含多种需求响应及电动汽车的微网虚拟电厂日前优化调度

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需求响应

电动汽车

虚拟电厂

优化调度

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在现代电力系统中，随着可再生能源的广泛应用以及电动汽车（Electric Vehicles, EVs）的普及，微网（Microgrid）和虚拟电厂（Virtual Power Plant, VPP）的概念日益受到重视。微网是由分布式能源（如风能、太阳能等）、储能装置、负荷以及控制设备组成的小型电力系统，而虚拟电厂则是一种通过集成多个分布式能源资源，实现集中管理和调度的新型电力运营模式。本文主要探讨的是在微网中结合多种需求响应策略以及电动汽车的VPP日前优化调度问题。需求响应（Demand Response, DR）是电力市场中的一种重要机制，它鼓励用户在特定时段调整其用电行为，以帮助平衡电网供需。这种策略可以减轻高峰时段的负荷压力，提高电力系统的稳定性和经济性。常见的需求响应类型包括价格响应、容量响应、紧急响应等。在微网中，电动汽车不仅是一种交通工具，还能作为移动储能单元参与电网的调度。它们在充电时可以吸收过剩的可再生能源，而在放电时则可以为微网提供额外的电力支持。因此，考虑电动汽车的充放电特性进行VPP的优化调度，对于提高微网的整体运行效率和经济效益具有重要意义。在“含多种需求响应及电动汽车的微网虚拟电厂日前优化调度”研究中，首先需要建立一个包含各种需求响应策略和电动汽车充放电模型的数学模型。这个模型会综合考虑微网内的各类能源（如风力、光伏、柴油发电机等）的出力特性，储能装置的状态，以及电网的电价和负荷需求等多方面因素。然后，通过优化算法（如遗传算法、粒子群优化或线性规划等）寻求最优的调度策略，以最小化运营成本、最大化收益或者最小化环境影响为目标。文件"VPP_ac_ev_new.m"很可能是一个MATLAB程序，用于实现上述的数学模型和优化算法。该程序可能包含了对微网中各元素的建模、需求响应策略的实施规则、电动汽车的充放电控制逻辑，以及优化调度过程。通过运行这个程序，可以模拟不同场景下微网的运行情况，分析不同需求响应策略和电动汽车参与调度的影响，从而为实际的微网运营提供决策支持。在实际应用中，这种优化调度方法可以帮助微网运营商更有效地管理能源资源，减少对传统电网的依赖，同时促进电动汽车的普及和可再生能源的利用。此外，对于政策制定者来说，了解并推广这类技术，也有助于推动电力市场的改革，创建更加灵活、可持续的能源系统。

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energies

Article

Stochastic Adaptive Robust Dispatch for Virtual

Power Plants Using the Binding Scenario

Identiﬁcation Approach

Guoqiang Sun

* , Weihang Qian

*, Wenjin Huang

, Zheng Xu

, Zhongxing Fu

Zhinong Wei

and Sheng Chen

College of Energy and Electrical Engineering, Hohai University, Nanjing 211100, China;

[email protected] (Z.W.); [email protected] (S.C.)

Yancheng Power Supply Company of State Grid Jiangsu Electric Power Company, Yancheng 224002, Jiangsu

Province, China; [email protected] (W.H.); [email protected] (Z.X.); [email protected] (Z.F.)

* Correspondence: [email protected] (G.S.); [email protected] (W.Q.);

Tel.: +86-136-0514-5395 (G.S.); +86-182-6005-3918 (W.Q.)

Received: 22 April 2019; Accepted: 15 May 2019; Published: 20 May 2019



 

Abstract:

The present study establishes a stochastic adaptive robust dispatch model for virtual power

plants (VPPs) to address the risks associated with uncertainties in electricity market prices and

photovoltaic (PV) power outputs. The model consists of distributed components, such as the central

air-conditioning system (CACS) and PV power plant, aggregated by the VPP. The uncertainty in the

electricity market price is addressed using a stochastic programming approach, and the uncertainty in

PV output is addressed using an adaptive robust approach. The model is decomposed into a master

problem and a sub-problem using the binding scenario identiﬁcation approach. The binding scenario

subset is identiﬁed in the sub-problem, which greatly reduces the number of iterations required

for solving the model, and thereby increases the computational eﬃciency. Finally, the validity of

the VPP model and the solution algorithm is veriﬁed using a simulated case study. The simulation

results demonstrate that the operating proﬁt of a VPP with a CACS and other aggregated units can

be increased eﬀectively by participating in multiple market transactions. In addition, the results

demonstrate that the binding scenario identiﬁcation algorithm is accurate, and its computation time

increases slowly with increasing scenario set size, so the approach is adaptable to large-scale scenarios.

Keywords:

virtual power plant (VPP); stochastic adaptive robust model; binding scenario

identiﬁcation approach; central air-conditioning system (CACS); multiple markets

1. Introduction

With the growth of electricity demand, fossil fuels have been widely used for electricity generation

in recent years as the cheapest source of energy. However, the use of fossil fuels causes a variety

of environmental eﬀects and may endanger human health [

]. In order to meet the challenges

associated with energy shortages and environmental pollution, the world-wide energy production

infrastructure is slowly moving in the direction of clean and low-carbon options based on renewable

energy sources (RESs) [

]. However, RESs suﬀer from the disadvantages of strong randomness, high

volatility, and weak controllability. Therefore, the continuous expansion of grid-connected electric

power facilities based on RESs poses a challenge to the safe and reliable operation of electric power

grids [

–

]. Virtual power plants (VPPs) have been developed to address this challenge. Through

advanced control, measurement, and communication technologies, a large number of RESs, controllable

loads, energy storage systems (ESSs), and other distributed energy resources are aggregated by VPPs

Energies 2019, 12, 1918; doi:10.3390/en12101918 www.mdpi.com/journal/energies

Energies 2019, 12, 1918 2 of 23

to participate in the power grid operation as a whole, which is conducive to the rational allocation and

utilization of resources [8–11].

In general, a VPP framework promotes the aggregation of various resources by simultaneously

participating in multiple markets, such as the day-ahead energy market (DAM) and real-time energy

market (RTM), which can improve the ﬂexibility of scheduling [

]. Existing studies have mostly only

considered VPP participation in the DAM, and participation has been rarely extended to multiple

markets. For example, a VPP model that considers only DAM participation has been established,

where the overall demand response (DR) was divided into incentive-based DR and price-based DR

mechanisms [

–

]. A DR was also applied in a multi-market model, where a VPP participates in

both the DAM and RTM simultaneously [

]. However, the DR in the above studies was regarded

strictly as an interruptible/transferable load, and no speciﬁc modeling analysis was applied.

Meanwhile, VPP operations are impacted by uncertain factors such as RES outputs in the

scheduling process, resulting in economic and security issues. Therefore, addressing uncertain factors

in VPP operations has become a topic of increasing interest [

]. Numerous approaches have been

applied toward addressing uncertainty in VPP operations, such as stochastic programming [

–

robust optimization [

], chance-constrained programming [

], and point estimation [

]. In contrast,

the application of adaptive robust optimization has been relatively rare in this case. However, this

approach is more ﬂexible than robust optimization because the decision making process is conducted

in stages, which to some extent can alleviate the conservativeness of robust optimization solutions.

Adaptive robust optimization considers the optimal solution under the worst-case conditions of

uncertain factors and is generally divided into two stages for decision making [

]. The ﬁrst stage

employs what are denoted as here-and-now variables to make decisions before the level of uncertainty

is known. The second stage employs what are denoted as wait-and-see variables to make decisions

after the level of uncertainty is known. For example, an adaptive robust unit commitment model was

established to account for uncertainties in wind power output by the active regulation of pumped

storage power stations [

], and an adaptive robust reactive power optimization model was proposed

to address the uncertainties in wind power output under conditions of high wind power penetration

integrated into active distribution networks [28].

At present, numerous methods have been applied for solving adaptive robust models, such as

the aﬃne policy, Benders decomposition, the column and constraint generation (CCG) algorithm,

and scenario-based algorithm. The aﬃne policy method uses the linear decision rule to establish the

aﬃne relationship between decision variables and uncertain parameters and transforms the two-stage

problem into a single-stage problem [

]. However, the results are conservative. A Benders/CCG

algorithm has been adopted for decomposing an original stochastic adaptive robust model problem

into a master problem and a sub-problem, but the Karush–Kuhn–Tucker (KKT) or duality method was

needed to transform the sub-problem into a single-level model, and a large number of integer terms

were introduced in the linearization process, leading to high model solution complexity in large-scale

problems [

]. The scenario-based algorithm was employed to transform a three-level adaptive

robust model into a single-level model by enumerating the uncertainty set based on the scenarios [

However, the computational eﬃciency of the scenario-based algorithm decreases as the scale of the

problem increases compared with the binding scenario identiﬁcation approach. This is particularly the

case for large-scale scenario sets, where the number of scenarios required for solving the problem is

quite large, resulting in a very large computational burden [33,34].

Based on the above analysis, the present study considers a VPP that aggregates a photovoltaic

(PV) power plant, a gas turbine, an ESS, a central air-conditioning system (CACS), and interruptible

load, and simultaneously participates in multiple market transactions in the DAM, RTM, and carbon

trading market (CTM). The contributions of this paper can be brieﬂy summarized as follows:

This paper establishes a stochastic adaptive robust model for VPP dispatch that considers CACS

and multiple markets. The stochastic programming approach is used to address the uncertainty of

market electricity price owing to the high accuracy of market price forecasting, and the adaptive

Energies 2019, 12, 1918 3 of 23

robust method is used to address the uncertainty of PV output owing to the low accuracy of PV

output forecasting.

The binding scenario identiﬁcation approach is used to solve the stochastic adaptive robust

model for VPP dispatch. The original problem is decomposed into a master problem for solving

the single-level optimization model with the binding scenario subset and a sub-problem for

identifying the binding scenario subset, which greatly reduces the number of scenarios and the

number of iterations required for the solution process. In addition, auxiliary variables are also

introduced rather than applying a cyclic solution process for the sub-problem to reduce the

number of times that the sub-problem must be solved.

This paper quantitatively eValuates the key factors aﬀecting VPP proﬁt, and the VPP scheduling

of aggregated units is analyzed. The results of a case study indicate that the binding scenario

identiﬁcation algorithm eﬀectively improves the computational eﬃciency of the solution process,

and is scalable to large-scale scenarios.

The remainder of this paper is organized as follows: Section 2 deﬁnes the modeling of a CACS.

The VPP model formulation is deﬁned in Section 3. Section 4 introduces the solution methodology.

Section 5 presents the case study and results. Section 6 concludes the paper. The overall framework of

this study is shown in Figure 1.

Energies 2019, 12, x FOR PEER REVIEW 3 of 24

forecasting, and the adaptive robust method is used to address the uncertainty of PV output

owing to the low accuracy of PV output forecasting.

2. The binding scenario identification approach is used to solve the stochastic adaptive

robust model for VPP dispatch. The original problem is decomposed into a master

problem for solving the single-level optimization model with the binding scenario

subset and a sub-problem for identifying the binding scenario subset, which greatly

reduces the number of scenarios and the number of iterations required for the

solution process. In addition, auxiliary variables are also introduced rather than

applying a cyclic solution process for the sub-problem to reduce the number of times

that the sub-problem must be solved.

3. This paper quantitatively evaluates the key factors affecting VPP profit, and the VPP

scheduling of aggregated units is analyzed. The results of a case study indicate that

the binding scenario identification algorithm effectively improves the computational

efficiency of the solution process, and is scalable to large-scale scenarios.

The remainder of this paper is organized as follows: Section 2 defines the modeling of a CACS.

The VPP model formulation is defined in Section 3. Section 4 introduces the solution methodology.

Section 5 presents the case study and results. Section 6 concludes the paper. The overall framework

of this study is shown in Figure 1.

Figure 1. Overall framework of this study.

2. Central Air-conditioning Systems

2.1. Comfort Index of the Human Body

A CACS is a kind of DR resource that can be beneficially regulated and controlled within a VPP

setting to decrease the peak load of power grids and alleviate conflicts between power supply and

demand. However, these systems must meet the comfort requirements of users. In this paper, the

Figure 1. Overall framework of this study.

Energies 2019, 12, 1918 4 of 23

2. Central Air-Conditioning Systems

2.1. Comfort Index of the Human Body

A CACS is a kind of DR resource that can be beneﬁcially regulated and controlled within a

VPP setting to decrease the peak load of power grids and alleviate conﬂicts between power supply

and demand. However, these systems must meet the comfort requirements of users. In this paper,

the comfort requirements of users are determined using the predicted mean vote (PMV) index, denoted

PMV

, which represents the thermal sensation registered by a majority of people within the same

environment [35,36].

To ensure human comfort within an acceptable range, the present work applies the following

constraint to the regulation and control processes of CACSs based on σ

PMV

[37]:

–0.5 ≤ σ

PMV

≤ 0.5 (1)

The relationship between

PMV

and the indoor temperature

can be expressed as follows [

PMV

(

0.3895 ×(T

−26), T

≥ 26

0.4065 ×(−T

+ 26), T

< 26

(2)

Therefore, the reasonable temperature range of human comfort can be determined according to

Equations (1) and (2).

2.2. Central Air-Conditioning System Model

According to the principle of energy conservation, the heat obtained by a public building over a

given period of time is the diﬀerence between the heat transferred in and the heat removed from the

inside over that period [40]. A diagram of public building energy conservation is shown in Figure 2.

Energies 2019, 12, x FOR PEER REVIEW 4 of 24

comfort requirements of users are determined using the predicted mean vote (PMV) index, denoted

PMV

, which represents the thermal sensation registered by a majority of people within the same

environment [35,36].

To ensure human comfort within an acceptable range, the present work applies the following

constraint to the regulation and control processes of CACSs based on

PMV

[37]:

PMV

0.5 0.5–

≤≤

(1)

The relationship between

PMV

and the indoor temperature

can be expressed as follows

[38,39]:

in in

PMV

in in

0.3895 ( 26), 26

0.4065 ( 26), 26



×− ≥



×− + <



(2)

Therefore, the reasonable temperature range of human comfort can be determined according to

Equations (1) and (2).

2.2. Central Air-conditioning System Model

According to the principle of energy conservation, the heat obtained by a public building over a

given period of time is the difference between the heat transferred in and the heat removed from the

inside over that period [40]. A diagram of public building energy conservation is shown in Figure 2.

Figure 2. Diagram of public building energy conservation.

This yields the following thermodynamic equation in a public building with a CACS [41]:

()0

γβα

+−−=

(3)

where

, and

are parameters determined according to the individual characteristics of

the public building and its CACS, and

is the total cold energy provided by the CACS.

Accordingly, the time-varying equation of

can be obtained for a public building as follows [42]:

in in

e(1e)()

ββ

γγ

ββ

−Δ −Δ

−

=+− −

(4)

out

wall wall cl d win win d s cl win win 1 2 3 he

nout n

4567le cl sh lh

( ) 1000

1000 1.01 38.5

t t

K A T T q A FFF K A T kkkP

kkkkP Cnq nq GT G

φφ

=++ +++

+++ +



(5)

wall wall win win

1.01KA KA G

=++



(6)

aa hin

CV S A

γρ

(7)

Figure 2. Diagram of public building energy conservation.

This yields the following thermodynamic equation in a public building with a CACS [41]:

+ βT

−(α −Q) = 0 (3)

where

, and

are parameters determined according to the individual characteristics of the

public building and its CACS, and

is the total cold energy provided by the CACS. Accordingly,

the time-varying equation of T

can be obtained for a public building as follows [42]:

= e

−

∆t

t−1

+ (1 −e

−

∆t

)(

−

) (4)

Energies 2019, 12, 1918 5 of 23

wall

+ T

) +

win

out

+ 1000k

1000k

+ C

nφq

+ nφq

+ 1.01G

out

+ 38.5G

(5)

β =

wall

win

+ 1.01G

(6)

γ = C

Vρ

+ S

(7)

In addition, we present Equations (5)–(7) for determining the values of

, and

for a public

building. In terms of the external walls and roofs of the building,

wall

, and

are respectively

the heat transfer coeﬃcient, total area, and the hourly value of the cooling load temperature, and

is a

correction value for

with respect to the regions. In terms of the outer windows of the building,

win

, and

win

are respectively the maximum solar heat gain, total area, correction coeﬃcient

based on the glass type, shading coeﬃcient associated with inner shading measures, cooling load

coeﬃcient, and heat transfer coeﬃcient, and

out

is the outdoor temperature. In terms of the electric

heating equipment of the building,

, and

are respectively the installation coeﬃcient, load

coeﬃcient, simultaneous utilization rate, and installed power. In terms of the lighting equipment of

the building,

, and

are respectively the simultaneous usage rate, heat storage coeﬃcient,

power consumption coeﬃcient of rectiﬁers, installation coeﬃcient, and installed power. In terms of

the human occupants of the building,

is the cooling load coeﬃcient reﬂecting the sensible heat

gain of a human body,

is the total number of persons in the public building,

is the coeﬃcient of

occupant aggregation, q

is the sensible heat gain per adult male, q

is the latent heat gain per adult

male, with all females and children converted into an adult male equivalence. Finally,

is the fresh

air volume of the building,

is the speciﬁc heat capacity of air at a constant pressure,

is the volume

of refrigeration space in the building,

is the air density,

is the heat storage coeﬃcient of interior

walls, and A

is the total area of interior walls.

A CACS is generally composed of chillers that produce cold energy

and thermal storage tanks

for the storage and release of cold energy, which are denoted as

and

, respectively. Accordingly,

can be given as follows [39]:

= Q

−Q

+ Q

(8)

The other constraints of a CACS can be expressed as follows:

0 ≤ Q

≤ Q

ch,max

(9)

0 ≤ Q

≤ Q

st,max

(10)

0 ≤ Q

≤ Q

re,max

(11)

0 ≤ S

≤ S

c,max

(12)

= S

t−1

+ (Q

−Q

/η

)∆t (13)

Here,

ch,max

is the maximum cold energy produced by chillers,

st,max

and

re,max

are the

maximum cold energy respectively stored and released by thermal storage tanks,

and

c,max

are the

respective cold energy in time period t and the cold energy capacity of thermal storage tanks, and

and

are the respective storage and release eﬃciencies of thermal storage tanks. Finally, the total

power consumption of the CACS

cold

is mainly a function of the power consumed by chillers and the

storage and release processes of thermal storage tanks, and can therefore be expressed as

cold

= Q

/µ

+ Q

(14)

where

, and

are the respective energy conversion eﬃciencies of chillers and of the storage

and release processes of thermal storage tanks.

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MATLAB代码：计及碳排放交易及多种需求响应的微网虚拟电厂日前优化调度注意：店铺内还有大量考虑碳交易的综合能源系统优化调度

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