy sharing amount between different multi-energy coupling elements under all sampling operation scenarios.The application improves the accuracy of integrated energy supply system reliability detection, and provides a scientific basis for subsequent planning and design and operation scheduling.

The invention relates to a light storage system configuration optimization method considering mutual assistance of buildings. The method comprises the following steps: firstly, constructing a system structure integrating photovoltaic (PV), electrochemical energy storage (ESS) and energy sharing among the buildings; secondly, establishing a key equipment model of photovoltaic output, energy storage electric quantity and inter-building electric energy transmission loss; then, by taking annual total cost minimization as a target and combining constraint conditions such as electric energy balance and equipment operation, a system optimization model is established; and finally, through multi-scene simulation analysis, optimization solution is carried out to determine the optimal configuration capacity of photovoltaic and energy storage, and inter-building electric energy mutual aid scheduling is realized. The method provided by the invention aims to improve the distributed photovoltaic consumption capability and the system economic benefit, is clear in logic and high in operability, can cover typical buildings such as museums, shopping malls and office buildings, and avoids the problems of poor economy and low photovoltaic consumption rate caused by the fact that a traditional method only pays attention to single equipment or independent operation.

The invention discloses a collaborative transaction and pricing system and method containing a pumped energy storage micro-grid group based on a game theory, which can realize fair and efficient energy sharing and income distribution in a multi-agent interaction environment, and mainly comprises the following steps: constructing a pumped energy storage supported multi-micro-grid group structure model, acquiring load, electricity price, distributed power supply and energy storage operation data of each microgrid; setting a hierarchical relationship between a leader and a follower, and establishing a game model containing an ambiguous pricing and point-to-point transaction mechanism; on the basis that a leader layer determines an optimal pricing strategy through a Stackelberg game, each micro-grid of a following layer participates in Nash equilibrium solution according to own economic and energy constraints to realize an optimal transaction decision; and outputting transaction power, price and income distribution results of each micro-grid and the pumping energy storage unit, thereby realizing fair transaction and global social welfare maximization in the micro-grid group.

A method and system for electrical energy transfer and allocation that includes a blockchain systems for identifying and tracking energy demands and requests by geographical and coordinates and other characteristics through a usage and / or consumption chain that includes consumers and producers (prosumers). A microgrid identifier can be used to tag a consumer and relate the consumer to a producer by geography or demand. Based on demand and location data an energy factor can be calculated and thereby serve to match consumers and producers. A federated learning model can be used to accommodate an energy sharing stage on the blockchain and thereby facilitate, by a server computer, the transport of excess available energy from one energy producer in a first microgrid to either an energy consumer in the first microgrid or an energy storage unit of a second microgrid.

This invention relates to a hybrid game-theoretic optimization scheduling method for an integrated electricity-heat energy system considering energy sharing across multiple industrial parks, belonging to the technical field of integrated energy system scheduling and energy market trading. The method includes: establishing an integrated electricity-heat energy system comprising multiple industrial parks, and constructing a cooperative game model for energy sharing among the parks and a master-slave game model between park operators and park users; transforming the master-slave game model into a single-layer mixed-integer linear programming model, constructing an overall optimization model for the integrated electricity-heat interactive energy system based on hybrid game theory, introducing Nash negotiation theory to decompose the cooperative game problem into two sub-problems, and using the alternating multiplier method for solving them, so as to realize the distribution of cooperative benefits based on the solution results. It aims to solve the technical problems existing in the collaborative operation of multiple industrial parks, such as imperfect energy sharing mechanisms, insufficient multi-entity pricing and scheduling coordination, and difficulty in coordinating the interests between parks and users.

This invention provides a distributed solution system for optimizing the operation of interconnected balanced subnets to improve the resilience of regional distribution networks. The system includes multiple balanced subnets, a DC interconnection network, and a network layer controller. Each balanced subnet has a built-in local optimizer to acquire operational data and construct and solve a local affine adjustable robust optimization model based on internal source-load uncertainties. This model generates an interactive power plan between the balanced subnet and the DC interconnection network and issues local control commands. The DC interconnection network is used to achieve energy sharing among the balanced subnets. The network layer controller receives the interactive power plans uploaded by each balanced subnet, solves the model based on a network layer coordinated optimization model aimed at minimizing the total transmission loss of the DC interconnection network, generates consistent auxiliary variables, updates the Lagrange multipliers using the alternating direction multiplier method, and coordinates the operation plans of each balanced subnet through iterative interaction with the local optimizers of each balanced subnet until global convergence is achieved.

The application relates to an industrial park-oriented carbon-energy collaborative management method, system, device and medium, which comprises the following steps: obtaining and preprocessing multi-source carbon-energy data of an industrial park to obtain a carbon-energy data set; constructing a park carbon-energy flow hypergraph model based on the carbon-energy data set to depict the correlation between energy flow and carbon emission flow among multiple subjects in the park; extracting carbon-energy evaluation indexes of each subject, calculating a comprehensive score value by using a comprehensive scoring model of the fusion of an analytic hierarchy process and an entropy weight method, determining a carbon quota allocation coefficient, and realizing reasonable allocation of the carbon quota; identifying output subjects and demand subjects of waste heat and surplus energy based on the carbon-energy flow hypergraph model, determining a waste heat and surplus energy sharing path and a sharing amount, and generating a waste heat and surplus energy sharing transaction scheme; and performing carbon-energy collaborative management on multiple subjects in the park according to the carbon quota allocation result and the waste heat and surplus energy sharing transaction scheme and generating a management report. The application has the effect of improving the collaborative efficiency of carbon-energy management of multiple subjects in the industrial park.

Energy Router for Peer-to-Peer Energy Sharing

The invention discloses a user side shared energy storage optimization scheduling method considering communication reliability, and belongs to the technical field of intelligent power grid technology and user side energy management. Comprising the following steps: establishing a user-side multi-dimensional load model and an energy storage system model; constructing a regional shared energy storage mechanism; realizing reasonable scheduling and optimal management of user-side energy; constructing a complete communication model from physical layer transmission characteristics to system-level control; and ensuring that the system keeps stable operation when the communication quality fluctuates, designing a communication-energy storage joint optimization model, carrying out multi-period joint optimization, and outputting an optimal energy storage scheduling strategy and a shared electric quantity distribution scheme. The method solves the problem of scheduling deviation caused by communication fluctuation, is suitable for scenes such as intelligent communities and industrial parks, preferentially guarantees energy sharing of users with high communication reliability on the basis of meeting the power utilization requirements of the users and energy storage operation constraints, reduces the power purchase cost of a power grid, and improves the economical efficiency and robustness of the system.

The invention relates to the technical field of electric vehicle energy supply, in particular to a shared battery system for a two-wheel electric vehicle and a battery replacing method. The invention provides a shared battery system for a two-wheeled electric vehicle. The shared battery system comprises a battery pack unit, a vehicle battery bin unit, a plurality of energy sharing station units and a communication control unit connected with all the units. The battery pack unit comprises a plurality of detachable battery packs with unified external interface specifications; the vehicle battery compartment unit is fixedly arranged on a two-wheeled electric vehicle and is provided with an interface matched with the battery pack unit, and the energy sharing station units are arranged in a distributed manner; the communication control unit comprises a local station controller arranged in each energy sharing station unit and a remote cloud platform server connected with all the local station controllers through a network. Rapid energy supply is realized, networked service is constructed, and intelligent operation management is realized.

The invention discloses a station-city integrated energy system collaborative design optimization method based on energy sharing, and the method comprises the steps: laying a plurality of energy stations in a target region based on a plurality of renewable energy sources, constructing a region-level energy sharing strategy, and achieving the energy sharing between different energy stations; constructing a double-layer energy system collaborative design optimization model comprising an upper-layer energy equipment configuration capacity optimization model and a lower-layer energy storage equipment operation parameter optimization model; establishing an upper and lower layer optimization target with the lowest total cost, the lowest carbon emission and the lowest energy consumption, and establishing constraint conditions based on characteristics including real-time energy balance of cooling, heating and power loads of each energy station; and based on the established optimization target and constraint conditions, adopting an NSGA II algorithm to carry out hierarchical optimization solution on the collaborative design optimization model of the double-layer energy system, and finally obtaining a regional energy system collaborative design optimization scheme containing optimal energy equipment configuration capacity and energy storage equipment operation parameter combination.

The invention discloses a building cluster energy scheduling optimization method and system based on shared energy storage, and relates to the technical field of building energy sharing, and the method comprises the steps: determining an operation cost optimization target of a building cluster through shared energy storage system based on the energy transaction characteristics of multi-agent cooperation; establishing a multi-dimensional constraint condition of the building cluster under shared energy storage based on an operation cost optimization target, and solving an operation cost optimization target function to obtain operation cost data; based on a collaborative cost reduction mechanism, according to the operation cost data, determining the rental price of the building for the virtual energy storage under the shared energy storage system; day-ahead distributed optimization scheduling is carried out based on the electricity-carbon collaborative coupling relationship and in combination with the lease price; according to the invention, power-carbon collaborative optimization of multi-agent collaborative interaction can be realized, economy and low-carbon property of building cluster energy scheduling are taken into consideration, and improvement of energy consumption efficiency and energy storage benefit is further taken into consideration.

An energy decentralized allocation system and method. The system comprises: an energy sharing end, provided with a plurality of energy sharing units that communicate with an energy sharing scheduling platform by means of the Internet of Things; the energy sharing scheduling platform, which grants registered users control authority over the energy sharing units; an energy digital display platform, which visualizes energy supply requests and energy consumption requests of the registered users, and publicly displays allocation among the registered users; a decentralized allocation module, which provides an allocation environment for the registered users; an allocation accounting module, which records the allocation; and a registered user end, which is provided with a plurality of registered users and provides a registration and login environment. The energy digital display platform, the registered user end, the decentralized allocation module, and the allocation accounting module join a consortium blockchain as nodes for data encryption. Reasonable energy scheduling is performed for different user entities and different energy supply units, thereby improving energy utilization efficiency.

The invention discloses a paper machine transmission frequency converter group and a control method applied to the same, the frequency converter group comprises a plurality of frequency converters, power supply terminals of the frequency converters are connected with a power grid, direct current bus terminals of the frequency converters are connected with direct current buses, the direct current buses comprise a positive direct current bus and a negative direct current bus, the paper machine transmission frequency converter group further comprises a control unit, and the direct current bus terminals comprise positive / negative terminals; the positive / negative terminal of each frequency converter is connected with a positive / negative direct current bus through a cable. The direct current bus terminal is connected in parallel with an energy storage capacitor, and the energy storage capacitor is connected in parallel with a super capacitor; the direct-current bus is connected with a voltage detection module, the signal output end of the voltage detection module is connected with the signal input end of a control unit, and the control unit outputs signals to control whether the frequency converter is connected with a power grid. According to the paper machine transmission frequency converter set and the control method applied to the paper machine transmission frequency converter set, the direct-current buses of all the frequency converters are connected, energy sharing is achieved, and the problem of direct-current bus overvoltage caused by excess regenerated energy of a single frequency converter is solved.

The invention relates to the technical field of energy storage power plant planning, in particular to a long-term energy storage virtual power plant planning method and device, electronic equipment and a storage medium, and the method comprises the steps: firstly obtaining a representative scene of virtual power plant planning and an energy sharing strategy of a virtual power plant and long-term energy storage; then, according to an energy sharing strategy of long-term energy storage, the installation duration of a virtual power plant system and the total working duration of operation and maintenance in a representative scene, a planning model of the virtual power plant and various limiting conditions of operation and maintenance of the virtual power plant are constructed; solving the planning model of the virtual power plant according to the plurality of limiting conditions by taking the minimum total duration of the virtual power plant as a target to obtain a virtual power plant planning scheme and an optimized operation result; and finally, establishing a plurality of polymers according to the optimal planning scheme of the virtual power plant, and calculating the total apportionment duration of each polymer by adopting a kernel method. According to the invention, the seasonal peak-valley difference can be reduced, and high-proportion new energy consumption can be assisted.

Example operations include one or more of determining, by the charging station, a first amount of energy required to fully charge the vehicle, determining, by the charging station, a second amount of energy that the vehicle will provide back to the charging station at a later time, and charging, by the charging station, the vehicle to a charge level equal to a difference between the first amount of energy and the second amount of energy.