# Active-reactive scheduling of active distribution system considering interactive load and battery storage

- Qixin Chen
^{1}, - Xiangyu Zhao
^{1}and - Dahua Gan
^{1}Email authorView ORCID ID profile

**2**:29

https://doi.org/10.1186/s41601-017-0060-2

© The Author(s) 2017

**Received: **18 April 2017

**Accepted: **3 July 2017

**Published: **7 August 2017

## Abstract

Distributed generation (DG) are critical components for active distribution system (ADS). However, this may be a serious impact on power system due to their volatility. To this problem, interactive load and battery storage may be a best solution. This paper firstly investigates operation characteristics of interactive load and battery storage, including operation flexibility, inter-temporal operation relations and active-reactive power relations. Then, a multi-period coordinated active-reactive scheduling model considering interactive load and battery storage is proposed in order to minimize overall operation costs over a specific duration of time. The model takes into accounts operation characteristics of interactive load and battery storage and focuses on coordination between DGs and them. Finally, validity and effectiveness of the proposed model are demonstrated based on case study of a medium-voltage 135-bus distribution system.

### Keywords

Active distribution system Active-reactive scheduling Interactive load Battery storage## 1 Introduction

Active distribution system (ADS) is defined as distribution networks that have systems in place to control a combination of distributed energy resources (DERs), including distributed generators (DGs), battery storage, demand response, etc. [1]. In recent, high levels of DERs that could be efficiently scheduled are being integrated in order to achieve specific operational objectives, for example, costs minimization. Therefore, it would be necessary for the Distribution System Operators (DSOs) to transform from the traditional “passive” uni-directional flow operation approach to novel “active” bi-directional flow operation approach [2]. To this end, a critical challenge is to formulate the operation characteristics of different kinds of DERs and integrate them into the scheduling scheme of ADS.

At present, many interesting researches related to the operation of ADS have been conducted [3–6]. Pilo et al. [1] and Keane et al. [7] proposed models and methodology to minimize system operation cost by optimizing the production of the local DGs, including the wind turbine, photovoltaic, considering power exchanges with the main distribution system. As power outputs of DGs are always restricted by meteorological factors [7], the volatility characteristics become a heavy burden to the DSOs. In this case, battery storage could serve as an option for accommodating volatile outputs of DGs [8]. An optimal model for ADS proposed in [9] contains DGs and battery storage, but only take the capacity limitation of battery storage into consideration. Further, the relation between active-reactive power outputs of battery storage is considered in [10–12], and the active-reactive coordination model for DGs and battery storage is proposed.

Though battery storage could solve the volatility of DGs, their high investment cost may increase the total operation cost of the distribution system [13]. Therefore, demand response may be another solution. In fact, demand response is a price mechanism between DSOs and the local users, and interactive load is an important type of demand response. Under the agreement, the DSOs could change the original load shape, while users could get some payback from the DSOs. Compared to battery storage, demand response could achieve similar aims and, at the same time, there would be hardly no investment cost. Dozens of demand response projects have been established and operated in many countries [14–18]. While an optimal model of ADS considering demand response and battery storage is not yet proposed.

Based on the above analysis, this paper focuses on multi-period coordinated active-reactive scheduling of ADS considering demand response and battery storage. Firstly, we design a new form of demand response, namely interactive load and the structure of battery storage is also analyzed. Then, the problem description and the mathematical model of interactive load and battery storage are presented. Based on these model, a novel multi-period active-reactive coordinated scheduling model is proposed for integrated operation of ADS, in order to minimize overall operation costs over a specific duration of time. The model takes into accounts operation characteristics of various DERs and formulates multi-period operation of ADS. Finally, validity and effectiveness of the proposed model are demonstrated based on case study of a medium-voltage 135-bus distribution system.

## 2 Flexible operation of interactive load and battery storage

### 2.1 Introduction to interactive load

According to the report of Federal Energy Regulatory Commission about demand response (DR) and advanced metering, DRs could be divided into 15 types on the basis of their response form, such as Direct Load Control, Interruptible Load, Critical Peak Pricing with Control, etc.

Interactive Load designed in this paper is a combination of Direct Load Control, Demand Bidding and Buyback. Its basic feature is that the DSOs would obtain the right to invoke the electrical equipment according to the agreement, thus the shape of power load could be changed to the most economical way. While at the same time, consumers could get economic compensation due to their participations in load shifting.

In fact, Peak Cutting Load is another category of Peak Shifting Load whose load cut during peak period wouldn’t be compensated. And considering that Peak Cutting Load may cause uncontrollable load rebound during valley period, this paper focuses on the Shifting one. Furthermore, it could be divided into two types, namely Shapeable Load and Removable Load. Their characteristic and modeling will be presented in the following chapters.

### 2.2 Characteristic and modeling of shapeable load

#### 2.2.1 Introduction to shapeable load

#### 2.2.2 Load shifting potential analysis of shapeable load

Thermal storage, such as large-scale central conditioning system, is an important resource of Demand Side Response. Its application could be described as Shapeable Load and its electrical characteristics is described in.

Load shifting potential analysis of thermal storage in China

Location | Project Name | Load Shifting Potential |
---|---|---|

Beijing | 94 Thermal Storage projects in 2002 | 200 MW |

Beijing | Industrial consumer | 100 MW(1996), 2.3% of the peak load |

Guangzhou | Cold storage project at Economic Trade Commission building in 2006 | 240 kW |

Guangxi Province | Thermal Equipment in 118 consumers | 162 MW, 2.3% of the peak load |

Shanghai | Cold storage project in Jindu Building | 220 kW |

Shanghai | Central Air conditions system in hotel and mall | 598 MW |

### 2.3 Characteristic and modeling of removable load

#### 2.3.1 Introduction to removable load

#### 2.3.2 Load shifting potential analysis of removable load

Removable Load can be used to describe the production process transfer of industrial user. Industrial production tend to have a relatively fixed production process. So when transferring their production process, their load shape should be the same.

Load shifting potential analysis of industrial users in Beijing

Industrial User Name | Load Shifting Potential(MW) |
---|---|

Shougang Corporation | 50 |

Tegang Corporation | 10 ~ 20 |

Yanhua Corporation | 5 ~ 10 |

Chemical Industry | 10 ~ 20 |

Building Materials Industry | 10 |

Total | 90 ~ 120 |

### 2.4 Characteristic and modeling of battery storage

## 3 Methods

### 3.1 Modeling of interactive load

This section is focus on formulations on operation characteristics of shapeable load and the removable one. The analyzed characteristics include load shifting cost curve, load shifting position and constraints for load shape and electricity consumption.

#### 3.1.1 Load shifting cost curve

*C*

^{ IL }denotes total load shifting cost of interactive load, including two parts, the cost of shapeable load and it of removable load.

*T*devotes the total period number.

*NSL*and

*NRL*respectively denote the number of shapeable load and removable load. \( {\lambda}_{i,j}^{shift} \) denotes the load shift cost of shapeable load or removable load

*j*at period

*i*. \( {P}_{i,j}^{SL,A} \) and \( {P}_{i,j}^{RL,A} \) respectively denote the load of shapeable load

*j*and removable load

*j*at period

*i*after their shifting.

#### 3.1.2 Load shifting position

*j*and removable load

*j*is shifted to period

*i*. It should be ensured that every head of shapeable load or removable load can be shifted to only one position. And in order to not affect operation of next day, the state variables from \( {\eta}_{T-{T}_0,j}^{SL} \) to \( {\eta}_{T,j}^{SL} \) and from \( {\eta}_{T-{T}_0,j}^{RL} \) to \( {\eta}_{T,j}^{RL} \) are set to 0. It could be expressed as:

Where \( {T}_{0,j}^{SL} \) and \( {\eta}_{0,j}^{RL} \) respectively denotes the length of shapeable load *j* and removable load *j*.

#### 3.1.3 Constraints for load shape and electricity consumption

*i*could be expresses as:

*j*and removable load

*j*at period

*i*before their shifting. \( {\underline{P}}_j^{SL} \) and \( {\overline{P}}_j^{SL} \) denote the upper and lower bounds of shapeable load

*j*.

*j*and removable load

*j*.

### 3.2 Modeling of battery storage

This section is focus on formulations on operation characteristics of battery storage. The analyzed characteristics include operation cost for battery, constraints for energy storage, power exchange and state transition number.

#### 3.2.1 Constraints for energy storage

*j*. \( {E}_j^{S,pre} \) denotes the initial stored energy. \( {P}_{i,j}^{S,C} \) and \( {P}_{i,j}^{S,D} \) respectively denote the active power charged or discharged between battery storage

*j*and the grid at period

*i*. \( {u}_j^S \) is the loss rate of the storage battery

*j*at charge process.

#### 3.2.2 Constraints for power exchange

*j*at period

*i*and \( {S}_j^S \) denote the power bound to the battery storage

*j*.

#### 3.2.3 Constraints for state transition number

*j*at period

*i*. It will be set to one when the battery is in discharge process, while zeros corresponds to the charge process. \( {\eta}_{i,j}^{S,CD} \) and \( {\eta}_{i,j}^{S,DC} \) respectively denote the operation state change from charge process to discharge process and from discharge process to charge process. It’s guaranteed by the second sub-formula in (8) that \( {\eta}_{i,j}^{S,CD} \) will be assigned as one if the operation state of battery storage

*j*is changed from charge process to discharge process at period

*i*. While it will be zero at other period. Similar situation can be implemented to \( {\eta}_{i,j}^{S,DC} \) as it will be assigned as one if the operation state of battery storage

*j*is changed from discharge process to charge process at period

*i*. Besides the third and fourth sub-formula guarantee that the state transition number would be just one.

#### 3.2.4 Operation cost for battery storage

*j*. \( {\lambda}_j^{S,P} \) and \( {\lambda}_j^{S,Q} \) are the active and reactive cost coefficients of battery storage

*j*.

## 4 Multi-period coordinated scheduling model considering battery storage and interactive load

### 4.1 Decision variables

The decision variables include continuous ones for active and reactive power of source bus, distributed generation, battery storage as well as interactive load, and “0–1” binary integer ones for operation states of battery storage and interactive load. Noted that there are two operation processes for battery storage, discharge and charge, three sets of decision variables would be assigned for each process.

#### 4.1.1 Continues decision variables

Continues decision variables include \( {P}_i^{Sou} \), \( {Q}_i^{Sou} \), \( {P}_{i,j}^{DG} \), \( {Q}_{i,j}^{DG} \), \( {P}_{i,j}^{SL,A} \), \( {Q}_{i,j}^{SL,A} \), \( {P}_{i,j}^{RL,A} \), \( {Q}_{i,j}^{RL,A} \), \( {P}_{i,j}^{S,C} \), \( {P}_{i,j}^{S,D} \), \( {Q}_{i,j}^S \), *V*
_{
i,j
}, *θ*
_{
i,j
}, where \( {P}_i^{Sou} \) and \( {Q}_i^{Sou} \) denote the active and reactive power of source bus at time interval *i* and \( {P}_{i,j}^{DG} \) and \( {Q}_{i,j}^{DG} \) are the active and reactive power of distributed generation *j* at time interval *i*. *V*
_{
i,j
} and *θ*
_{
i,j
} denote the voltage amplitude and angle of bus *j* at time interval *i*.

#### 4.1.2 “0–1” binary integer decision variables

“0–1” binary integer decision variables include \( {\eta}_{i,j}^{SL} \), \( {\eta}_{i,j}^{S,S} \), \( {\eta}_{i,j}^{CD} \), \( {\eta}_{i,j}^{DC} \).

### 4.2 Objective function

Where *λ* denotes cost coefficients. The superscripts of the variables and parameters in (10) are used to distinguish different kinds of DERs (*Sou*, *DG* and *S,P*) and active and reactive power output (*P*, *Q*). *NG* and *NS* respectively denote sets of distribution generation and battery storage.

In (9), generation costs of the source bus are related to its active and reactive power. The costs of reactive power might come from contracts or auxiliary markets, these two mechanisms could both be reflected by cost coefficients. The same situation would be implemented to distributed generations.

### 4.3 Constraints

Constraints mainly consist of two categories, respectively related to system operation and various DERs.

#### 4.3.1 System operation constraints

System operation constraints are safety operation constraints for the distribution system, including constraints for power balance, bus voltage and transmission power flow.

*j*at time interval

*i*.

*V*

_{ i }is vector of bus voltage magnitude and

*θ*

_{ i }is vector of bus voltage angle at time interval

*i*.

*F*

_{1}and

*F*

_{2}are active and reactive power flow functions.

Note that circuit parameters and operation state of distribution system are quite different from those of transmission system, transmission power flow should be calculated based on AC power flow.

Where \( {\overline{S}}_j^{line} \) and \( {\underline{S}}_j^{line} \) are upper and lower capacity limitations of line *j*. \( {P}_{i,j}^{line} \) and \( {Q}_{i,j}^{line} \) are the active and reactive transmission power flow of line *j* at time interval *i*.

*V*

_{ i,s }and

*θ*

_{ i,s }denote voltage magnitude and angle of source bus. \( {\overline{V}}_j^b \) and \( {\underline{V}}_j^b \) respectively denote upper and lower limitation of voltage magnitude of bus

*j*.

#### 4.3.2 DER operation constraints

Operation constraint constraints on distributed generation, battery storage and interactive load are established based on their operation characteristics.

*j*at period

*i*and \( {\overline{P}}_{i,j}^G \), \( {\underline{P}}_{i,j}^G \), \( {\overline{Q}}_{i,j}^G \) and \( {\underline{Q}}_{i,j}^G \) are their upper and lower bounds. \( {C}_j^G \) is the controlled power factor between active and reactive power of distributed generation

*j*. \( {V}_{i,j}^G \) is the bus voltage which distributed generation

*j*is connected to and \( {V}_j^{G, set} \) indicates the controlled voltage level.

Formulations on operation of interactive load and battery storage have been discussed in chapter III including formula (2–8).

### 4.4 Solution method

Obviously the formulated multi-period coordinated scheduling model is essentially a typical nonlinear mixed integer programming problem. GAMS could be used to solve this problem.

## 5 Case study

This profit minimization problem is a standard SOCP problem. We used MATLAB on a computer with a Pentium-M (2.0 GHz) processor and 1GB of DDR-RAM and selected CPLEX 12.0 as the solver.

### 5.1 Basic data

#### 5.1.1 System data

The proposed model is implemented on the tested REDS (Repository of Distribution Systems) 135-bus distribution system. The test system has been extended from single-period to multi-period, with 1 day as the scheduled duration and 1 h as basic time interval.

### 5.2 DER data

Eight DGs are added, including five GTs, two WTs and one PV; one SD and one CL are added as well.

Characteristics of the distributed generators

Num | Bus | Type | Power Factor | Voltage | Ramp Rate (kW/15 min) |
---|---|---|---|---|---|

| 2 | W | 0.8 | - | - |

| 22 | W | 0.8 | - | - |

| 37 | G | - | 1.05 | 100 |

| 46 | G | 0.8 | - | 100 |

| 62 | G | - | 1.05 | 100 |

| 86 | G | 0.8 | - | 100 |

| 101 | G | - | 1.05 | 100 |

| 121 | P | 0.8 | - | - |

Characteristics of the battery storage

Num | Bus | Initial electricity/kWh | Maximum capacity/kWh | Maximum exchanging power/kW | Power exchange loss |
---|---|---|---|---|---|

1 | 39 | 4000 | 8000 | 500 | 0.05 |

## 6 Results and discussion

### 6.1 Schedules of the source bus

### 6.2 Schedules of the DGs

No curtailments are observed for WTs and PV, as their capacities are relatively low in this tested system; therefore, the fluctuations could be easily offset by the source bus and the GTs. Reactive power schedules of DG 3, 5 and 7 are appropriately adjusted to keep the bus voltages at the set range, as they adopt CVC control strategy. Therefore, schedules of reactive power are independent of that of active power. However, For DG 4 and 6, as they adopt CPFC strategy, reactive power schedules are proportional to that of active output.

### 6.3 Schedules of the storage battery

### 6.4 Schedules of the interactive load

## 7 Conclusions

Implementation of DGs imposes great challenges on traditional distribution system operation. And interactive load and battery storage would reduce their volatility. So scheduling coordinated DG and them will be an important research topic, which imposes remarkable impacts on system economics and security. This paper firstly investigates operation characteristics of interactive load and battery storage. Load shifting cost, load shifting positive, load shifting shape and the relation between active and reactive load of interactive load are respectively discussed and formulated. And to battery storage, constraints for energy storage, power exchange, state transition number and operation cost are also formulated in detail. Then, a multi-period coordinated scheduling model is proposed for integrated operation of ADS, with the object of costs minimizing. A tested case is studied, which is based on a 135-bus distribution system with eight DGs, one SD and one CL connected. Solution of the proposed model includes optimal schedules of the DERs, which help to smooth bus load and cut distribution losses in the premise of secure operation constraints.

## Declarations

### Authors’ contributions

QC: Initiated the research and established models and schedules used for this study, XZ: Cope with establishing the formulation on Operation of Interactive Load and Battery Storage. DG: Manipulated the load data and summarized results in the case study. All authors read and approved the final manuscript.

### Competing interests

The authors declare that they have no competing interests.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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