# Reliability Evaluation Method Considering Demand Response (DR) of Household Electrical Equipment in Distribution Networks

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## Abstract

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## 1. Introduction

- The load characteristic of two typical items of household electrical equipment is elaborately analyzed.
- An electricity price-based DR model and an incentive-based DR model are proposed for two typical items of high-power electrical equipment, considering charging behavior and thermodynamic property.
- A load shedding strategy is introduced to improve the traditional reliability evaluation method for distribution networks, while taking into account the capacity constraints.
- A reliability calculation method of distribution networks with shortage of power supply capacity and faults taken into consideration is presented.

## 2. DR Modeling

#### 2.1. DR Modeling of EVs Based on Electricity Price

#### 2.1.1. Optimization Objective

_{t}represent the charging power of EV and time-of-use electricity price at time t, Δt is the length of one time interval, and T is the number of time intervals within the scheduling time.

#### 2.1.2. Constraints

_{ch}represents the charging efficiency of the battery; E

_{B}is the energy capacity of battery, and the unit is kW·h; Soc

_{max}and Soc

_{min}represent the upper and lower limit of SOC, respectively.

_{td}and Soc

_{exp}respectively represent the actual and expected SOC of the battery at t

_{d}; t

_{d}denotes the time when EV plugs out, which is with strong uncertainty and can be approximately estimated according to the historical data of EVs.

_{max}

^{EV}represents the maximum of charging power of EV.

_{s}represents the time when an EV plugs into the grid.

#### 2.2. DR Modeling of Air Conditioners Based on Incentive

#### 2.2.1. Optimization Objective

_{th}air conditioner in time t; ${\overline{P}}^{\mathrm{D}}$ is the mean value of the total load in the dispatching period; N represents the total number of air conditioners; T is the number of time intervals within the scheduling time; x

_{k,t}is the binary decision variable indicating whether the k

_{th}air conditioner participates in load reduction at time t; x

_{k,t}is equal to 1 if the air conditioner k participates in scheduling at time t, and 0 otherwise.

#### 2.2.2. Constraints

_{A}and f

_{A}represent the operating power and frequency of air conditioners, respectively. a and b are constants. Equation (10) denotes the relationship between refrigerating capacity and frequency of air conditioners, where Q

_{A}represents the refrigerating capacity of air conditioners. m, n, and q are coefficients.

_{in,t+}

_{1}and θ

_{in,t}represent the indoor temperature at time t + 1 and t, respectively; θ

_{out,t+}

_{1}denotes the outdoor temperature at time t + 1; Q

_{t}is the air conditioning refrigerating capacity at time t; R and C are the equivalent heat resistance and heat capacity of air conditioning, with the units of °C/kW kW h/°C, respectively.

_{k}represents the operating frequency of the k

_{th}air conditioner; f

_{max,k}and f

_{min,k}denote the maximum and minimum operating frequency of the k

_{th}air conditioner, respectively.

_{c,k}is the maximum dispatchable number of the k

_{th}air conditioner.

#### 2.2.3. Control Method

_{1}to θ

_{2}, the air conditioning would operate with the lowest frequency at the first time, and then the air conditioning frequency would be adjusted to stable value for θ

_{2.}

_{th}air conditioner in stable operation at time t.

## 3. Reliability Evaluation of Distribution Networks Considering DR

#### 3.1. Model of Load Transfer Capacity

_{lz}represents the power supplied by the tie line; P

_{l}is the load of a line itself; P

_{l}

_{max}is the maximum transmission power of the line l; β

_{l}is the line loss ratio of the line l.

#### 3.2. Load Shedding Strategy

_{i}is the importance coefficient of load point i for reliability requirement; S represents the collection set of all load points on the feeder; P

_{i}(t) is the power demand of load point i at time t. Equation (18) describes the power supply capacity constraint and node voltage constraint, where P

_{S}

_{max}represents the upper limit of the power transmitted by the feeder and U

_{i}, U

_{i,}

_{max}, and U

_{i,}

_{min}are the voltage of node i and its maximum and minimum values, respectively.

## 4. Analysis of the Influence of DR on Distribution Network Reliability

#### 4.1. Load Point Reliability Index

_{outage,i}denotes the outage probability of load point i; X(I, t) is a binary decision variable for operation state of load point i at time t, which is equal to 1 in normally operating state, and 0 otherwise.

#### 4.2. System Reliability Index

## 5. Improved Reliability Evaluation Method Based on Load Clustering

#### 5.1. Improved Reliability Evaluation Method

- (1)
- When power supply capacity is insufficient in normal operation state, the load shedding strategy in Section 3.2 should be applied to supply power as much as possible with the feeder maximum capacity constraint respected. Calculate the system reliability indexes with and without DR, respectively.
- (2)
- When a failure occurs in the distribution network, parts of the loads of Type B cannot get power supply due to restricted transfer capacity if the maximum capacity limit of feeders are considered.

#### 5.2. Reliability Calculation Method of Distribution Networks Considering Load Clustering

## 6. Case Study

#### 6.1. Case 1

#### 6.1.1. Residential Electricity Load Analysis

#### 6.1.2. Analysis on DR of Residential Load

#### 6.2. Case 2

#### 6.2.1. Simulation Settings

#### 6.2.2. Load Profile Considering DR

#### 6.2.3. Influence of Real-Time Electricity Price on DR

#### 6.2.4. Reliability Evaluation Considering DR

- Case 1: DR is not taken into consideration.
- Case 2: DR based on electricity price and incentive is considered.
- Case 3: Case 1 with sufficient spare capacity of tie lines.
- Case 4: Case 2 with sufficient spare capacity of tie lines.
- The reliability index of the four cases is shown in Table 2.

## 7. Conclusions

- (1)
- DR can improve the load curve and reduce the peak loads. DR based on electricity price has a certain randomness and is greatly affected by real-time electricity price. Unreasonable real-time electricity price may lead to “peak-on-peak” or unnecessary load reduction.
- (2)
- Both DR based on electricity price and DR based on incentive can improve the reliability index of distribution networks. Compared with the reliability results attained by employing a single DR strategy, comprehensive DRs can improve reliability
- (3)
- DR has no influence on the distribution network reliability index if transmission capacity of tie lines is assumed to be infinite. Under the premise of considering the tie line capacity limit, DR reduces the peak loads of the systems and decreases the probability of insufficient power supply capacity in normal operation, and meanwhile increases the possibility of the load point being transferred when a failure occurs.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Load Number (Class) | Average Load (kW) | Load Number (Class) | Average Load (kW) | Load Number (Class) | Average Load (kW) | Load Number (Class) | Average Load (kW) |
---|---|---|---|---|---|---|---|

LP1(II) | 165.9 | LP7(I) | 210.1 | LP13(III) | 250.1 | LP19(III) | 155.4 |

LP2(III) | 180.8 | LP8(III) | 155.4 | LP14(III) | 155.4 | LP20(II) | 186.1 |

LP3(III) | 250.1 | LP9(I) | 283.1 | LP15(II) | 186.1 | LP21(I) | 283.1 |

LP4(III) | 243.1 | LP10(II) | 158.5 | LP16(II) | 158.5 | LP22(II) | 158.5 |

LP5(I) | 207.0 | LP11(III) | 155.4 | LP17(III) | 250.1 | LP23(I) | 210.1 |

LP6(II) | 165.9 | LP12(II) | 158.5 | LP18(III) | 243.1 |

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**Figure 5.**Comparison of load profile between base loads and loads with demand response (DR) taken into account.

**Figure 7.**Comparison of load profile between base loads and loads with electric vehicles (EVs) taken into account

**Figure 8.**Comparison of load profile between base loads and loads with air conditioning taken into account.

Type | Daily Load Rate | Percent |
---|---|---|

A | 0.633253 | 56% |

B | 0.647609 | 11% |

C | 0.74984 | 33% |

**Table 2.**System reliability index (SAIFI, system average interruption frequency index; SAIDI, system average interruption duration index; CAIDI, customer average interruption duration index; ENS, energy not supplied).

Case | SAIFI/(times/a) | SAIDI/(h/a) | CAIDI/(h/times) | ENS/(MW h/a) |
---|---|---|---|---|

1 | 2.253 | 5.67 | 2.517 | 67.93 |

2 | 2.2052 | 5.2483 | 2.3798 | 59.31 |

3 | 2.2052 | 3.519 | 1.596 | 43.22 |

4 | 2.2052 | 3.519 | 1.596 | 40.76 |

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## Share and Cite

**MDPI and ACS Style**

Chen, H.; Tang, J.; Sun, L.; Zhou, J.; Wang, X.; Mao, Y.
Reliability Evaluation Method Considering Demand Response (DR) of Household Electrical Equipment in Distribution Networks. *Processes* **2019**, *7*, 799.
https://doi.org/10.3390/pr7110799

**AMA Style**

Chen H, Tang J, Sun L, Zhou J, Wang X, Mao Y.
Reliability Evaluation Method Considering Demand Response (DR) of Household Electrical Equipment in Distribution Networks. *Processes*. 2019; 7(11):799.
https://doi.org/10.3390/pr7110799

**Chicago/Turabian Style**

Chen, Hongzhong, Jun Tang, Lei Sun, Jiawei Zhou, Xiaolei Wang, and Yeying Mao.
2019. "Reliability Evaluation Method Considering Demand Response (DR) of Household Electrical Equipment in Distribution Networks" *Processes* 7, no. 11: 799.
https://doi.org/10.3390/pr7110799