# Research on Stochastic Optimal Operation Strategy of Active Distribution Network Considering Intermittent Energy

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Formulation

## 3. Solution Methodology

## 4. Demonstration Application for Optimal Operation

#### 4.1. Basic Optimization Scenario

#### 4.2. Different Intermittent Energy Uncertainty

#### 4.3. Different Objective Function Weight Selection

#### 4.4. Optimization Results Analysis

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

ADN | Active Distribution Network |

SUC | Stochastic Unit Commitment |

MILP | Mixed-integer Linear Programming |

HVAC | Heating, Ventilation and Air Conditioning |

TCL | Thermostatically Controlled load |

ESS | Energy Storage System |

SOC | Status of Charge |

V2G | Vehicle-to-Grid |

DSO | Distribution System Operator |

Sets | |

$\Phi $ | Set of power regulation devices |

$\Gamma $ | Set of energy storage devices |

$\mathrm{H}$ | Set of intermittent energy |

$B$ | Set of all buses |

$L$ | Set of all feeders |

Parameters | |

$T$ | Time periods in optimization horizon, in this paper the horizon is to be 24 h |

${\kappa}_{step}$ | Time span for optimization, in this paper each time span is to be one hour |

${\chi}_{i}^{t}$ | Output for power regulation device $i$ in time period $t$ |

${\vartheta}_{i}^{t}$ | Output for energy storage device $i$ in time period $t$ |

${\vartheta}_{i,eq}^{t}$ | Equivalent output for energy storage device $i$ in time period $t$ |

${p}_{i}^{t}$ | Output for intermittent energy $i$ in time period $t$ |

${e}_{\vartheta ,i}^{r}$ | Rated capacity for energy storage device $i$ in time period $t$ |

${\vartheta}_{i}^{r}$ | Rated power for energy storage device $i$ in time period $t$ |

${\chi}_{i}^{r}$ | Rated power for power regulation device $i$ in time period $t$ |

${p}_{\psi ,i}^{t}$ | Forecasted output for intermittent energy $i$ in time period $t$ |

${p}_{\psi +,i}^{t}$ | Upper deviation for intermittent energy $i$ in time period $t$ |

${p}_{\psi -,i}^{t}$ | Lower deviation for intermittent energy $i$ in time period $t$ |

${\eta}_{t,i}^{+}$, ${\eta}_{t,i}^{-}$ | Binary decision variables represent the status of deviation for ${p}_{\psi ,i}^{t}$ |

${\alpha}_{up,i}$ | Ramp-up limit for power regulation device $i$ |

${\alpha}_{down,i}$ | Ramp-down limit for power regulation device $i$ |

${L}_{low,i}$ | Minimum power limit for power regulation device $i$ |

${L}_{up,i}$ | Maximum power limit for power regulation device $i$ |

${S}_{soc,i}^{1}$ | Initial state of charge (SOC) for energy storage device $i$ in optimization horizon |

${S}_{soc,i}^{T+}$ | Final state of charge (SOC) for energy storage device $i$ in optimization horizon |

${S}_{soc,i}^{t}$ | State of charge (SOC) for energy storage device $i$ at the start of time period $t$ |

${S}_{soc,i}^{\mathrm{max}}$ | Maximum state of charge for energy storage device $i$ |

${S}_{soc,i}^{\mathrm{min}}$ | Minimum state of charge for energy storage device $i$ |

${\lambda}_{t}$ | Electricity price in time period $t$ |

$\zeta $ | Profit for peak-valley regulation per kWh |

${V}_{\zeta}$ | Peak-valley difference in optimization horizon |

${V}_{\zeta}^{0}$,${V}_{\zeta}^{rslt}$ | Initial state and optimized state for peak-valley difference |

${S}_{\lambda}^{t}$ | Network loss in time period $t$ |

${S}_{\lambda ,t}^{0}$, ${S}_{\lambda ,t}^{rslt}$ | Initial state and optimized state for network loss in time period $t$ |

${D}_{t}$ | Load in time period $t$ |

${V}_{b}^{t}$ | Voltage for bus $b$ in time period $t$ |

${I}_{l}^{t}$ | Transmission current for feeder $l$ in time period $t$ |

${h}_{up}$, ${h}_{low}$ | Extra variables for peak-valley difference calculation |

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**Figure 4.**Forecast Value Deviation for Intermittent Energies: (

**a**) Power Deviation for WTP1 and WTP2; (

**b**) Power Deviation for PV2&4; (

**c**) Power Deviation for PV1&3.

**Figure 5.**Optimization result for energy storage devices: (

**a**) Active Power for BESS; (

**b**) Active Power for EV.

**Figure 6.**Optimization result for power regulation devices: (

**a**) Active Power for CCHP and Hydro; (

**b**) Active Power for Flexild.

**Figure 16.**Optimization result for energy storage devices in the second scenario: (

**a**) Active Power for BESS; (

**b**) Active Power for EV.

**Figure 17.**Optimization result for power regulation devices in the second scenario: (

**a**) Active Power for CCHP and Hydro; (

**b**) Active Power for Flexild.

**Figure 18.**Summary of Optimization Results. (

**a**) Network Loss Comparison; (

**b**) Peak-valley Difference Comparison.

Name | Types of Devices | Capacity of Devices | |
---|---|---|---|

PV1 | Photovoltaic | Intermittent energies | 32.4 kW |

PV2 | 91.8 kW | ||

PV3 | 32.4 kW | ||

PV4 | 91.8 kW | ||

WTP1 | Wind turbine | 100 kW | |

WTP2 | 100 kW | ||

BESS1 | Battery energy storage system | Energy storage devices | 100 kW/200 kWh |

BESS2 | 100 kW/200 kWh | ||

EV1 | Electric vehicle | 100 kW/200 kWh | |

EV2 | 10 kW/30 kWh | ||

EV3 | 10 kW/30 kWh | ||

EV4 | 10 kW/30 kWh | ||

Hydro | Hydropower | 10,000 kW | |

CCHP | Cooling-heating-power supply | Power regulation devices | 500 kW |

Flexild | HVAC |

Name | Weight Selection |
---|---|

${\epsilon}_{1}$ | 0.005 |

${\epsilon}_{2}$ | 0.495 |

${\epsilon}_{3}$ | 0.25 |

${\epsilon}_{4}$ | 0.25 |

Name | Intermittent Energy Uncertainty | |
---|---|---|

Time Period When ${\mathit{\eta}}_{\mathit{t},\mathit{i}}^{+}=1$ | Time Period When ${\mathit{\eta}}_{\mathit{t},\mathit{i}}^{-}=1$ | |

PV1 | 19 | 14,15,16,17 |

PV2 | 19,20 | 13,14,15,16,17,18 |

PV3 | 19 | 14,16,17 |

PV4 | 19,20 | 13,14,15,16,18 |

WTP1 | 19,20 | 13,14,15,16,17 |

WTP2 | 19,20 | 13,14,15,16,17 |

Name | Intermittent Energy Uncertainty | |
---|---|---|

Time Period when ${\mathit{\eta}}_{\mathit{t},\mathit{i}}^{+}=1$ | Time Period when ${\mathit{\eta}}_{\mathit{t},\mathit{i}}^{-}=1$ | |

PV1 | 7,10,11,12,19 | 8,9,13,14,15,16,17,18 |

PV2 | 7,10,12,19 | 8,9,13,14,15,16,17,18 |

PV3 | 7,10,12,19 | 8,9,13,14,15,16,17,18 |

PV4 | 7,10,12,19 | 8,9,13,14,15,16,17,18 |

WTP1 | 19,20 | 13,14,15,16,17 |

WTP2 | 19,20 | 13,14,15,16,17 |

Name | Weight Selection |
---|---|

${\epsilon}_{1}$ | 0 |

${\epsilon}_{2}$ | 0.5 |

${\epsilon}_{3}$ | 0 |

${\epsilon}_{4}$ | 0.5 |

Name | Weight Selection |
---|---|

${\epsilon}_{1}$ | 0.01 |

${\epsilon}_{2}$ | 0.49 |

${\epsilon}_{3}$ | 0.375 |

${\epsilon}_{4}$ | 0.125 |

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**MDPI and ACS Style**

Chen, F.; Liu, D.; Xiong, X. Research on Stochastic Optimal Operation Strategy of Active Distribution Network Considering Intermittent Energy. *Energies* **2017**, *10*, 522.
https://doi.org/10.3390/en10040522

**AMA Style**

Chen F, Liu D, Xiong X. Research on Stochastic Optimal Operation Strategy of Active Distribution Network Considering Intermittent Energy. *Energies*. 2017; 10(4):522.
https://doi.org/10.3390/en10040522

**Chicago/Turabian Style**

Chen, Fei, Dong Liu, and Xiaofang Xiong. 2017. "Research on Stochastic Optimal Operation Strategy of Active Distribution Network Considering Intermittent Energy" *Energies* 10, no. 4: 522.
https://doi.org/10.3390/en10040522