Robust energy storage scheduling for imbalance reduction of strategically formed energy balancing groups
Introduction
The number of Power Producer and Supplier (PPS) in the power and energy market is increasing rapidly due to the liberalization in power market in Japan [1]. With the increase in market share of PPSs, the potential of demand-centric business opportunity increases. As of 2014, the electricity market in Japan is dominated by regional monopolies, where 85% of the installed generating capacity is produced by 10 privately owned companies. However, the rising of Power Producer and Supplier (PPS) (i.e. Electric Power Retailer) in the electricity market is inevitable due to the full-fledged deregulation [1] that will eventually break the monopolies. PPPs face challenge while keeping the on-line supply and demand matched with the highest precision, and thus reducing the imbalance (gap between contracted supply and demand) in demand side low-voltage network. In off-line, the PPS can intelligently group the customers to increase the demand predictability of each group and procures volume of energy (utilizing day-ahead energy prediction). The procured energy refers as the supply contract for each group. Flexible power distribution as such is attainable through Digital grid architecture [2]. In ideal world, the contracted supply matches with actual demand at each granular (typically, 30-min). However, due to the uncertainty in on-line energy consumption as well as energy supply, the gap between supply and demand is highly likely to occur. The current practice is to buy (in case of demand is higher than the supply) or sell (in case of supply is higher than the demand) energy from/to Energy Imbalance Market (EIM) (EIM can be a part of Utility or be an independent body or the Utility itself, [3]). The EIM mitigates such mismatch between on-line supply and demand by transacting necessary energy with the PPS. The involvement of EIM goes higher with the increasing gap between the supply and the demand. The price setting of EIM, on the other hand, is significantly higher compared to the conventional energy tariff ([3], page 4). Therefore, the reduction of imbalance cost casts itself as one of the important problems to tackle for demand side based energy service of PPS.
Two fundamental yet interconnected problems are, therefore, identified for a PPS, 1) strategic demand aggregation for balancing group creation, and 2) on-line imbalance energy and cost reduction for formed balancing groups. A PPS serves multiple commercial settings (e.g. apartment buildings, commercial buildings, shopping mall, factory, and similar setting.). Therefore, it is essential for the PPS to effectively and strategically identify the customers' demand based grouping for energy balancing purpose, i.e. balancing group. Groupings as such are also necessary for service and price differentiations. In case of the imbalance energy reduction service, it is critically important for the PPS to define appropriate demand aggregation criterion and demand aggregation strategy so that it can effectively identify clusters of similar customers (e.g. buildings), the associated aggregated demand with reduced variance and potential imbalance energy bound. In this paper, we present a probabilistic programming [4] approach that utilizes a Bayesian Markov Chain Monte Carlo (MCMC) sampling method [5], [6] in order to form multiple balancing groups. Initially, a demand aggregation criterion is identified as a statistical observation, then a probabilistic model of the observation is devised and finally posteriors of the model parameters are determined through Bayesian MCMC. The process is recursively conducted, which divides a parent observation into two based on the posterior analysis of the model parameters. Therefore, a divide-and-conquer approach is designed to solve balancing group formation problem.
As for the on-line operation, the reduction of the group-wise imbalance cost can be realized by the effective on-line energy storage management; more particularly, the on-line charge/discharge (CD) scheduling of energy storage. However, since the imbalance energy tariff is non-linear to the imbalance energy, typical straight-forward method of CD scheduling leads to an inefficient solution. Therefore, we present an efficient CD scheduling for multiple spatially distributed energy storages where the schedule is robust against demand prediction uncertainty. The robust scheduling method essentially minimizes the expected imbalance energy and imbalance cost considering a number of demand prediction scenarios. Battery storage system is utilized as the energy storage system. The designed scheduling approach first performs a short-term demand prediction, then generates a number of statistical scenarios of the predicted demands utilizing a joint distribution of probability density function (PDF) of prediction error with the PDF of variability of preceding periods; and finally solves a multi-objective optimization problem that decides the CD scheduling (with power dispatch) of batteries while minimizing both imbalance energy and cost. The required aggregated battery power-rating information is drawn from the posterior distribution knowledge that had been conducted while forming groups. The problem in hand is non-linear due to the imbalance pricing scheme, storage dynamics and associated non-linear constraints. The optimization problem is, therefore, transformed into an equivalent Mixed Integer Linear Programming (MILP) problem [7] followed by an additional transformation to Mixed Logical Dynamical (MLD) System [8], and finally solved by a branch-and-cut linear solver [9].
Clustering has been a useful analytical and operational tool in energy domain (e.g. energy market, [10]). Applications of clustering methods in high- and medium-voltage power networks for large scale integration of customers have been reported in articles like [11], [12]. In Ref. [11], a comprehensive overview of clustering methods are presented and the necessity of these methods while identifying effective customer grouping are highlighted (from the perspective of an Energy Supplier). The supervised clustering algorithms (e.g. Hierarchical clustering, K-means, Fuzzy K-means) are discussed [12] that analyzes the similarity within customers. Meanwhile, at the low-voltage network, energy based clustering for planning and operation (from the perspective of market operators such as Distribution Network Operators, DNOs) is reported in Ref. [13]. In Ref. [13], household smart-meter data are analyzed for demand variability and a finite mixture model based clustering algorithm is proposed that discovers a number of distinctive behavior groups. Therefore, it is evident that clustering methods play important roles for planning and operation of market operators such as energy suppliers, DNOs and PPSs. We employed a Bayesian inference coupled with MCMC method to determine the energy balancing groups based on a statistical demand measurement. The Bayesian MCMC is chosen over other clustering methods due to its advantages of accounting the uncertainty presented in the models and parameters as well as its ability to present useful insights regarding the model (inferred from the posterior distribution of model's parameters). For example, the applied Bayesian MCMC method provides an upper-bound of required group-wise energy storage aggregated power-rating (and consequently energy capacity rating).
For on-line operation, which requires fast solution, it has been widely advised by the experts to deploy advanced mathematical optimization algorithms that accounts for system uncertainty and predictability of future states or conditions [14]. The working mechanism of the proposed CD scheduling method, therefore, aligns with that of Model Predictive Control (MPC), which measures up to the aforementioned requirements. MPC (and its variants) has been an active research area in the power system arena. In Ref. [15], an energy management system for Microgrid operation considering PV, Diesel Generators, and energy storage is presented. A stochastic MPC for solving Unit Commitment with wind power is documented in Ref. [16]. Robust scheduling of resources is critically important when the optimization model is exposed to various uncertainties presented in the model states. For example, in Ref. [17], a robust cost optimization method is presented that essentially schedules of renewable energy generators with combined heat and power (CHP) generators considering the uncertainty in net energy demand and electricity price. Another stream of research has been conducted on stochastic MPC considering the uncertainty in the model. For example, in Ref. [18], a stochastic MPC is presented for efficient controlling in building's HVAC system while focusing on energy minimization. On the other hand, MILP based mathematical optimization is the current industry trend of operation research oriented towards resource scheduling and optimization. For instance, in the arena of Unit Commitment (one of the important problems in Power System Planning and Operation), MILP provides efficient, fast and scalable solutions [19], [20]. These outstanding researches create platform for applying robust MILP based optimization algorithm, which minimizes the expected imbalance energy and cost over a set predicted demand scenarios, as a core optimizer of the proposed on-line CD scheduling method.
Section snippets
Forming energy balancing groups
An energy balancing group contains a number of customersl sharing similarity in their demand profiles where their aggregated demand profile exhibits higher predictability. It is, therefore, essential to identify appropriate criterion based on which such aggregation and group formation will be performed. The following is one such criterion.
On-line storage scheduling for imbalance reduction
In this section, an on-line stochastic scenario based robust storage scheduling method is proposed that reduces the imbalance energy and imbalance cost of a particular balancing group. Even, the balancing groups are formed strategically in order to maximize the aggregated demand predictability (which is utilized in the forward and day-ahead market to determine supply contract), in real-time, the imbalance of energy is still inevitable due to the prediction error. The PPS, therefore, interacts
Numerical simulations and discussions
This section presents the numerical simulations, analysis, results and discussions associated with formation of balancing groups and robust CD scheduling. A total of 103 apartments building in Tokyo are taken as customers and their demand data are utilized for the analysis. More particularly, the demand data of January and February 2013 are taken and broken down to two phases.
- 1
Analysis and training phase: Data from January 1st to January 20th are utilized to perform the balancing group formation
Conclusion
In this paper, we propose novel solution strategies for two of the fundamental yet interconnected problems of PPS. The 1st problem deals with formation of energy based balancing groups within a particular class of customers. In this paper, apartment buildings are taken as customers. To solve the group formation problem, we apply a Bayesian MCMC based divide-and-conquer strategy that takes a statistical measure (periodical demand standard deviation of each customer) and produces a number of
Acknowledgement
The authors would like to thank Digital Grid Co., Ltd. and The University of Tokyo. This work is a part of collaborative research program with these entities.
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