# Effects of a Battery Energy Storage System on the Operating Schedule of a Renewable Energy-Based Time-of-Use Rate Industrial User under the Demand Bidding Mechanism of Taipower

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- A demand bidding mechanism is designed to make a collaboration between customers and suppliers on demand response to perform peak shaving and realize energy conservation.
- An improved DSM incorporated with a three-state DP is proposed to solve the operating schedule of a TOU rate industrial user under the demand bidding mechanism of Taipower.
- Several operational strategies of a BESS are evaluated for a TOU rate industrial user to maximize the total incentive obtained from the TPC.
- Numerical results are provided to assess the impact and economic benefits of the installation of a BESS for executing the DBP. The proposed DSM is also efficient and suitable for practical applications.

## 2. Problem Formulation and System Modeling

#### 2.1. Notation

TOC | : Total electricity cost of the TOU rate industrial user (NT$). |

$CBL({d}^{*})$ | : Customer baseline load for the day d* (kW). |

$P{U}_{\mathrm{max}}({d}^{*})$ | : Maximum demand during DR-execution time for the day d* (kW). |

${P}_{D}^{bt}({d}^{*})$ | : Load demand in period bt for the day d* (kW). |

$BDT({d}^{*})$ | : DR-execution time (2 h or 4 h) for the day d* (hours). |

$ABP({d}^{*})$ | : Actual load-reduction amount for the day d* (kW). |

${F}_{BD}(d)$ | : Total incentive for the day d (NT$/h). |

${F}_{PE}(t,d)$ | : Cost of the purchased power at interval t for the day d (NT$/h). |

${C}_{BD}(d)$ | : Bidding price during the DR-execution time for the day d (NT$/ kWh). |

${C}_{PE}(t,d)$ | : Tariff of the purchased power at interval t for the day d (NT$/kWh). |

d | : Index for day intervals (one day). |

D | : Total observation days (days). |

t | : Index for time intervals (15 min interval). |

T | : Number of time intervals (one day). |

j | : Index for non-dispatchable units. |

ND | : Number of non-dispatchable units in system. |

${P}_{D}(t,d)$ | : System load demand at interval t for the day d (kW). |

${P}_{NDj}(t,d)$ | : Power of non-dispatchable unit j at interval t for the day d (kW). |

${P}_{grid}(t,d)$ | : Power of purchased from utility grid at interval t for the day d (kW). |

${P}_{grid}^{\mathrm{max}}$ | : Maximum output power from utility grid (namely, the contract capacity) (kW). |

${P}_{bat}(t,d)$ | : Charging/discharging power of battery storage system at interval t for the day d (positive for discharging and negative for charging) (kW). |

${P}_{bat}^{\mathrm{max}}$ | : Maximum power from the battery storage system (kW). |

$SOC(t,d)$ | : State of charge of the battery at interval t for the day d (kWh). |

$SO{C}_{\mathrm{min}}$ | : Minimum battery state of charge (kWh). |

$SO{C}_{\mathrm{max}}$ | : Maximum battery state of charge (kWh). |

${\eta}_{B}$ | : Battery round-trip efficiency. |

$\Delta \mathrm{t}$ | : Sampling time interval. |

${P}_{Wj}^{*}(t,d)$ | : Available power of wind power generation unit j at interval t for the day d (kW). |

${P}_{Wj}^{\mathrm{max}}$ | : Maximum power of wind power generation unit j (kW). |

${\varphi}_{j}(\u2022)$ | : Wind power curve of wind power generation unit j (kW). |

$v(t,d)$ | : Wind speed at interval t for the day d. |

${v}_{Ij}$ | : Cut in wind speed for wind power generation unit j. |

${v}_{Rj}$ | : Rated wind speed for wind power generation unit j. |

${v}_{Oj}$ | : Cut out wind speed for wind power generation unit j. |

${P}_{PVj}^{*}(t,d)$ | : Available power of solar power generation unit j at interval t for the day d (kW). |

${\delta}_{j}(\u2022)$ | : Radiation/ambient temperature power curve of solar power generation unit j (kW). |

${P}_{PVj}^{\mathrm{max}}$ | : Maximum power of solar power generation unit j (kW). |

${S}_{r}(t,d)$ | : Intensity of solar radiation at interval t for the day d. |

${T}_{r}(t,d)$ | : Ambient temperature at interval t for the day d. |

SD | : Minimum intensity of solar radiation. |

SU | : Maximum intensity of solar radiation. |

${P}_{vir}(bt+l)$ | : Virtual price at period bt+l (NT$/kWh). |

α | : Coefficient of virtual price. |

${P}_{D}^{\mathrm{max}}$/${P}_{D}^{\mathrm{min}}$ | : Maximum/minimum load demand during the DR-executing time (kW). |

PLC | : Price of peak load periods (NT$/kWh). |

LLC | : Price of off-peak load periods (NT$/kWh). |

#### 2.2. Demand Bidding Mechanism of Taipower

#### 2.3. Objective Function

#### 2.4. Operational Constraints

_{bat}> 0 represents discharging, while P

_{bat}< 0 implies charging. On the other hand, references [25,26] show that loads could be classified into non-controllable, controllable comfort-based loads. However, this paper focuses on the power dispatch problem, the investigated load demand profile is statistical data from TPC customers and is regarded as an uncontrollable load. The operational constraints of the hybrid system with a RES and BESS are introduced as below.

#### 2.4.1. System Constraints

- Power balance constraint$$\sum _{j=1}^{ND}{P}_{NDj}(t,d)}+{P}_{grid}(t,d)+{P}_{bat}(t,d)={P}_{D}(t,d)$$

#### 2.4.2. Non-Dispatchable Unit Constraints

- Wind power curve constraints$${P}_{Wj}^{*}{(t,d)}_{}=\text{\hspace{0.33em}}\left\{\begin{array}{c}\hspace{1em}\hspace{1em}0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}v(t,d)\le {v}_{Ij}\text{\hspace{0.33em}}or\text{\hspace{0.33em}}v(t,d)>{v}_{Oj}\\ {\varphi}_{j}(v(t,d))\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{v}_{Ij}\le v(t,d)\le {v}_{Rj}\\ \hspace{1em}{P}_{Wj}^{\mathrm{max}}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{v}_{Rj}\le v(t,d)\le {v}_{Oj}\end{array}\right.$$
- Solar radiation/ambient temperature power curve constraints$${P}_{PVj}^{*}{(t,d)}_{}=\text{\hspace{0.33em}}\left\{\begin{array}{c}0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{S}_{r}(t,d)\le SD\\ {\delta}_{j}({S}_{r}(t,d),\text{\hspace{0.33em}}{T}_{r}(t,d))\hspace{1em}\hspace{1em}\hspace{1em}SD\le {S}_{r}(t,d)\le SU\\ {P}_{PVj}^{\mathrm{max}}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{S}_{r}(t,d)\ge SU\end{array}\right.$$

#### 2.4.3. Battery Constraints

- Limits of charge/discharge power$$-{P}_{bat}^{\mathrm{max}}\le {P}_{bat}^{}(t,d)\le {P}_{bat}^{\mathrm{max}}$$
- Upper and lower limits for state of charge$$SO{C}_{\mathrm{min}}\le SOC(t,d)\le SO{C}_{\mathrm{max}}$$
- State of charge for battery storage system$$SOC(t,d)=\left\{\begin{array}{l}SOC(t-1,d)-{P}_{bat}(t,d)\times {\eta}_{B}\times \Delta tif{P}_{bat}(t,d)0\\ SOC(t-1,d)-{P}_{bat}(t,d)\times \frac{\Delta t}{{\eta}_{B}}if{P}_{bat}(t,d)\ge 0\end{array}\right.$$

#### 2.4.4. Constraints of the Utility Grid

- Limit of the purchased power$$0\le {P}_{grid}(t,d)\le {P}_{grid}^{\mathrm{max}}$$

## 3. Evaluation of Operating Policy for the TOU Rate Industrial User

#### 3.1. Development of the DSM Software

_{1}, and reduced factor K. The previous work on the DSM approaches used a larger initial step size S

_{1}for effective search, and the step size was then successively refined until the calculation step was less than the predetermined resolution. Clearly, the DSM with a coarse convergence step can enhance the global exploration ability; however, it causes an incapability to find nearby extreme points (exploitation problem). By contrast, the DSM with a refined convergence step can enhance the local exploitation ability; however, it is easily trapped in local minima (exploration problem). Consequently, the standard DSM cannot guarantee that the solutions are optimal, or even close to the optimal, due to the deficiency in the balance between global exploration and local exploitation. Providing a well-balanced mechanism between these abilities is critical to avoid early convergence.

_{1}and a low K is recommended. From our numerical experience, S

_{1}= 10% of upper limit for BESS and K = 5 are applied in this study.

#### 3.2. Assessment of Operational Strategy for Executing the DBP

## 4. Numerical Examples

_{1}= 18 kW, the reduced factor K = 5, and the predetermined resolution ε = 0.01 kW. All the computation is performed on a PC Intel(R) Core(TM) i5-4570 CPU, up to 3.2 GHz. Several scenarios are taken into account and discussed as follows:

#### 4.1. Performance of the Proposed DSM Algorithm

#### 4.2. Prediction of Electricity Cost Savings for Executing the DBP

#### 4.3. Effects of BESS on the Operating Schedule for Load-Reduction Day

#### 4.4. Effects of BESS on the Operating Schedule for Non-Load-Reduction Day

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Chen, F.; Lu, S.M.; Wang, E.; Tseng, K.T. Renewable energy in Taiwan. Renew. Sustain. Energy Rev.
**2010**, 14, 2029–2038. [Google Scholar] [CrossRef] - Bouzguenda, M.; Rahman, S. Value analysis of intermittent generation sources from the system operations perspective. IEEE Trans. Energy Convers.
**1993**, 8, 484–490. [Google Scholar] [CrossRef] - Alqunun, K.; Guesmi, T.; Albaker, A.F.; Alturki, M.T. Stochastic Unit Commitment Problem, Incorporating Wind Power and an Energy Storage System. Sustainability
**2020**, 12, 10100. [Google Scholar] [CrossRef] - Su, W.; Wang, J.; Roh, J. Stochastic energy scheduling in microgrids with intermittent renewable energy resources. IEEE Trans. Smart Grid
**2013**, 5, 1876–1883. [Google Scholar] [CrossRef] - Behabtu, H.A.; Messagie, M.; Coosemans, T.; Berecibar, M.; Anlay Fante, K.; Kebede, A.A.; Mierlo, J.V. A Review of Energy Storage Technologies’ Application Potentials in Renewable Energy Sources Grid Integration. Sustainability
**2020**, 12, 10511. [Google Scholar] [CrossRef] - Chen, C.L. Optimal wind–thermal generating unit commitment. IEEE Trans. Energy Convers.
**2008**, 23, 273–280. [Google Scholar] [CrossRef] - Ramli, M.A.M.; Bouchekara, H.R.E.H.; Alghamdi, A.S. Efficient Energy Management in a Microgrid with Intermittent Renewable Energy and Storage Sources. Sustainability
**2019**, 11, 3839. [Google Scholar] [CrossRef] [Green Version] - Ejaz, W.; Naeem, M.; Shahid, A.; Anpalagan, A.; Jo, M. Efficient energy management for the internet of things in smart cities. IEEE Commun. Mag.
**2017**, 55, 84–91. [Google Scholar] [CrossRef] [Green Version] - Sundt, S.; Rehdanz, K.; Meyerhoff, J. Consumers’ Willingness to Accept Time-of-Use Tariffs for Shifting Electricity Demand. Energies
**2020**, 13, 1895. [Google Scholar] [CrossRef] - Chen, Z.; Wu, L.; Fu, Y. Real-time price-based demand response management for residential appliances via stochastic optimization and robust optimization. IEEE Trans. Smart Grid
**2012**, 3, 1822–1831. [Google Scholar] [CrossRef] - Yu, Z.; Jia, L.; Murphy-Hoye, M.C.; Pratt, A.; Tong, L. Modeling and stochastic control for home energy management. IEEE Trans. Smart Grid
**2013**, 4, 2244–2255. [Google Scholar] [CrossRef] [Green Version] - Tarasak, P.; Chai, C.C.; Kwok, Y.S.; Oh, S.W. Demand bidding program and its application in hotel energy management. IEEE Trans. Smart Grid
**2014**, 5, 821–828. [Google Scholar] [CrossRef] - Taiwan Power Company, Demand Bidding Measures. Available online: https://dbp.taipower.com.tw/TaiPowerDBP/Portal/proj_data/%E9%9C%80%E9%87%8F%E7%AB%B6%E5%83%B9%E6%8E%AA%E6%96%BDDM.pdf (accessed on 20 February 2020).
- Yao, L.; Lim, W.H. Optimal purchase strategy for demand bidding. IEEE Trans. Power Syst.
**2017**, 33, 2754–2762. [Google Scholar] [CrossRef] - Lee, T.Y. Operating schedule of battery energy storage system in a time-of-use rate industrial user with wind turbine generators: A multipass iteration particle swarm optimization approach. IEEE Trans. Energy Convers.
**2007**, 22, 774–782. [Google Scholar] [CrossRef] - Cheng, Y.S.; Liu, Y.H.; Hesse, H.C.; Naumann, M.; Truong, C.N.; Jossen, A. A pso-optimized fuzzy logic control-based charging method for individual household battery storage systems within a community. Energies
**2018**, 11, 469. [Google Scholar] [CrossRef] [Green Version] - Samuel, O.; Javaid, S.; Javaid, N.; Ahmed, S.H.; Afzal, M.K.; Ishmanov, F. An Efficient Power Scheduling in Smart Homes Using Jaya Based Optimization with Time-of-Use and Critical Peak Pricing Schemes. Energies
**2018**, 11, 3155. [Google Scholar] [CrossRef] [Green Version] - Chen, C.L. Non-convex economic dispatch: A direct search approach. Energy Convers. Manag.
**2007**, 48, 219–225. [Google Scholar] [CrossRef] - Kazarlis, S.A.; Bakirtzis, A.G.; Petridis, V. A genetic algorithm solution to the unit commitment problem. IEEE Trans. Power Syst.
**1996**, 11, 83–92. [Google Scholar] [CrossRef] - Selvakumar, A.I.; Thanushkodi, K. A new particle swarm optimization solution to nonconvex economic dispatch problems. IEEE Trans. Power Syst.
**2007**, 22, 42–51. [Google Scholar] [CrossRef] - Demand Bidding Program, Southern California Edison. Available online: https://www.sce.com/sites/default/files/inline-files/0804_Com.pdf (accessed on 9 March 2021).
- Delavaripour, H.; Khazaee, A.; Ghasempoor, M.; Hooshmandi, H. Reduced peak-time energy use by the demand bidding program in Iran. Cired-Open Access Proc. J.
**2017**, 2017, 1959–1962. [Google Scholar] [CrossRef] - Hosseini, S.M.; Carli, R.; Dotoli, M. Robust optimal energy management of a residential microgrid under uncertainties on demand and renewable power generation. IEEE Trans. Autom. Sci. Eng.
**2020**, 1–20. [Google Scholar] [CrossRef] - Sperstad, I.B.; Korpås, M. Energy storage scheduling in distribution systems considering wind and photovoltaic generation uncertainties. Energies
**2019**, 12, 1231. [Google Scholar] [CrossRef] [Green Version] - Carli, R.; Dotoli, M. Decentralized control for residential energy management of a smart users’ microgrid with renewable energy exchange. IEEE/CAA J. Autom. Sin.
**2019**, 6, 641–656. [Google Scholar] [CrossRef] - Scarabaggio, P.; Grammatico, S.; Carli, R.; Dotoli, M. Distributed Demand Side Management With Stochastic Wind Power Forecasting. IEEE Trans. Control Syst. Technol.
**2021**, 1–16. [Google Scholar] [CrossRef] - Lu, T.C.; Huang, C.Y.; Chen, Y.Y.; Chen, C.L.; Lee, T.Y. Efficient Energy Management of a Time-of-Use Rate Industrial User for Smart Cities. In Proceedings of the 2018 International Conference on System Science and Engineering (ICSSE), New Taipei, Taiwan, 28–30 June 2018; pp. 1–6. [Google Scholar]

**Figure 3.**State transition diagram of the battery energy storage system (BESS) for dynamic programming (DP).

**Table 1.**Comparison of iterations and total electricity cost (TOC) under various S in the TOU system.

Convergence | Iterations | TOC (NT$) |
---|---|---|

Initialization | - | 12,975.646 |

S_{1} = 18 kW | 0 | 12,975.646 |

S_{2} = 3.6 kW | 23 | 12,611.493 |

S_{3} = 0.72 kW | 24 | 12,556.483 |

S_{4} = 0.144 kW | 24 | 12,545.985 |

S_{5} = 0.0288 kW | 12 | 12,544.726 |

S_{6} = 0.00576 kW | 7 | 12,544.588 |

Run | Initialization (NT$) | TOC (NT$) |
---|---|---|

1 | 31,211,025 | 12,544.537 |

2 | 27,560,846 | 12,544.554 |

3 | 22,997,452 | 12,544.547 |

4 | 27,190,036 | 12,544.555 |

5 | 25,530,881 | 12,544.548 |

6 | 25,004,720 | 12,544.545 |

7 | 24,011,364 | 12,544.560 |

8 | 24,318,074 | 12,544.539 |

9 | 20,842,510 | 12,544.548 |

10 | 27,207,412 | 12,544.546 |

Case | BESS | DBP (Load-Reduction Day) | DBP (Non-Load-Reduction Day) | TOC (NT$) | Saving (%) |
---|---|---|---|---|---|

1 | Without | Without | Without | 12,975.646 | - |

2 | With | Without | Without | 12,544.546 | 3.32% |

3 | With | With | Without | 10,445.745 | 19.49% |

4 | With | Without | With | 12,544.546 | 3.32% |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tsai, C.-T.; Cheng, Y.-S.; Lin, K.-H.; Chen, C.-L.
Effects of a Battery Energy Storage System on the Operating Schedule of a Renewable Energy-Based Time-of-Use Rate Industrial User under the Demand Bidding Mechanism of Taipower. *Sustainability* **2021**, *13*, 3576.
https://doi.org/10.3390/su13063576

**AMA Style**

Tsai C-T, Cheng Y-S, Lin K-H, Chen C-L.
Effects of a Battery Energy Storage System on the Operating Schedule of a Renewable Energy-Based Time-of-Use Rate Industrial User under the Demand Bidding Mechanism of Taipower. *Sustainability*. 2021; 13(6):3576.
https://doi.org/10.3390/su13063576

**Chicago/Turabian Style**

Tsai, Cheng-Ta, Yu-Shan Cheng, Kuen-Huei Lin, and Chun-Lung Chen.
2021. "Effects of a Battery Energy Storage System on the Operating Schedule of a Renewable Energy-Based Time-of-Use Rate Industrial User under the Demand Bidding Mechanism of Taipower" *Sustainability* 13, no. 6: 3576.
https://doi.org/10.3390/su13063576