A Multi-layer Optimization Scheduling Model for Active Distribution Network Based on Consistency Constraint

Abstract

With the increasing penetration of distributed generation (DG), active distribution network (ADN) is the development trend of future smart grid. Due to the features of uncertainties of DG, the difficulty of scheduling increases. For this concern, an optimization scheduling model of intra-layer autonomy and inter-layer coordination of ADN is proposed in this work. Aiming at intra-layer autonomy, an optimization model is established with the goals of the smallest electricity purchase cost for the ADN, the most profitable purchase and sale of electricity of microgrids and the most profitable and comfortable users. Aiming at inter-layer coordination, a "distribution network-microgrid" electricity price formation method that maximizes renewable energy sharing between microgrids and a "microgrid-user" electricity price formation method that maximizes users' willingness to generate electricity are proposed. In this paper, the modified IEEE 33-bus distribution system is built as case study, which verified the great scheduling capability and performance of the proposed model.

1 Introduction

Due to the massive access to energy storage (ES) and DG, the scheduling for ADN is affected by the diversity of scheduling purposes and uncertain output of DG, which result in more difficult and complicate scheduling optimization. The microgrids in the ADN contain a great deal of responsive resources. Due to its strong operation autonomy, which is also complicate, the hierarchical scheduling for ADN faces the problem of coordination between various agents. With the continuous development of ADN, the research on distribution network scheduling has changed greatly such as objective functions and constraints, like references [1,2,3,4,5,6]. In [7], an optimization method is proposed with multiple objectives, aiming to solve task-scheduling problems. Reference [8] presents a two-layer scheduling model considering the opportunity cost and the immediate cost, which is verified with great economic merit. At present, lots of researchers have studied the hierarchical scheduling models for ADN. When the model contains multiple decision-making agents, the optimization scheduling problem can be divided into different levels, that is, multi-layered optimization methods [9,10,11]. Please note that the first paragraph of a section or subsection is not indented. The first paragraphs that follows a table, figure, equation etc. does not have an indent, either.

This paper proposes an optimization scheduling model of intra-layer autonomy and inter-layer coordination of ADN. Aiming at intra-layer autonomy, an optimization model is established with the goals of the smallest electricity purchase cost for the ADN, the most profitable purchase and sale of electricity of micro-grids and the most profitable and comfortable users. Aiming at inter-layer coordination, a “distribution network-microgrid” electricity price formation method that maximizes the new energy sharing ability between microgrids and a “microgrid-user” electricity price formation method that maximizes users’ willingness to generate electricity are proposed. As a study case, the modified IEEE 33-bus distribution network is built to verify the performance of the multi-layer optimization structure. Subsequent paragraphs, however, are indented.

2 Economic Model of ADN

2.1 Transaction Coordinator Model F₁

The active distribution network aims to minimize the purchase cost of electricity.

$$ \min C_{dm} = \left[ {q_{dm}^{buy} p_{dm}^{buy} + q_{ds}^{buy} p_{ds}^{buy} - \left( {q_{dis}^{load} + q_{dis}^{loss} } \right) - q_{dm}^{sell} p_{dm}^{sell} } \right] $$

(1)

where $q_{dm}^{buy}$ and $q_{dm}^{sell}$ are the total power purchased and sold from the distribution network to all microgrids, respectively, which are positive. $q_{dm}^{buy}$ $P_{dm}^{buy}$ and $p_{dm}^{sell}$ are the power purchase price and sale price from the distribution network to all microgrids. $q_{dis}^{load}$ and $q_{dis}^{loss}$ represent the total load and loss of the distribution network. $q_{ds}^{buy}$ means the power bought from the main grid to the distribution network. $p_{ds}^{buy}$ represents electricity purchase price from the main grid to the distribution network.

Constraints:

$q_{ds}^{buy}$ is equal to the sum of the power from the distribution network to the microgrids and the total load and loss of the distribution network.

$$ 0 \le q_{ds}^{buy} - q_{ds}^{sell} = q_{dm}^{sell} + q_{dis}^{load} + q_{dis}^{loss} - q_{dm}^{buy} \le P_{ds}^{\max } $$

(2)

where $q_{ds}^{sell}$ means the electricity sold to the main grid. $P_{ds}^{\max }$ means the maximum transmission power of the transmission lines among the distribution network and the main grid.

Besides, transaction coordinator needs to consider line flow constraints to simplify the network.

$$ P_{dis,ab}^{\min } \le P_{dis,ab} \le P_{dis,ab}^{\max } $$

(3)

2.2 Microgrid Dispatch Model F₂

The microgrid aims to optimize the economy. Its objective function is:

$$ \left\{ {\begin{array}{*{20}c} {F_2 = \max \left\{ {p_t \sum_{t = 1}^T {\left( {\Delta L_{ind\_up,t} + \Delta L_{ind\_down,t} } \right) + C_{IDR} - C_{stor} } } \right\}} \\ {C_{stor} = c_{stor} \sum_{t = 1}^T {\left( {P_{stor\_d,t} + L_{stor\_c,t} } \right)} } \\ \end{array} } \right. $$

(4)

where $C_{stor}$ indicates the total operation and maintenance cost of energy storage. $c_{stor}$ is the cost per unit of charging/discharging. The first term of the objective function is the cost reduction due to the reduction of electricity purchase by customers, the second term is the subsidy received by the microgrid for participating in demand response, and The third term is the cost of energy storage operation paid by the microgrid.

Constraints:

Energy storage constraints:

$$ \left\{ {\begin{array}{*{20}c} {P_{stor}^{\min } \le P_{stor\_d,t} - L_{stor\_c,t} \le P_{stor}^{\max } } \\ {SOC_{stor,t} = SOC_{stor,t - 1} + L_{stor\_c,t} \alpha_{stor} - P_{stor\_d,t} /\beta_{stor} } \\ {SOC_{stor}^{\min } \le SOC_{stor,t} \le SOC_{stor}^{\max } } \\ \end{array} } \right. $$

(5)

where $SOC_{stor}^{\min }$ is the lower limit of the state of charge (SOC) of the energy storage.

Electric vehicle Constraints:

$$ \left\{ {\begin{array}{*{20}c} {SOC_{ev,t} = SOC_{ev,t - 1} + L_{ev,t} } \\ {SOC_{ev}^{\min } \le SOC_{ev,t} \le SOC_{ev}^{\max } } \\ {L_{ev,t} = 0,\forall t \in T_{off} } \\ \end{array} } \right. $$

(6)

where $SOC_{ev,t}$ means the state of charge of electric vehicles. $SOC_{ev}^{\min }$ and $SOC_{ev}^{\max }$ mean the maximum and minimum thresholds of the state of charge. $T_{off}$ means the non-charging time collection of electric vehicles.

2.3 Terminal User Model F₃

The load aims at improving the comprehensive contentment of load electricity consumption. The objective function is:

$$ \max S_A = \left( {\delta_1 \delta_W + \delta_2 \delta_E } \right) $$

(7)

$$ S_W = 1 - \frac{{l_{i,j}^* - l_{i,j} }}{{l_{i,j}^* }} $$

(8)

$$ S_E = 1 - \frac{{p_{mic}^{sell} l_{i,j} - \left( {p_{mic}^{sell} } \right)^* l_{i,j}^* }}{{\left( {p_{mic}^{sell} } \right)^* l_{i,j}^* }} $$

(9)

where $S_A$ is the comprehensive satisfaction of load electricity consumption, $S_W$ is the satisfaction of the load power consumption mode, $S_E$ is the satisfaction of load electricity consumption. $\delta_1$ and $\delta_2$ are respectively the satisfaction weight of load electricity consumption mode and the satisfaction weight of load electricity consumption cost, which meet the equation $\delta_1 + \delta_2 = 1$. $l_{i,j}^\ast$ and $l_{i,j}$ respectively represent the power consumption of load j in the i-th microgrid before and after participating in demand response. $\left( {p_{mic}^{sell} } \right)^\ast$ and $p_{mic}^{sell}$ indicate the electricity sale price for the users, before and after which participating in demand response.

3 Electricity Price

3.1 “DIstribution Network-Microgrid” Electricity Price

According to the supply and demand ratio of ADN, which is expressed as:

$$ \eta_{dm} = \frac{{q_{dm}^{buy} }}{{q_{dm}^{sell} }} $$

(10)

where $q_{dm}^{buy}$ is the power purchased from the microgrid to the ADN, $q_{dm}^{sell}$ is the power sold from the ADN to the microgrid.

Define the electricity purchase price from the microgrid to the ADN as:

$$ p_{dm}^{buy} = f\left( {\eta_{dm} } \right) = \left\{ {\begin{array}{*{20}l} {\frac{{p_{ds}^{buy} p_{ds}^{sell} }}{{\left( {p_{ds}^{buy} - p_{ds}^{sell} } \right)\eta_{dm} + p_{ds}^{sell} }}} \hfill & {0 \le \eta_{dm} \le 1} \hfill \\ {p_{ds}^{sell} } \hfill & {\eta_{dm} > 1} \hfill \\ \end{array} } \right. $$

(11)

Define the electricity purchase price from the ADN to the microgrid as:

$$ p_{dm}^{sell} = g\left( {\eta_{dm} } \right) = \left\{ {\begin{array}{*{20}l} {p_{dm}^{buy} \eta_{dm} + p_{ds}^{sell} \left( {1 - \eta_{dm} } \right)} \hfill & {0 \le \eta_{dm} \le 1} \hfill \\ {p_{ds}^{sell} } \hfill & {\eta_{dm} > 1} \hfill \\ \end{array} } \right. $$

(12)

3.2 “MIcrogrid-User” Electricity Price

Define $\mu_{mic}^{buy}$ as the ratio of the maximum predicted output of DG to the sum of the maximum predicted output of DG and the dischargeable power of ES in microgrid i.

$$ \mu_{mic}^{buy} = \frac{{q_{G,i}^* }}{{q_{G,i}^* + q_{S,i,dch}^* }} $$

(13)

Define $\mu_{mic}^{sell}$ as the ratio of the load demand in microgrid i to the sum of the load demand in i-th microgrid and the chargeable power of the ES.

$$ \mu_{mic}^{sell} = \frac{{q_{mic,i}^{sell} }}{{q_{mic,i}^{sell} - q_{S,i,ch}^* }} $$

(14)

Set the internal transaction electricity price in the microgrid according to $\mu_{mic}^{buy}$ and $\mu_{mic}^{sell}$:

$$ p_{mic}^{buy} = \left( {p_{mic}^{buy} } \right)^* e^{\left( {\mu_{mic}^{buy} - 1} \right)} $$

(15)

$$ p_{mic}^{sell} = \left( {p_{mic}^{sell} } \right)^* e^{\left( {\mu_{mic}^{sell} - 1} \right)} $$

(16)

4 Solution of Multi-layer Optimization Scheduling Model

The proposed multi-layer optimization scheduling model is composed of the ADN layer, the microgrid layer, and the user layer optimization scheduling model. The consistency constraint is introduced as $\varepsilon_1 = q_{dm}^{sell} - \sum {q_{md,i}^{buy} = 0,\varepsilon_2 = q_{dm}^{buy} } - \sum {q_{md,i}^{sell} = 0,\varepsilon_3 = \sum_{i = 0} {\left( {q_{mic,i}^{sell} - \sum {l_{i,j} } } \right) = 0} }$.

The solution process is as follows:

• Step 1: Let $h = 0$.

• Step 2: Input the value $q_{dm}^{buy} \left( h \right),q_{dm}^{sell} \left( h \right),q_{G,i}^\ast ,q_{S,i,dch}^\ast ,q_{S,i,ch}^\ast$.

• Step 3: Calculate the value of $\eta_{dm} \left( h \right),\mu_{mic}^{buy} \left( h \right),\mu_{mic}^{sell} \left( h \right)$.

• Step 4: Based on the “distribution network-microgrid” and “microgrid-user” electricity price mechanism, calculate the value of $p_{dm}^{buy} \left( h \right),p_{dm}^{sell} \left( h \right),p_{mic}^{buy} \left( h \right),p_{mic}^{sell} \left( h \right)$.

• Step 5: Substitute $p_{dm}^{buy} \left( h \right)$ and $p_{dm}^{sell} \left( h \right)$ into F₁, solve F₁, calculate, $q_{dm}^{sell} \left( {h + 1} \right)$,$q_{dm}^{buy} \left( {h + 1} \right)$, and $q_{ds}^{buy} \left( {h + 1} \right)$; substitute $p_{mic}^{buy} \left( h \right)$ and $p_{mic}^{sell} \left( h \right)$ into F₂, solve F₂, obtain $q_{md,i}^{sell} \left( {h + 1} \right)$ or $q_{md,i}^{buy} \left( {h + 1} \right)$; substitute $\left( {p_{mic}^{sell} } \right)^\ast$ and $p_{mic}^{sell} \left( h \right)$ into F₃, solve F₃, obtain the load after user load response l_i,j(h+1).

• Step 6: When $\varepsilon_1 + \varepsilon_2 \le e^{ - 6}$, output the final results; or let $h = h + 1$, and go to the next step.

• Step 7: Repeat Step 2, Step 3, Step 4 and Step 5 in order, then go to Step 8.

• Step 8: When $\varepsilon_1 + \varepsilon_2 + \varepsilon_3 \le e^{ - 4}$, output the final results; or let $h = h + 1$, and go to Step 6.

5 Case Study

5.1 Simulation Model

The IEEE 33-bus system with DGs is built for the simulation in PowerFactory with four microgrids. The simulation is implemented in the Windows 10 environment on a PC as the calculation platform. The structure of the ADN is shown in Fig. 1.

Fig. 1.

The structure of the ADN

The curve of the 24-h system load demand is shown in Fig. 2(a). The forecast curves of 24-h PV output of each microgrid are shown in Fig. 2(b).

Fig. 2.

(a)The curve of the 24-h system load demand; (b) The forecast curves of 24-h PV output of each microgrid

The model proposed in this work takes economy and safety comprehensively as optimization scheduling goals considering renewable energy consumption and user satisfaction with electricity consumption. The scheduling consequences of the optimization method are plotted in Fig. 3(a).

Fig. 3.

(a)MG1-MG4 optimization results of the proposed method

6 Conclusion

In this paper, a multi-layer optimization scheduling model based on ADN layer, microgrid layer and user layer is proposed to process the safety and economy concerns of the ADN. The main conclusions can be summarized as follows:

• (1) Transaction coordinators and microgrid operators and terminal users’ model have been built. Electricity price mechanisms are proposed to maximize energy sharing and economic benefits.

• (2) The modified IEEE 33-bus distribution network is established. The results of the simulation show that the proposed multi-layer scheduling method of ADN can effectively promote the energy sharing within the microgrids and guarantee the reliable and economical operation of the ADN.

In terms of the future work, the action decision of ES should be carried out to enhance the energy sharing performance of the ADN.