# Scheduling of electricity storage for peak shaving with minimal device wear

Thijs van der Klauw, Johann L. Hurink, Gerardus J.M. Smit

### Abstract

In this work, we investigate scheduling problems for electrical energy storage systems and formulate an algorithm that finds an optimal solution with minimal charging cycles in the case of a single device. For the considered problems, the storage system is used to reduce the peaks of the production and consumption within (part of) the electricity distribution grid, while minimizing device wear. The presented mathematical model of the storage systems captures the general characteristic of electrical energy storage devices while omitting the details of the specific technology used to store the energy. In this way, the model can be applied to a wide range of settings. Within the model, the wear of the storage devices is modeled by either: (1) the total energy throughput; or (2) the number of switches between charging and discharging, the so-called charging cycles. For the first case, where the energy throughput determines the device wear, a linear programming formulation is given. For the case where charging cycles are considered, an NP-hardness proof is given for instances with multiple storage devices. Furthermore, several observations about the structure of the problem are given when considering a single device. Using these observations, we develop a polynomial time algorithm of low complexity that determines an optimal solution. Furthermore, the solutions produced by this algorithm also minimize the throughput, next to the charging cycles, of the device. Due to the low complexity, the algorithm can be applied in various decentralized smart grid applications within future electricity distribution grids.
Original language English 465 19 Energies 9 6 https://doi.org/10.3390/en9060465 Published - 17 Jun 2016

### Fingerprint

Electricity
Scheduling
Wear of materials
Throughput
Energy storage
Storage System
Cycle
Energy Storage
Linear programming
Low Complexity
Optimal Solution
Energy
Hardness
Switches
Polynomials
Mathematical models
Grid
Smart Grid
NP-hardness
Polynomial-time Algorithm

### Keywords

• EWI-27058
• device aging
• mixed integer linear program (MILP)
• IR-100529
• Peak Shaving
• polynomial time optimal algorithm
• METIS-317218
• electrical energy storage

### Cite this

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title = "Scheduling of electricity storage for peak shaving with minimal device wear",
abstract = "In this work, we investigate scheduling problems for electrical energy storage systems and formulate an algorithm that finds an optimal solution with minimal charging cycles in the case of a single device. For the considered problems, the storage system is used to reduce the peaks of the production and consumption within (part of) the electricity distribution grid, while minimizing device wear. The presented mathematical model of the storage systems captures the general characteristic of electrical energy storage devices while omitting the details of the specific technology used to store the energy. In this way, the model can be applied to a wide range of settings. Within the model, the wear of the storage devices is modeled by either: (1) the total energy throughput; or (2) the number of switches between charging and discharging, the so-called charging cycles. For the first case, where the energy throughput determines the device wear, a linear programming formulation is given. For the case where charging cycles are considered, an NP-hardness proof is given for instances with multiple storage devices. Furthermore, several observations about the structure of the problem are given when considering a single device. Using these observations, we develop a polynomial time algorithm of low complexity that determines an optimal solution. Furthermore, the solutions produced by this algorithm also minimize the throughput, next to the charging cycles, of the device. Due to the low complexity, the algorithm can be applied in various decentralized smart grid applications within future electricity distribution grids.",
keywords = "EWI-27058, device aging, mixed integer linear program (MILP), IR-100529, Peak Shaving, polynomial time optimal algorithm, METIS-317218, electrical energy storage",
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In: Energies, Vol. 9, No. 6, 465, 17.06.2016.

TY - JOUR

T1 - Scheduling of electricity storage for peak shaving with minimal device wear

AU - van der Klauw, Thijs

AU - Hurink, Johann L.

AU - Smit, Gerardus J.M.

N1 - eemcs-eprint-27058

PY - 2016/6/17

Y1 - 2016/6/17

N2 - In this work, we investigate scheduling problems for electrical energy storage systems and formulate an algorithm that finds an optimal solution with minimal charging cycles in the case of a single device. For the considered problems, the storage system is used to reduce the peaks of the production and consumption within (part of) the electricity distribution grid, while minimizing device wear. The presented mathematical model of the storage systems captures the general characteristic of electrical energy storage devices while omitting the details of the specific technology used to store the energy. In this way, the model can be applied to a wide range of settings. Within the model, the wear of the storage devices is modeled by either: (1) the total energy throughput; or (2) the number of switches between charging and discharging, the so-called charging cycles. For the first case, where the energy throughput determines the device wear, a linear programming formulation is given. For the case where charging cycles are considered, an NP-hardness proof is given for instances with multiple storage devices. Furthermore, several observations about the structure of the problem are given when considering a single device. Using these observations, we develop a polynomial time algorithm of low complexity that determines an optimal solution. Furthermore, the solutions produced by this algorithm also minimize the throughput, next to the charging cycles, of the device. Due to the low complexity, the algorithm can be applied in various decentralized smart grid applications within future electricity distribution grids.

AB - In this work, we investigate scheduling problems for electrical energy storage systems and formulate an algorithm that finds an optimal solution with minimal charging cycles in the case of a single device. For the considered problems, the storage system is used to reduce the peaks of the production and consumption within (part of) the electricity distribution grid, while minimizing device wear. The presented mathematical model of the storage systems captures the general characteristic of electrical energy storage devices while omitting the details of the specific technology used to store the energy. In this way, the model can be applied to a wide range of settings. Within the model, the wear of the storage devices is modeled by either: (1) the total energy throughput; or (2) the number of switches between charging and discharging, the so-called charging cycles. For the first case, where the energy throughput determines the device wear, a linear programming formulation is given. For the case where charging cycles are considered, an NP-hardness proof is given for instances with multiple storage devices. Furthermore, several observations about the structure of the problem are given when considering a single device. Using these observations, we develop a polynomial time algorithm of low complexity that determines an optimal solution. Furthermore, the solutions produced by this algorithm also minimize the throughput, next to the charging cycles, of the device. Due to the low complexity, the algorithm can be applied in various decentralized smart grid applications within future electricity distribution grids.

KW - EWI-27058

KW - device aging

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KW - IR-100529

KW - Peak Shaving

KW - polynomial time optimal algorithm

KW - METIS-317218

KW - electrical energy storage

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