# Reduction of Power Imbalances Using Battery Energy Storage System in a Bulk Power System with Extremely Large Photovoltaics Interactions

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## Abstract

**:**

## 1. Introduction

## 2. Operation and Schedule Update Method for Generators and a Large BESS

#### 2.1. Time Chart of the Schedule Update

#### 2.1.1. Case 1 (Base Case)

#### 2.1.2. Case 2 (Proposed Case)

#### 2.2. Problem Formulation

#### 2.2.1. Optimization Problem

#### 2.2.2. Economic Dispatch

## 3. Simulation

#### 3.1. Simulation Conditions

#### 3.1.1. Power and Control Resources

#### 3.1.2. Load Demand Data

#### 3.1.3. PV Power Output Data

#### 3.2. Simulation Results

#### 3.2.1. Total Imbalance and Cost

#### 3.2.2. Daily generation curves

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

BESS | Battery energy storage system |

LFC | Load frequency control |

LT | Local time |

MBE | Mean bias error |

MILP | Mixed integer linear programming |

MSM | Meso-scale model |

PV | Photovoltaic |

RMSE | Root mean square error |

RT | Release time |

SoC | State of charge |

UC | Unit commitment |

## Nomenclature

Parameters | |

$\Delta T$ | Time interval of unit commitment calculation |

$\eta $ | BESS charging efficiency |

$\gamma $ | The schedule cycle |

${\lambda}_{i}^{k}$ | gradient of interval k of piece-wise linear fuel cost function of unit i |

${\mathit{a}}_{i},\phantom{\rule{0.166667em}{0ex}}{b}_{i},\phantom{\rule{0.166667em}{0ex}}{c}_{i}$ | parameters of fuel cost function for generator i |

${\mathrm{C}}_{\mathrm{init}}^{\mathit{b}}$ | Initial charge of the BESS |

${\mathrm{C}}_{\mathrm{max}}^{\mathit{b}}$ | Maximum charge of the BESS |

${\mathrm{C}}^{\mathit{h}}$ | Total LFC regulating capacity of hydro power plants [ MW ] |

${\mathrm{C}}_{i}^{\mathit{lfc}}$ | LFC regulating capacity of generator i |

${\mathrm{C}}_{\mathrm{soc}}$ | Penalty cost for SoC difference |

${\mathrm{DT}}_{i}$ | Down time of generator i |

${\mathrm{FC}}_{i}\left(p\right)$ | Fuel cost function at power p for generator i [ JPY/h ] |

${\mathrm{LC}}_{t}$ | Load curtailment cost of time j [ JPY/h ] |

$\mathrm{N}$ | Number of thermal power plants [h] |

${\mathrm{PC}}_{t}$ | PV curtailment cost of time j [ JPY/h ] |

${\mathrm{p}}_{d,t}^{a}$ | The estimated PV power output at time t on day d |

${\mathrm{p}}_{d,t,RT}^{f}$ | The forecasted PV power output at time t on day d that was released at time $RT$ |

${\mathrm{P}}_{inv}^{\mathit{bc}}$ | Rated charging power of the BESS |

${\mathrm{P}}_{inv}^{\mathit{bd}}$ | Rated discharging power of the BESS |

${\mathrm{P}}^{\mathit{h}}$ | Total output of Hydro Power |

${\mathrm{P}}_{t}^{\mathit{ld}}$ | Forecasted load demand at time t |

${\mathrm{P}}_{i}^{\mathit{max}}$ | Maximum rated output of generator i |

${\mathrm{P}}_{i}^{\mathit{min}}$ | Minimum output of generator i |

${\mathrm{P}}^{\mathit{nu}}$ | Total output of Nuclear Power |

${\mathrm{P}}_{t}^{\mathit{pv}}$ | Forecasted PV power output at time t (Actual PV power output for $t={t}_{c}$ in Case 2.) |

${\mathrm{R}}^{d}$ | Ratio of required LFC regulation capacity to load demand |

${\mathrm{R}}_{i}^{down}$ | Ramp up rate of generator i |

${\mathrm{R}}^{o}$ | Ratio of upward reserve capacity |

${\mathrm{R}}^{pv}$ | Ratio of required LFC regulation capacity to PV power output |

${\mathrm{R}}_{i}^{up}$ | Ramp up rate of generator i |

${\mathrm{SC}}_{i}$ | Startup cost of generator i |

$\mathrm{T}$ | Number of Time steps |

${\mathrm{T}}^{cu}$ | Current time in wall time |

${\mathrm{t}}_{\mathrm{c}}$ | Current time index |

${\mathrm{t}}_{\mathrm{mn}}$ | time index at midnight |

${\mathrm{UT}}_{i}$ | Up time of generator i |

${\mathrm{U}}_{i,t}$ | The generator schedule calculated by UC. 1 if generator i at time interval t is on and 0 otherwise |

Decision Variables | |

${c}_{t}^{\mathrm{B}}$ | charge of the BESS at time t |

${curt}_{t}^{ld}$ | load curtailment at time t |

${curt}_{t}^{pv}$ | PV curtailment at time t |

${d}_{i,t}$ | 1 if generator i is shutdown at time interval t. 0 otherwise. |

${p}_{i,t}$ | Output power of generator i at time t |

${p}_{t}^{\mathrm{bc}}$ | charging power for 100% efficient BESS at time t |

${p}_{t}^{\mathrm{bd}}$ | discharging power for BESS at time t |

${s}_{i,t}$ | 1 if generator i is started at time interval t. 0 otherwise. |

${u}_{i,t}$ | 1 if generator i at time interval t is on and 0 otherwise |

${v}_{i,t}^{k}$ | value of interval k of piece-wise linear fuel cost function of unit i at time interval t |

Auxiliary Variables | |

${w}_{i,t}^{k}$ | value of interval k of piece-wise linear fuel cost function of unit i at time interval t |

${x}_{soc}$ | Upper bound of SoC difference. |

${x}_{t}$ | 1 if BESS is charging at time interval t is on and 0 otherwise |

${y}_{t}$ | 1 if BESS is discharging at time interval t is on and 0 otherwise |

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**Figure 1.**Case 1 time chart; unit commitment (UC) and battery energy storage system (BESS) schedule is calculated once a day from 19:00 LT of day n to 24:00 of day n+1 using forecast at 18:30 LT on day n.

**Figure 2.**Case 2 schedule for UC and BESS operations. Vertical axis represent the current time and horizontal axis represents the time interval of BESS and UC schedules.

**Figure 3.**Error analysis from April 2 to 30. (

**a**) Mean bias error (MBE) of the day-ahead and intraday PV power forecasts. (

**b**) RMSE of the day-ahead and intraday PV power forecasts.

**Figure 4.**Error analysis from January 2 to 30. (

**a**) MBE of the day-ahead and intraday PV power forecasts. (

**b**) RMSE of the day-ahead and intraday PV power forecasts.

**Figure 5.**The simulation results averaged per day with installed PV capacity of 50 GW for Case 1 and Case 2 with BESS capacities of 0, 100 and 200 GWh for the simulation period from April 2 to 30 (29 days).

**Figure 6.**The simulation results averaged per day with installed PV capacity of 100 GW for Case 1 and Case 2 with BESS capacities of 0, 100 and 200 GWh for the simulation period from April 2 to 30 (29 days).

**Figure 7.**The simulation results averaged per day with installed PV capacity of 50 GW for Case 1 and Case 2 with BESS capacities of 0, 100 and 200 GWh for the simulation period from January 2 to 30 (29 days).

**Figure 8.**The simulation results averaged per day with installed PV capacity of 100 GW for Case 1 and Case 2 with BESS capacities of 0, 100 and 200 GWh for the simulation period from January 2 to 30 (29 days).

**Table 1.**Installed nuclear, hydro and thermal capacity in MW in the Kanto Area of Japan [24].

Installed Capacity (MW) | |
---|---|

Nuclear | 6000 |

Hydro | 1200 |

Thermal | 60,850 (168 machines) |

Rated Output (MW) | Lower Limit (MW) | Coefficient of Fuel Cost Function | Start-up Cost (JPY) | Ramp -Up Rate (%MW /min.) | Ramp -Down Rate (%MW /min.) | Up Time (h) | Down Time (h) | Num- ber of Gene- Rators | Total Capacity (MW) | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{a}}_{\mathit{i}}$ (JPY /MWh) | ${\mathit{b}}_{\mathit{i}}$ (JPY /MWh) | ${\mathit{c}}_{\mathit{i}}$ (JPY /MW ^{2}h) | ||||||||||

Coal | 1000 | 300 | 550,000 | 400 | 0.70 | 2,380,000 | 3.0 | 3.0 | 3.0 | 3.0 | 12 | 12,000 |

700 | 105 | 182,000 | 1300 | 0.16 | 1,670,000 | 3.0 | 3.0 | 3.0 | 3.0 | 4 | 2800 | |

CC | 250 | 63 | 120,000 | 1400 | 1.66 | 378,000 | 5.0 | 5.0 | 1.5 | 1.5 | 74 | 18,500 |

100 | 30 | 104,000 | 900 | 0.73 | 151,000 | 5.0 | 5.0 | 1.5 | 1.5 | 21 | 2100 | |

LNG | 700 | 140 | 117,000 | 2400 | 0.40 | 1,060,000 | 3.0 | 3.0 | 1.5 | 1.5 | 19 | 13,300 |

200 | 80 | 66,000 | 2200 | 2.50 | 302,000 | 3.0 | 3.0 | 1.5 | 1.5 | 13 | 2600 | |

Oil | 700 | 175 | 260,000 | 5000 | 0.38 | 1,060,000 | 3.0 | 3.0 | 1.5 | 1.5 | 4 | 2800 |

500 | 100 | 200,000 | 5000 | 0.05 | 756,000 | 3.0 | 3.0 | 1.5 | 1.5 | 6 | 3000 | |

250 | 50 | 316,000 | 4600 | 1.05 | 378,000 | 3.0 | 3.0 | 1.5 | 1.5 | 15 | 3750 | |

Total | 168 | 60,850 |

Installed PV capacity (GW) | 50 | 100 | |||||

Installed BESS capacity (GWh) | 0 | 100 | 200 | 0 | 100 | 200 | |

April(2–30) | Total energy demand (GWh) (Daily average) | 694 | |||||

Hourly average demand (GW) | 28.9 | ||||||

Total PV energy production (GWh) (Daily average before curtailment) | 219 | 438 | |||||

Hourly average PV power from 7 to 15 h (GW) (Before curtailment) | 22.5 | 45.1 | |||||

Total curtailed PV energy (GWh) (Daily average for Case 2) | 61.2 | 7.4 | 2.7 | 241 | 147 | 73.6 | |

PV curtailment ratio ( % ) (Case 2) | 28.0 | 3.4 | 1.2 | 55.1 | 33.6 | 16.8 | |

PV curtailment reduction ratio ( % ) (Case 2 with BESS) | - | 88.0 | 95.7 | - | 39.1 | 69.5 | |

January(2–30) | Total energy demand (GWh) (Daily average) | 866 | |||||

Hourly average demand (GW) | 36.1 | ||||||

Total PV energy production (GWh) (Daily average for before curtailment) | 140 | 280 | |||||

Hourly average PV power from 7 to 15 h (GW) (Before curtailment) | 15.6 | 31.2 | |||||

Total curtailed PV energy (GWh) (Daily average for Case 2) | 6.9 | 0.0 | 0.0 | 95.3 | 17.1 | 7.4 | |

PV curtailment ratio ( % ) (Case 2) | 5.0 | 0.0 | 0.0 | 34.0 | 6.1 | 2.6 | |

PV curtailment reduction ratio ( % ) (Case 2 with BESS) | - | 99.9 | 100 | - | 88.9 | 95.2 |

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## Share and Cite

**MDPI and ACS Style**

Udawalpola, R.; Masuta, T.; Yoshioka, T.; Takahashi, K.; Ohtake, H.
Reduction of Power Imbalances Using Battery Energy Storage System in a Bulk Power System with Extremely Large Photovoltaics Interactions. *Energies* **2021**, *14*, 522.
https://doi.org/10.3390/en14030522

**AMA Style**

Udawalpola R, Masuta T, Yoshioka T, Takahashi K, Ohtake H.
Reduction of Power Imbalances Using Battery Energy Storage System in a Bulk Power System with Extremely Large Photovoltaics Interactions. *Energies*. 2021; 14(3):522.
https://doi.org/10.3390/en14030522

**Chicago/Turabian Style**

Udawalpola, Rajitha, Taisuke Masuta, Taisei Yoshioka, Kohei Takahashi, and Hideaki Ohtake.
2021. "Reduction of Power Imbalances Using Battery Energy Storage System in a Bulk Power System with Extremely Large Photovoltaics Interactions" *Energies* 14, no. 3: 522.
https://doi.org/10.3390/en14030522