Description:FORM 2
THE PATENTS ACT, 1970
(39 of 1970)
&
THE PATENT RULES, 2003
COMPLETE SPECIFICATION
(See Section 10 and Rule 13)
Title of invention:
SYSTEMS AND METHODS FOR GENERATING OPTIMAL INTRADAY BIDS AND OPERATING SCHEDULES FOR DISTRIBUTED ENERGY RESOURCES
Applicant
Tata Consultancy Services Limited
A company Incorporated in India under the Companies Act, 1956
Having address:
Nirmal Building, 9th floor,
Nariman point, Mumbai 400021,
Maharashtra, India
Preamble to the description:
The following specification particularly describes the invention and the manner in which it is to be performed.
TECHNICAL FIELD
The disclosure herein generally relates to distributed energy resources, and, more particularly, to systems and methods for generating optimal intraday bids and operating schedules for distributed energy resources.
BACKGROUND
Owing to their stochastic nature, Distributed Energy Resources (DERs) are more suited to participate in short-term or intraday electricity markets. The trading horizon of these markets is shorter than day-ahead markets but longer than flex/regulation markets. Very few of the existing works on DER trading in intraday markets satisfactorily model the different aspects of this problem. Customers at the distribution side are investing in DER assets like storage systems, solar PV and becoming more flexible with their load requirements. Such DER assets are a need of time as they can provide various kinds of services to the grid and help in relieving the stress on power system. Also, they create revenue potential for the owner in return for their services. This is possible only if they are operated in a coordinated manner and utilized to their maximum potential. However, it is very difficult for the asset owner to manage their operation when interacting with the markets on his/her own. They do not have the necessary knowledge and the right infrastructure to do so. Hence, they need someone who can facilitate it and create operation schedules of their assets i.e., tell when and for how much time to switch on/off their assets. This is where an aggregator comes into play. The DER assets subscribe to the aggregator with the requirement of explaining them how to operate their assets so as to maximize its utilization and earn revenue. The aggregator has a large number of DER assets subscribed to it. These DER assets are usually located at different nodes in the distribution system, and hence the aggregator must manage all these resources as a group, interact with market and create an optimal operation schedule for all the assets. However, creating an operating schedule of these multiple assets while abiding by the several technical constraints, behavioral preferences and network constraints is a huge technical challenge.
SUMMARY
Embodiments of the present disclosure present technological improvements as solutions to one or more of the above-mentioned technical problems recognized by the inventors in conventional systems.
For example, in one aspect, there is provided a processor implemented method for generating optimal intraday bids and operating schedules for distributed energy resources. The method comprises obtaining, via one or more hardware processors, an input comprising (i) historical data pertaining to generation and demand of energy, (ii) historical intraday market data, (iii) a specification of a plurality of distributed energy resources (DERs) connected to a network specific to an aggregator, (iv) a preference of one or more subscribers, and (v) information associated with the network specific to the aggregator; forecasting, via the one or more hardware processors, a generation and demand of energy by the plurality of DERs for a plurality of delivery slots in an initialized optimization window based on the input; estimating, via the one or more hardware processors, a two-dimensional (2D) distribution of price-volume for the plurality of delivery slots in the initialized optimization window based on the forecasted generation and demand of the energy by the plurality of DERs; and executing, an optimization model via the one or more hardware processors, using the estimated two-dimensional (2D) distribution of price-volume for the plurality of delivery slots in the initialized optimization window to obtain at least one of (i) an optimal intraday operating schedule for one or more DERs from the plurality of DERs, and (ii) an intraday bid associated with the plurality of DERs for the plurality of delivery slots to be traded in an intraday market, wherein the step of executing the optimization model comprises: formulating a mixed integer non-linear programming (MINLP) problem based on the input and the estimated two-dimensional (2D) distribution of price-volume for the plurality of delivery slots in the initialized optimization window; converting the formulated MINLP problem to an NLP problem; and executing the NLP problem to obtain the at least one of (i) the optimal intraday operating schedule for one or more DERs from the plurality of DERs, and (ii) the intraday bid associated with the plurality of DERs for the plurality of delivery slots to be traded in an intraday market.
In an embodiment, the method further comprises executing, an intraday market clearing model via the one or more hardware processors, based on the intraday bid associated with the plurality of DERs for the plurality of delivery slots to be traded in the intraday market, to obtain an intraday market output, wherein the intraday market output comprises information pertaining to at least one of (i) number of cleared buy bids, and (ii) number of cleared sell bids; and generating a final optimal intraday operating schedule for the plurality of DERs based on the intraday market output.
In an embodiment, the method further comprises repeating the steps of forecasting, estimating, and executing the optimization model based on the final optimal intraday operating schedule generated for the plurality of DERs to obtain (i) a subsequent optimal intraday operating schedule for one or more DERs from the plurality of DERs, and (ii) a subsequent intraday bid associated with the plurality of DERs for the plurality of delivery slots to be traded in the intraday market for a subsequent optimization window.
In an embodiment, the optimal intraday operating schedule for a first DER type comprises at least one of (i) whether to charge or discharge in each delivery slot of the initialized optimization window, (ii) a charging level or a discharging level in each delivery slot of the initialized optimization window; and (iii) a state of charge (SOC) value of a DER of the first DER type at an end of each delivery slot.
In an embodiment, the optimal intraday operating schedule for a second DER type comprises quantity of energy required to be provided to a power grid in each delivery slot.
In an embodiment, the optimal intraday operating schedule for a third DER type comprises information pertaining to scheduling of an operation of a flexible load at one or more delivery slots.
In an embodiment, the intraday bid comprises a decision to place a buy bid or a sell bid and a corresponding price-volume pair for each delivery slot pertaining to one or more DERs.
In an embodiment, the NLP problem is obtained by relaxing at least one (i) a first integer variable, and (ii) a second integer variable comprised in the MINLP, wherein the first integer variable is based on a decision of a type of the intraday bid, and wherein the second integer variable is based on a constraint specific to a DER type.
In another aspect, there is provided a processor implemented system for generating optimal intraday bids and operating schedules for distributed energy resources. The system comprises: a memory storing instructions; one or more communication interfaces; and one or more hardware processors coupled to the memory via the one or more communication interfaces, wherein the one or more hardware processors are configured by the instructions to: obtain an input comprising (i) historical data pertaining to generation and demand of energy, (ii) historical intraday market data, (iii) a specification of a plurality of distributed energy resources (DERs) connected to a network specific to an aggregator, (iv) a preference of one or more subscribers, and (v) information associated with the network specific to the aggregator; forecast a generation and demand of energy by the plurality of DERs for a plurality of delivery slots in an initialized optimization window, based on the input; estimate a two-dimensional (2D) distribution of price-volume for the plurality of delivery slots in the initialized optimization window based on the forecasted generation and demand of the energy by the plurality of DERs; and execute, an optimization model, using the estimated two-dimensional (2D) distribution of price-volume for the plurality of delivery slots in the initialized optimization window to obtain at least one of (i) an optimal intraday operating schedule for one or more DERs from the plurality of DERs, and (ii) an intraday bid associated with the plurality of DERs for the plurality of delivery slots to be traded in an intraday market, wherein the step of executing the optimization model comprises: formulating a mixed integer non-linear programming (MINLP) problem based on the input and the estimated two-dimensional (2D) distribution of price-volume for the plurality of delivery slots in the initialized optimization window; converting the formulated MINLP problem to an NLP problem; and executing the NLP problem to obtain the at least one of (i) the optimal intraday operating schedule for one or more DERs from the plurality of DERs, and (ii) the intraday bid associated with the plurality of DERs for the plurality of delivery slots to be traded in an intraday market.
In an embodiment, the one or more hardware processors are further configured by the instruction to execute an intraday market clearing model based on the intraday bid associated with the plurality of DERs for the plurality of delivery slots to be traded in the intraday market, to obtain an intraday market output, wherein the intraday market output comprises information pertaining to at least one of (i) number of cleared buy bids, and (ii) number of cleared sell bids; and generate a final optimal intraday operating schedule for the plurality of DERs based on the intraday market output.
In an embodiment, the one or more hardware processors are further configured by the instruction to repeat the steps of forecasting, estimating, and executing the optimization model based on the final optimal intraday operating schedule generated for the plurality of DERs to obtain (i) a subsequent optimal intraday operating schedule for one or more DERs from the plurality of DERs, and (ii) a subsequent intraday bid associated with the plurality of DERs for the plurality of delivery slots to be traded in the intraday market for a subsequent optimization window.
In an embodiment, the optimal intraday operating schedule for a first DER type comprises at least one of (i) whether to charge or discharge in each delivery slot of the initialized optimization window, (ii) a charging level or a discharging level in each delivery slot of the initialized optimization window; and (iii) a state of charge (SOC) value of a DER of the first DER type at an end of each delivery slot.
In an embodiment, the optimal intraday operating schedule for a second DER type comprises quantity of energy required to be provided to a power grid in each delivery slot.
In an embodiment, the optimal intraday operating schedule for a third DER type comprises information pertaining to scheduling of an operation of a flexible load at one or more delivery slots.
In an embodiment, the intraday bid comprises a decision to place a buy bid or a sell bid and a corresponding price-volume pair for each delivery slot pertaining to one or more DERs.
In an embodiment, the NLP problem is obtained by relaxing at least one (i) a first integer variable, and (ii) a second integer variable comprised in the MINLP, wherein the first integer variable is based on a decision of a type of the intraday bid, and wherein the second integer variable is based on a constraint specific to a DER type.
In yet another aspect, there are provided one or more non-transitory machine-readable information storage mediums comprising one or more instructions which when executed by one or more hardware processors cause generating optimal intraday bids and operating schedules for distributed energy resources by: obtaining an input comprising (i) historical data pertaining to generation and demand of energy, (ii) historical intraday market data, (iii) a specification of a plurality of distributed energy resources (DERs) connected to a network specific to an aggregator, (iv) a preference of one or more subscribers, and (v) information associated with the network specific to the aggregator; forecasting a generation and demand of energy by the plurality of DERs for a plurality of delivery slots in an initialized optimization window, based on the input; estimating a two-dimensional (2D) distribution of price-volume for the plurality of delivery slots in the initialized optimization window based on the forecasted generation and demand of the energy by the plurality of DERs; and executing, an optimization model, using the estimated two-dimensional (2D) distribution of price-volume for the plurality of delivery slots in the initialized optimization window to obtain at least one of (i) an optimal intraday operating schedule for one or more DERs from the plurality of DERs, and (ii) an intraday bid associated with the plurality of DERs for the plurality of delivery slots to be traded in an intraday market, wherein the step of executing the optimization model comprises: formulating a mixed integer non-linear programming (MINLP) problem based on the input and the estimated two-dimensional (2D) distribution of price-volume for the plurality of delivery slots in the initialized optimization window; converting the formulated MINLP problem to an NLP problem; and executing the NLP problem to obtain the at least one of (i) the optimal intraday operating schedule for one or more DERs from the plurality of DERs, and (ii) the intraday bid associated with the plurality of DERs for the plurality of delivery slots to be traded in an intraday market.
In an embodiment, the one or more instructions which when executed by the one or more hardware processors further cause executing, an intraday market clearing model based on the intraday bid associated with the plurality of DERs for the plurality of delivery slots to be traded in the intraday market, to obtain an intraday market output, wherein the intraday market output comprises information pertaining to at least one of (i) number of cleared buy bids, and (ii) number of cleared sell bids; and generating a final optimal intraday operating schedule for the plurality of DERs based on the intraday market output.
In an embodiment, the one or more instructions which when executed by the one or more hardware processors further cause repeating the steps of forecasting, estimating, and executing the optimization model based on the final optimal intraday operating schedule generated for the plurality of DERs to obtain (i) a subsequent optimal intraday operating schedule for one or more DERs from the plurality of DERs, and (ii) a subsequent intraday bid associated with the plurality of DERs for the plurality of delivery slots to be traded in the intraday market for a subsequent optimization window.
In an embodiment, the optimal intraday operating schedule for a first DER type comprises at least one of (i) whether to charge or discharge in each delivery slot of the initialized optimization window, (ii) a charging level or a discharging level in each delivery slot of the initialized optimization window; and (iii) a state of charge (SOC) value of a DER of the first DER type at an end of each delivery slot.
In an embodiment, the optimal intraday operating schedule for a second DER type comprises quantity of energy required to be provided to a power grid in each delivery slot.
In an embodiment, the optimal intraday operating schedule for a third DER type comprises information pertaining to scheduling of an operation of a flexible load at one or more delivery slots.
In an embodiment, the intraday bid comprises a decision to place a buy bid or a sell bid and a corresponding price-volume pair for each delivery slot pertaining to one or more DERs.
In an embodiment, the NLP problem is obtained by relaxing at least one (i) a first integer variable, and (ii) a second integer variable comprised in the MINLP, wherein the first integer variable is based on a decision of a type of the intraday bid, and wherein the second integer variable is based on a constraint specific to a DER type.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.
BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated in and constitute a part of this disclosure, illustrate exemplary embodiments and, together with the description, serve to explain the disclosed principles:
FIG. 1 depicts an exemplary system for generating optimal intraday bids and operating schedules for distributed energy resources, in accordance with an embodiment of the present disclosure.
FIG. 2 depicts an exemplary flow chart illustrating a method for generating optimal intraday bids and operating schedules for distributed energy resources, using the system of FIG. 1, in accordance with an embodiment of the present disclosure.
FIG. 3 illustrates an exemplary IEEE 13 bus radial distribution network as implemented by the system of FIG. 1, in accordance with an embodiment of the present disclosure.
FIG. 4 depicts various bidding timelines in intraday markets, in accordance with an embodiment of the present disclosure.
FIGS. 5A through 5D depict a histogram of two-dimensional (2D) distributions for some of delivery hours at different trading hours, in accordance with an embodiment of the present disclosure.
FIG. 6 depicts an exemplary flow chart illustrating a method for executing the optimization model (or a non-linear programming problem), using the systems of FIG. 1, in accordance with an embodiment of the present disclosure.
FIG. 7 depicts a graphical representation illustrating a comparison of revenue earned by a baseline trading technique (ID3) and the method of the present disclosure trading techniques across individual days, in accordance with an embodiment of the present disclosure.
FIG. 8A depicts a heatmap of buy bids placed by the baseline trading technique (ID3) over a sample day (day 3), in accordance with an embodiment of the present disclosure.
FIG. 8B depicts a heatmap of buy bids placed by the method of the present disclosure trading techniques over a sample day (day 3), in accordance with an embodiment of the present disclosure.
FIG. 9A depicts a graphical representation of a performance of the baseline trading technique (ID3) and the method of the present disclosure under a higher generation (twice the solar panel sizes with all other parameters remaining the same), in accordance with an embodiment of the present disclosure.
FIG. 9B depicts a graphical representation of a performance of the method along with the baseline trading technique for a period June 2020, in accordance with an embodiment of the present disclosure.
FIG. 9C depicts a graphical representation of a performance of the method along with the baseline trading technique (ID3 – conventional approach) on a set of 250 DERs, in accordance with an embodiment of the present disclosure.
DETAILED DESCRIPTION OF EMBODIMENTS
Exemplary embodiments are described with reference to the accompanying drawings. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. Wherever convenient, the same reference numbers are used throughout the drawings to refer to the same or like parts. While examples and features of disclosed principles are described herein, modifications, adaptations, and other implementations are possible without departing from the scope of the disclosed embodiments.
Power systems are undergoing significant changes due to increasing penetration of Distributed Energy Resources (DERs) such as solar, wind farms, electric vehicles, energy storage systems and flexible demand. These DERs are usually owned by end users connected to low and medium voltage distribution networks. Unlike traditional centralized generators, these DERs have smaller capacities. However, due to their large numbers and flexible nature, these DERs can inject clean energy and provide valuable services to the grid. Nevertheless, an uncontrolled and a disorderly inclusion of DERs can make it harder for system operators to keep the grid running.
In this context, aggregators are emerging as new players in the power system. An aggregator’s goal is to coordinate the DERs and provide services to the power system through appropriate markets while earning revenue. In such a set-up, aggregators are expected to provide the necessary technology to communicate and control the DERs. Aggregators improve the economic efficiency of the power system by enhancing the existing grid’s robustness with little investment. Simultaneously, they also create private value by allowing their subscribers to earn revenue through market participation. It is economically inefficient for DERs to participate individually in markets by themselves due to the high transaction costs and low individual capacities.
Given this strong business case for aggregation, a plethora of work has been done to address the research challenges involved. In one of the research works, an optimization framework for an aggregator of flexible loads participating in Nordic markets has been discussed (e.g., refer Aleksandra Roosa, Stig Ø. Ottesenb, and Torjus F. Bolkesjøa. 2014. Modeling consumer flexibility of an aggregator participating in the wholesale power market and the regulation capacity market. In Renewable Energy Research Conference. Oslo, Norway). The relationship between aggregator-storage units and effect of aggregator on system welfare is also discussed (e.g., J. E. Contreras-Ocaña, M. A. Ortega-Vazquez, and B. Zhang. 2019. Participation of an Energy Storage Aggregator in Electricity Markets. IEEE Transactions on Smart Grid 10, 2 (2019), 1171–1183.).
Certain works considered participation of DERs in single markets such as day-ahead or flexibility while others consider simultaneous participation of DERs in multiple markets such as energy, regulation, and reserve. There are also works that describe how DERs can be controlled to provide other services for the network such as voltage regulation.
The uncertainties associated with the DERs are higher than the conventional loads and generation sources. Therefore, these are better suited for markets that operate with short lead times. While one may consider ancillary services market or real time markets to be a good avenue for DERs to participate, such markets are not fully governed by economics. These are rather driven by system conditions prevailing in the time window when the services are asked for. Therefore, such markets provide little room for the DER aggregator to play with. DERs are ideally suited for economics driven markets with a trading horizon shorter than day-ahead markets and longer than real-time markets. There is a class of electricity markets called "short-term" or "intraday" markets which operate in this time range.
On the other hand, intraday markets support continuous trades (similar to stock markets) and follow pay-as-you-bid market clearing. Also, these markets allow for a bid (buy or sell) to be partially cleared in a single transaction. The uncleared volume may get cleared in subsequent transactions. Consequently, the clearing prices in intraday markets exhibit more volatility – for the same delivery slot, the market clearing price could change depending on when the trade happens. This increases the complexity of doing trades optimally in intraday markets.
There has been some research that focuses on DERs trading in intraday markets, either exclusively or in combination with other markets. These works aim to either reduce the cost of energy procurement or maximize the revenue generated through trading.
Given the importance of DERs and aggregation, considerable research on this topic exists in literature. For instance, Vaya et. al., (e.g., refer “Marina González Vayá and Göran Andersson. 2014. Optimal bidding strategy of a plug-in electric vehicle aggregator in day-ahead electricity markets under uncertainty. IEEE transactions on power systems 30, 5 (2014), 2375–2385.”) discuss a model for aggregator of electric vehicles (EVs) participating as a buyer in a day ahead electricity market. Here, the aggregator is considered as a price maker and the problem is formulated as a bilevel optimization problem. Khajeh et.al., (refer “Hosna Khajeh, Asghar Akbari Foroud, and Hooman Firoozi. 2019. Robust bidding strategies and scheduling of a price-maker microgrid aggregator participating in a pool-based electricity market. IET Generation, Transmission & Distribution 13, 4 (2019), 468–477.”) proposed a model for a microgrid aggregator with ‘price-maker’ bidding strategies in a pool market. The uncertainties in renewable generation are modeled in a robust optimization framework. Somma et. al., (e.g., “Marialaura Di Somma, Giorgio Graditi, and Pierluigi Siano. 2018. Optimal bidding strategy for a DER aggregator in the day-ahead market in the presence of demand flexibility. IEEE Transactions on Industrial Electronics 66, 2 (2018), 1509–1519.”) presented a model for an aggregator utilizing demand flexibility for trading in day-ahead markets. Uncertainties in the DER generation and the market prices are considered in a stochastic mixed-integer linear programming framework. Bessa et. al. (e.g., refer “Ricardo J Bessa, Manuel A Matos, Filipe Joel Soares, and João A Peças Lopes. 2012. Optimized bidding of a EV aggregation agent in the electricity market. IEEE Transactions on Smart Grid 3, 1 (2012), 443–452.”) discussed a bidding model for EV aggregator participating in the day-ahead and reserve markets. Their model focused on the higher flexibility and variability of EV as compared to the conventional loads. In Han et. al. (e.g., refer “Bing Han, Shaofeng Lu, Fei Xue, and Lin Jiang. 2019. Day-ahead electric vehicle aggregator bidding strategy using stochastic programming in an uncertain reserve market. IET Generation, Transmission & Distribution 13, 12 (2019), 2517–2525.”) a model was presented for EV aggregator which jointly optimizes bidding strategy for reserve capacity in day-ahead market and reserve deployments in real-time markets while considering the market uncertainties. Iria et.al. (e.g., refer “José Iria, Filipe Soares, and Manuel Matos. 2019. Optimal bidding strategy for an aggregator of prosumers in energy and secondary reserve markets. Applied Energy 238 (2019), 1361–1372.”) proposed a stochastic optimization model for an aggregator optimizing prosumers’ flexibility and minimizing the net cost of buy and sell in day-ahead and real time market. Valsomatzis et. al., (e.g., refer “Emmanouil Valsomatzis, Torben Bach Pedersen, and Alberto Abelló. 2018. Day-Ahead Trading of Aggregated Energy Flexibility. In Proceedings of the Ninth International Conference on Future Energy Systems (Karlsruhe, Germany) (e-Energy’18). Association for Computing Machinery, New York, NY, USA, 134–138.”) discussed a strategy to trade the flexibility offered by EVs in European day-ahead flex markets. Dannel et. al. (e.g., refer “Dominik Danner, Jan Seidemann, Michael Lechl, and Hermann de Meer. 2021. Flexibility Disaggregation under Forecast Conditions. In Proceedings of the Twelfth ACM International Conference on Future Energy Systems (Virtual Event, Italy) (e-Energy ’21). Association for Computing Machinery, New York, NY, USA, 27–38.”) proposed a strategy to forecast the flexibility potential of heterogeneous DERs. They also present a method for dispatching the network’s flexibility requirement among the participating DER groups. Attarha et. al., (e.g., refer “Ahmad Attarha, Paul Scott, and Sylvie Thiébaux. 2020. Network-Aware Participation of Aggregators in NEM Energy and FCAS Markets. In Proceedings of the Eleventh ACM International Conference on Future Energy Systems (Virtual Event, Australia) (e-Energy ’20). Association for Computing Machinery, New York, NY, USA, 14–24.”) proposed a strategy for aggregators to participate in both energy and frequency control ancillary service markets. They modeled the inter-dependencies in simultaneous market participation and also factored in the constraints placed by the network.
In regard to DERs and intraday markets, Bouskas et. al., (e.g., refer “Ioannis Boukas, Damien Ernst, Thibaut Théate, Adrien Bolland, Alexandre Huynen, Martin Buchwald, Christelle Wynants, and Bertrand Cornélusse. 2021. A deep reinforcement learning framework for continuous intraday market bidding. Machine Learning (2021), 1–53.”) discussed a strategy for a grid connected storage to trade in intraday markets using a deep reinforcement learning framework. They model the trading problem as a Markov Decision Process and present an asynchronous distributed version of the fitted Q iteration algorithm. There are also approaches that use stochastic differential equations to derive optimal trading strategies for renewable generators (e.g., refer “R Aid, P. Gruet, and H Pham. 2016. An optimal trading problem in intraday electricity markets. Financial Economics 10, 1 (2016), 49–85.”). Limmer et. al., (e.g., refer “Ilham Naharudinsyah and Steffen Limmer. 2018. Optimal Charging of Electric Vehicles with Trading on the Intraday Electricity Market. Energies 11, 6 (2018)”) proposed a strategy to charge EVs optimally by trading in the intraday markets. They also assume that a retailer is available as a fall-back source to supply the required electricity during times of need. Sanchez et. al., (e.g., refer “Pedro Sánchez-Martín, Sara Lumbreras, and Antonio Alberdi-Alén. 2016. Stochastic Programming Applied to EV Charging Points for Energy and Reserve Service Markets. IEEE Transactions on Power Systems 31, 1 (2016), 198–205.”) proposed a strategy for EVs to trade in both day-ahead and intraday markets. In the first stage, EVs trade in the day-ahead market based on the forecasts while in the second stage, they trade in the intraday market to account for deviations in the forecast. Jacobsen et. al., (e.g., refer “Christoph Goebel and Hans-Arno Jacobsen. 2016. Aggregator-Controlled EV Charging in Pay-as-Bid Reserve Markets with Strict Delivery Constraints. IEEE Transactions on Power Systems 31, 6 (2016), 4447–4461.”) discussed a technique for EVs to participate in both regulation and intraday markets. However, the electricity costs are not optimized since the required energy is bought late irrespective of the prices. A common feature in all the aforesaid works is that they assume homogeneity in the DER population (i.e., the solution is targeted for a specific DER type). Hence, they cannot be applied in a heterogeneous DER setting.
Ayon et.al., (e.g., refer “Xiaolin Ayón, María Ángeles Moreno, and Julio Usaola. 2017. Aggregators’ Optimal Bidding Strategy in Sequential Day-Ahead and Intraday Electricity Spot Markets. Energies 10, 4 (2017).”) proposed a probabilistic optimization method that produces optimal bidding curves to be submitted by an aggregator to the day-ahead electricity market and the intraday market in a sequential manner. Their formulation entails different linear optimization problems that follow the natural temporal sequence of day-ahead and intraday markets. The overall trade optimization is performed in three steps: First, the optimal bidding curves are produced and submitted to the day-ahead market; Second, after the day-ahead market clearing, temporal constraints related to the flexible consumption are fulfilled through a rescheduling process; and finally, new optimal bidding curves are produced and submitted to the intraday market, trying to take advantage of the lower lead time and the knowledge gained on the marginal prices through the day-ahead market clearing. While this work models heterogeneous DERs, they do not take into consideration the constraints that may be placed by the network. Further, they also assume that different price scenarios to be equiprobable which may not be true.
While all the above research works are notable contributions, they possess one or more of the following gaps: (i) They assume only one type of DER such as storage or EVs. Heterogeneity in the nature of DERs is not considered. (ii) They do not model the continuous price fluctuations in the market. They assume the clearing price to remain constant over certain duration, which is hardly the case. (iii) They do not model constraints placed by the network operator for injecting or withdrawing power at network buses. (iv) They do not provision for energy exchanges to happen within the DER pool managed by an aggregator.
In the present disclosure, system and method described herein determine an optimal intraday operating schedule and intraday bids for aggregators managing a set of DERs (e.g., (both energy resources that are homogeneous and heterogeneous in nature). In particular, system and method of the present disclosure model a joint price-volume dynamics present in intraday markets, wherein such modeling of the joint price-volume dynamics allows for the trades/bids placed earlier to be corrected based on the revised forecasts of demand and generation while allowing for energy exchanges within the DER pool.
More specifically, the system and method of the present disclosure (i) model the price volume behavior in intraday markets as a two-dimensional (2D) distribution which is obtained using at least historical market logs, wherein the forecasted (2D) distribution is used to optimize the intraday bids placed by the aggregator in the intraday energy market(s), and (ii) model the optimal bidding problem of aggregators in an intraday market as a (potentially non-convex) MINLP and a relaxation wherein the integer variables from the formulation are removed and the MINLP problem is converted to an NLP problem.
Present disclosure provides systems and methods to determine/generating an optimal strategy (e.g., optimal intraday operating schedule and intraday bid) for aggregators managing DERs (both energy resources that are homogeneous and heterogeneous in nature) to trade in intraday markets. The system and method of the present disclosure model the joint price-volume dynamics present in such markets through a two-dimensional (2D) distribution (e.g., histograms, and the like) and use it in decision making. The above method of the present disclosure also allows for the trades/bids placed earlier to be corrected based on the revised forecasts of demand and generation in the DER pool. The system and method of the present disclosure model the optimal bidding problem of aggregators in an intraday market as a mixed-integer non-linear programming (MINLP) problem. More specifically, the present disclosure presents a reformulation of the problem which leverage different aspects of the problem’s structure. The relaxation converts the MINLP to an NLP problem. Furthermore, the system and method test the performance against commonly used approaches. In this regard, the system and method of the present disclosure have used real world intraday market logs from a specific region/country in the experiments. The results indicated that the relaxation mentioned above improves the revenue performance of the aggregator by 19% relative to the commonly followed trading practices. Also, the performance gap between the baseline and the method implemented by the present disclosure remains robust to changes in subscriber generation volumes. Further, it is also observed by the present disclosure that enabling pool interactions within the DER set is helpful. Based on the observations, such enabling improves the revenue performance of aggregator by 2.5%.
Referring now to the drawings, and more particularly to FIG. 1 through 9C, where similar reference characters denote corresponding features consistently throughout the figures, there are shown preferred embodiments and these embodiments are described in the context of the following exemplary system and/or method.
FIG. 1 depicts an exemplary system 100 for generating optimal intraday bids and operating schedules for distributed energy resources, in accordance with an embodiment of the present disclosure. In an embodiment, the system 100 includes one or more hardware processors 104, communication interface device(s) or input/output (I/O) interface(s) 106 (also referred as interface(s)), and one or more data storage devices or memory 102 operatively coupled to the one or more hardware processors 104. The one or more processors 104 may be one or more software processing components and/or hardware processors. In an embodiment, the hardware processors can be implemented as one or more microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, logic circuitries, and/or any devices that manipulate signals based on operational instructions. Among other capabilities, the processor(s) is/are configured to fetch and execute computer-readable instructions stored in the memory. In an embodiment, the system 100 can be implemented in a variety of computing systems, such as laptop computers, notebooks, hand-held devices (e.g., smartphones, tablet phones, mobile communication devices, and the like), workstations, mainframe computers, servers, a network cloud, and the like.
The I/O interface device(s) 106 can include a variety of software and hardware interfaces, for example, a web interface, a graphical user interface, and the like and can facilitate multiple communications within a wide variety of networks N/W and protocol types, including wired networks, for example, LAN, cable, etc., and wireless networks, such as WLAN, cellular, or satellite. In an embodiment, the I/O interface device(s) can include one or more ports for connecting a number of devices to one another or to another server.
The memory 102 may include any computer-readable medium known in the art including, for example, volatile memory, such as static random-access memory (SRAM) and dynamic-random access memory (DRAM), and/or non-volatile memory, such as read only memory (ROM), erasable programmable ROM, flash memories, hard disks, optical disks, and magnetic tapes. In an embodiment, a database 108 is comprised in the memory 102, wherein the database 108 comprises (i) historical data pertaining to generation and demand of energy by a plurality of distributed energy resources (DERs) connected to a network specific to an aggregator, (ii) historical intraday market data, (iii) a specification of the plurality of distributed energy resources (DERs) connected to the network specific to the aggregator, (iv) a preference of one or more subscribers, and (v) information associated with the network specific to the aggregator. The database 108 further comprises various models, such as optimization model(s), intraday market clearing model(s), and the like. The memory 102 further comprises (or may further comprise) information pertaining to input(s)/output(s) of each step performed by the systems and methods of the present disclosure. In other words, input(s) fed at each step and output(s) generated at each step are comprised in the memory 102 and can be utilized in further processing and analysis.
FIG. 2, with reference to FIG. 1, depicts an exemplary flow chart illustrating a method for generating optimal intraday bids and operating schedules for distributed energy resources, using the system 100 of FIG. 1, in accordance with an embodiment of the present disclosure. In an embodiment, the system(s) 100 comprises one or more data storage devices or the memory 102 operatively coupled to the one or more hardware processors 104 and is configured to store instructions for execution of steps of the method by the one or more processors 104. The steps of the method of the present disclosure will now be explained with reference to components of the system 100 of FIG. 1, and the flow diagram as depicted in FIG. 2.
The system and method of the present disclosure consider a centralized set-up wherein an aggregator orchestrates the operations of a set of DERs. The system 100 assumes that the aggregator has the knowledge of the characteristics (size, ratings, constraints, and preferences) of the participating DERs. A subscriber s can have a generation source (e.g., solar PV), demand, energy storage systems (e.g., battery) or any combination of these. The aggregator has the ability to forecast the renewable generation and overall demand of its subscribers using historical logs and other pertinent information.
A subscriber s has two kinds of demands: fixed demand, d_(t,s)^fix, and flexible demand, d_(t,s)^flex. As the name indicates, fixed demand is that part of the customer load that remains fixed and must be supplied at the specified time t. Flexible demand is that part of the customer load where there is flexibility in terms of the time(s) at which this demand can be satisfied. While the quantum of flexible demand is decided by the customer, its schedule is decided by the aggregator. The aggregator can split a customer’s overall demand into flexible and fixed components by leveraging information about customer’s appliance set and operational preferences (which can be periodically collected).
With the knowledge of customer preferences, demands, asset constraints, and the generation availability, an aggregator participates in an intraday market. Market participation is for both procuring and selling power. Aggregator places the bids in a such a way that the revenue obtained through market participation is maximized. The aggregator also schedules the operations of the individual DERs based on the cleared market commitments.
Intraday markets for electricity are also referred as continuous markets as the trading happens in continuous time slots until the trade window closure. Trading in these markets typically starts after the day-ahead market clearing. In intraday markets, the bids for a given delivery time can be placed anywhere from the previous afternoon to few minutes before the delivery. The exact gate opening and closing times varies across geographies. Different exchanges offer varying products that range from simple products (which are limited to one time slot) to block products (which span multiple continuous time slots). In the present disclosure, the system and method assume that the aggregator is interested in simple one slot energy product.
Intraday markets typically follow pay-as-bid pricing for bid clearing and the system and method further assume the same clearing model. Under this clearing model, the market operator matches an incoming bid order with the best opposite order as soon as it is submitted. If there is no suitable match, the incoming order stays in the order book until its expiry condition. The best opposite order is defined as the highest priced buy order or lowest priced sell order. If the best opposite order matches with the price condition of an incoming order, a transaction happens. An order can get fulfilled either completely or partially. If an order is cleared partially, the remaining quantity stays in the order book.
Referring to steps of FIG. 2, at step 202 of the method of the present disclosure, the one or more hardware processors 104 obtain an input comprising (i) historical data pertaining to generation and demand of energy by a plurality of distributed energy resources (DERs) connected to a network specific to an aggregator, (ii) historical intraday market data, (iii) a specification of the plurality of distributed energy resources (DERs), (iv) a preference of one or more subscribers, and (v) information associated with the network specific to the aggregator. The plurality of DERs connected to the network of the aggregator may be identical in nature (e.g., homogeneous DERs or networks of a single DER type, say only batteries, only solar photovoltaic cells, only flexible load(s) and the like) or similar. The plurality of DERs connected to the network of the aggregator may be different from each other or heterogeneous in nature. For instance, the DERs in the network of the aggregator may include, but are not limited to, batteries, solar photovoltaic cells, flexible load(s), fixed loads, and the like. Below Table 1 and Table 2 illustrate exemplary historical data pertaining to generation and demand of energy by a DER (e.g., say on an hourly basis) respectively.
Table 1
Generation
Date Hour Generation (MW)
1/1/2020 5:00 0
1/1/2020 6:00 12
1/1/2020 7:00 23
Table 2
Demand
Date Hour Demand (MW)
1/1/2020 5:00 22
1/1/2020 6:00 36
1/1/2020 7:00 43
Below Table 3 illustrates historical intraday market data consisting of price-volume pairs bid at different transaction hours for each delivery hour.
Table 3
Date Transaction time Delivery Hours Volume (MW) Price (EUR)
1/1/2020 9:05 14:00 10 33.2
1/1/2020 10:22 14:00 30 34.99
1/1/2020 12:35 15:00 5 30.1
Below Table 4 illustrates various examples of DERs connected to the network of the aggregator.
Table 4
Type Description of DER Number of DERs Average Size
(KW)
I Fixed and flexible demand 6 300; 50
II Fixed + flexible demand with Solar 4 400; 350; 2300
III Fixed + flexible demand with Storage 7 400; 400; 2650
IV Solar with Storage 5 1690 and 2480
V Fixed/flexible demand with Solar &
Storage 4 600, 330; 2000; 3300
The preference of the one or more subscribers corresponds (or pertains) to the availability of the battery and flexible demand which is communicated on a day ahead basis to the aggregator. The distribution network used in the model is shown in FIG. 3. More specifically, FIG. 3, with reference to FIGS. 1-2, illustrates an exemplary IEEE 13 bus radial distribution network as implemented by the system 100 of FIG. 1, in accordance with an embodiment of the present disclosure. The network information includes, but is not limited to, maximum and minimum import power limits of each node in the network. Below Table 5 illustrates information pertaining to the network:
Table 5
Node Import Limit (MW) Export Limit (MW)
1 1250 1250
2 251 251
… … …
13 543 470
At step 204 of the method of the present disclosure, the one or more hardware processors 104 forecast a generation and demand of energy by the plurality of DERs for a plurality of delivery slots in an initialized optimization window, based on the input.
Without loss of generality, the system and method consider time to be slotted. Given a delivery slot of h, let the aggregator’s trading window be the sequence of t consecutive slots from h - t - r till h - r, where r is the minimum lead time allowed by the market operator. The aim of the optimal trading strategy is to answer the following questions: (1) Given a delivery time slot h and a trading slot t ? [h - t -r,h - r ], determine the volume of the buy or sell bids the aggregator has to place in the market at ?? for h. (2) Determine the price for the buy or sell bids the aggregator has to be place in the market at t for h. (3) The volumes and prices have to be determined such that the revenue earned by the aggregator is maximized and the demand requirements of the DERs in the aggregator’s subscriber pool are met.
Moving window optimization: Notations used in the present disclosure are summarized in below Table 6.
Table 6
Symbol Description
h Time slot at which power/energy should be delivered
t Current time slot
r Minimum lead time for trading allowed by market operator
t Window of time slots over which the aggregator trades for h
s Subscriber index
N Set of nodes in a distribution network
S_n Set of DERs connected at bus n
S Set of all subscribers of the aggregator
W^t The window of optimization – the range of h values for which
the aggregator optimizes the bids at t; given by [t +r ,t +r +t]
d_(h,s)^fix Fixed demand of subscriber s for h as forecasted at t
G_(h,s) Generation of subscriber s for delivery slot h as forecasted at t
?Lim?_n Import/export limit at node n for the aggregator that has been determined by the network operator. The operator communicates
this limit to the aggregator at least t slots before h.
R_s^chg (.) and R_s^dsg(.) Function that specifies the maximum charge/discharge rate of battery available with subscriber ?? as per the SOC.
P_h^L and P_h^H Lower and Higher limit of market price for delivery slot h
M and k Large positive numbers
x_(h,n) Net energy at node n during h that is traded in the market
x_(h,n)^pool Net energy at node n during h that is traded within the pool
x_h^tot Total aggregated volume which has to be traded with market
b_(h,s)^chg, b_(h,s)^dsg Charging and Discharging volume of subscriber s’s battery during h.
d_(h,s)^flex Subscriber s’s flexible demand scheduled during h.
?SOC?_(h,s) State of charge of battery with subscriber s during hour h
?SOC?_s^min, ?SOC?_s^max Maximum and minimum limits of the state of charge of the battery available with s
z_(t,s) Binary variable indicating the status of battery operation during t (1=charging, 0=discharging)
d_h Binary variable indicating whether the aggregator will place sell offer or buy bid at h (1 = sell and 0 = buy)
Qb_h^clear, Qs_h^clear Present value of aggregator’s sell and buy volume for h that has been cleared in the market.
?qs?_h, ?ps?_h Sell offer volume and price for the aggregator during h
?qb?_h, ?pb?_h Buy bid volume and price for the aggregator during h
f^(t,h) (p,q) Relative fraction of bids with price p and volume q found in the historical cleared market transactions at t for delivery slot h.
F_sell^(t,h) (p,q),
F_buy^(t,h) (p,q) A measure of market’s propensity to clear sell and buy bids respectively at t for delivery slot h.
Let S be the set of DERs who have subscribed to the services of an aggregator. Let these DERs be connected to the distribution network across N different buses with S_n denoting the set of DERs connected at bus n. Let the current (trading) time be t. The range of delivery slots for which the aggregator can optimize the bids at t is given by [t + r ,t + r + t]. The system and method refer to this range of h values as the optimization window W^t. As t advances, so does W^t. The aggregator can place its first bid for delivery slot h at t = h - ?? - ?? based on the forecasts available at t about the generations and demands in its DER pool at h. This bid can be revised by the aggregator in the time slots t = h - t + 1 – r to h - r using the updated forecast values available in these time slots about the generations and demands at h. In the present disclosure, the system and method implement a forecasting model (not shown in FIGS. – but comprised in the memory 102 and executed to perform steps described herein) for generation and demand of each DER. The forecasting model(s) is/are trained using the corresponding historical input data. The trained model(s) is/are used to forecast the generation and demand of all delivery hours in the initialized optimization window. In the present disclosure, the system and method implemented as a stacked LSTM network” model which served as the forecasting model. The various timelines involved in the bidding process are shown in FIG. 4. FIG. 4, with reference to FIGS. 1 through 3, depicts various bidding timelines in intraday markets, in accordance with an embodiment of the present disclosure.
At step 206 of the method of the present disclosure, the one or more hardware processors 104 estimate a two-dimensional (2D) distribution of price-volume for the plurality of delivery slots in the initialized optimization window based on the forecasted generation and demand of the energy by the plurality of DERs. The historical intraday market data is used to estimate the 2D distribution of price-volume for all the delivery slots/hours in the optimization window. This estimation is done by closest fitting of the non-linear 2D function. 2D distributions for some of delivery hours at different trading hours are shown in FIGS. 5A through 5D. FIGS. 5A through 5D, with reference to FIGS. 1 through 4, depict a histogram of 2D distributions for some of delivery hours at different trading hours, in accordance with an embodiment of the present disclosure. More specifically, FIGS. 5A through 5D depict a histogram illustrating cleared price-volume for h = 7 and h = 23 for two trading slots, in accordance with an embodiment of the present disclosure.
At step 208 of the method of the present disclosure, the one or more hardware processors 104 execute, an optimization model, using the estimated two-dimensional (2D) distribution of price-volume for the plurality of delivery slots in the initialized optimization window to obtain at least one of (i) an optimal intraday operating schedule for one or more DERs from the plurality of DERs, and (ii) an intraday bid associated with the plurality of DERs for the plurality of delivery slots to be traded in an intraday market. The optimal intraday operating schedule for the one or more DERs is extracted values of the variables such as G_(h,s), d_(h,s)^flex, d_(h,s)^fix, and r_(h,s) obtained after completing the execution of the NLP problem. Similar, the intraday bids include, but are not limited to, extracted values of the variables such as but ?ps?_h, ?qs?_h, ?pb?_h, and ?qb?_h obtained after completing the execution of the NLP problem.
Execution of the optimization model comprises various steps being carried out by the system. FIG. 6, with reference to FIGS. 1 through 5D, depicts an exemplary flow chart illustrating a method for executing the optimization model (or a non-linear programming problem), using the systems of FIG. 1, in accordance with an embodiment of the present disclosure. For instance, at step 208a of the method of the present disclosure, the one or more hardware processors 104 formulate a mixed integer non-linear programming (MINLP) problem based on the input and the estimated two-dimensional (2D) distribution of price-volume for the plurality of delivery slots in the initialized optimization window. At step 208b of the method of the present disclosure, the one or more hardware processors 104 convert the formulated MINLP problem to an NLP problem. At step 208c of the method of the present disclosure, the one or more hardware processors 104 execute (or solve) the NLP problem to obtain the at least one of (i) the optimal intraday operating schedule for one or more DERs from the plurality of DERs, and (ii) the intraday bid associated with the plurality of DERs for the plurality of delivery slots to be traded in an intraday market. The NLP problem is obtained by relaxing at least one (i) a first integer variable, and (ii) a second integer variable comprised in the MINLP. The first integer variable is based on a decision of a type of the intraday bid (e.g., either to sell generated energy/power or buy energy (or demand). The second integer variable is based on a constraint specific to a DER type (e.g., charging and discharging rates and levels of batteries). The intraday bid comprises a decision to place a buy bid or a sell bid and a corresponding price-volume pair for each delivery slot pertaining to one or more DERs. For instance, for each hour delivery slot, the aggregator must decide to place a buy or sell bid based on the aggregate power (x_h^tot) in that slot. If x_h^tot>0, it means the aggregator has surplus generation and it needs to place a sell bid. If x_h^tot<0, it indicates that the aggregator has excess demand, and it needs to place a buy bid. The constraints (equations (10) through (17) for MINLP problem and equations (10), (17), (21), and (22) for NLP model) govern this decision. Below Table 7 illustrates intraday bid obtained as an output from the execution of the optimization model.
Table 7
Delivery hour x_h^tot Sell bid Buy bid
Price (Euro) Volume (MW) Price (Euro) Volume (MW)
6:00 0.49 - - 9.10 0.49
7:00 0.61 - - 7.34 0.61
8:00 0.36 19.94 0.36 - -
9:00 0.29 19.42 0.29 - -
The optimal intraday operating schedule for a first DER type (e.g., say battery) comprises at least one of (i) whether to charge or discharge in each delivery slot of the initialized optimization window, (ii) a charging level or a discharging level in each delivery slot of the initialized optimization window; and (iii) a state of charge (SOC) value of a DER of the first DER type at an end of each delivery slot. For instance, the first DER type is a battery. The constraints (e.g., equations (1), (4), (5), (6), and (7) for MINLP problem and equations (1), (5), (19), (20) for NLP problem) govern the schedule of this DER type. As battery is a bi-directional in nature, it can export as well as import. A sample optimal schedule of one battery for the initialized optimization window is shown in below Table 8.
Table 8
Delivery hour r SOC
6:00 -15 15
7:00 10 25
8:00 8 33
9:00 2 35
A positive value of r indicates battery charging whereas negative value of r indicates battery discharging. The absolute value of r is charging/discharging level.
The optimal intraday operating schedule for a second DER type (e.g., say solar photovoltaic or energy or power generators) comprises quantity of energy required to be provided to a power grid in each delivery slot. For instance, say, the second DER type is a solar PV. As it is a pure generation source, the optimal schedule for this DER type is a net power that is exported to the power grid. A sample operating schedule of a solar PV is shown in below Table 9.
Table 9
Delivery hour Solar export (kW)
6:00 11
7:00 40
8:00 83
9:00 101
The optimal intraday operating schedule for a third DER type comprises information pertaining to scheduling of an operation of an electrical load (e.g., such as flexible load or flexible demand) at one or more delivery slots. For instance, the third DER type is the flexible load. Here the aggregator knows the total flexible load, but the aggregator has to decide in which delivery hours to schedule the flexible load such that its operating cost is minimum. The constraints (e.g., equations (1), (8), and (9)) govern the schedule of this DER type. A sample schedule of a flexible load DER is shown in below Table 10.
Table 10
Delivery hour Flexible load (KW)
6:00 12
7:00 13
8:00 0
9:00 0
Examples of fixed and flexible load(s), include, but are not limited to residential (or commercial) air conditioners, water heaters, refrigerators, commercial HVAC (Heating, ventilation, and air conditioning) systems, pumps for irrigation, pool cleaning or heating, appliances to be scheduled for operation in office buildings, houses, and the like.
The steps 208a through 208c are better understood by way of following description:
Market and pool trading: For a delivery hour h, the generation available with the aggregator at a node n is equal to the sum of the battery discharge volumes (b_(h,s)^dsg) and local generation (G_(h,s)) of subscribers under that node. This is represented as the first term in right hand side of equation (1). Similarly, the demand of the aggregator at node n is equal to the sum of battery charging volume (b_(h,s)^chg), fixed loads of customers attached to n (d_(h,s)^fix), and flexible loads of customers attached to n that are being scheduled (d_(h,s)^flex) as reflected in the second term in the right hand side of equation (1) below.
x_(h,n)+x_(h,n)^pool=?_(s?S_n)¦?(G_(h,s)+b_(h,s)^dsg )-(d_(t,s)^fix+d_(h,s)^flex+b_(h,s)^chg)? ?n?N,?h?W^t (1)
The net amount of energy exchanged at a node is split between market (x_(h,n)) and pool (x_(h,n)^pool) components as in equation (1). Positive values of x_(h,n) and x_(h,n)^pool indicate that excess power is either exported to the markets or used to meet the demands of its own subscriber pool across nodes. Similarly, negative values x_(h,n) and x_(h,n)^pool indicate that the demand is met either through market imports or from the generation of other subscribers in the pool. Market exports increase the revenue earned by the aggregator while pool exports decrease the revenue outflow. The converse holds for market and pool imports. The underlying assumption is that there could be asymmetry between the successful market clearing of a sell bid and a buy bid with the same price and volume values. Equation 2 balances the power exchange occurring within the pool i.e., the total power exported onto the pool should always be equal to the power imported into the pool.
?_(x?N)¦?x_(h,n)^pool=0?,?h (2)
Network and battery constraints: The amount of power that can be injected by the DERs into the network could be limited by the hosting capacity and other operational limits of the network. Such limits are assumed to be communicated by the network operator to the aggregators at least t slots in advance. Equation (3) enforces the nodal limits set by the network operator on the aggregator.
|?x_(h,n)+x?_(h,n)^pool |=?Lim?_n, ?n?N (3)
Equations (4), and (5) enforce the relationship between the state of charge (SOC) and charge/discharge volumes of batteries available with subscribers.
?SOC?_(h,s)=?SOC?_(h-1,s)+b_(h,s)^chg-b_(h,s)^dsg, ?h?W^t, ?s?S (4)
?SOC?_s^min=?SOC?_(h,s)=?SOC?_s^max, ?h?W^t, ?s?S (5)
It is noted here that the values of ?SOC?_(t+r-1,s) is be determined by the optimal solution discovered in the previous window W^(t-1). Equations (6) and (7) limit the charging/discharging rates of batteries as determined by the battery characteristics. Also, the binary variable z_(h,s) ensures that the battery is either charging or discharging (but not both) in each h.
b_(h,s)^chg=z_(h,s)×R_s^chg (?SOC?_(h-1,s)), ?h?W^t, ?s?S (6)
b_(h,s)^dsg=(1-z_(h,s) )×R_s^dsg (?SOC?_(h-1,s) ), ?h?W^t, ?s?S (7)
Lithium-ion batteries (found in electric vehicles and home electricity storage products) must be charged carefully so as to not trigger any thermal effects that can affect the battery life. Finding optimal strategies to quickly charge Li-ion cells under high efficiency without damaging them is an active area of research. Several methods exist for charging Li-ion batteries such as constant current – constant voltage, multi-step charging, and pulse charging, to name a few. In some of these charging techniques, the time taken to charge from 10% to 20% state of charge (SoC) may not be same as that of charging from 70% to 80% SoC. So, for a given battery size, the maximum (dis)charging rate – R_s^chg () and R_s^dsg(), may depend on the SoC level and could be non-linear.
Demand constraints: Equations (8) and (9) are constraints for scheduling the flexible demands. Equation (8) ensures that the flexible demand scheduled in the entire optimization window is always equal to the expected total flexible demand. Also, the flexible demand scheduled in each slot should be less than the maximum limit allowed in a slot as indicated in equation (9) below:
?_h¦?d_(h,s)^flex=d_s^totflex ?, ?s?S (8)
0=d_(h,s)^flex=d_s^maxflex, ?h?W^t, ?s?S (9)
Trade volume revisions: x_(h,n) quantifies the net power available at node n to trade with the market during slot h. This volume estimation is being done during time slot t. It is possible that, a similar volume estimation for h was done during the slots t - 1,t -2,· · · ,h - t - r. Based on these earlier estimates, buy or sell bids might have been placed in the market during t - 1,t - 2,· · · ,h -t - r, resulting in prior market commitment for the aggregator. Let Qb_h^clear and Qs_h^clear h indicate the cumulative quanta of buy and sell commitments made in the market respectively before t for delivery slot h. Given these prior commitments, the total aggregated power available with the aggregator for delivery at h that needs to be traded in the intraday market is defined by equation (10) below:
x_h^tot=Qb_h^clear-Qs_h^clear+?_(n=1)^N¦x_(h,n) , ?h?W^t (10)
It is observed that equation (10) also allows for revisions to be made in the trade volume based on the latest forecasts available at t about generations and demands in W^t. This provision to adjust for the trade volume also supports spill over trades from day-ahead markets. In such cases, the initial values of Qb_h^clear and Qs_h^clear can be set to the volumes cleared in the day-ahead market.
Buy vs Sell: The total quantity x_h^tot can be either positive or negative depending on the states and requirements of the DERs at h. If x_h^tot is positive, it implies that the aggregator has surplus generation and needs to place sell offers in market. If x_h^tot is negative, it means that the aggregator has excess demand and needs to place buy bids in market. This decision is made by the binary variable d_h in equation (11).
-M(1-d_h)=x_h^tot=Md_h, ?h?W^t (11)
If d_h=1, the aggregator places sell offers; otherwise, it places buy bids. This is represented in equations (A) and (B) respectively. Also, both these constraints ensure that the aggregator places either buy bids or sell offers but not both.
x_h^tot d_h=?qs?_h, ?h?W^t (A)
x_h^tot (d_h-1)=?qb?_h, ?h?W^t (B)
The above two constraints are nonlinear in nature. In order to make it easier for solvers to find the solution, the system and method of the present disclosure linearize them.
Constraint A is linearized through equations (12) and (13). Similarly, constraint B is linearized through equations (14), (15), and (16).
-Md_h=?qs?_h=Md_h, ?h?W^t (12)
x_h^tot-M(1-d_h )=?qs?_h=x_h^tot+M(1-d_h ), ?h?W^t (13)
-M(1-d_h )=q ^b_h=M(1-d_h ), ?h?W^t (14)
x_h^tot-M(d_h )=q ^b_h=x_h^tot+Md_h, ?h?W^t (15)
?qb?_h=-q ^b_h, ?h?W^t (16)
Equation (17) constrains the buy/sell prices to be within their maximum and minimum limits obtained from the historical data.
P_h^L=?pb?_h=P_h^H, ?h?W^t (17)
Objective function: Given the above relations, the aggregator at time t has to decide the amount of energy to buy (or sell) in the market during h. It should also determine the prices of the buy bids and sell offers. The values of these decision variables have to be determined so that the revenue earned by the aggregator through trading is maximized. This is defined by the objective function in equation (18).
max-(p_h,q_h )???_(h?W^t)¦??ps?_h ?qs?_h.F_sell^(t,h) ?(p_h,q_h)?-?_(h?W^t)¦??pb?_h ?qb?_h (1-.F_sell^(t,h) (p_h,q_h )) ? (18)
where p_h=(?ps?_h ?pb?_h) and q_h=(?qs?_h ?qb?_h)
In each slot t, the market clears bids corresponding to different delivery slots h. Among the bids cleared during t for delivery at h, let f^(t,h) (p,q) be the relative fraction of bids with price p and volume q that are found in the historical logs. It is noted that here that f^(t,h) (p,q) captures the market’s bid clearing dynamics as a function of bid price and volume. It is clear that f^(t,h) (p,q) does not represent the probability of a
bid getting cleared in the intraday market at t for delivery at h. This is because f^(t,h) (p,q) is obtained from the cleared market transactions. Rather, this term is the conditional probability of finding a
transaction in the bids cleared at t for delivery at h.
The distribution f^(t,h) (p,q), however, divulges the market’s relative preference in clearing the bids. The probability of the market fully clearing a sell bid with quantity q_1 and price p_1 at transaction slot t for delivery at h increases with f^(t,h) (p_1,q_1 )+f^(t,h) (p_2,q_1 )…+f^(t,h) (p_n,q_1 ) where p_1