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A micro-market module design for university demand-side management using self-crossover genetic algorithms
Applied Energy 252 (2019) 113456
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
A micro-market module design for university demand-side management using self-crossover genetic algorithms ⁎
T
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Fangyuan Xua, Wanli Wua, Fei Zhaoa, Ya Zhoub,c, , Yongjian Wangc, , Runji Wua, Tao Zhangd, Yongchen Wena, Yiliang Fana, Shengli Jiange a
School of Automation, Guangdong University of Technology, Guangzhou 510006, China Institute Environmental and Ecological Engineering, Guangdong University of Technology, Guangzhou 510006, China c School of Management, Guangdong University of Technology, Guangzhou 510520, China d Institute for Innovation and Entrepreneurship, Loughborough University London, London E15 2GZ, UK e MUFG Securities EMEA plc, London EC2Y 9AJ, UK b
H I GH L IG H T S
G R A P H I C A L A B S T R A C T
scheme is proposed • Aformicro-market demand side management in university campus.
model of university micro• Detail market is developed for scheme supports.
new optimization algorithm, the • Aself-crossover genetic algorithm is proposed.
numerical study shows that the • Aproposed scheme can reduce system costs.
A R T I C LE I N FO
A B S T R A C T
Keywords: Micro-market Demand side management Smart grid Power market Microgrid
Demand Side Management (DSM) is an effective measure in load configuration for microgrid power cost control and power system operation. In most extant studies, DSM in microgrid only consider directly controllable devices for load modification. The load triggered by non-controllable devices with sub-decision-makers are regarded as unchangeable load and generally not considered in DSM. A critical reason for unchangeable load is that the sub-decision makers in these microgrids may not sense and react to external dynamic electricity prices. However, these non-changeable loads in some microgrids contribute significantly to the overall power consumption of the system. Thus, a new demand side management scheme is required for these special microgrids so that the load triggered by these sub-decision makers can also response to external dynamic electricity prices. Based on a case study of a university campus, this study proposes a micro-market module to facilitate the participative behaviours of sub-decision makers in a microgrid with extra financial incentives. A university microgrid DSM optimization model is formulated to optimize the total system cost, the control of the microgrid controllable load, the behaviour of sub-decision makers and the micro-market operations are modelled. A new optimization algorithm, the self-crossover genetic algorithm, is proposed. Empirical data from a university is used to conduct a numerical study to test the proposed module and algorithm. The results show that DSM with the micro-market module can reduce the overall electricity cost of the system, and the proposed self-crossover genetic algorithm out-performs traditional optimization algorithms for the proposed model.
⁎
Corresponding authors. E-mail addresses: [email protected] (Y. Zhou), [email protected] (Y. Wang).
https://doi.org/10.1016/j.apenergy.2019.113456 Received 25 January 2019; Received in revised form 27 May 2019; Accepted 7 June 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.
Applied Energy 252 (2019) 113456
F. Xu, et al.
Nomenclature
PNint,s Pexr,s s R ar PBB bp_initt,s
total number of consumers of type s at time t power of the rth device in the office or lab 0 means student, 1 means staff device number 0 means device close, 1 means device open preferred behavioural boundary traditional office arrival probability by consumer type s at time t bpt,s office arrival probability by consumer type s at time t bp_maxt,s, proportion of consumers who believe that “working at time t” is acceptable. Nums,z consumer number for the zth behaviour unit for consumer type s. f(PEOttijk,t,s,z) student number at time t from unit z for a certain class timetable Su promised subsidy value Suss,z minimum subsidy requirement given by unit z SRt,s office arrival rate at time t and consumer type s gt,s,z(Su) consumer number of the zth behaviour unit for consumer type s at time t under subsidy Su L*t,s boundary value of the PBB at time t for consumer type s Ltrat,s traditional load at time t for consumer type s β ratio of cost reduction to subsidy generation Su−1 generated subsidy Billnew school electric bill under micro-market Billtra school electric traditional bill g't,s,z(Su) consumer number of the zth behaviour unit for consumer type s obtained subsidy k2t(Lcont,k) transfers the time index from k (the time slot index) to t Lnoncont,t non-controllable load at the time t Sub_pay extra payment is generated for subsidies in the micromarket Su* solution of Eqs. (12) and (13) SR*t,s office arrival rate at time t and consumer type s under subsidy Su*
fluctuation degree of class hours in different weeks of each course B fluctuation degree of the total class hours In each week WD number matrix of classes for each week and course C course number W week number Ivx a column vector filled with ones with a dimension of x cut (WD, x) removes the xth column of WD and outputs the remainder matrix wdc,w the element at the cth row and wth column of WD esc the number of classes for the cth course in the education schedule wdmax maximum number of weekly classes for each independent course roommax maximum available space ttijk course number occurs in classroom i, on day j and at the kth time slot. Lcont,k controllable load at the kth time slot H number of work days in a week I classroom number J day number K time slot number pow(i,j,k) power consumed in classroom i, on day j and at the kth time slot. rec(ttijk, c) determine if c and course number occurs in classroom i, on day j and at the kth time slot are equal. MC maximum number of classes from one course SSku satisfaction score for course u at the kth time slot Smin minimum average satisfaction Lt,s power used at time t for consumer type s Prit dynamic electricity price bpt,s office arrival probability at time t for consumer type s Pins power used by each consumer in the office or lab A
1. Introduction
performed on fully controllable devices. Another example is given by Yau and Rismanchi [25]. Load flexibility is mostly provided by shifting or shedding small non-critical loads. A thermal energy storage system for building cooling applications is proposed. This system can balance the energy demand between the peak (daytimes) and off-peak hours (nights). All critical devices in this system are fully controllable. In Chen et al. [26], authors have summarized several measures for improving the flexibility of commercial/residential buildings and developed a systematic methodological framework to evaluate energy demand flexibility. All smart appliances in buildings with home energy management systems, e.g. dishwashers, washing machines, tumble dryers and electric vehicles, can be fully controlled. Such loads can be managed straightforwardly at the user level [27,28]. Therefore, an underlying assumption of these studies is that the load under DSM is fully controllable. The reason for this assumption is that microgrid owners usually have usage rights for power devices inside a microgrid. In other words, the microgrid owner is the only decision maker that controls these devices. Practically, though, some microgrid consumers do not obtain full usage rights for their main power-consuming devices. This situation is true in most universities. These institutions face dynamic electricity prices and pay the bill while the usage rights for devices are distributed to staff and students, forming a structure comprising multiple decision makers. Price fluctuation is not transmitted to sub-decision makers like staff and students so that most of the power consumptions do not respond to price variation. Energy efficiency improvements in universities from the behavioural optimization perspective is complex. Thus, universities’ electricity cost reduction and power market participation are
1.1. Background Initiative load is important to power system development. It increases the flexibility of supply-demand balance control [1,2], enhances the power system flexibility [3], regulates the grid frequency [4], facilitates the flexibility improvement in the joint dispatch problem of energy and reserve [5], therefore improving grid reliability and economic performance [6,7]. Some examples of initiative load include demand response (DR) [8,9], load management [10,11], demand-side management (DSM) [12,13], storage control [14,15], virtual power plants [16], and di-directional load flow with distributed generation [17,18]. Multiple studies have shown that initiative load yields improvements in grid performance [19,20]. In most extant studies on initiative load inside microgrids, microgrid behaviour under DSM is assumed to be fully controllable by grid owners. For example, Ramin et al. [21] and Aghajani et al. [22] indicate that flexible consumers can be divided into two types: (1) single energy-intensive industrial units that are qualified to individually participate in energy or capacity markets and (2) small distributed loads such as residential or small commercial consumers. In both types, device behaviour under DSM is fully controllable. The controllable behaviour can be found not only on consuming equipment, but also on the new resources such as distributed generators, solar panels, and storage units [23,24]. Ramin et al. [21] proposes a scheduling model for a multi-stage and multi-line process for optimal operation in multiple power markets, and all operations in a metal casting foundry are 2
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The rest of this paper is organized as follows. Section 2 describes the micro-market module in detail and discusses the differences between the DSM with micro-market and the traditional DSM structure. Section 3 explains the model’s treatment of controllable and non-controllable loads in the case of a university. Section 4 introduces the SCGA. Finally, Section 5 applies real-world empirical data derived from a typical university in a numerical study.
difficult. For example, universities can select only controllable devices such as central air-conditioning systems for DSM. Many single airconditioning units are controlled by staff and students, thus contributing less to the university’s overall electricity cost reduction. These types of consumers are referred to as load-not-completely-controllable consumers (LNCCCs). 1.2. Original contribution
2. DSM in universities with micro-market
Given the issue above, this paper initiates a new DSM scheme referred to as a micro-market for university campus. This scheme constructs a small market module inside a university. It take initiatives on the energy load for each sub-decision makers using financial incentives. The module is then applied to a case of a university DSM. Using this module, university decision makers can create a comprehensive DSM strategy that manages both controllable and non-controllable loads. The specific contributions of this paper are listed below.
There are two main functions of a University: education and research, both of which use electricity. Thus, the power load of a university is mainly generated by the two sections. Education wise, a closed-loop is generated in Fig. 1. The main decision maker adjusts the lecturing timetable to change the time of classroom power usage (Central Air-Conditioning, Projectors and Lights). The altered power usage leads to different electricity bills with dynamic electricity price from the power market, and these electricity bills can be returned to the main decision maker. Because the lecturing schedule is controlled by the main decision maker, the electricity consumption of lecturing belongs to controllable load and is mainly deterministic, excluding small consumption variation within each lecture. Fig. 1 also shows the electricity consumption of research activities in a university. Research activities and office work occur in offices or laboratories. Universities seldom control the behaviour of staff or students in offices or labs. Staff and students control their air-conditioners, computers, lights and experimental equipment in their own interests and their behaviour causes electricity consumption. Bills of electricity consumption for research is usually paid by university main decision maker. This is an open-loop mode in which the main decision maker cannot adjust the electricity consumption caused by research activities with dynamic electricity price. Traditionally, universities respond to dynamic market information
• A micro-market module is introduced for universities. This module •
•
increases the reach of load initiatives and improves the market participation flexibility. The micro-market module is applied to a case of DSM in a university. An integrated model of controllable load and non-controllable load is constructed to generate a DSM strategy for the university. The results of a numerical study using empirical data suggest that the university can achieve improved load flexibility and greater cost reductions with this model. A modified genetic algorithm, i.e. the self-crossover genetic algorithm (SCGA), is developed to tackle the nonlinear integer optimization problem associated with universities’ DSM. The numerical study shows that this modified genetic algorithm achieves greater convergence than the general genetic algorithm.
University Main Decision Maker Lecturing Schedule
Reseath Staff/Studects
Classroom Usage Distribution
Office Usage
Central Air Conditioning Projector
Office Air Computer Conditioning Monitor Lighters
Lighters
Building Material
Power from lecturing
Lab Usage .
equipment 1 equipment 2 . . equipment n
Student/ Staff NO
Temperature
Power from Research
Price from PM Bill from controllable load
Bill from noncontrollable load
Providing Educational Services
Scientific or Engineering Services
Fig. 1. University electricity bill generation procedure. 3
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university’s load is the electricity consumption of non-lecture operations such as research. Researchers who control laboratory and office devices often do not respond to dynamic power market information or course timetabling. Forcing researchers to change their working patterns could decrease the effectiveness of research. A university spends much more time on research than on lectures. In a typical university in China, postgraduate students attend lectures for only 2–4 h per day, but they often spend more than 6 h per day in offices or labs for research. Therefore, a DSM that includes a module for enabling non-controllable load can maximize the flexibility of demand response. Fig. S1 in Appendix B shows a schematic of all core sub-sections used in modelling.
using the controllable load. Fig. 2 schematically shows a DSM within universities. The decision making of DSM in traditional universities is located at the level of the main decision maker, who sends operation orders or deterministic planning to controllable devices. For example, the main decision maker sends order directly to central air-conditioning systems or constructs timetable for lectures to control the power consumption in classrooms. Therefore, the outcomes of electricity consumption behaviour change based only on load changes of controllable devices. Because no economic incentives are passed on to sub-decision makers, sub-decision makers inside the traditional DSM do not change their routinised behavioural patterns. These patterns may not correspond to the microgrid DSM strategy. To encourage these sub-decision makers to correspond to the strategy, a controllable financial incentive scheme should be established between the main decision maker and the sub-decision makers. Departing from the traditional DSM, the micro-market module aims to construct a small market environment between the main decision maker and multiple sub-decision makers, as shown in Fig. 2. The main decision maker adjusts the triggering parameters to influence the market operations, thus influencing the behaviour of the sub-decision makers. This can achieve variations of non-controllable load. Fairness and non-lost participations are important features in the market design. Non-lost participation means that any sub-decision maker who does not take part in the micro-market will not suffer an extra cost from behaving as normal in the micro-market environment. This feature prevents complaints from non-participants. With the micro-market module, an university can manage and operate the micro-market to control the loads of both controllable devices (e.g. projectors, computers and lights in classrooms) and non-controllable devices (e.g. airconditioners, experimental equipment and other devices in offices and labs).
3.1. Modelling of controllable load in university campuses The timetabling of a university aims to distribute each course into a specific classroom at a specific time. There are three requirements for university course timetabling. Firstly, the classes for each course should not be condensed into a short period, as the condensation can lead to excessive study pressure for students over each term. This requirement applies both daily and weekly [29]. Secondly, the classes for each course should not result in decreases in students’ satisfaction [30,31]. Thirdly, the electricity cost of the entire timetable should be reduced. As a result of the class scheduling requirements noted above, the timetabling is separated into weekly and daily components.
• Weekly Component The weekly component of timetabling mainly focuses on the issue of imbalanced class distribution. The aim of this component is to distribute classes for a course evenly among all weeks in a term. Eq. (1) shows the objective function of the weekly component. The objective function in Eq. (1) tries to minimize the unbalanced distribution of classes on a weekly basis for each course. There are two considerations for this: consideration of element A tries to fairly distribute classes of each courses into different weeks, and consideration of element B tries to fairly distribute total classes into different weeks.
3. Micro-market implementation modelling on a university campus The mail decision maker in a university can adjust the timetable of courses to sufficiently satisfy lecturers and students. Changes to the timetable represents a load variation. Another contribution to the
min:Obj _1 = A + B
Traditional DSM
DSM with Micro-Market
Power Market / Load Serving Entity
Power Market / Load Serving Entity
Power Price
Power Load & Cost
University Main Decision Maker Power Load
Control Orders
Power Load & Cost
Power Price
University Main Decision Maker
Power Load
Operation Management
Power Load
No Power Economic Information Transmission
Control Orders
University Sub-Decision Makers
Micro Market Winning Bidders
Bids
University Sub-Decision Makers
Control Orders University Controllable Devices
Power Load
Responsed Control Orders
Devices Under Sub-Decision Makers
University Controllable Devices
Devices Under Sub-Decision Makers
Fig. 2. Schemes of operation in traditional dsm and dsm with the micro-market module in universities. 4
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A = Ivw − 1T × |cut (WD , W ) − cut (WD, 1)|T × IvC B=
Ivw − 1T
× |[cut (WD , W ) − cut (WD ,
1)]T
(1)
Satisfaction is another aspect of class timetabling. A questionnaire was given to the lecturer of each course on their time preferences (see Table S1 in Appendix A). Their time preferences were divided into 5 categories: most preferred (MP), preferred (P), acceptable (A), weakly acceptable (WA) and disliked (DL). Each category was scored with a number: MP was scored as 100, P as 75, A as 50, WA as 25 and DL as 0. This satisfaction constraint was included using Eq. (8). Smin is given by the main decision maker, which limits that satisfaction of any candidate solutions should not lower than Smin.
× IvC |
The weekly balancing optimization algorithm should follow several additional constraints. First, the total of any optimization solution in Eq. (1) should equal the number of classes for each course in the university’s education schedule. Eq. (2) introduces this constraint as follows:
⎧ Const1 − 1: ∀ c ∈ [1, C ]| ⎨ ⎩
W
∑
(wdc, w ) = esc
w=1
⎫ ⎬ ⎭
(
⎧ mean ∑kK= 1 ∑Hj =×1W ∑iI= 1 Sat (i, j, k , u) ≥ Smin ⎪ Const 2 − 3: Sat (i, j, k , u) = SS ku ⎨ ⎪u = ttijk ⎩
(2)
The second constraint is that the maximum number of weekly classes for each independent course should be limited. This constraint prevents the phenomenon where a course’s classes are balanced on average is but imbalanced independently. Eq. (3) introduces this constraint below:
Const1 − 2: 0 ≤ wdc, w ≤wdmax
In addition to class timetabling, consumption inside offices and labs for research activities is another important part of university electricity usage. This type of consumption is completely determined by staff and student behaviour. A micro-market module is constructed for these subdecision makers to encourage them to alter their behaviour to optimize the university’s electricity costs along with the controllable load.
(3)
C
• Definition of Behaviour Unit
(4)
• Daily Component
A behaviour unit is an entire group that can decide its behaviour. Any individual person is a behaviour unit, as is a research group in close cooperation. For convenience, a research group was determined to be a behaviour unit in this paper, because load monitoring using smart metres is much more convenient and inexpensive for units composed of groups. It would be more expensive to install smart metres for individuals, while giving one metre to each group requires fewer metres and reduces the data processing requirements. Any individual conducting research is also recognized as a research group.
In the daily component, the objective is to determine a class timetable that minimizes the power cost. For cost minimization, a supporting 3-dimensional matrix, TT, is generated (Fig. S2 in Appendix B). One dimension of TT represents the class schedule each day. This paper considers 5 time slots per day: 8:00–10:00, 10:00–12:00, 14:00–16:00, 16:00–18:00 and 18:00–20:00. The remaining two dimensions represent the days and classrooms. Element ttijk is the course number, which represents a class from course ttijk that occurs in classroom i, on day j and at the kth time slot. Using TT, the controllable load function for the daily modelling component is as follows: H ×W
Lcont , k =
• Non-Loss Participation Non-loss participation means that under the new pricing scheme, any behaviour unit in the micro-market will not receive a higher electricity bill than in the traditional environment. This feature ensures that no participants lose and prevents complaints regarding the micromarket module. Anyone who dislikes the micro-market may proceed with their original behaviour patterns without extra cost. A similar study can be found in [32]. In this paper, financial subsidies were offered to consumers based on their demand response as long as the load variation exceeded a given threshold value. Consumers that did not alter their behaviour did not pay an extra cost. The aim of constructing the micro-market was to encourage non-controllable consumers to respond to the dynamic electricity prices received by the microgrid. Thus, an acceptable PBB can be constructed as a target behaviour. The micro-market module requires that any behaviour unit whose average load stays below the threshold of the PBB will receive a subsidy. This subsidy comes from the cost reductions associated with the response of non-controllable consumers. Those consumers that behave in their traditional patterns will pay the traditional cost.
I
∑ ∑ pow (i, j, k ) (5)
j=1 i=1
where H represents the number of days in a week. The function pow() computes the power consumed in each class, whose details are introduced in Eq. (S.1) in Appendix C. In the daily component, the distribution of classes should follow the optimization results of the weekly component. Thus, the weekly classes distribution result derived from Obj_1 should be strictly limited as an equality constraint. Eq. (6) shows the detail of this constraint as follows.
⎧ ∀ c ∈ [1, C ], ∀ w ∈ [1, W ] K I ⎪∑H × w ∑ ∑ rec (ttijk , c ) = wdc, w ⎪ j = H × (w − 1) + 1 k = 1 i = 1 ⎪ Const 2 − 1: wdc, w ∈ WD = argmin (Obj _1) Const1 − 1,2,3 ⎨ ⎪ 1, ttijk = c ⎧ ⎪ rec (ttijk , c ) = ⎪ ⎨ ⎩ 0, ttijk ≠ c ⎩
(6)
• Preferred Behaviour Boundary
In addition to the class distribution determined in the weekly component, the daily component also limits the placement of too many classes from one course into a short period of time. Eq. (7) shows this constraint as follows. MC is given by the main decision maker, representing that classes from any courses should not exceed MC. K
Const 2 − 2:
This study uses a 24-hour load curve as the PBB. When the average daily load curve of a behaviour unit remained under the PBB, the behaviour unit is recognized to have responded to the dynamic price and is entitled to receive a subsidy. The PBB should include the features defined below.
I
∑ ∑ rec (ttijk, c ) ≤ MC k=1 i=1
(8)
3.2. Modelling of non-controllable load under the micro-market module
The third constraint is that the total number of classes in any week should not exceed the space available (number of classrooms). Eq. (4) introduces this constraint, as follows:
⎫ ⎧ Const1 − 3: ∀ w ∈ [1, W ]| ∑ (wdc, w ) = roommax ⎬ ⎨ c = 1 ⎭ ⎩
)
(7)
– Price Response. The aim of the PBB is to encourage behavioural 5
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above. The generated subsidy Su−1 comes from the cost reduction obtained from behaviours changing of bid-winning units.
variation in return for cost reduction. Thus, the PBB should respond to the dynamic price shape. – Working Time Insurance. The PBB should not force researchers to reduce their total workload, thus allowing researchers to work as much time as previously. – Unconventional Behaviour Rejection (UBR). The PBB should consider researchers’ preferences regarding unconventional behaviour. For example, nearly 90% of researchers would prefer not to work at 2:00 am. Therefore, the PBB should not strongly encourage working at 2:00 am, even though the price at that time is lower. The questionnaire and statistical results used to determine UBR are shown in Table S2 in Appendix A.
H ×W I ⎧ ⎧ Nums, z − ∑ j = 1 ∑i = 1 f (PEOttijk , t , s, z ), Su ≥ Suss, z ⎪ gt , s, z (Su) = ⎪ ⎨ 0, Su < Suss, z ⎩ ⎨ Z ∑z = 1 gt , s, z (Su) ⎪ SRt , s = ⎪ ∑Z z = 1 Nums, z ⎩
(12) 1
Considering the features above, the PBB can be obtained by optimizing the results of Eqs. (9)–(11). Eq. (9) aims to determine a PBB with the greatest potential for cost reduction. Obj_3 is the electricity bill under PBB. Eq. (10) ensures that no change to working time occurs during optimization, representing working time insurance. Eq. (11) rejects unconventional behaviour.
T
Const 3 − 1:
t=1
t=1
Const 3 − 2: bpt , s ≤ bp _maxt , s
(14)
Const 2 − 4: Su = Su−1 (9)
• Final Target Function of the Microgrid DSM
T
∑ bpt,s = ∑ bp _initt,s
(13)
A feasible micro-market trade requires balancing the promised subsidy and the generated subsidy; that is, Su in Eq. (12) and Su−1 in Eq. (13) should be the same. Thus, the subsidy should be the solution that satisfies both Eqs. (12) and (13), as shown in Eq. (14).
T
⎧ min:Obj _3 = ∑t = 1 Lt , s × Prit ⎪ ⎪ Lt , s = bpt , s × Pins × PNint , s ⎨ Pins = ∑R (αr × Per , s ) r=1 ⎪ ⎪ PBB = argmin (Obj _3) × Pins × PNint , s = [⋯Lt , s ⋯] ⎩
T
⎧ Billnew = ∑s = 0 ∑t = 1 [(1 − SRt , s )·Ltrat , s + SRt , s ·L∗t , s ] × Prit ⎪ ⎪ L∗t , s = argmin (Obj _3) Const 3 − 1,2 ⎪ (Billnew − Billtra) × β Su = − 1 ' ⎨ ∑1s = 0 ∑Z z = 1 gs, z (Su−1 ) ⎪ ⎪ ' ⎧ Nums, z , Su ≥ Suss, z ⎪ gs, z (Su) = ⎨ 0, Su < Sus s, z ⎩ ⎩
Based on the micro-market module for controllable load and noncontrollable load, the university manager can obtain its objective in Eq. (15), which calculates the contributions from controllable and noncontrollable load. Additionally, an extra payment is generated for
(10) (11)
• Micro-Market module for a University Campus
Start of Each Trading Period
Using the PBB, the micro-market module for universities can be constructed in Fig. 3. As shown in Fig. 3, the market manager will compute the PBB and release it to all behaviour units at the beginning of each trading period. Next, behaviour units can consider how to vary their behaviour based on the PBB and submit their minimum subsidy requirements, which are called bits, for obeying the PBB to the market manager. The market manager will then begin subsidy making (SM) and announce the successful bits and the promised subsidy. Finally, the market manager will examine the average load of each successful behaviour unit throughout the trading period. If any behaviour unit does not meet the requirements of the PBB, it should pay an extra fee to the market manager for the unexpected benefit reduction.
Situation of UBR
PBB Construction and Release
Submitted Bids Behavior Units
• Subsidy Making for the Micro-Market Given the non-loss participation feature, the subsidy will be deducted from the cost reduction experienced by the LNCCC because of the response of successful behaviour units. The following two aspects should be satisfied. First, a certain subsidy value can incentivise a group of behaviour units to join the micro-market. This aspect represents the effect of market participation willingness based on the subsidy. Second, the reduction in the university’s costs generated by the change in behaviour must cover the subsidy. This aspect ensures that the subsidy can be offered. Trading can occur only when the subsidies for both aspects are the same. The flow diagram is introduced in Fig. S3 in Appendix B. The SM process is shown in Eqs. (12) and (13). Eq. (12) calculates how the subsidy value influences the office arrival rate by using information from all submitted bids and represents the first aspect referred to above. The promised subsidy Su in Eq. (12) comes from the promised winning bids. Eq. (13) shows how the office arrival rate influences the subsidy value and represents the second aspect mentioned
Won Bids with Subsidy Promise
Normal Arrival Situation
Market Manager Biddings and Subsidy Making
Behavior Units Outside MicroMarket
Behavior Units with Subsidy Promise
Load under Normal Pattern
Load with PBB Boundary
PBB Broken Exam and Extra Compensation Requirement
+ Total Load of Market Manager
+ Total Power Cost of Microgrid
+
Dynamic Electricity Price for Microgrid End of Each Trading Period Fig. 3. Micro-market module for a university. 6
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subsidies in the micro-market.
⎧ min:Obj2 = [k 2t (Lcont , k ) + Lnoncont , t ] × Prit + Sub _pay ⎪ Sub = Su ∗ × ∑1 ∑Z g ' (Su∗) pay s=0 z = 1 s, z ⎪
•
∑Z z = 1 gt , z (Su ∗)
⎨ SR∗t , s = ∑Z ⎪ z = 1 Numz ⎪ 1 = ∑s = 0 [(1 − SR∗t , s )·Ltrat , s + SR∗t , s ·L∗t , s ] L ⎩ noncont , t
(15)
•
The extra compensation for unexpected benefit reduction is shown in Eq. (S.2) in Appendix C. 4. Micro-market DSM optimization and the self-crossover genetic algorithm
argument (Courses Time Table) transmits through two paths to influence Obj_2. One path is controllable load (Load of Classrooms) and the other is non-controllable load (Load of Offices and Labs). Optimization of Obj_1 contributes to the constraints of courses scheduling. Optimization of Obj_1 is to construct optimal weekly distribution of courses. The result of this optimization will be set as boundary of constraint 2-1, which is in Eq. (6). Then constraint 2-1, 2-2 and 2-3 forms the constraints of courses distribution. Optimization of Obj_3 contributes to PBB constructions. Before the market biddings, market manager raises the PBB with consideration of Price Response, Working Time Insurance and Unconventional Behaviour Rejection. This PBB will be the target load for bid setting of each consumers. And the result of the optimization will be exactly L* in Eqs. (S.2) and (15), which is a boundary value in Obj_2.
4.1. Micro-market DSM optimization 4.2. Self-Crossover Genetic Algorithm (SCGA) Section 3 described the modelling of the controllable and noncontrollable loads for a typical university. Construction of the DSM strategy depends on 3 main optimizations and one equilibrium. Fig. 4 shows the flow chart of the micro-market DSM. Detail introduction of the proposed DSM in Fig. 4 is listed below:
Following the structure shown in Fig. 4, a preliminary experiment is conducted in Table S3 in Appendix A. The result shows that the traditional Lagrangian multiplier method (an analytic method) and the genetic algorithm (a stochastic method) have difficulties in finding the optimal solution for Obj_2. Further failure analysis demonstrates that nearly all failure optimization methods stop iteration because constraint 2-1 is violated. This phenomenon can be explained by the fact that Obj_2 is an integer non-linear optimization problem with equality and inequality constraints. The equality constraint in Eq. (6) limits the solution to a lower-dimensional space. However, the search still operates in highdimensional space and cannot be fine-tuned (unlike continuous arguments, it is difficult to fine-tune integer arguments to a sufficiently small step). This process can be likened to searching for a feasible point in 3D space when all solutions are located only on a line. Given this issue, this paper presents a new genetic algorithm to
• The final objective function is Obj_2. It covers controllable load and non-controllable load. The argument is the Course Time Table. • The influencing chain from argument to objective function. The Courses Time Table firstly leads to power consumption of classroom, which is the controllable load section in Obj_2. Also, Courses Time Table influence the staff/student arrivals in offices and labs. These arrivals will then influence the biddings in micro-market. Different biddings will lead to different winners and subsidy levels. Then proportion of unsuccessful behaviour units and successful behaviour units are changed. The proportion variation finally leads to variation of non-controllable load section in Obj_2. In summary, impact of the
Fig. 4. Microgrid DSM with the micro-market module on a university campus. 7
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eliminate individuals which break the constraints. After elimination of constraint-unsatisfied individuals, the individual with the best fitting function value will survive first. The rest population survivals depend on Roulette Selections.
process this optimization with the equality constraint. Lemma 1. Constraint 2-1 in Eq. (6) requires that the total number of classes for each course in a specific week should equal some constant value. For a given constant value, any two solutions that satisfy this constraint can be transformed into each other using value elementary transformation (VET). The VET step involves finding two locations in matrix TT and exchanging their values.
5. Numerical study 5.1. Background of the numerical study
Each iteration contains V times VET steps and form a new timetable. The value V depends on the rate S. Rate S is a positive value. Eq. (16) introduces the computation of V. For example, if S is 2.6, V covers the integer section of S, which is 2. The rest 0.6 is recognized as 60% probability and generate 0 or 1 randomly by this probability. So if S is 2.6, V is 40% to be 2 and 60% to be 3.
V = int (S ) + rand (S − int (S ))
The Electrical Engineering department of a typical university has been selected for a numerical study to assess the effectiveness of the proposed model. The university is assumed to modify its course timetable every 12 weeks. The students number and total classes of each course is introduced in Table S5 in Appendix A. The number of people and subsidy requirements of each group unit is introduced in Table S6 in Appendix A. On the basis of the database of the entrance guard system (Table S1 in Appendix A), the arrival rate of not-attending-class staff and students is shown in Fig. S5 in Appendix B. The other parameters of numerical study are introduced in Table S8 in Appendix A.
(16)
Lemma 1 implies that the optimal solution can be found within several VET steps from any initial value that satisfies constraint 2-1. Proof of Lemma 1 is shown in Table S4 in Appendix A. Because the VET step is similar to the crossover in the genetic algorithm but works only on an individual, the VET step can be referred to as self-crossover (SCO). Fig. S4 in Appendix B selects a 1 classroom 5 days time-table as an example to introduces VET steps. Thus, a new optimization algorithm can be generated by changing the crossover step into SCO. Additionally, mutation in the traditional genetic algorithm should be deleted because it would violate constraint 2-1. Fig. 5 shows the details of the SCGA. The SCGA firstly requires an initial population whose individuals all satisfy constraint 2-1. During each iteration, inheritance is similar to the traditional GA. However, the crossover step in the traditional GA is replaced by SCO. Additionally, mutation is removed because it violates constraint 2-1. During the elimination step in the SCGA, the following 3 actions are considered.
5.2. Results comparison between microgrid with/without micro-market The PBB is the basis for the micro-market module. The dynamic prices experienced by the university are shown in Fig. S6 in Appendix B. Fig. 7(a) shows the results of PBB construction. Fig. 7(b) shows the converging process of Obj_2 optimization in traditional DSM and DSM with micro-market. Fig. 7(b) shows that university’s total cost reduce under DSM with micro-market. The traditional DSM on controllable load (course timetable) only will increase the total cost instead. Both results satisfy the satisfaction constraint in Table 1. The variation in average satisfaction during optimization is shown in Fig. S7 in Appendix B. The cost variation of controllable load and cost variation of non-controllable load during the whole converging process are shown in Figs. S8 and S9 in Appendix B. The optimization results from traditional DSM and DSM with the Micro-Market scheme is shown in Fig. S10 in Appendix B. Table 1 reveals average satisfaction, cost of controllable load and cost of non-controllable load at initial state, after traditional DSM and after DSM with Micro-Market. In traditional DSM on controllable load only, cost of controllable load decreases. This reduction comes from distributing courses to lower price time period. Thus, it will promote the consumption of offices/labs to higher price time period. So the cost of offices/labs of traditional DSM will increase. As cost increasing of offices/labs is larger than cost reduction of time tabling, the total cost of traditional DSM will increase. In comparison, DSM with micro-market distributes the course to higher price time period. It will increase the cost of courses in classroom. But this distribution will promote usage of
• Individuals that violate other constraints should be removed. • The optimal individual in each iteration must survive into the next iteration. • Survival of other individuals depends on roulette selection. Given that individuals in the initial population should satisfy constraint 2-1, Fig. 6 shows a candidate initialization algorithm with optimal satisfaction. The SCGA looks similar to GA but it uses self-crossover step instead and does not contains mutation section. In each iteration, each individual generates one more same individual in Inheritance section. Then each individual in newly born population will implement its own self-crossover on rate S. It means that each individual uses Eq. (16) to generate its V value and implements V times VET steps. After self-crossover section, the population will firstly
Fig. 5. Flow chart for the self-crossover genetic algorithm. 8
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Fig. 6. Initialization algorithm for the SCGA initial population generation.
Fig. 7a. Traditional arrival rate and arrival rate for the PBB. Fig. 8a. Determining the subsidy for the optimal solution from Fig. 7(b).
traditional DSM ignores the impact of non-controllable load. DSM with micro-market can influence the behaviours of non-controllable load and can reduce the total cost. Subsidies are a necessary component of micromarket operation. Fig. 8(a) shows the subsidy associated with the optimal solution from Fig. 7(b). Based on the requirements of Eqs. (13)–(15), Su in Eq. (13) and Su−1 in Eq. (14) should be the same. Thus, the final subsidy balance occurs at 107.4 CNY, which encourages approximately 16% of the population to join the micro-market. On the left side of Fig. 8(a), Su−1 is higher than Su. The university decision maker can attempt to encourage more people to participate in the micro-market. On the right space of Fig. 8(a), Su−1 is smaller than Su, indicating that the benefit generated from the micro-market is not sufficiently to support the promised subsidy. Thus, the intersection of Su and Su−1 is the best solution. The micro-market module encourages a group of behaviour units to change their behaviour. Fig. 8(b) shows the variations in behaviour and critical load. As shown in the figure, the micro-market module mainly shifts consumption that occurred from 14:00–18:00 to 9:00–11:00. The period between 00:00–6:00 does not include a large shift in consumption even though the price is low, because many consumers refuse to work at night. The PBB considers this phenomenon and does not force people to shift their load into this time period.
Fig. 7b. Total cost variation during optimization.
offices/labs into lower price time periods and decrease the cost of offices/labs. Because the reduction of offices/labs cost is larger than cost increase in time tabling, the total cost of DSM with micro-market decreases. In summary, the cost of traditional DSM may increase because Table 1 Simulation results of traditional DSM and new DSM. Item Names
Initial
Traditional DSM
DSM with Micro-Market
Average Satisfaction Cost of the Controllable Load Cost of the Non-controllable Load
70.601 12906.446 949879.611
68.202 12494.744 961835.835
68.313 14162.361 889982.199
9
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Table 3 Comparison between SCGA and other optimization methods. SCGA
GA
LM-KKT
PSO
SA
Case 1: 10 courses, 1 week only Constraint satisfies the initial value Better solution achieved within 200 repeated optimization
Y 200
Y 7
Y 3
Y 0
Y 25
Case 2: 100 courses, 12 weeks Constraint satisfies the initial value Better solution achieved within 200 repeated optimization
Y 200
Y 0
Y 0
Y 0
Y 0
6. Conclusion and future work
Fig. 8b. Micro-market impacts on the average daily load curve.
6.1. Conclusions
5.3. Analysis of results: micro-market impacts on load distribution
In summary, key findings of this paper are listed below:
Table 2 reveals simulation details of Traditional DSM and New DSM. As lectures scheduling is the only control direction of university decision maker, lectures are shifted to low price period. Then this lecture scheduling naturally forces staff and students to shift their time in offices/slabs into high price period. So traditional DSM cannot directly influence the behaviour of non-controllable load. In new DSM, MicroMarket provides an influencing path to behaviours modification in noncontrollable section. Lectures are not fully shifted to low price period, which allows people to shift some of consumption in offices/labs into this period. Thus, it is more likely to obtain a global minimum for the main decision maker. In summary, traditional DSM has more courses in period of lower price and obtain a lower cost of classrooms only. DSM with microgrid fully considers both controllable load and non-controllable load. It can obtain a global optimal. Finally, cost per electricity unit of DSM with micro-market is 0.7977 CNY / kWh, comparing with 0.8504 CNY / kWh in traditional DSM.
• A demand side management scheme with Micro-market module
•
•
5.4. Analysis of results: performance of the self-crossover genetic algorithm In this section, the performance of typical optimization methods is compared with that of the SCGA. Four typical optimization methods are assessed: the traditional GA (in the MATLAB Toolbox), Lagrange multiplier optimization (in the MATLAB Toolbox), PSO and SA. Parameters of this numerical study is shown in Table S9 in Appendix A. Table 3 shows that the low performances of the traditional GA, LMKKT, PSO and SA are mainly due to constraint 2-1. In all cases that did not achieve a solution, this failure was due to the fact that constraint 21 was violated. Compared with traditional methods, the SCGA ensures the satisfaction of constraint 3-1 by SCO and has the best performance during optimization. The sensitivity analysis of rate S is shown in Fig. S11 in Appendix B.
is proposed. Because microgrids contain load-not-completely-controllable consumers, this paper integrates a small market environment into demand side management. With this new module, these originally non-controllable loads from sub-decision makers are able to be influenced. A University Based demand side management model with Micro-market is created. As university is a typical microgrid containing load-not-completely-controllable consumers. This paper constructs the model of controllable load section (courses timetable) and the model of non-controllable load section (devices usages in offices and labs). An optimization is finally created whose objective function is the total bill of both controllable and non-controllable loads. The relevant constraints include courses distribution, courses time satisfaction, office/lab working time insurance, unconventional behavior rejection and subsidy balancing. A Self-Crossover Genetic Algorithm is proposed for optimization solving. The target optimization is a nonlinear integer programming problem with equality and inequality constraints. This paper proposed a modified genetic algorithm (i.e. the self-crossover genetic algorithm) to solve this problem effectively. This algorithm contains a Self-Crossover section and can naturally ensure the target equality constraint satisfaction for all individuals if the initial population satisfy the same constraint. The proposed self-crossover genetic algorithm performs effectively in finding the optimal solution than traditional algorithms.
6.2. Future work Practically, universities are not the unique sites that contain loadnot-completely-controllable consumer. For example, some clustering factories pay the total power bill together but each sub-manufacturing unit plans schedule in its own way. So the proposed demand side management scheme with the micro-market module has the potential to
Table 2 Simulation details of traditional DSM and new DSM. Item Names
Initial
Traditional DSM
DSM with Micro-Market
NO. of Courses at 8:00–10:00 NO. of Courses at 10:00–12:00 NO. of Courses at 14:00–16:00 NO. of Courses at 16:00–18:00 NO. of Courses at 18:00–20:00 Cost of classroom Cost of Office/Lab Cost Per kWh
578 555 23 90 279 12906.446 949879.611 0.8394
600 588 17 11 369 12494.744 961835.835 0.8504
452 474 142 147 310 14162.361 889982.199 0.7977
10
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be extended to other flexible structures in the power market. New models and new market structures can be studied in the future to optimize microgrid operations.
[11] Amini MH, Nabi B, Haghifam M. Load management using multi-agent systems in smart distribution network. 2013 IEEE power & energy society general meeting, Vancouver, BC. 2013. p. 1–5. [12] Palensky P, Dietrich D. Demand side management: demand response, intelligent energy systems, and smart loads. IEEE Trans Ind Inf 2011;7(3):381–8. [13] Noor Sana, Yang Wentao, Guo Miao, van Dam Koen H, Wang Xiaonan. Energy demand side management within micro-grid networks enhanced by blockchain. Appl Energy 2018;228:1385–98. [14] Malysz P, Sirouspour S, Emadi A. An optimal energy storage control strategy for grid-connected microgrids. IEEE Trans Smart Grid 2014;5(4):1785–96. [15] Liegmann E, Majumder R. An efficient method of multiple storage control in microgrids. IEEE Trans Power Syst 2015;30(6):3437–44. [16] Wei Congying, Jian Xu, Liao Siyang, Sun Yuanzhang, Jiang Yibo, Ke Deping, Zhang Zhen, Wang Jing. A bi-level scheduling model for virtual power plants with aggregated thermostatically controlled loads and renewable energy. Appl Energy 2018;224:659–70. [17] Perera D, Meegahapola L, Perera S, Ciufo P. Characterisation of flicker emission and propagation in distribution networks with bi-directional power flows. Renew. Energy 2014;63(8):172–80. [18] Paterakis NG, Erdinç O, Pappi IN, Bakirtzis AG, Catalao JPS. Coordinated operation of a neighborhood of smart households comprising electric vehicles energy storage and distributed generation. IEEE Trans Smart Grid 2016;7(6):2736–47. [19] Haider HT, See OH, Elmenreich W. A review of residential demand response of smart grid. Renew Sustain Energy Rev 2016;59:1086–94. [20] Mian Hu, Xiao Jiang-Wen, Cui Shi-Chang, Wang Yan-Wu. Distributed real-time demand response for energy management scheduling in smart grid. Int J Electr Power Energy Syst 2018;99(1364–0321):233–45. [21] Ramin D, Spinelli S, Brusaferri A. Demand-side management via optimal production scheduling in power-intensive industries: the case of metal casting process. Appl Energy 2018;225:622–36. [22] Aghajani GR, Shayanfar HA, Shayeghi H. Demand side management in a smart micro-grid in the presence of renewable generation and demand response. Energy 2017;126:622–37. [23] Mehra Varun, Amatya Reja, Ram Rajeev J. Estimating the value of demand-side management in low-cost, solar micro-grids. Energy 2018;163:74–87. [24] Gomez-Herrera Juan A, Anjos Miguel F. Optimal collaborative demand-response planner for smart residential buildings. Energy 2018;161:370–80. [25] Yau YH, Rismanchi B. A review on cool thermal storage technologies and operating strategies. Renew Sustain Energy Rev 2012;16(1):787–97. [26] Chen Yongbao, Peng Xu, Jiefan Gu, Schmidt Ferdinand, Li Weilin. Measures to improve energy demand flexibility in buildings for demand response (DR): a review. Energy Build 2018;177:125–39. [27] Nan S, Zhou M, Li G. Optimal residential community demand response scheduling in smart grid. Appl Energy 2018;210:1280–9. [28] Mateska Aleksandra Krkoleva, Borozan Vesna, Krstevski Petar, Taleski Rubin. Controllable load operation in microgrids using control scheme based on gossip algorithm. Appl Energy 2018;210:1336–46. [29] Soria-Alcaraz JA, Özcan E, Swan J, Kendall G, Carpio M. Iterated local search using an add and delete hyper-heuristic for university course timetabling. Appl Soft Comput 2016;40:581–93. [30] Song K, Kim S, Park M, Lee HS. Energy efficiency-based course timetabling for university buildings. Energy 2017;139:394–405. [31] Qaurooni D, Akbarzadeh-T MR. Course timetabling using evolutionary operators. Appl Soft Comput J 2013;13(5):2504–14. [32] Vallés M, Bello A, Reneses J, Frías P. Probabilistic characterization of electricity consumer responsiveness to economic incentives. Appl Energy 2018;216:296–310.
Acknowledgements This research was supported in part by the National Natural Science Foundation of China (51707041, 71704029, 71802056), in part by the Education Department of Guangdong Province (The Power Market Advanced Service for Load Monitoring Technologies, 2016KQNCX047), in part by the State Grid Energy Research Institute Project (Penetration Capability Research of Distribution Grid and The algorithm of Relevant Analyse Optimization Model) and in part by the State Grid (Suzhou) City & Energy Research Institute project (Critical Data Acquisition and Obtaining Method research on City Energy Research). Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apenergy.2019.113456. References [1] Dehnavi E, Abdi H. Optimal pricing in time of use demand response by integrating with dynamic economic dispatch problem. Energy 2016;109:1086–94. [2] Amini MH, Talari S, Arasteh H, Mahmoudi N, Catalao JPS. Demand response in future power networks: panorama and state-of-the-art. Sustain Interdependent Netw II 2019:167–91. [3] Giaouris Damian, Papadopoulos Athanasios I, Patsios Charalampos, Walker Sara, Ziogou Chrysovalantou, Taylor Phil, et al. A systems approach for management of microgrids considering multiple energy carriers, stochastic loads, forecasting and demand side response. Appl Energy 2018;226:546–59. [4] Muhssin MT, Cipcigan LM, Sami SS, Obaid Z. A Potential of demand side response aggregation for the stabilization of the grids frequency. Appl Energy 2018;220:643–56. [5] Zhang Menglin, Ai Xiaomeng, Fang Jiakun, Yao Wei, Zuo Wenping, Chen Zhe, Wen Jinyu. A systematic approach for the joint dispatch of energy and reserve incorporating demand response. Appl Energy 2018;230:1279–91. [6] Mirakhorli Amin, Dong Bing. Model predictive control for building loads connected with a residential distribution grid. Appl Energy 2018;230:627–42. [7] Jin M, Feng W, Liu P, Marnay C, Spanos C. MOD-DR: Microgrid optimal dispatch with demand response. Appl Energy 2017;187:758–76. [8] Qadrdan M, Cheng M, Wu J, Jenkins N. Benefits of demand-side response in combined gas and electricity networks. Appl Energy 2017;192:360–9. [9] Vuelvas José, Ruiz Fredy, Gruosso Giambattista. Limiting gaming opportunities on incentive-based demand response programs. Appl Energy 2018;225:668–81. [10] Yongli W, Yujing H, Yudong W, Ming Z, Fang L, Yunlu W, et al. Energy management of smart micro-grid with response loads and distributed generation considering demand response. J Cleaner Prod 2018;197:1069–83.
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Contents lists available at ScienceDirect
Applied Energy journal homepage: www.elsevier.com/locate/apenergy
A micro-market module design for university demand-side management using self-crossover genetic algorithms ⁎
T
⁎
Fangyuan Xua, Wanli Wua, Fei Zhaoa, Ya Zhoub,c, , Yongjian Wangc, , Runji Wua, Tao Zhangd, Yongchen Wena, Yiliang Fana, Shengli Jiange a
School of Automation, Guangdong University of Technology, Guangzhou 510006, China Institute Environmental and Ecological Engineering, Guangdong University of Technology, Guangzhou 510006, China c School of Management, Guangdong University of Technology, Guangzhou 510520, China d Institute for Innovation and Entrepreneurship, Loughborough University London, London E15 2GZ, UK e MUFG Securities EMEA plc, London EC2Y 9AJ, UK b
H I GH L IG H T S
G R A P H I C A L A B S T R A C T
scheme is proposed • Aformicro-market demand side management in university campus.
model of university micro• Detail market is developed for scheme supports.
new optimization algorithm, the • Aself-crossover genetic algorithm is proposed.
numerical study shows that the • Aproposed scheme can reduce system costs.
A R T I C LE I N FO
A B S T R A C T
Keywords: Micro-market Demand side management Smart grid Power market Microgrid
Demand Side Management (DSM) is an effective measure in load configuration for microgrid power cost control and power system operation. In most extant studies, DSM in microgrid only consider directly controllable devices for load modification. The load triggered by non-controllable devices with sub-decision-makers are regarded as unchangeable load and generally not considered in DSM. A critical reason for unchangeable load is that the sub-decision makers in these microgrids may not sense and react to external dynamic electricity prices. However, these non-changeable loads in some microgrids contribute significantly to the overall power consumption of the system. Thus, a new demand side management scheme is required for these special microgrids so that the load triggered by these sub-decision makers can also response to external dynamic electricity prices. Based on a case study of a university campus, this study proposes a micro-market module to facilitate the participative behaviours of sub-decision makers in a microgrid with extra financial incentives. A university microgrid DSM optimization model is formulated to optimize the total system cost, the control of the microgrid controllable load, the behaviour of sub-decision makers and the micro-market operations are modelled. A new optimization algorithm, the self-crossover genetic algorithm, is proposed. Empirical data from a university is used to conduct a numerical study to test the proposed module and algorithm. The results show that DSM with the micro-market module can reduce the overall electricity cost of the system, and the proposed self-crossover genetic algorithm out-performs traditional optimization algorithms for the proposed model.
⁎
Corresponding authors. E-mail addresses: [email protected] (Y. Zhou), [email protected] (Y. Wang).
https://doi.org/10.1016/j.apenergy.2019.113456 Received 25 January 2019; Received in revised form 27 May 2019; Accepted 7 June 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.
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Nomenclature
PNint,s Pexr,s s R ar PBB bp_initt,s
total number of consumers of type s at time t power of the rth device in the office or lab 0 means student, 1 means staff device number 0 means device close, 1 means device open preferred behavioural boundary traditional office arrival probability by consumer type s at time t bpt,s office arrival probability by consumer type s at time t bp_maxt,s, proportion of consumers who believe that “working at time t” is acceptable. Nums,z consumer number for the zth behaviour unit for consumer type s. f(PEOttijk,t,s,z) student number at time t from unit z for a certain class timetable Su promised subsidy value Suss,z minimum subsidy requirement given by unit z SRt,s office arrival rate at time t and consumer type s gt,s,z(Su) consumer number of the zth behaviour unit for consumer type s at time t under subsidy Su L*t,s boundary value of the PBB at time t for consumer type s Ltrat,s traditional load at time t for consumer type s β ratio of cost reduction to subsidy generation Su−1 generated subsidy Billnew school electric bill under micro-market Billtra school electric traditional bill g't,s,z(Su) consumer number of the zth behaviour unit for consumer type s obtained subsidy k2t(Lcont,k) transfers the time index from k (the time slot index) to t Lnoncont,t non-controllable load at the time t Sub_pay extra payment is generated for subsidies in the micromarket Su* solution of Eqs. (12) and (13) SR*t,s office arrival rate at time t and consumer type s under subsidy Su*
fluctuation degree of class hours in different weeks of each course B fluctuation degree of the total class hours In each week WD number matrix of classes for each week and course C course number W week number Ivx a column vector filled with ones with a dimension of x cut (WD, x) removes the xth column of WD and outputs the remainder matrix wdc,w the element at the cth row and wth column of WD esc the number of classes for the cth course in the education schedule wdmax maximum number of weekly classes for each independent course roommax maximum available space ttijk course number occurs in classroom i, on day j and at the kth time slot. Lcont,k controllable load at the kth time slot H number of work days in a week I classroom number J day number K time slot number pow(i,j,k) power consumed in classroom i, on day j and at the kth time slot. rec(ttijk, c) determine if c and course number occurs in classroom i, on day j and at the kth time slot are equal. MC maximum number of classes from one course SSku satisfaction score for course u at the kth time slot Smin minimum average satisfaction Lt,s power used at time t for consumer type s Prit dynamic electricity price bpt,s office arrival probability at time t for consumer type s Pins power used by each consumer in the office or lab A
1. Introduction
performed on fully controllable devices. Another example is given by Yau and Rismanchi [25]. Load flexibility is mostly provided by shifting or shedding small non-critical loads. A thermal energy storage system for building cooling applications is proposed. This system can balance the energy demand between the peak (daytimes) and off-peak hours (nights). All critical devices in this system are fully controllable. In Chen et al. [26], authors have summarized several measures for improving the flexibility of commercial/residential buildings and developed a systematic methodological framework to evaluate energy demand flexibility. All smart appliances in buildings with home energy management systems, e.g. dishwashers, washing machines, tumble dryers and electric vehicles, can be fully controlled. Such loads can be managed straightforwardly at the user level [27,28]. Therefore, an underlying assumption of these studies is that the load under DSM is fully controllable. The reason for this assumption is that microgrid owners usually have usage rights for power devices inside a microgrid. In other words, the microgrid owner is the only decision maker that controls these devices. Practically, though, some microgrid consumers do not obtain full usage rights for their main power-consuming devices. This situation is true in most universities. These institutions face dynamic electricity prices and pay the bill while the usage rights for devices are distributed to staff and students, forming a structure comprising multiple decision makers. Price fluctuation is not transmitted to sub-decision makers like staff and students so that most of the power consumptions do not respond to price variation. Energy efficiency improvements in universities from the behavioural optimization perspective is complex. Thus, universities’ electricity cost reduction and power market participation are
1.1. Background Initiative load is important to power system development. It increases the flexibility of supply-demand balance control [1,2], enhances the power system flexibility [3], regulates the grid frequency [4], facilitates the flexibility improvement in the joint dispatch problem of energy and reserve [5], therefore improving grid reliability and economic performance [6,7]. Some examples of initiative load include demand response (DR) [8,9], load management [10,11], demand-side management (DSM) [12,13], storage control [14,15], virtual power plants [16], and di-directional load flow with distributed generation [17,18]. Multiple studies have shown that initiative load yields improvements in grid performance [19,20]. In most extant studies on initiative load inside microgrids, microgrid behaviour under DSM is assumed to be fully controllable by grid owners. For example, Ramin et al. [21] and Aghajani et al. [22] indicate that flexible consumers can be divided into two types: (1) single energy-intensive industrial units that are qualified to individually participate in energy or capacity markets and (2) small distributed loads such as residential or small commercial consumers. In both types, device behaviour under DSM is fully controllable. The controllable behaviour can be found not only on consuming equipment, but also on the new resources such as distributed generators, solar panels, and storage units [23,24]. Ramin et al. [21] proposes a scheduling model for a multi-stage and multi-line process for optimal operation in multiple power markets, and all operations in a metal casting foundry are 2
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The rest of this paper is organized as follows. Section 2 describes the micro-market module in detail and discusses the differences between the DSM with micro-market and the traditional DSM structure. Section 3 explains the model’s treatment of controllable and non-controllable loads in the case of a university. Section 4 introduces the SCGA. Finally, Section 5 applies real-world empirical data derived from a typical university in a numerical study.
difficult. For example, universities can select only controllable devices such as central air-conditioning systems for DSM. Many single airconditioning units are controlled by staff and students, thus contributing less to the university’s overall electricity cost reduction. These types of consumers are referred to as load-not-completely-controllable consumers (LNCCCs). 1.2. Original contribution
2. DSM in universities with micro-market
Given the issue above, this paper initiates a new DSM scheme referred to as a micro-market for university campus. This scheme constructs a small market module inside a university. It take initiatives on the energy load for each sub-decision makers using financial incentives. The module is then applied to a case of a university DSM. Using this module, university decision makers can create a comprehensive DSM strategy that manages both controllable and non-controllable loads. The specific contributions of this paper are listed below.
There are two main functions of a University: education and research, both of which use electricity. Thus, the power load of a university is mainly generated by the two sections. Education wise, a closed-loop is generated in Fig. 1. The main decision maker adjusts the lecturing timetable to change the time of classroom power usage (Central Air-Conditioning, Projectors and Lights). The altered power usage leads to different electricity bills with dynamic electricity price from the power market, and these electricity bills can be returned to the main decision maker. Because the lecturing schedule is controlled by the main decision maker, the electricity consumption of lecturing belongs to controllable load and is mainly deterministic, excluding small consumption variation within each lecture. Fig. 1 also shows the electricity consumption of research activities in a university. Research activities and office work occur in offices or laboratories. Universities seldom control the behaviour of staff or students in offices or labs. Staff and students control their air-conditioners, computers, lights and experimental equipment in their own interests and their behaviour causes electricity consumption. Bills of electricity consumption for research is usually paid by university main decision maker. This is an open-loop mode in which the main decision maker cannot adjust the electricity consumption caused by research activities with dynamic electricity price. Traditionally, universities respond to dynamic market information
• A micro-market module is introduced for universities. This module •
•
increases the reach of load initiatives and improves the market participation flexibility. The micro-market module is applied to a case of DSM in a university. An integrated model of controllable load and non-controllable load is constructed to generate a DSM strategy for the university. The results of a numerical study using empirical data suggest that the university can achieve improved load flexibility and greater cost reductions with this model. A modified genetic algorithm, i.e. the self-crossover genetic algorithm (SCGA), is developed to tackle the nonlinear integer optimization problem associated with universities’ DSM. The numerical study shows that this modified genetic algorithm achieves greater convergence than the general genetic algorithm.
University Main Decision Maker Lecturing Schedule
Reseath Staff/Studects
Classroom Usage Distribution
Office Usage
Central Air Conditioning Projector
Office Air Computer Conditioning Monitor Lighters
Lighters
Building Material
Power from lecturing
Lab Usage .
equipment 1 equipment 2 . . equipment n
Student/ Staff NO
Temperature
Power from Research
Price from PM Bill from controllable load
Bill from noncontrollable load
Providing Educational Services
Scientific or Engineering Services
Fig. 1. University electricity bill generation procedure. 3
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university’s load is the electricity consumption of non-lecture operations such as research. Researchers who control laboratory and office devices often do not respond to dynamic power market information or course timetabling. Forcing researchers to change their working patterns could decrease the effectiveness of research. A university spends much more time on research than on lectures. In a typical university in China, postgraduate students attend lectures for only 2–4 h per day, but they often spend more than 6 h per day in offices or labs for research. Therefore, a DSM that includes a module for enabling non-controllable load can maximize the flexibility of demand response. Fig. S1 in Appendix B shows a schematic of all core sub-sections used in modelling.
using the controllable load. Fig. 2 schematically shows a DSM within universities. The decision making of DSM in traditional universities is located at the level of the main decision maker, who sends operation orders or deterministic planning to controllable devices. For example, the main decision maker sends order directly to central air-conditioning systems or constructs timetable for lectures to control the power consumption in classrooms. Therefore, the outcomes of electricity consumption behaviour change based only on load changes of controllable devices. Because no economic incentives are passed on to sub-decision makers, sub-decision makers inside the traditional DSM do not change their routinised behavioural patterns. These patterns may not correspond to the microgrid DSM strategy. To encourage these sub-decision makers to correspond to the strategy, a controllable financial incentive scheme should be established between the main decision maker and the sub-decision makers. Departing from the traditional DSM, the micro-market module aims to construct a small market environment between the main decision maker and multiple sub-decision makers, as shown in Fig. 2. The main decision maker adjusts the triggering parameters to influence the market operations, thus influencing the behaviour of the sub-decision makers. This can achieve variations of non-controllable load. Fairness and non-lost participations are important features in the market design. Non-lost participation means that any sub-decision maker who does not take part in the micro-market will not suffer an extra cost from behaving as normal in the micro-market environment. This feature prevents complaints from non-participants. With the micro-market module, an university can manage and operate the micro-market to control the loads of both controllable devices (e.g. projectors, computers and lights in classrooms) and non-controllable devices (e.g. airconditioners, experimental equipment and other devices in offices and labs).
3.1. Modelling of controllable load in university campuses The timetabling of a university aims to distribute each course into a specific classroom at a specific time. There are three requirements for university course timetabling. Firstly, the classes for each course should not be condensed into a short period, as the condensation can lead to excessive study pressure for students over each term. This requirement applies both daily and weekly [29]. Secondly, the classes for each course should not result in decreases in students’ satisfaction [30,31]. Thirdly, the electricity cost of the entire timetable should be reduced. As a result of the class scheduling requirements noted above, the timetabling is separated into weekly and daily components.
• Weekly Component The weekly component of timetabling mainly focuses on the issue of imbalanced class distribution. The aim of this component is to distribute classes for a course evenly among all weeks in a term. Eq. (1) shows the objective function of the weekly component. The objective function in Eq. (1) tries to minimize the unbalanced distribution of classes on a weekly basis for each course. There are two considerations for this: consideration of element A tries to fairly distribute classes of each courses into different weeks, and consideration of element B tries to fairly distribute total classes into different weeks.
3. Micro-market implementation modelling on a university campus The mail decision maker in a university can adjust the timetable of courses to sufficiently satisfy lecturers and students. Changes to the timetable represents a load variation. Another contribution to the
min:Obj _1 = A + B
Traditional DSM
DSM with Micro-Market
Power Market / Load Serving Entity
Power Market / Load Serving Entity
Power Price
Power Load & Cost
University Main Decision Maker Power Load
Control Orders
Power Load & Cost
Power Price
University Main Decision Maker
Power Load
Operation Management
Power Load
No Power Economic Information Transmission
Control Orders
University Sub-Decision Makers
Micro Market Winning Bidders
Bids
University Sub-Decision Makers
Control Orders University Controllable Devices
Power Load
Responsed Control Orders
Devices Under Sub-Decision Makers
University Controllable Devices
Devices Under Sub-Decision Makers
Fig. 2. Schemes of operation in traditional dsm and dsm with the micro-market module in universities. 4
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A = Ivw − 1T × |cut (WD , W ) − cut (WD, 1)|T × IvC B=
Ivw − 1T
× |[cut (WD , W ) − cut (WD ,
1)]T
(1)
Satisfaction is another aspect of class timetabling. A questionnaire was given to the lecturer of each course on their time preferences (see Table S1 in Appendix A). Their time preferences were divided into 5 categories: most preferred (MP), preferred (P), acceptable (A), weakly acceptable (WA) and disliked (DL). Each category was scored with a number: MP was scored as 100, P as 75, A as 50, WA as 25 and DL as 0. This satisfaction constraint was included using Eq. (8). Smin is given by the main decision maker, which limits that satisfaction of any candidate solutions should not lower than Smin.
× IvC |
The weekly balancing optimization algorithm should follow several additional constraints. First, the total of any optimization solution in Eq. (1) should equal the number of classes for each course in the university’s education schedule. Eq. (2) introduces this constraint as follows:
⎧ Const1 − 1: ∀ c ∈ [1, C ]| ⎨ ⎩
W
∑
(wdc, w ) = esc
w=1
⎫ ⎬ ⎭
(
⎧ mean ∑kK= 1 ∑Hj =×1W ∑iI= 1 Sat (i, j, k , u) ≥ Smin ⎪ Const 2 − 3: Sat (i, j, k , u) = SS ku ⎨ ⎪u = ttijk ⎩
(2)
The second constraint is that the maximum number of weekly classes for each independent course should be limited. This constraint prevents the phenomenon where a course’s classes are balanced on average is but imbalanced independently. Eq. (3) introduces this constraint below:
Const1 − 2: 0 ≤ wdc, w ≤wdmax
In addition to class timetabling, consumption inside offices and labs for research activities is another important part of university electricity usage. This type of consumption is completely determined by staff and student behaviour. A micro-market module is constructed for these subdecision makers to encourage them to alter their behaviour to optimize the university’s electricity costs along with the controllable load.
(3)
C
• Definition of Behaviour Unit
(4)
• Daily Component
A behaviour unit is an entire group that can decide its behaviour. Any individual person is a behaviour unit, as is a research group in close cooperation. For convenience, a research group was determined to be a behaviour unit in this paper, because load monitoring using smart metres is much more convenient and inexpensive for units composed of groups. It would be more expensive to install smart metres for individuals, while giving one metre to each group requires fewer metres and reduces the data processing requirements. Any individual conducting research is also recognized as a research group.
In the daily component, the objective is to determine a class timetable that minimizes the power cost. For cost minimization, a supporting 3-dimensional matrix, TT, is generated (Fig. S2 in Appendix B). One dimension of TT represents the class schedule each day. This paper considers 5 time slots per day: 8:00–10:00, 10:00–12:00, 14:00–16:00, 16:00–18:00 and 18:00–20:00. The remaining two dimensions represent the days and classrooms. Element ttijk is the course number, which represents a class from course ttijk that occurs in classroom i, on day j and at the kth time slot. Using TT, the controllable load function for the daily modelling component is as follows: H ×W
Lcont , k =
• Non-Loss Participation Non-loss participation means that under the new pricing scheme, any behaviour unit in the micro-market will not receive a higher electricity bill than in the traditional environment. This feature ensures that no participants lose and prevents complaints regarding the micromarket module. Anyone who dislikes the micro-market may proceed with their original behaviour patterns without extra cost. A similar study can be found in [32]. In this paper, financial subsidies were offered to consumers based on their demand response as long as the load variation exceeded a given threshold value. Consumers that did not alter their behaviour did not pay an extra cost. The aim of constructing the micro-market was to encourage non-controllable consumers to respond to the dynamic electricity prices received by the microgrid. Thus, an acceptable PBB can be constructed as a target behaviour. The micro-market module requires that any behaviour unit whose average load stays below the threshold of the PBB will receive a subsidy. This subsidy comes from the cost reductions associated with the response of non-controllable consumers. Those consumers that behave in their traditional patterns will pay the traditional cost.
I
∑ ∑ pow (i, j, k ) (5)
j=1 i=1
where H represents the number of days in a week. The function pow() computes the power consumed in each class, whose details are introduced in Eq. (S.1) in Appendix C. In the daily component, the distribution of classes should follow the optimization results of the weekly component. Thus, the weekly classes distribution result derived from Obj_1 should be strictly limited as an equality constraint. Eq. (6) shows the detail of this constraint as follows.
⎧ ∀ c ∈ [1, C ], ∀ w ∈ [1, W ] K I ⎪∑H × w ∑ ∑ rec (ttijk , c ) = wdc, w ⎪ j = H × (w − 1) + 1 k = 1 i = 1 ⎪ Const 2 − 1: wdc, w ∈ WD = argmin (Obj _1) Const1 − 1,2,3 ⎨ ⎪ 1, ttijk = c ⎧ ⎪ rec (ttijk , c ) = ⎪ ⎨ ⎩ 0, ttijk ≠ c ⎩
(6)
• Preferred Behaviour Boundary
In addition to the class distribution determined in the weekly component, the daily component also limits the placement of too many classes from one course into a short period of time. Eq. (7) shows this constraint as follows. MC is given by the main decision maker, representing that classes from any courses should not exceed MC. K
Const 2 − 2:
This study uses a 24-hour load curve as the PBB. When the average daily load curve of a behaviour unit remained under the PBB, the behaviour unit is recognized to have responded to the dynamic price and is entitled to receive a subsidy. The PBB should include the features defined below.
I
∑ ∑ rec (ttijk, c ) ≤ MC k=1 i=1
(8)
3.2. Modelling of non-controllable load under the micro-market module
The third constraint is that the total number of classes in any week should not exceed the space available (number of classrooms). Eq. (4) introduces this constraint, as follows:
⎫ ⎧ Const1 − 3: ∀ w ∈ [1, W ]| ∑ (wdc, w ) = roommax ⎬ ⎨ c = 1 ⎭ ⎩
)
(7)
– Price Response. The aim of the PBB is to encourage behavioural 5
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above. The generated subsidy Su−1 comes from the cost reduction obtained from behaviours changing of bid-winning units.
variation in return for cost reduction. Thus, the PBB should respond to the dynamic price shape. – Working Time Insurance. The PBB should not force researchers to reduce their total workload, thus allowing researchers to work as much time as previously. – Unconventional Behaviour Rejection (UBR). The PBB should consider researchers’ preferences regarding unconventional behaviour. For example, nearly 90% of researchers would prefer not to work at 2:00 am. Therefore, the PBB should not strongly encourage working at 2:00 am, even though the price at that time is lower. The questionnaire and statistical results used to determine UBR are shown in Table S2 in Appendix A.
H ×W I ⎧ ⎧ Nums, z − ∑ j = 1 ∑i = 1 f (PEOttijk , t , s, z ), Su ≥ Suss, z ⎪ gt , s, z (Su) = ⎪ ⎨ 0, Su < Suss, z ⎩ ⎨ Z ∑z = 1 gt , s, z (Su) ⎪ SRt , s = ⎪ ∑Z z = 1 Nums, z ⎩
(12) 1
Considering the features above, the PBB can be obtained by optimizing the results of Eqs. (9)–(11). Eq. (9) aims to determine a PBB with the greatest potential for cost reduction. Obj_3 is the electricity bill under PBB. Eq. (10) ensures that no change to working time occurs during optimization, representing working time insurance. Eq. (11) rejects unconventional behaviour.
T
Const 3 − 1:
t=1
t=1
Const 3 − 2: bpt , s ≤ bp _maxt , s
(14)
Const 2 − 4: Su = Su−1 (9)
• Final Target Function of the Microgrid DSM
T
∑ bpt,s = ∑ bp _initt,s
(13)
A feasible micro-market trade requires balancing the promised subsidy and the generated subsidy; that is, Su in Eq. (12) and Su−1 in Eq. (13) should be the same. Thus, the subsidy should be the solution that satisfies both Eqs. (12) and (13), as shown in Eq. (14).
T
⎧ min:Obj _3 = ∑t = 1 Lt , s × Prit ⎪ ⎪ Lt , s = bpt , s × Pins × PNint , s ⎨ Pins = ∑R (αr × Per , s ) r=1 ⎪ ⎪ PBB = argmin (Obj _3) × Pins × PNint , s = [⋯Lt , s ⋯] ⎩
T
⎧ Billnew = ∑s = 0 ∑t = 1 [(1 − SRt , s )·Ltrat , s + SRt , s ·L∗t , s ] × Prit ⎪ ⎪ L∗t , s = argmin (Obj _3) Const 3 − 1,2 ⎪ (Billnew − Billtra) × β Su = − 1 ' ⎨ ∑1s = 0 ∑Z z = 1 gs, z (Su−1 ) ⎪ ⎪ ' ⎧ Nums, z , Su ≥ Suss, z ⎪ gs, z (Su) = ⎨ 0, Su < Sus s, z ⎩ ⎩
Based on the micro-market module for controllable load and noncontrollable load, the university manager can obtain its objective in Eq. (15), which calculates the contributions from controllable and noncontrollable load. Additionally, an extra payment is generated for
(10) (11)
• Micro-Market module for a University Campus
Start of Each Trading Period
Using the PBB, the micro-market module for universities can be constructed in Fig. 3. As shown in Fig. 3, the market manager will compute the PBB and release it to all behaviour units at the beginning of each trading period. Next, behaviour units can consider how to vary their behaviour based on the PBB and submit their minimum subsidy requirements, which are called bits, for obeying the PBB to the market manager. The market manager will then begin subsidy making (SM) and announce the successful bits and the promised subsidy. Finally, the market manager will examine the average load of each successful behaviour unit throughout the trading period. If any behaviour unit does not meet the requirements of the PBB, it should pay an extra fee to the market manager for the unexpected benefit reduction.
Situation of UBR
PBB Construction and Release
Submitted Bids Behavior Units
• Subsidy Making for the Micro-Market Given the non-loss participation feature, the subsidy will be deducted from the cost reduction experienced by the LNCCC because of the response of successful behaviour units. The following two aspects should be satisfied. First, a certain subsidy value can incentivise a group of behaviour units to join the micro-market. This aspect represents the effect of market participation willingness based on the subsidy. Second, the reduction in the university’s costs generated by the change in behaviour must cover the subsidy. This aspect ensures that the subsidy can be offered. Trading can occur only when the subsidies for both aspects are the same. The flow diagram is introduced in Fig. S3 in Appendix B. The SM process is shown in Eqs. (12) and (13). Eq. (12) calculates how the subsidy value influences the office arrival rate by using information from all submitted bids and represents the first aspect referred to above. The promised subsidy Su in Eq. (12) comes from the promised winning bids. Eq. (13) shows how the office arrival rate influences the subsidy value and represents the second aspect mentioned
Won Bids with Subsidy Promise
Normal Arrival Situation
Market Manager Biddings and Subsidy Making
Behavior Units Outside MicroMarket
Behavior Units with Subsidy Promise
Load under Normal Pattern
Load with PBB Boundary
PBB Broken Exam and Extra Compensation Requirement
+ Total Load of Market Manager
+ Total Power Cost of Microgrid
+
Dynamic Electricity Price for Microgrid End of Each Trading Period Fig. 3. Micro-market module for a university. 6
-
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subsidies in the micro-market.
⎧ min:Obj2 = [k 2t (Lcont , k ) + Lnoncont , t ] × Prit + Sub _pay ⎪ Sub = Su ∗ × ∑1 ∑Z g ' (Su∗) pay s=0 z = 1 s, z ⎪
•
∑Z z = 1 gt , z (Su ∗)
⎨ SR∗t , s = ∑Z ⎪ z = 1 Numz ⎪ 1 = ∑s = 0 [(1 − SR∗t , s )·Ltrat , s + SR∗t , s ·L∗t , s ] L ⎩ noncont , t
(15)
•
The extra compensation for unexpected benefit reduction is shown in Eq. (S.2) in Appendix C. 4. Micro-market DSM optimization and the self-crossover genetic algorithm
argument (Courses Time Table) transmits through two paths to influence Obj_2. One path is controllable load (Load of Classrooms) and the other is non-controllable load (Load of Offices and Labs). Optimization of Obj_1 contributes to the constraints of courses scheduling. Optimization of Obj_1 is to construct optimal weekly distribution of courses. The result of this optimization will be set as boundary of constraint 2-1, which is in Eq. (6). Then constraint 2-1, 2-2 and 2-3 forms the constraints of courses distribution. Optimization of Obj_3 contributes to PBB constructions. Before the market biddings, market manager raises the PBB with consideration of Price Response, Working Time Insurance and Unconventional Behaviour Rejection. This PBB will be the target load for bid setting of each consumers. And the result of the optimization will be exactly L* in Eqs. (S.2) and (15), which is a boundary value in Obj_2.
4.1. Micro-market DSM optimization 4.2. Self-Crossover Genetic Algorithm (SCGA) Section 3 described the modelling of the controllable and noncontrollable loads for a typical university. Construction of the DSM strategy depends on 3 main optimizations and one equilibrium. Fig. 4 shows the flow chart of the micro-market DSM. Detail introduction of the proposed DSM in Fig. 4 is listed below:
Following the structure shown in Fig. 4, a preliminary experiment is conducted in Table S3 in Appendix A. The result shows that the traditional Lagrangian multiplier method (an analytic method) and the genetic algorithm (a stochastic method) have difficulties in finding the optimal solution for Obj_2. Further failure analysis demonstrates that nearly all failure optimization methods stop iteration because constraint 2-1 is violated. This phenomenon can be explained by the fact that Obj_2 is an integer non-linear optimization problem with equality and inequality constraints. The equality constraint in Eq. (6) limits the solution to a lower-dimensional space. However, the search still operates in highdimensional space and cannot be fine-tuned (unlike continuous arguments, it is difficult to fine-tune integer arguments to a sufficiently small step). This process can be likened to searching for a feasible point in 3D space when all solutions are located only on a line. Given this issue, this paper presents a new genetic algorithm to
• The final objective function is Obj_2. It covers controllable load and non-controllable load. The argument is the Course Time Table. • The influencing chain from argument to objective function. The Courses Time Table firstly leads to power consumption of classroom, which is the controllable load section in Obj_2. Also, Courses Time Table influence the staff/student arrivals in offices and labs. These arrivals will then influence the biddings in micro-market. Different biddings will lead to different winners and subsidy levels. Then proportion of unsuccessful behaviour units and successful behaviour units are changed. The proportion variation finally leads to variation of non-controllable load section in Obj_2. In summary, impact of the
Fig. 4. Microgrid DSM with the micro-market module on a university campus. 7
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eliminate individuals which break the constraints. After elimination of constraint-unsatisfied individuals, the individual with the best fitting function value will survive first. The rest population survivals depend on Roulette Selections.
process this optimization with the equality constraint. Lemma 1. Constraint 2-1 in Eq. (6) requires that the total number of classes for each course in a specific week should equal some constant value. For a given constant value, any two solutions that satisfy this constraint can be transformed into each other using value elementary transformation (VET). The VET step involves finding two locations in matrix TT and exchanging their values.
5. Numerical study 5.1. Background of the numerical study
Each iteration contains V times VET steps and form a new timetable. The value V depends on the rate S. Rate S is a positive value. Eq. (16) introduces the computation of V. For example, if S is 2.6, V covers the integer section of S, which is 2. The rest 0.6 is recognized as 60% probability and generate 0 or 1 randomly by this probability. So if S is 2.6, V is 40% to be 2 and 60% to be 3.
V = int (S ) + rand (S − int (S ))
The Electrical Engineering department of a typical university has been selected for a numerical study to assess the effectiveness of the proposed model. The university is assumed to modify its course timetable every 12 weeks. The students number and total classes of each course is introduced in Table S5 in Appendix A. The number of people and subsidy requirements of each group unit is introduced in Table S6 in Appendix A. On the basis of the database of the entrance guard system (Table S1 in Appendix A), the arrival rate of not-attending-class staff and students is shown in Fig. S5 in Appendix B. The other parameters of numerical study are introduced in Table S8 in Appendix A.
(16)
Lemma 1 implies that the optimal solution can be found within several VET steps from any initial value that satisfies constraint 2-1. Proof of Lemma 1 is shown in Table S4 in Appendix A. Because the VET step is similar to the crossover in the genetic algorithm but works only on an individual, the VET step can be referred to as self-crossover (SCO). Fig. S4 in Appendix B selects a 1 classroom 5 days time-table as an example to introduces VET steps. Thus, a new optimization algorithm can be generated by changing the crossover step into SCO. Additionally, mutation in the traditional genetic algorithm should be deleted because it would violate constraint 2-1. Fig. 5 shows the details of the SCGA. The SCGA firstly requires an initial population whose individuals all satisfy constraint 2-1. During each iteration, inheritance is similar to the traditional GA. However, the crossover step in the traditional GA is replaced by SCO. Additionally, mutation is removed because it violates constraint 2-1. During the elimination step in the SCGA, the following 3 actions are considered.
5.2. Results comparison between microgrid with/without micro-market The PBB is the basis for the micro-market module. The dynamic prices experienced by the university are shown in Fig. S6 in Appendix B. Fig. 7(a) shows the results of PBB construction. Fig. 7(b) shows the converging process of Obj_2 optimization in traditional DSM and DSM with micro-market. Fig. 7(b) shows that university’s total cost reduce under DSM with micro-market. The traditional DSM on controllable load (course timetable) only will increase the total cost instead. Both results satisfy the satisfaction constraint in Table 1. The variation in average satisfaction during optimization is shown in Fig. S7 in Appendix B. The cost variation of controllable load and cost variation of non-controllable load during the whole converging process are shown in Figs. S8 and S9 in Appendix B. The optimization results from traditional DSM and DSM with the Micro-Market scheme is shown in Fig. S10 in Appendix B. Table 1 reveals average satisfaction, cost of controllable load and cost of non-controllable load at initial state, after traditional DSM and after DSM with Micro-Market. In traditional DSM on controllable load only, cost of controllable load decreases. This reduction comes from distributing courses to lower price time period. Thus, it will promote the consumption of offices/labs to higher price time period. So the cost of offices/labs of traditional DSM will increase. As cost increasing of offices/labs is larger than cost reduction of time tabling, the total cost of traditional DSM will increase. In comparison, DSM with micro-market distributes the course to higher price time period. It will increase the cost of courses in classroom. But this distribution will promote usage of
• Individuals that violate other constraints should be removed. • The optimal individual in each iteration must survive into the next iteration. • Survival of other individuals depends on roulette selection. Given that individuals in the initial population should satisfy constraint 2-1, Fig. 6 shows a candidate initialization algorithm with optimal satisfaction. The SCGA looks similar to GA but it uses self-crossover step instead and does not contains mutation section. In each iteration, each individual generates one more same individual in Inheritance section. Then each individual in newly born population will implement its own self-crossover on rate S. It means that each individual uses Eq. (16) to generate its V value and implements V times VET steps. After self-crossover section, the population will firstly
Fig. 5. Flow chart for the self-crossover genetic algorithm. 8
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Fig. 6. Initialization algorithm for the SCGA initial population generation.
Fig. 7a. Traditional arrival rate and arrival rate for the PBB. Fig. 8a. Determining the subsidy for the optimal solution from Fig. 7(b).
traditional DSM ignores the impact of non-controllable load. DSM with micro-market can influence the behaviours of non-controllable load and can reduce the total cost. Subsidies are a necessary component of micromarket operation. Fig. 8(a) shows the subsidy associated with the optimal solution from Fig. 7(b). Based on the requirements of Eqs. (13)–(15), Su in Eq. (13) and Su−1 in Eq. (14) should be the same. Thus, the final subsidy balance occurs at 107.4 CNY, which encourages approximately 16% of the population to join the micro-market. On the left side of Fig. 8(a), Su−1 is higher than Su. The university decision maker can attempt to encourage more people to participate in the micro-market. On the right space of Fig. 8(a), Su−1 is smaller than Su, indicating that the benefit generated from the micro-market is not sufficiently to support the promised subsidy. Thus, the intersection of Su and Su−1 is the best solution. The micro-market module encourages a group of behaviour units to change their behaviour. Fig. 8(b) shows the variations in behaviour and critical load. As shown in the figure, the micro-market module mainly shifts consumption that occurred from 14:00–18:00 to 9:00–11:00. The period between 00:00–6:00 does not include a large shift in consumption even though the price is low, because many consumers refuse to work at night. The PBB considers this phenomenon and does not force people to shift their load into this time period.
Fig. 7b. Total cost variation during optimization.
offices/labs into lower price time periods and decrease the cost of offices/labs. Because the reduction of offices/labs cost is larger than cost increase in time tabling, the total cost of DSM with micro-market decreases. In summary, the cost of traditional DSM may increase because Table 1 Simulation results of traditional DSM and new DSM. Item Names
Initial
Traditional DSM
DSM with Micro-Market
Average Satisfaction Cost of the Controllable Load Cost of the Non-controllable Load
70.601 12906.446 949879.611
68.202 12494.744 961835.835
68.313 14162.361 889982.199
9
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Table 3 Comparison between SCGA and other optimization methods. SCGA
GA
LM-KKT
PSO
SA
Case 1: 10 courses, 1 week only Constraint satisfies the initial value Better solution achieved within 200 repeated optimization
Y 200
Y 7
Y 3
Y 0
Y 25
Case 2: 100 courses, 12 weeks Constraint satisfies the initial value Better solution achieved within 200 repeated optimization
Y 200
Y 0
Y 0
Y 0
Y 0
6. Conclusion and future work
Fig. 8b. Micro-market impacts on the average daily load curve.
6.1. Conclusions
5.3. Analysis of results: micro-market impacts on load distribution
In summary, key findings of this paper are listed below:
Table 2 reveals simulation details of Traditional DSM and New DSM. As lectures scheduling is the only control direction of university decision maker, lectures are shifted to low price period. Then this lecture scheduling naturally forces staff and students to shift their time in offices/slabs into high price period. So traditional DSM cannot directly influence the behaviour of non-controllable load. In new DSM, MicroMarket provides an influencing path to behaviours modification in noncontrollable section. Lectures are not fully shifted to low price period, which allows people to shift some of consumption in offices/labs into this period. Thus, it is more likely to obtain a global minimum for the main decision maker. In summary, traditional DSM has more courses in period of lower price and obtain a lower cost of classrooms only. DSM with microgrid fully considers both controllable load and non-controllable load. It can obtain a global optimal. Finally, cost per electricity unit of DSM with micro-market is 0.7977 CNY / kWh, comparing with 0.8504 CNY / kWh in traditional DSM.
• A demand side management scheme with Micro-market module
•
•
5.4. Analysis of results: performance of the self-crossover genetic algorithm In this section, the performance of typical optimization methods is compared with that of the SCGA. Four typical optimization methods are assessed: the traditional GA (in the MATLAB Toolbox), Lagrange multiplier optimization (in the MATLAB Toolbox), PSO and SA. Parameters of this numerical study is shown in Table S9 in Appendix A. Table 3 shows that the low performances of the traditional GA, LMKKT, PSO and SA are mainly due to constraint 2-1. In all cases that did not achieve a solution, this failure was due to the fact that constraint 21 was violated. Compared with traditional methods, the SCGA ensures the satisfaction of constraint 3-1 by SCO and has the best performance during optimization. The sensitivity analysis of rate S is shown in Fig. S11 in Appendix B.
is proposed. Because microgrids contain load-not-completely-controllable consumers, this paper integrates a small market environment into demand side management. With this new module, these originally non-controllable loads from sub-decision makers are able to be influenced. A University Based demand side management model with Micro-market is created. As university is a typical microgrid containing load-not-completely-controllable consumers. This paper constructs the model of controllable load section (courses timetable) and the model of non-controllable load section (devices usages in offices and labs). An optimization is finally created whose objective function is the total bill of both controllable and non-controllable loads. The relevant constraints include courses distribution, courses time satisfaction, office/lab working time insurance, unconventional behavior rejection and subsidy balancing. A Self-Crossover Genetic Algorithm is proposed for optimization solving. The target optimization is a nonlinear integer programming problem with equality and inequality constraints. This paper proposed a modified genetic algorithm (i.e. the self-crossover genetic algorithm) to solve this problem effectively. This algorithm contains a Self-Crossover section and can naturally ensure the target equality constraint satisfaction for all individuals if the initial population satisfy the same constraint. The proposed self-crossover genetic algorithm performs effectively in finding the optimal solution than traditional algorithms.
6.2. Future work Practically, universities are not the unique sites that contain loadnot-completely-controllable consumer. For example, some clustering factories pay the total power bill together but each sub-manufacturing unit plans schedule in its own way. So the proposed demand side management scheme with the micro-market module has the potential to
Table 2 Simulation details of traditional DSM and new DSM. Item Names
Initial
Traditional DSM
DSM with Micro-Market
NO. of Courses at 8:00–10:00 NO. of Courses at 10:00–12:00 NO. of Courses at 14:00–16:00 NO. of Courses at 16:00–18:00 NO. of Courses at 18:00–20:00 Cost of classroom Cost of Office/Lab Cost Per kWh
578 555 23 90 279 12906.446 949879.611 0.8394
600 588 17 11 369 12494.744 961835.835 0.8504
452 474 142 147 310 14162.361 889982.199 0.7977
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be extended to other flexible structures in the power market. New models and new market structures can be studied in the future to optimize microgrid operations.
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Acknowledgements This research was supported in part by the National Natural Science Foundation of China (51707041, 71704029, 71802056), in part by the Education Department of Guangdong Province (The Power Market Advanced Service for Load Monitoring Technologies, 2016KQNCX047), in part by the State Grid Energy Research Institute Project (Penetration Capability Research of Distribution Grid and The algorithm of Relevant Analyse Optimization Model) and in part by the State Grid (Suzhou) City & Energy Research Institute project (Critical Data Acquisition and Obtaining Method research on City Energy Research). Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apenergy.2019.113456. References [1] Dehnavi E, Abdi H. Optimal pricing in time of use demand response by integrating with dynamic economic dispatch problem. Energy 2016;109:1086–94. [2] Amini MH, Talari S, Arasteh H, Mahmoudi N, Catalao JPS. Demand response in future power networks: panorama and state-of-the-art. Sustain Interdependent Netw II 2019:167–91. [3] Giaouris Damian, Papadopoulos Athanasios I, Patsios Charalampos, Walker Sara, Ziogou Chrysovalantou, Taylor Phil, et al. A systems approach for management of microgrids considering multiple energy carriers, stochastic loads, forecasting and demand side response. Appl Energy 2018;226:546–59. [4] Muhssin MT, Cipcigan LM, Sami SS, Obaid Z. A Potential of demand side response aggregation for the stabilization of the grids frequency. Appl Energy 2018;220:643–56. [5] Zhang Menglin, Ai Xiaomeng, Fang Jiakun, Yao Wei, Zuo Wenping, Chen Zhe, Wen Jinyu. A systematic approach for the joint dispatch of energy and reserve incorporating demand response. Appl Energy 2018;230:1279–91. [6] Mirakhorli Amin, Dong Bing. Model predictive control for building loads connected with a residential distribution grid. Appl Energy 2018;230:627–42. [7] Jin M, Feng W, Liu P, Marnay C, Spanos C. MOD-DR: Microgrid optimal dispatch with demand response. Appl Energy 2017;187:758–76. [8] Qadrdan M, Cheng M, Wu J, Jenkins N. Benefits of demand-side response in combined gas and electricity networks. Appl Energy 2017;192:360–9. [9] Vuelvas José, Ruiz Fredy, Gruosso Giambattista. Limiting gaming opportunities on incentive-based demand response programs. Appl Energy 2018;225:668–81. [10] Yongli W, Yujing H, Yudong W, Ming Z, Fang L, Yunlu W, et al. Energy management of smart micro-grid with response loads and distributed generation considering demand response. J Cleaner Prod 2018;197:1069–83.
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