Integrated scheduling of energy supply and demand in microgrids under uncertainty: A robust multi-objective optimization approach

Energy 130 (2017) 1e14

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Integrated scheduling of energy supply and demand in microgrids under uncertainty: A robust multi-objective optimization approach Luhao Wang a, Qiqiang Li a, *, Ran Ding a, Mingshun Sun b, Guirong Wang a, c a

250061, School of Control Science and Engineering, Shandong University, Jinan, China 85719, Electrical and Computer Engineering, Arizona State University, Tucson, United States c 250101, Key Laboratory of Building Renewable Energy Utilization Technologies, Ministry of Education, Jinan, China b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 8 October 2016 Received in revised form 18 April 2017 Accepted 21 April 2017 Available online 24 April 2017

As a Demand Response (DR) based working mode, the integrated scheduling of energy supply and demand provides an effective approach to improve economic and environmental benefits for Microgrids (MGs). However, it is still a challenging issue to cover uncertainties caused by intermittent renewable energy and random loads while optimizing multiple objectives in economy and environment. To tackle this issue, an integrated scheduling approach for MGs is proposed based on robust multi-objective optimization. Firstly, load shifting in a finite time is introduced to express an acceptable DR program for industrial customers. A minimax multi-objective optimization model is formulated to seek the minimum operation costs and emissions under the worst-case realization of uncertainties, which are captured by the robust sets with budgets of uncertainty. Secondly, a strong duality based model transformation method is implemented to cope with the strong coupling and nonlinearity in the proposed formulation. Also, Multi-Objective Cross Entropy (MOCE) algorithm is adopted to solve the reconstructed model for simultaneously optimizing all the objectives. Finally, detailed comparative experiments are conducted in problem level, model level and algorithm level. The simulation results show that the proposed scheduling approach can effectively attenuate the disturbances of uncertainties as well as achieve optimal economic and environmental benefits, compared with single-objective robust optimization scheduling approaches and deterministic multi-objective optimization scheduling approaches. Meanwhile, the validity and effectiveness of the robust multi-objective optimization approach for the MG integrated scheduling problem under uncertainty are confirmed. © 2017 Published by Elsevier Ltd.

2016 MSC: 00-01 99-00 Keywords: Microgrid Demand scheduling Uncertainty Robust optimization Multi-objective optimization

1. Introduction In China, large portions of electricity are consumed by industrial customers [1]. Especially, in summer, the majority of power lines are often under full load operation. To guarantee residential electricity, grid corporation has to switch off some industrial electricity. As an effective complement and substitute for centralized power plants, Microgrids (MGs) integrated with Distributed Generations (DGs) and energy storage devices are established in the industrial park to ensure orderly production and reduce fossil energy consumption. Some similar demonstrations and commercial projects are reported in Ref. [2]. However, the advantages of economy and environment are not obvious in the operation of MGs, relative to

* Corresponding author. E-mail address: [email protected] (Q. Li). http://dx.doi.org/10.1016/j.energy.2017.04.115 0360-5442/© 2017 Published by Elsevier Ltd.

centralized energy generation modes. One reason is that carbon emissions are roughly translated into costs in traditional economic scheduling. The resulting one scheduling scheme may not adapt to the different focuses in economy and environment [3]. Another reason is that intermittent renewable energy and uncertain loads can cause the energy supply contract violation and increase dependence on power grid [4]. Therefore, it is necessary to design an effective scheduling approach to mitigate the disturbances of uncertainties while optimizing economic and environmental benefits in the operation of MGs. Here, the operational planning for MGs could be seen as an uncertain multi-objective optimization problem, in which energy supply and demand are managed in a cost-effective and low-emission way. Furthermore, in view of the uniqueness of MG structure and load patterns, it may prove to be a meaningful and challenging research work to help system operators improve operational performance of MGs. In general, MGs are run in the “ load-tracking ” manner. In order

2

L. Wang et al. / Energy 130 (2017) 1e14

to meet the energy demand and reduce the impacts of randomness of renewable energy generation, various energy generation scheduling strategies are employed in MG operation [5]. Without the participation of demand-side resources, scheduling decision is just a theoretical optimization rather than an optimal decision in actual application [6]. Therefore, several works focused on the management of Demand Response (DR) in MGs. To address the tieline power fluctuation and reduce the size of energy storage systems in a MG, a hierarchical control strategy for battery storage and demand-side resources is proposed in Ref. [7]. Normally, DR programs consisting of Price-Based Program (PBP) and Incentive-Based Program (IBP) are formulated as a price elasticity model to participate in the market transactions directly [8]. However, discrete features of load are not described in the elasticity model, and it is difficult to obtain the complete and exact price-elastic demand curve in the real world [9]. Then, the concept of demand scheduling proposed by Ref. [10] is introduced to improve operating performance of a MG. Based on the price-quantity offer package, the formulations of load curtailment for residential, commercial, and industrial consumers are implemented in integrated scheduling of a MG [11]. A similar DR program is employed in multi-objective optimization operation for a MG and cover energy generation uncertainty [12]. Although the roles of these demand scheduling programs are positive, load reduction is undesirable for customers from a psychological perspective, especially for industrial customers. Combined with physical features of loads, Wang et al. [13] have gone a step further in the MG management by applying energy consumption scheduling formulation proposed by Ref. [14], in which load reduction is converted to load shifting. After then, an improved model for the DR program, including interruptible and uninterruptible loads, is proposed to maximize economic benefits of a MG [15]. However, the volatility of non-schedulable loads is not included in the studies mentioned above. In this work, uncertainties in power, cooling and heating loads are fully considered. Besides, different from the direct response of DR programs to the price and incentive, in our study, the demand-side resources are regarded as the generation units with negative output power, which are controlled by system operators to seek comprehensive benefits. As pointed out before, intrinsic uncertainties, such as renewable generation, energy demand or market information and so on, might hamper the potential profit in the operation of MGs. Some recent literatures have investigated the operation of hybrid energy systems under uncertainties. An economic operations optimizer for two specific nuclear hybrid energy system configurations is proposed to address the variability raised from wholesale electricity markets and renewable generation [16]. Authors of [17] have gone a step further by designing a control strategy to manage prediction error and energy storage elements to avoid the energy imbalance problem in a hybrid energy system. Moreover, a storage integration optimization method among different MG subsections is developed to achieve robust and economic power supply [18]. In Ref. [19], authors propose a stochastic energy management system to handle energy demand and supply uncertainties in MG operation. However, the effects of uncertainties on environment benefits of MGs are not considered in these studies, which might make their outcomes tricky to meet stringent emissions requirements. Here, environmental concerns change the classical economic operation problem into a multi-objective economic and environmental operation problem [20]. Uncertainty handling in a multi-objective framework is still a key point for the operation of MGs. Considering the bounds of variations in load demand and renewable energy generation, a deterministic three stage optimization framework is designed to minimize economic and environmental objectives of a MG [21]. Based on extreme scenarios of probabilistic

forecasts, a deterministic Mixed Integer Linear Programming (MILP) planning model of a MG is formulated under the objectives of minimizing total cost, batteries usage, and peak load [22]. Although uncertainties can be addressed in multi-objective optimization, the results in these works are overly conservative. Also, operational flexibility of MGs is reduced. In order to guarantee the stability and raise comprehensive benefits of a multi-objective optimization of MGs, different tools such as stochastic programming or fuzzy programming are used to handle uncertainties. Based on scenarios of probabilistic forecasts, a Mixed Integer Non-Linear Programming (MINLP) model for the generating side and demand side management of MGs is developed to reduce the operational costs and air pollution [23]. Here, uncertainty factors are represented by a large number of scenarios. Similar description has also appeared in Ref. [20], a stochastic multi-objective method is applied to distribution systems to schedule DG units and manage DR programs under the objectives of minimizing operational costs and emissions. With an increase in the number of scenarios, accuracy of the scheduling schemes of MGs increases. However, a larger scenario set will significantly expand the size of multi-objective operational planning problem of MGs and be computationally expensive [24]. Therefore, Chance Constrained Programming (CCP) is used in the multi-objective design of a hybrid energy system to deal with uncertainty in renewable resources [25]. A multi-objective stochastic optimal method for stand-alone MGs is presented in Ref. [26], in which uncertainties are assumed to follow some classic distributions, such as the wind speed follows a Weibull distribution. Although robustness of scheduling schemes could be effectively controlled by adjusting the probability of constraints to be violated, there are still practical limitations in such stochastic optimization based multiobjective approaches. Unlike renewable energy resources, it is difficult to use an accurate probability distribution to express the uncertain loads with market and emotional factors. Also, a highrisk operation may exist in MGs since this approach only provides probabilistic guarantees for the system reliability. As an alternative, Chaouachi and Kamel [27] present a linear multi-objective programming model with fuzzy logic, in which uncertain parameters are handled by a fuzzy logic expert system with the experience of decision-makers. However, as a new research field, experiential knowledge of MG operation is limited. To overcome these disadvantages of the above methods in the operation of MGs, some concise uncertainty models should be further investigated to capture the most significant characteristics of uncertainties and achieve simple calculation. Also, the relationship between the multiobjective operational planning problem and uncertainty factors should be further refined to balance the robustness and Pareto features of the scheduling schemes of MGs. Accordingly, in this paper, we employ a robust multi-objective approach to optimize the scheduling of MGs. It does not require any probabilistic information and experiential knowledge [28]. Also, its optimal solution hedges against all realizations of the uncertain data in a multiobjective framework. In recent years, robust optimization approaches are shown to be effective to ensure operational reliability for MGs [29e34]. In Ref. [29], a robust optimization approach based on prediction interval is proposed to evaluate the overall MG reliability under different levels of uncertainty. To minimize the total cost in a deregulated environment, a robust optimization based MG management approach is presented in Ref. [30]. A new flexible robust optimization model of MGs can be found in Ref. [5], in which the uncertainty is confined by reference distributions and field measurements. Similarly, Xiang et al. [31] develop a scenario-based robust energy management approach to maximize the exchange cost and minimize social benefits cost for MGs with uncertain

L. Wang et al. / Energy 130 (2017) 1e14

renewable generation and load. In Ref. [32], a minimax regret nonlinear formulation aiming at minimizing the total operation cost is implemented. The existing researches of the MG robust optimization strategy mostly focus on economic objectives, but few of them associated to economic and environmental benefits. In order to minimize fuel cost and emission simultaneously, a robust hierarchical dynamic dispatch approach is proposed to address the uncertainty of wind power output [33]. However, the conservativeness regulation in the proposed robust formulation has not been considered. Based on the economic robustness measure, a multi-objective model between the worst-case cost problem and the expected cost problem is developed in Ref. [34]. Although the model robustness can be effectively adjusted, the impacts of economy and environment have not been analyzed independently for the MG planning. This paper emphasizes on the simultaneous optimization of multiple objectives and the adjustment of the robustness in the scheduling process by a robust multi-objective optimization approach. Compared with load curtailment for customers, load shifting in a finite time is introduced in this paper to express the willingness of industrial customers in DR programs. To the best of our knowledge, previous studies have not fully considered uncertainties handling while optimizing economic and environmental benefits in the MG supply and demand scheduling problem. The main contributions of this paper are listed as follows:
A MG supply and demand scheduling problem is studied not only to minimize the total cost and carbon emissions, but also to mitigate the disturbances of intermittent renewable energy and uncertain loads.
A robust multi-objective optimization based MG integrated scheduling approach is proposed to derive Pareto optimal scheduling schemes with robustness, which could provide system operators more options to coordinate economic and environmental benefits under uncertainty.
Uncertainties are captured by the robust sets with budgets of uncertainty, which allows the robustness of the optimal scheduling schemes to be controlled in a multi-objective framework. Based on the strong duality principle, the prime problem is transformed into a deterministic multi-objective optimization problem, which can be effectively solved by MOCE algorithm.

cooling/heating energy can be imported from the Ground Source Heat Pump (GSHP). Electricity loads are collectively fulfilled by the Photovoltaic generation (PV) and the CCHP. If there exists excess electricity, it is adopted to charge the Battery (BT) or sell to the Power Grid (PG), and vice versa. Relative to the randomness of solar energy, geothermal energy is a stable energy supply on a daily or hourly basis. Then, the PV output power, cooling/heating loads, and non-schedulable electrical loads are considered as uncertainties in the MG operation. In order to maximize comprehensive benefits of the MG, the main scheduling decisions include not only the amount of power to be produced on the energy supply side, but also the determination of when and how much the schedulable loads to be consumed on the energy demand side. Therefore, based on scheduling the energy supply-side and demand-side resources, the MG integrated scheduling problem is to alleviate the disturbances of uncertainties in each hour, as well as minimize operation costs and emissions in the 24-h period. Combined with the robust multi-objective approach, the ultimate goal of this problem is to determine the optimal scheduling schemes and ensure the robustness of schemes in the multi-objective framework. 3. Robust multi-objective optimization In this section, a robust multi-objective optimization approach is briefly introduced through an example. Developing a robust multi-objective theory has been started only in recent years [35]. Based on the classical concept of minimax robustness, researchers have proposed two kinds of robust multi-objective approaches. The first one is set-based minimax robustness proposed in Ref. [36], in which robust solution is a minimum set of the maximum case for the inverted multi-objective programming problem. However, this method is controversial in highly robustness and suffers from a heavy computational burden. The second one is point-based minimax robustness, which is obtained by introducing the worstcase scenario of uncertainty in a multi-objective optimization problem [37]. And similar methods have been implemented in cancer treatment [38] and internet routing [39]. Compared with the first method, the second one has stronger operability and applicability. Especially the degree of conservatism in models can be effectively controlled. In our work, the second approach is applied to schedule energy demand and supply to cover uncertainties in a cost-effective and low-emission way. We consider the following multi-objective programming problem (S1) subject to the data uncertainty in the constraints.

The paper is organized as follows. The problem statement of the MG demand and supply scheduling is given in Section 2. Section 3 introduces the robust multi-objective optimization approach. In Section 4, the robust multi-objective formulation of the MG integrated scheduling problem is described in detail, and the corresponding solving process is provided based on MOCE algorithm. Combined with the multi-level simulation experiments, the results and discussions are given in Section 5. Finally, some conclusions are drawn in Section 6.

v2V;

2. Problem statement

w2W:

In this paper, a hybrid configuration grid-connected MG driven by multiple energy resources, is used as a research platform to design the integrated scheduling scheme. The illustration of the MG is depicted in Fig. 1, where heating pipeline is not marked. On the demand side, electricity loads denote industrial electricity, which can be categorized in schedulable and non-schedulable loads. Here, schedulable loads are regarded as the generation units with negative output power to participate in the MG scheduling. On the supply side, the Combined Cooling Heating and Power (CCHP) runs in the thermal load tracking mode, and the remaining required

3

S1 : s:t:

min v;w

f ðv; wÞ

(1)

Av þ Q w  b;

(2) (3) (4)

In constraint (2), we assume that variables

v2V4ℝs

have

deterministic coefficients A ¼ ½a1 a2 …ajKj T 2ℝjKjs and variables w2W 4ℝjNj

have

uncertain

coefficients

Q ¼ ½q1 q2 …qjKj T

2ℝjKjjNj , where K represents a set of indices of the constraints in S1. Moreover, b ¼ ½b1 b2 …bjKj T 2ℝjKj is also affected by uncertainty. Then, there are simultaneous right-hand and left-hand sides uncertainties in all the constraints of S1. A vector-valued function f ðv; wÞ ¼ ½f1 ðv; wÞf2 ðv; wÞ…fjMj ðv; wÞ2ℝjMj is assumed to be deterministic. Based on a polyhedral uncertainty model proposed by

4

L. Wang et al. / Energy 130 (2017) 1e14

Fig. 1. A simplified illustration of microgrid with industrial customers.

Ref. [40], for each i2K, uncertainty set Ui can be described as follows:

~ij ¼ qij þ xq b q ; q 9 8 ij ij i > h > > > > b b ~ qij 2 qij  q ij ; qij þ q ij ; > > > > > > > > > = < b ~ b bhi ¼ bi þ xi b i ; i Ui ¼ ~2 b b > b b i ; bi þ b bi ; > > > i i > > > >     > > > > > > ; : P  q   b  xij  þ xi   Gi : j2N     j2N

S2 :

s:t:

min f ðv; wÞ

(6)

v;w

ai v þ

X

qij wj þ

j2N

(5)

8 > max > > > xq ;xb > > < > > > > > > :

P

 

 





  xqij bq ij wj 

 

þ

     P  q   b  xij  þ xi   Gi ;   j2N  

j2N

q

1  9

  xbi bb i w0 A; > > >

b



1  xij  1; 1  xi  1:

> > > = > > > > > > ;

 bi (7)

where j2N represents the index of uncertain variables in constraint i. qij and bi are the nominal value, b q ij and b b i stand for ~ ~ and b are the actual constant perturbation (which are positive), q ij

i

v2V;

(8)

w2W:

(9)

q

value, xij and xbi are the uncertainty coefficients of q and b for

i2K; j2N. Budgets of uncertainty Gi 2½0; n þ 1 represents the number of the worst-case realization of all the uncertainties in constraint i. In other words, it is unlikely that all the uncertainties will encounter the worst case simultaneously for a constraint. Thus, the level of conservatism in the model can be controlled by adjusting G. Because the worst-case scenario sorting in a multi-objective framework is not clear, the concept of robust single-objective optimization cannot be extended directly to robust multiobjective optimization problems. Then, the robust efficiency conception for S1 is introduced. The feasible solution ðv; wÞ of S1 is a robust efficient solution, if there does not exist another solution ðv0 3 ; w0 Þ such that fg ðv0 ; w0 Þ  fg ðv; wÞ for all g2M with at least one strict inequality [39]. In this way, the total order of robust solutions is defined in multi-objective functions. Moreover, U i is nonempty and bounded for every i2K. Also, uncertainty set U may be represented as U ¼ U 1  U 2  …  U jKj . Therefore, solving for the robust efficient solution of S1 is equivalent to solve its robust counterpart in the multi-objective framework, the corresponding proof is shown in Refs. [28,39]. Here, all possible realizations of uncertainties in S1 can be taken over by the supremum of U i . The form of robust counterpart for S1 can be written as follows:

where w0 ¼ 1, and the uncertainties are transferred to the lefthand side of Eq. (7). S2, including the minimum problem with ðv; wÞ and the maximum problem with ðxq ; xb ; wÞ, is a bi-level multi-objective optimization problem. However, the upper-level and lower-level problems have a strong coupling with each other and make the overall problem difficult to solve. In this paper, we reconstruct S2 by replacing the lower-level problem. Theorem 1 S2 has an equivalent multi-objective formulation as follows:

S3 : min f ðv; wÞ

(10)

v;w;y; z;b;a

s:t:

ai v þ

X

qij wj þ zi Gi þ

j2N

X

aij þ bi  bi ; ci2K

(11)

j2N

q ij yj ; ci2K; j2N zi þ aij  b

(12)

b i ; ci2K zi þ bi  b

(13)

L. Wang et al. / Energy 130 (2017) 1e14

yj  wj  yj ; cj2N

(14)

zi  0; yj  0; ci2K; j2N

(15)

5

constraints of xdt .

xdmin  xdt  xdmax ; ct2T; d2D

(24)

To complete a production order in a finite time, device d should

aij  0; bi  0; ci2K; j2N

(16)

start to work after ad 2T and finish before bd 2T. Here, ad and bd are set by system operators. Considering the schedulable loads

v2V; w2W:

(17)

information is known, then energy consumption xdt also subjects to the following constraints:

Proof 1 For a given w, the lower-level problem in Eq. (7) is a linear programming. Therefore, based on strong duality principle, its dual form is given by:

min

z;b;a;y

s:t:

X

b X d

t¼a

xdt ¼ Ed ; cd2D

(25)

d

aij þ zi Gi þ bi

(18) where Ed is the total energy consumption for device d. Constraints (24) and (25) determine the minimum/maximum completion time

j2N

q ij yj ; ci2K; j2N zi þ aij  b

(19)

zi þ bi  b b i ; ci2K

(20)

yj  wj  yj ; cj2N

(21)

d d d . To reduce the Tmin and Tmax in horizon T. Obviously, bd  ad  Tmax

device switching frequency, the on/off state ydt should satisfy the following constraints: b X d

zi  0; yj  0; ci2K; j2N

(22)

aij  0; bi  0; ci2K; j2N

(23)

d Tmin 

t¼ad

d ydt  Tmax ; cd2D

(26)

In addition, if t;½ad ; bd , then ydt ¼ 0. For interruptible loads, ydt

    where wj  ¼ yj , z, a, and b are dual variables. Considering Ui is non-

can freely choose 0 or 1 in ½ad ; bd  based on constraint (26). In contrast, uninterruptible load once starts operation, and then its devices need to continue until production process finish. This kind of loads is commonly seen in the process industry. At each time slot

empty and bounded, their objective values are coincident at opti      b  b b i w0 . Hence, the lowerq mality aij þ zi Gi þ bi ¼ xq j þ xi b ij ij wj

t, an auxiliary binary variable mdt is introduced to describe the running state of device d [14]. If device d starts operation at hour t,

level problem in S2 can be replaced with Eq (18)e(23). S3 is identified as an equivalent form for S2. ◊ Through a series of transformations, S3 is also an equivalent form of S1, in which the minimax problem is replaced by minimization one. As a deterministic multi-objective problem with a finite number of constraints, S3 could be solved by a general multiobjective algorithm. Likewise, the level of conservatism for compromise solutions in S3 can be controlled by adjusting G. 4. Robust multi-objective formulation and solution for the microgrid integrated scheduling problem 4.1. Robust multi-objective formulation 4.1.1. Energy demand side In realistic electricity market, majority of industrial loads are insensitive to the electricity price and incentive due to the urgency and timeliness of commodity contracts. Therefore, demand resources scheduling in a finite time is an efficient path to maximize benefits. The schedulability of loads depends on the strength of timeliness in commodity contracts, which correspond to the power consumption of devices. The schedulable loads consisting of interruptible and uninterruptible loads, are considered to be determinate consumptions in the low timeliness orders. Similarly, the non-schedulable loads represent power demand in the strong timeliness orders, the emergency and alteration orders. These loads are indeterminate consumptions in each hour. Let D denotes the set of devices belonging to the low timeliness orders in the horizon T. For each device d2D, the energy con-

then mdt b1, and vice versa. We have: d bd T þ1 min X

t¼ad

mdt ¼ 1; cd2D

(27)

d where the upper bound bd  Tmin þ 1 ensures that the order can be d þ 1, then mdt b0. For device finished by time b . If t;½ad ; b  Tmin d in the uninterruptible load, the relations between the running d

d

state mdt and on/off state ydt are shown as follows:

ydt  mdt ; ydtþ1  mdt ; …; ydtþT d

min

1

 mdt ; ct2T; d2D

(28)

Constraint (28) shows that the production order can be finished d . Similarly, if at least in the minimum completion time Tmin d  1  bd , then the order can be finished at any time in t þ Tmax d ; T d . ½Tmin max Next, considering stochastic characteristics in cooling/heating loads and non-schedulable electrical loads, the robust set is used to capture uncertainties, which are represented by the following constraints:

i h el el el el el b el el b el ~el b ~ p t ¼ pt þ x p t ; pt 2 pt  p t ; pt þ p t ; ct2T

(29)

i h hl hl hl hl hl ~hl b hl hl b hl b ~ p t ¼ pt þ x p t ; pt 2 pt  p t ; pt þ p t ; ct2T

(30)

sumption and on/off state in time interval t2T can be defined as xdt

i h cl cl cl cl cl ~cl b cl cl b cl b ~ p t ¼ pt þ x p t ; pt 2 pt  p t ; pt þ p t ; ct2T

(31)

and ydt 2f0; 1g, respectively. Similar to the power limitations for generating units, there are the minimum/maximum power

hl where pel t is non-schedulable electrical loads in time interval t, pt

6

L. Wang et al. / Energy 130 (2017) 1e14

and pcl t are heating and cooling loads in industrial production, respectively. Here, the meanings of some specific symbols can be el

hl

cl

found in Eq. (5). The uncertainty coefficient x , x , and x values between 1 and 1. To avoid artificial load peak in each time slot, we have:

~el p t þ

X

xdt  Emax ; ct2T

take

  1  ch dis E1 ; ct2T SOCt ¼ SOCt1 þ pch hdis t h  pt

(42)

where SOC is the state of charge of the BT, E is the battery capacity,

(32)

d2D

   el  x   G1

be expressed as follows:

(33)

where Emax is the maximum value of the load peak. The role of G1 2½0; 1 is to adjust the level of conservatism for constraint (32), ~el which means the worst case realization of p t may not appear in this constraint. Note that the cooling/heating loads shifting caused by the electrical loads shifting is omitted because of the trivial demand. 4.1.2. Energy supply side In the CCHP, electricity and cool/heat energy can be generated simultaneously. Firstly, a Micro Turbine (MT) generates power pmt t and releases the waste heat by burning natural gas ftmt . Then, a Heat Recovery (HR) device recycles the waste heat energy, and supplies to an Absorption Chiller (AC) or thermal loads [41]. In this way, heat energy might be transformed into cool energy. These statements can be mathematically described as:

hch and hdis represent the charging and discharging efficiency, dis respectively. pch t and pt are the charging and discharging power at time t, respectively. Noted that the charging and discharging process cannot appear at the same time. If the BT runs in the process of ch bt dis charging, then pbt t ¼ pt , otherwise pt ¼ pt . The corresponding power and SOC constraints is expressed as:

bt bt pbt min  pt  pmax ; ct2T

(43)

SOCmin  SOCt  SOCmax ; ct2T

(44)

SOC0 ¼ SOCjTj ;

(45)

To ensure the safety of the PG, the power restriction can be written as follows: pg

pg

pg

pmin  pt  pmax ; ct2T

(46)

Moreover, the power output of the PV can be represented as:

 pv pv pv pv  pv b pv pv b pv ~pv b ~ p t ¼ pt þ x p t ; pt 2 pt  p t ; pt þ p t ; ct2T

(47)

mt f e pmt t ¼ ft h f ; ct2T

(34)

where xpv 2½1; 1.

mt f e s hr phr t ¼ ft h ð1  f  f Þf ; ct2T

(35)

4.1.3. Energy supply-demand balance According to [42], balance equality constraints can be described

ac hr pac t ¼ pt COP ; ct2T

(36)

where hf is the heat value of natural gas, fhr is the recovery efficiency of the HR, fe and fs are the generation efficiency and loss hr factor of the MT, respectively. pac t and pt represent the cool and heat energy output of the CCHP at time t, respectively. COPac is the coefficient of performance for the AC. Moreover, the minimum/ maximum power constraints and ramping up/down constraints in the CCHP are expressed by:

ac ac pac min  pt  pmax ; ct2T

(37)

as inequalities, where pes and pchs are introduced to represent the supply shortage/excess in electricity and cooling/heating. Then, energy balance and the corresponding conservatism constraints can be written as follows: pg mt bt es ~el ~pv p t þ pt þ pt þ pt þ pt  pt þ

X

ehp

xdt þ pt

; ct2T

(48)

d2D

     el   pv   x  þ x   G2 pg bt mt ~ el ~pv p t þ pt þ pmax þ pmax  pt þ

(49) X

xdt þ r e ; ct2T

(50)

d2D mt mt pmt min  pt  pmax ; ct2T

(38)

U mt ED  pmt t  pt1  E ; ct2T

(39)

Unlike the CCHP driven by fossil energy, the GSHP absorbs the low quality geothermal energy to convert into high-grade energy by consuming a small amount of electricity. The power output of the GSHP is expressed as: gshp

pt

ehp

¼ pt

COPgshp ; ct2T

(40)

ehp

where pt is the electrical consumption of the GSHP, COPgshp is the coefficient of performance for the GSHP. The power constraint of the GSHP is expressed as:

pgshp min



pgshp t



pgshp max ; ct2T

(41)

As an electrical energy transfer station, the storage level of the BT closely related to the charging/discharging state and power, can

     el   pv   x  þ x   G3 gshp

pt

chs ~hl þ phr p t ; ct2T t þ pt

(51) (52)

   hl   x   G4

(53)

chs ~ cl þ pac p pgshp t ; ct2T t þ pt t

(54)

   cl   x   G5

(55)

where constraint (50) represents the reserve constraint in payload, r e is the maximum electrical load fluctuation, constraint (48) represents the electrical power balance, constraints (52) and (54) represent heating and cooling balance respectively. Moreover, G2 , G3 , G4 , and G5 restrict the level of conservatism in the above

L. Wang et al. / Energy 130 (2017) 1e14

constraints. Here, G2 ¼ G3 .



4.1.4. Multi-objective function As two main evaluation indicators in the MG operation, in this paper, the minimum total cost and carbon emissions are chosen to study the demand and supply scheduling problem. The cost objective F1 , including fuel cost, maintenance cost, purchasing and selling electricity cost, battery depreciation cost, and penalty cost, can be expressed as follows:

F1 ¼

8 > > > jTj > < X

cfuel ftmt þ

X

dg

cdg pt

9 > > > > =

dg2A  buy pg pg sell pg þ zpg c t pt t ct pt þ 1  zt      bt bt es  es  chs  chs  þs pt þ s pt  þ s pt 

> :

t¼1 > > >

MG,

> > > > ;

represents the maintenance cost of DG units, buy ct

pdg t

denotes

csell t

and are the purthe power output of DG units at time t, chasing and selling electricity prices, respectively. Note that selling and purchasing electricity within a period is an impermissible action. If

pg pt

 0, then

pg zt

¼ 1, and vice versa.

sbt

jTj  X

fuel mt εpg ppg ft t þε



4.2. Equivalent form of robust multi-objective formulation As mentioned before, uncertainties exist in the constraints of the robust multi-objective formulation. Also, all the uncertainty sets are nonempty and bounded. The proposed formulation is equivalent to its robust counterpart, which is the worst case of the MG integrated scheduling problem. The same as S2, the robust counterpart materializes in a bi-level multi-objective problem apparently hard to solve. According to Theorem 1 in Section 3, it is equivalent to the following deterministic multi-objective formulation:

Fr ; ct2T; dg2A; d2D

(58)

z;b

s:t:

pel t

þ

X

xdt

þ z1 G1 þ b1  Emax ; ct2T

(59)

ppv t 

pmt t

þ X

d2D

þ

ppg t

þ

ehp

xdt þ pt

pbt t

þ

þ pel t ;

pes t

(62)

gshp

chs þ pac þ z5 G5 þ b7  pcl t þ pt t ; ct2T

(63)

pt

el z1 þ b1  b p t ; ct2T

(64)

b pv b el z2 þ b2  p t ; z2 þ b3  p t ; ct2T

(65)

b pv b el z3 þ b4  p t ; z3 þ b5  p t ; ct2T

(66)

hl p t ; ct2T z4 þ b6  b

(67)

b cl z5 þ b7  p t ; ct2T

(68)

zi  0; bj  0; ci2I; j2J

(69)

and the following constraints (24)e(31) and (34)e(47), ydt 2½0; 1 for d2D. Here, I is set of indices of constraints affected by uncertainties, J is set of indices of b. z and b are dual variables. In Eq. (58), r represents the number of the objective function. If r ¼ 1, then the integrated scheduling problem reduces to a robust single objective optimization problem. Moreover, the size of uncertainty set in the deterministic multi-objective formulation can be controlled through adjusting Gi .

þ z2 G2 þ b2 þ b3

In order to simultaneously optimize all the objectives, in this paper, we employ a multi-objective heuristic algorithm to solve the problem. Cross Entropy (CE) algorithm has the goal directness and high degree of accuracy than other heuristic algorithms, then it is used to solve the proposed formulation. It considers the optimization problem as an estimation problem, in which parameters of a family of probability density functions are estimated based on importance sampling techniques [43]. Combined with the Pareto ranking principles proposed by Ref. [44], this algorithm called Multi-Objective Cross Entropy (MOCE) can be applied in multiobjective problems [45]. For the MG integrated scheduling problem, the algorithm is described below. Step 1: Loading input data. Update load profiles, which include the predicted information in non-schedulable electrical loads and cooling/heating loads, as well as real information in schedulable electrical loads. Update the predicted output power of the PV. Define parameters for the MG structure and operating condition. Step 2: Initialization parameters. Set the distribution parameters for continuous variables vXL i and discrete variables vYL , and initialize iterations L)0. Generate the continuous variables sample L ; X L ; …; X L ÞT for i2C and discrete variables sample X Li ¼ ðXi1 i2 iG

d2D



chs þ phr þ z4 G4 þ b6  phl t þ pt t ; ct2T

4.3. Solution technique

where εpg and εfuel are the carbon dioxide emission conversion factors for electricity and gas, respectively.

min

gshp

pt

(57)

t¼1

pg d d pdg t ;pt ;xt ;yt ;

(61)

d2D

represents the

depreciation cost of BT. ses and schs are the penalty cost of the supply shortage/excess in electricity and cooling/heating, respectively. Here, the penalty cost for production orders violation is included in the supply penalty cost. The load adjustment cost is trivial for industrial consumers, and it is not considered in Eq. (56). In addition, the carbon emissions objective F2 contains coal and natural gas combustion emissions, since the coal-fired power generation is the main source of grid in China. This function is expressed as:

F2 ¼



(56)

where cfuel is the price of natural gas, A is the set of DG units in the cdg

pg bt mt ppv t þ pt þ pmax þ pmax þ z3 G3 þ b4 þ b5 X xdt þ r e þ pel  t ;

7

Y L ¼ ðY1L ; Y2L ; …; YGL ÞT according to the constraints (24)e(28),

 (60)

(34)e(46) and (59)e(69). Here, XiL represents the auxiliary variables, the output power of the DG units and demand-side resources. C is the set of indices of continuous variables. G is the size of the sample. Step 3: Ranking. Calculate the fitness values based on the

8

L. Wang et al. / Energy 130 (2017) 1e14

objective functions (56) and (57). Implement non-domination ranking and crowding distance ranking for the overall samples. Step 4: Importance sampling. Set the quantile r of the sample, L

then the quantile for the fitness values is q ¼ Fðr,GÞ . Select the non-dominated solutions and add them to the elite set X Lie and Y Le . Step 5: Updating parameters. Combined with a Markov process, the distribution parameters for the continuous variables and discrete variables are updated by solving the program

. Qr$GS vXL i ¼ Sj¼1 XijL Qr$GS; cXijL 2X Lie ; i2C

(70)

. Qr$GS vYL ¼ Sj¼1 YjL Qr$GS; cYjL 2Y Le

(71)

Step 6: Smoothing parameters. Set parameter a and execute the smoothing functions, as follows: i i vXLþ1 ¼ avXLþ1 þ ð1  aÞvXL i ; ci2C

(72)

vYLþ1 ¼ avYLþ1 þ ð1  aÞvYL

(73)

i Step 7: Termination. If vXLþ1 and vYLþ1 converge to the expected

     and pchs  approach 0, then the robust Pareto value, as well as pes t t optimal solution ðXi ; Y  Þ is obtained, otherwise L)L þ 1 and goes to Step 2. According to the characteristics of the proposed formulation, the solution flowchart for the MG integrated scheduling problem is shown in Fig. 2. As shown in Fig. 2, the integrated scheduling of energy supply and demand in the MG under uncertainty can be constructed as the deterministic multi-objective formulation by implementing the robust multi-objective optimization approach. Here, the characteristics of user's consumption and MG may be represented as the linear constraints with discrete variables and continuous variables. The underlying uncertainty is replaced with the worst-case realization of the uncertainty, which is easily obtained by the statistical and predictive technology. Moreover, the developed multiobjective formulation can be solved by a general multi-objective algorithm. Therefore, in this paper, the proposed scheduling approach has universal significance for MGs in other countries and districts. 5. Results and discussion A detailed comparative study is performed to evaluate the

Fig. 2. Solution flowchart of the MG demand and supply scheduling problem.

L. Wang et al. / Energy 130 (2017) 1e14

9

Fig. 3. Operating condition (a) Daily PV output power (b) Daily load demand.

Table 1 Input data. Technologies

Value

Unit

Technologies

Value

CCHP

pac max ¼ 282

kW

GSHP

COPgshp ¼ 4:09

pac min ¼ 20

kW

PG

pmt max ¼ 195

kW

pmax ¼ 400 ¼ 200 ppg min

pmt min ¼ 20

kW

ED ¼ 72 fe ¼ 0:3

kW h

pg

kW kW kg=m3 kW

εfuel ¼ 1:96 BT

pbt max ¼ 50

kW

pbt min ¼ 100 E ¼ 250 SOCmax ¼ 1

fs ¼ 0:23 fhr ¼ 0:9 hf ¼ 9:7 εpg ¼ 0:872

Unit

SOCmin ¼ 0:2

kW h=m3 kg=kW h

hch ¼ 0:95 hdis ¼ 0:98

COPac ¼ 1:1

performance of the robust multi-objective optimization based integrated scheduling approach. Then, this section includes four parts: (1) operating condition introduction; (2) verification in the problem level; (3) verification in the model level; (4) verification in the algorithm level. 5.1. Operating condition introduction The proposed model is tested on the MG commercial project in a small industrial park, which includes some schedulable production lines and loads [46]. The technical aspects of the DGs installed in a building are taken from Ref. [32]. A representative day in summer is selected as the simulation condition, which is divided into 24 h periods. The nominal values of the PV output power, cooling loads, and electrical loads for each period are shown in Fig. 3, which are estimated by the statistical and predictive technology. Since the heat demand is trivial in summer, heating loads are not considered in this paper. Parameters associated with the MG configuration are shown in Table 1. In addition, market information is adopted as an important part of input data. The price of natural gas is 4.14 CNY/m3 and the selling price of electricity is 1.12 CNY/kW h. Time-of use price is used in electricity purchased, which is shown in Table 2. The depreciation cost of the BT is 0.1 CNY/kW. The USD-CNY exchange rate is 6.8706 CNY. In order to ensure the supply shortage/excess converge to zero, the corresponding penalty costs are set as a large value M. Normally, the production orders should be completed in

kW

the daytime from ad ¼ 7 a:m: to bd ¼ 6 p:m: for d2D.

5.2. Verification in the problem level In the problem level, the simulation results are analyzed in three different case studies. In case 1, the uncertainties are ignored in the MG integrated scheduling problem, which is optimized by a deterministic multi-objective scheduling approach. In case 2, the MG integrated scheduling problem is optimized by a singleobjective robust scheduling approach to seek the optimal costs or emissions. Without demand-side resources participation, the energy generation scheduling approach is examined in case 3. Moreover, the comparisons between the proposed scheduling approach and the above three approaches are conducted. We define the degree of uncertainty in the MG operation is supreme, as Gi ¼ 1Yi . Yi represents the number of uncertainties in constraint i, for i2I. Table 2 Purchase electricity price (1USD ¼ 6.8706CNY). Time

Electricity price period

Price

Unit

½1; 7Þ; ½23; 24Þ ½7; 8Þ; ½11; 18Þ ½8; 10Þ; ½18; 19Þ; ½21; 23Þ ½10; 11Þ; ½19; 21Þ

Lower price period Average price period Higher price period Peak price period

0.307 0.702 1.053 1.218

CNY/kW CNY/kW CNY/kW CNY/kW

h h h h

10

L. Wang et al. / Energy 130 (2017) 1e14

Fig. 4. (a) Pareto optimal solution in the MG multi-objective optimization scheduling with and without uncertainty (b) Scheduled demand-side resources in different optimizations (c) Scheduled supply-side resources with uncertainty in (4573.7, 2463.3) (d) Scheduled supply-side resources without uncertainty in (2711.9, 1603.5).

5.2.1. Case 1: multi-objective optimization for the MG integrated scheduling without uncertainty In this part, the results of the MG integrated scheduling are analyzed with and without considering uncertainty. Without considering uncertainty, case 1 is a deterministic multi-objective optimization problem, which occurs in Gi ¼ 0. As shown in Fig. 4(a), its Pareto optimal front is significantly less than that of the case with uncertainty. This is because the supply-side and demandside resources need not be scheduled to attenuate the disturbances of uncertainties. With fewer energy supplies and more loads shifting in the scheduling process, the operation costs and emissions decrease. In other words, in case 1, system operators only need to seek multi-objective benefits for the MG scheduling, without having to consider the uncertainty. On the demand side, Fig. 4(b) shows the load consumption with optimization is shifted from peak price period [10,11) to average price period [7,8) and [11,18), relative to the schedulable load curve without optimization. With considering uncertainty, there is still a small amount of load demands in higher price period [8,10) and peak price period [10,11) to address uncertainty. This demonstrates that multi-objective and uncertainty in the MG scheduling can be optimized simultaneously. In comparison, during 8:00e12:00, case 1 only has the load consumption at 10 a.m. Thus, the total completion time of production

orders in case 1 is less than that in the case with uncertainty. On the supply side, we can see that energy supplies in Fig. 4(c) are higher than that in Fig. 4(d). More energy needs to be provided by the CCHP, the GSHP and the PG to cover uncertainties. Moreover, each SOC curve contains charging at lower price period and discharging at higher price period, namely the general trends are consistent. Since the disturbances of the PV output power and load may appear during 6:00e19:00, there is a lower level of SOC during 11:00e18:00 in Fig. 4(c). This means that if the uncertainties are considered, then the scheduling scheme for case 1 will be altered significantly. These results show that the proposed robust multiobjective optimization scheduling approach not only obtains multi-objective benefits, but also handles uncertainty by allocating the supply-side and demand-side resources properly. 5.2.2. Case 2: operation costs/emissions optimization for the MG integrated scheduling In this part, the results of the MG integrated scheduling problem are compared in three different cases including costs optimization, emissions optimization, as well as simultaneous optimization of costs and emissions. As shown in Fig. 5(a), Pareto optimal front is a trade-off between the optimal costs and the optimal emissions. Note that these two optimal solutions are not the upper and lower

L. Wang et al. / Energy 130 (2017) 1e14

11

Fig. 5. (a) Comparison of optimal solution in different optimizations (b) Scheduled demand-side resources in different optimizations (c) Scheduled supply-side resources in (4521.5, 2613.2) in costs optimization (d) Scheduled supply-side resources in (4682.8, 2363) in emissions optimization.

bounds for the Pareto optimal front. The main reason is that a part of compromise solutions are removed by importance sampling techniques in MOCE. On the demand side, Fig. 5(b) shows the difference of load shifting with different optimization approaches. In costs optimization, all the loads are scheduled in average price period [7,8) and [11,18) to obtain economic benefit. In contrast, the size of load shifting in emissions optimization is small during 7:00e18:00, and there are still load consumptions in peak price period [10,11). Likewise, the distribution of load consumptions and the total completion time in multi-objective optimization are considered as a compromise between the previous two results. On the supply side, a large amount of electricity from the PG and cooling energy from the GSHP are purchased to reduce the cost caused by the expensive CCHP unit in Fig. 5(c). The BT is fully utilized by increasing the depth of the charge and discharge in the peak-valley price interval. However, when the goal is the optimal emissions, utilization of the PG with the higher emissions is reduced and the BT is not scheduled to provide energy during 14:00e19:00. Also, it charges at higher price period [21, 23) and discharges at lower price period [23, 24). Here, the CCHP unit with the lower emissions becomes a main force on the supply side. Compared with Fig. 5(c) and Fig. 5(d), Fig. 4(c) is a compromise scheme, in which all the DG units are not overly used. Although the optimal costs or emissions can be achieved in single objective

optimization cases, other benefits may be ignored. As a consequence, through implementing the proposed scheduling approach, a variety of compromised operation schemes are provided to system operators to coordinate the conflicting economy and environment objectives in the MG integrated scheduling problem. 5.2.3. Case 3: energy generation scheduling without demand-side resources response In this part, the results of the MG scheduling problem are analyzed with and without the demand-side resources response. In Fig. 6, we can see that the operation costs and emissions can be reduced by 5% and 15% when the demand-side resources are involved in the MG scheduling. The main reason is that the effects of demand scheduling in handling uncertainty and multi-objective optimization are abandoned. Here, the interactive bilateral mechanism is replaced by a unilateral optimization mechanism, i.e., energy generation scheduling in the MG. Therefore, the output powers from the DG units in Fig. 6(b) are significantly higher than that in Fig. 4(c). Although the trends of SOC are consistent, there is a lower level of SOC during 11:00e21:00 in Fig. 6(b). Moreover, the effect of responsive loads is limited in this paper. This is because demand scheduling only contains load shifting in a finite time and there is no change in the total load consumption. Also, the lower price periods are not included in a defined period of time.

12

L. Wang et al. / Energy 130 (2017) 1e14

Fig. 6. (a) Pareto optimal solution in the MG scheduling with and without the demand response (b) Scheduled supply-side resources in (4792.1, 2823.4) without the demand response.

Fig. 7. (a) Pareto optimal solution in different Gi (b) Scheduled demand-side resources in different Gi (c) Scheduled supply-side resources in (3223.5, 1829.8) (d) Scheduled supplyside resources in (3862.2, 2124.9).

L. Wang et al. / Energy 130 (2017) 1e14

Fig. 8. Pareto optimal solution in MOCE algorithm and NSGA-II algorithm.

Therefore, load scheduling decision is more advantageous to decrease emissions relative to decrease costs in this paper. 5.3. Verification in the model level As a feature in the proposed formulation, the robustness of the optimal scheduling schemes can be controlled in the multiobjective framework by adjusting Gi , i2I. In practice, the worst case for the uncertainty is a small probability event. Hence, budget of uncertainty Gi is not necessarily integer, might take any value in ½0; jYi j. In this section, three cases including 0:2Yi , 0:6Yi , and 1Yi , are conducted to verify this feature. With an increase in Gi , uncertainty is closer to the worst case, i.e. available PV output power even lower and a load demand level even higher. As shown in Fig. 7(a), the costs and emissions increase significantly to cover uncertainties, which means that system operators have to schedule more energy and loads to immunize against a higher degree of uncertainties. On the demand side, Fig. 7(b) shows the total completion time in different Gi are 8, 11, and 12, respectively. This is because loads are shifted to compensate the difference between energy supply and the growing uncertainty. However, the load consumption trend is not clear in the time domain under the dual influences of multi-objective optimization and uncertainties handling. On the supply side, as shown in Fig. 7(c), Fig. 7(d), and Fig. 4(c), the output powers from the DG units increase with rising Gi . Therefore, the energy generation and loads scheduling are altered significantly by adjusting Gi . In other words, the proposed scheduling approach gives system operators capability of controlling the robustness of operation schemes in the multi-objective framework based on real scenarios in the MG. 5.4. Verification in the algorithm level In this section, the different results of the MG integrated scheduling problem are solved by MOCE algorithm and NSGA-II algorithm. We define Gi ¼ 1Yi . For MOCE algorithm, the population size is 150, the number of iteration is 300, r is 0.01 and a is 0.75.

13

For NSGA-II algorithm, the population size is 150, the number of iteration is 400, the crossover rate is 0.9 and the mutation rate is 0.2. The corresponding comparison results are shown in Fig. 8 and Table 3. As shown in Fig. 8, although Pareto optimal solutions under the two algorithms are distributed uniformly, the distribution area in MOCE algorithm is significantly less than that in NSGA-II algorithm. This is because only part of the elite solution set is retained in each iteration to generate a new sample, i.e., a part of compromise solution are removed by importance sampling techniques in MOCE algorithm. The same meaning can be found in the first and second row in Table 3. We can see that Pareto optimal solution of MOCE algorithm is less than that of NSGA-II algorithm. Moreover, there is a significantly difference in the computational times, relative to the number of Pareto optimal solution. The main reason is that the scheduling problem in MOCE algorithm is considered as an estimation problem with the goal directness, which enhances the convergence rate. Thus, MOCE algorithm is more advantageous than NSGA-II algorithm for solving the MG integrated scheduling problem. 6. Conclusions In this paper, a robust multi-objective optimization based integrated scheduling approach is proposed and investigated to solve the MG supply and demand scheduling problem under uncertainty. Firstly, a minimax multi-objective optimization formulation, including load shifting and energy generation scheduling, is developed to simultaneously minimize operation costs and emissions under the worst-case realization of intermittent renewable energy and uncertain loads. Secondly, by implementing the strong duality based model transformation method, the proposed formulation can be transformed into a deterministic multiobjective optimization model, which is effectively solved by MOCE algorithm. Moreover, the proposed formulation allows adjusting the robustness of the optimal scheduling schemes in the multi-objective framework, in order to react to variations from uncertainty. Finally, the simulation results indicate that the proposed scheduling approach can achieve the optimal operation costs and emissions as well as mitigate the disturbances of renewable energy and loads compared with other scheduling approaches. The participation of loads scheduling can not only relieve the stress of supply side in handling uncertainties, but also significantly reduce the total cost (about 5%) and carbon emissions (about 15%) in the MG operation. Although the proposed approach is the first attempt for scheduling energy supply and demand of MGs under uncertainty, the results obtained reveal that this scheduling approach could contribute to more efficient market operation for MGs. By using the proposed energy demand model, the consumption patterns of customers could be changed to respond to uncertainties. The adjustment of conservativeness in the proposed formulation could provide useful insights, which help system operators balance robustness and comprehensive benefits of the MG operation. With the current emphasis on environmental issues, emissions requirements are flexible in different economic development periods. This approach could provide a variety of compromised operation

Table 3 Comparison of results (1USD ¼ 6.8706CNY). Algorithm

Cost (CNY)

Emission (kg)

No. of iterations

Solution time(s)

MOCE NSGA-II

ð4540  4640Þ ð4527  4673Þ

ð2400  2550Þ ð2389  2600Þ

65 73

228.1 336.5

14

L. Wang et al. / Energy 130 (2017) 1e14

schemes, which are adaptable to different concerns about economy and environment in the natural world. In our future work, the efficiency of the scheduling approach will be further improved to facilitate large-scale integration of DR and renewable energy in regional integrated energy systems.

[21] [22]

[23]

Acknowledgments The authors would like to thank the anonymous reviewers for the thoughtful and constructive comments and suggestions. This work is supported by Natural Science Foundation of Shandong Provincial (Grant no. ZR2014FM036).

[24]

[25]

[26]

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