Hierarchical aggregation method for a scalable implementation of demand side management

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Hierarchical aggregation method for a scalable implementation of demand side management Bhagya Amarasekara∗, Chathurika Ranaweera, Rob Evans, Ampalavanapillai Nirmalathas Department of Electrical and Electronic Engineering, The University of Melbourne, Australia

a r t i c l e

i n f o

Article history: Received 27 February 2017 Revised 19 August 2017 Accepted 18 October 2017 Available online xxx Keywords: Demand side management Aggregation Residential users Distribution grids Scalability Optimization

a b s t r a c t Demand side management (DSM) aims to efficiently manage power flow by engaging energy customers, through offering incentives via price signals to alter their consumption patterns or directly controlling their loads. However, the integration of renewable energy generators and batteries in residential premises requires new approaches for DSM as they offer more flexibility. Moreover, as there are often a large number of residential energy customers within a distribution network, it is quite challenging to accommodate all of them in the DSM. In this paper, we propose an Aggregated Method (AM) that allows the treatment of distribution grid as a composition of several microgrids, which helps to aggregate underlying energy customers’ power and energy constraints and operating preferences. In addition, we provide methods for distributing the aggregated energy demand decisions among the participating energy customers. In contrast to the alternative centralized method, our approach requires less computational time to obtain decisions and hence scales well with increasing network size. Moreover, our results indicate that when using our method, energy customers receive more benefits through satisfying their energy requirements and operating conditions. Our overall analyses showed that the proposed framework can be easily adopted by the electricity market operators to create scalable DSM programs. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction The changes in the electricity distribution grid have resulted in rethinking of the electricity market (Aliprantis et al., 2010; Brown and Salter, 2011). Previously, electricity providers were more focused on the supply assuming that energy customers were unwilling or unable to change their power consumption patterns (Spees and Lave, 2007). Moreover, for demand side management (DSM) programs that aim to match the demand to the supply, industrial loads were the major contributors while residential and commercial energy customers contributed less (Eid et al., 2015). However, today, distribution level energy customers are increasingly participating in demand response programs by changing their consumption within desired limits according to the price. In addition, as energy customers can also integrate their own renewable energy sources on site (Mutale, 2006) and even storage capabilities (web, 2015), they could participate directly in the energy market to maximize benefits through an active orchestration of demand, usage patterns, generation, and storage of energy. With such changing customer expectations and behavior, it is also becoming necessary for the operators to maintain the quality and bal∗

Corresponding author. E-mail address: [email protected] (B. Amarasekara).

ance in the electricity grid through appropriate DSM mechanisms (Vandael et al., 2013). However, accommodating a large number of residential energy customers in DSM is challenging due to the large scale of the network. The computational complexity of designing DSM is tackled in literature through decision-making tools such as optimization (Anderson et al., 2011; Galus et al., 2010; Tushar et al., 2014) and game theory (Rasoul et al., 2015; Reka and Ramesh, 2016; Stephens et al., 2015; Tushar et al., 2015). However, integrating a large number of energy customers into these tools is problematic because as the number of decision variables increase, the time to compute the optimal decisions increases due to limited resources such as memory (Galus et al., 2010; Tushar et al., 2014). Therefore, in this paper, we investigate and provide an effective solution to the scalability of the DSM when incorporating a large number of distribution grid energy customers. We propose a hierarchical structure that scales well with increasing number of energy customers in the DSM. We begin by decomposing the distribution electricity grid as a set of microgrids interconnected by a transmission network (Asmus, 2010; Hatziargyriou et al., 2005). The microgrid is an island of the electricity network that interconnects electricity generators (both of traditional and distributed renewable), electrical loads from residential and commercial energy customers, and storage elements. As

https://doi.org/10.1016/j.cor.2017.10.008 0305-0548/© 2017 Elsevier Ltd. All rights reserved.

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Fig. 1. Architecture of the proposed framework.

these microgrids have an inbuilt energy generation and storage capacity to meet the energy demands inside the grid, they can be operated as isolated units at least partially over a certain operational time window. In addition, it is possible to manage the excess and shortfall in energy through the interconnection of microgrids and the transmission network. We represent these microgrids using an aggregation framework that sums up both physical and cost characteristics of the microgrid’s lower level entities to include in the DSM problem. This methodology allows DSM to be seen as a hierarchical system as illustrated in Fig. 1 - the transmission network as the upper level and the microgrids in the bottom level and thus this method is neither a fully centralized nor a distributed problem-solving approach. We then use those aggregated values of microgrid energy customers as opposed to individual energy customer integration for obtaining the optimal decisions through an optimization algorithm. This algorithm also incorporates the transmission network elements such as generators and industrial loads. In addition, we provide methods for distributing the optimal aggregated energy generation and demand decisions to individual energy customers in microgrids. We demonstrate the scalability of this approach by applying it to a standard network and then by increasing the size of the network and the number of time intervals in the scheduling horizon. In particular, our main unique contributions in this work are as follows: •

•

•

Formulation of an aggregation model for a microgrid in terms of its energy generation, storage capacity, and consumption patterns to fulfill DSM objectives. Development of specific algorithms to first optimize energy plans in DSM and then to distribute the optimal aggregated energy plans to individual microgrid energy customers. Evaluation of the proposed approach and a comparison of the performance with the benchmark model of the centralized approach.

Our analyses show that the proposed approach significantly decreases the computational time with increasing scale while suc-

cessfully achieving the goals of individual microgrid energy customers in DSM. The remainder of the paper is organized as follows. Section 2 presents related work and Section 3 describes the model of the transmission network, microgrids, and gateways. The formulation of aggregated models for microgrids, participation of these aggregated models in DSM, and distribution of optimal decisions obtained by aggregated entities to individual energy customers are presented in Section 4. Section 5 describes a use case of applying the proposed aggregated model into power markets and the comparison model. The key results of our model followed by comparative analyses are presented in Section 6. Section 7 concludes the paper. 2. Related work Approaches on incorporating residential energy customers in DSM has been explored in previous studies (Anderson et al., 2011; Galus et al., 2010; Li et al., 2011; Rasoul et al., 2015; Reka and Ramesh, 2016; Shi et al., 2014; Stephens et al., 2015; Tushar et al., 2015; 2014). The first approach is the centralized method (CM) in which energy scheduling is carried out by a centralized controller. This allows optimal energy schedules being achieved by using techniques like global optimization (Anderson et al., 2011; Galus et al., 2010; Tushar et al., 2014). A major problem of this method is the increasing computational complexity with the size of the network (Tushar et al., 2014). As a solution, approximation methods and algorithms such as gradient method (Zhang et al., 2014), evolutionary algorithm (Li et al., 2016; Vidal et al., 2014), and genetic algorithm (Awais et al., 2015) are proposed to solve the optimization problem. However, authors in Galus et al. (2010) showed that when the scale of the network increases, the controller could potentially face problems of running out of memory space even with approximation methods as the optimization space grows exponentially with the number of users. The second method is the distributed approach, where the above global optimization problem is distributed across the number of participants in DSM program and each participant is then

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charged with solving a local optimization problem (Li et al., 2011; Shi et al., 2014). Many proposals favor this distributed approach as entities can utilize their private information in local optimization problems rather than sending them to a global problem solver. Game theoretical methods can be also used as the solving method in distributed DSM problems (Rasoul et al., 2015; Reka and Ramesh, 2016; Stephens et al., 2015; Tushar et al., 2015). Particularly in Tushar et al. (2015), authors presented a game theorybased distributed model for incorporating large-scale participants. However, to reach an optimum value in this distributed scheme, DSM entities have to exchange locally optimized values in repetitive iterations. This creates a significant communication overload between the DSM entities, raising a scalability issue with increasing size of the network. To mitigate the issues associated with the previous proposals, in this paper, we propose and demonstrate a hierarchical approach towards a scalable DSM framework. This approach includes aggregated models of the energy customers clustered in microgrids of the distribution grid. Formation of aggregated models to represent the distribution grid has been previously investigated for different applications. For instance, authors in Parvania et al. (2013) have proposed a demand response aggregation framework, where aggregators accumulate energy customers with the same demand response strategies and policies, such as load curtailment and load shifting. Moreover, authors in Nguyen and Le (2015) have extended the model proposed in Parvania et al. (2013) by incorporating the risk of getting low profits of microgrid aggregators. However, the models proposed in Parvania et al. (2013) and Nguyen and Le (2015) are only combining demand response strategies without considering the physical device constraints. In addition, an aggregation model of a fleet of electrical vehicles (EV) for DSM is presented in Vandael et al. (2013). This work considered the physical device constraints and cost characteristics of EVs when formulating the aggregated model. As opposed to Vandael et al. (2013), our work incorporates different microgrid entities without only considering EVs and proposes different decomposition methods for the obtained aggregated decisions. Moreover, aggregators are widely formed in electricity market bidding schemes where agents that represent microgrids are first formed in order to calculate energy schedules of underlying entities and then they submit bids to the market (Joo et al., 2015; Kim and Thottan, 2011; Li et al., 2016; Parhizi et al., 2016; Parvania et al., 2013). In these schemes, aggregators have their own objective of maximizing profit. Thus, two optimization problems are formed (Gkatzikis et al., 2013; Joo et al., 2015; Kim and Thottan, 2011; Manshadi and Khodayar, 2016; Parhizi et al., 2016; Parvania et al., 2013; Yang et al., 2015), one at the upper transmission level network considering representative models for the lower level, and another at the lower level to distribute the decisions made by the upper level. However, solving two centralized optimization problems might still lead to a problem in terms of scalability. Thus, in this paper, we develop a hierarchical framework for the DSM problem, which incorporates aggregators that simply represent underlying network entities, but do not have their own objectives as in Gkatzikis et al. (2013). We accommodate them in such a way that the supply-demand balance is maintained and individual objectives of the energy customer are fulfilled. Moreover, rather than solving another optimization framework at the lower level for distributing the values obtained by aggregators, we present simplified methods of obtaining energy schedules for individual energy customers. The scope of this paper is to propose a scalable DSM that incorporates all the electricity network elements. Therefore, in this work, we consider electricity grid customers such as generators, batteries, and consumers such as industrial, commercial, and residential. In particular, for residential customers, we control their individual household appliances within the acceptable power and

3

comfort limits to achieve cost-effective supply-demand balance. It is also noteworthy that there are significant studies conducted in home energy management by using methods such as modelpredictive control techniques (Godina et al., 2016; Rodrigues et al., 2017), linear programming (Chen et al., 2013), and game theory (Rottondi et al., 2017). 3. System model In this section, we introduce the modeling of the electricity network components, which is needed for our aggregation framework presented in the next section. We decompose the electricity grid into four units: microgrids, gateways, transmission network, and transshipment nodes as illustrated in Fig. 1. Transshipment nodes are components in the power system, which do not consume or generate the electricity such as transformers that only change the voltage level of the network. Moreover, throughout the formulation, we make the following assumptions: 1. All energy customers in the electricity network actively participate in the DSM; 2. The reactive power demand inside the grid is catered for, and all energy customers receive the voltage within the acceptable limits; 3. All investment costs have already been paid over, and the operational and maintenance costs are negligible for nondispatchable generators; 4. We ignore the startup and shutdown costs and consider only costs associated with the electricity generation for dispatchable generators; 5. The factors that limit the power output and input of batteries, such as temperature and internal resistance, are included in the battery efficiency parameters; 6. All of the installation costs of the batteries have already been paid; 7. The network is built with perfect conductors, which allow zero power loss in transmission lines. Note that hereafter, the aggregated power, energy, and cost models of the microgrid are denoted by capital letters while individual device constraints are denoted by lower case letters. 3.1. Microgrids A microgrid consists of both conventional and renewable power generation entities, residential and commercial loads, and energy storage entities. The detailed modeling of these entities is presented in Table 1. In this work, we consider solar, wind, and diesel as energy sources inside a microgrid. The power generated by solar panel, wind plant, and diesel generator in the kth microgrid are i,k i,k denoted by pi,k s , pw , and pd , respectively. The cost of the diesel

generator is denoted by cdi,k . We denote the power consumed by the commercial customer j j as pc . For a residential customer, we consider that a house will have three types of appliances depending on their power requirement and operational time, C1 , C2 , and C3 . Class 1 load (C1 ) is a l, j,k non-interruptible load that requires constant power ( pr1 ) during its operational period, for example, lighting. A Class 2 device (C2 ) such as a washer, a dryer, and an electrical vehicle has a fixed l, j,k,req energy requirement (er2 ) that should be fulfilled before the device’s leaving time. The third type is the Class 3 device (C3 ) that allows changing its power consumption within certain limits, for example, an iron, an air condition unit, a space heater, and an entertainment device. The power and energy of C2 and power l, j,k l, j,k l, j,k of C3 devices are denoted by pr2 , er2 , and pr3 , respectively. Each residential energy customer that owns a C3 device would

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B. Amarasekara et al. / Computers and Operations Research 000 (2017) 1–12 Table 1 Individual element models in kth microgrid. Element

Model

Battery m ∈ B

pm,k (t ) ≤ pb ≤ pm,k b b

m,k

em,k b em,k b m,k

(1)

(t + 1 ) = (t ) + pm,k (t ) × t (2) b m,k (3) ≤ em,k (t ) ≤ e (τ ) = em,k,req (4) b em,k b

e where maximum and minimum capacity limits, end of the scheduling horizon energy, minimum discharging and maximum charging rates of m,k m,k , em,k,req , pm,k , and pb , respectively the mth battery are eb , em,k b b b  m,k T −2 m,k (Chen et al., 2009). cbm,k = αbm,k t∈T pm,k ( t ) − β t=0 pb (t + b b  1 ) pm,k (t ) + γbm,k t∈T (min( pm,k (t ) − δ m,k em,k,max , 0 ))2 +  m,k (5) b b b where, αbm,k , βbm,k , γbm,k , δbm,k , and  m, k are positive constants and

Photovoltaic panel (PV) i ∈ PV

Wind plant i ∈ WP

Generator i ∈ MG

αbm,k > βbm,k (Li et al., 2011). i,k i,k Ai,k pi,k s (t ) = ξs s rs (t ) (6) i,k where, ξsi,k is the efficiency, Ai,k s is the PV panel area, and rs (t ) is the

solar irradiation at time t (Chedid et al., 1998; Villalva et al., 2009). ⎧ for v ≤ vi and v ≥ v0 ⎨0, pi,k w (t ) =

⎩

pi,k wr (v−vi ) v r −v i , pi,k wr ,

for vi ≤ v ≤ vr

(7)

for vr ≤ v ≤ vo

where pi,k wr , v , vi , vr , and vo represent rated power of the wind plant, wind speed, cut-in wind speed, rated wind speed, and cut-out wind speed, respectively. (Wang and Gooi, 2011). (8) (t ) ≤ pi,k pi,k ≤ pi,k d d d i,k

where pi,k is minimum and pd is maximum power generation limits. d cdi,k

Residential customer j ∈ LR

=α

i,k d



()

pi,k t d i,k i,k , , d d

2

β

γ

()

t + di,k (9) + di,k pi,k d and di,k are ith generator related (10) l ∈ C1 pl,r1j,k t = l, j,k t

γ constants. where, α β () μ () Class 1 device where, μl, j, k (t) is a time varying constant. Class 2 device l ∈ C2 l, j,k pl,r2j,k ≤ pl,r2j,k (t ) ≤ pr2 , for t = tsl,2j,k , . . . , tel,2j,k (11) tel,2j,k l, j,k l, j,k,req (12) l, j,k pr2 (t ) = er2 ts2

el,r2j,k (t + 1 ) = el,r2j,k (t ) + pl,r2j,k (t ) × t, for t = tsl,2j,k , . . . , tel,2j,k

(13)

l, j,k

Commercial customer j ∈ LC

where, pr2 , pl,r2j,k , tsl,2j,k , and tel,2j,k are maximum and minimum power limits and start and end time of the device. Class 3 device l ∈ C3 l, j,k pl,r3j,k ≤ pl,r j,k (t ) ≤ pr , for t = tsl,3j,k , . . . , tel,3j,k (14) where, minimum and maximum power limits and arrival and l, j,k departure time are denoted by pl,r3j,k , pr3 , tsl,3j,k , and tel,3j,k , respectively. User utility function for C3 devices is, ul,r j,k (t ) = ωl, j,k ( pl,r3j,k (t ) − pl,roj,k )2 , l ∈ C3 (15) pcj (t ) = θ j (t ) (16) where, θ j (t) is a time varying constant.

like to operate the device to experience a maximum satisfaction l, j,k level. We capture this desire by a convex utility function ur (t ) for devices l ∈ C3 in Eq. (15), which shows the deviation from a l, j,k set point of power consumption ( pro ) decided by the individual customer. This utility function indicates the customer dissatisfaction and ωl, j, k , the weighing factor is changing among energy customers. The power, energy, and cost of operating a battery is denoted by pm,k , em,k , and cbm,k , respectively. Also, three b b terms in the battery cost model correspond to fast charging, charging/discharging cycles, and deep discharging, respectively. 3.2. Gateways There are two types of gateways that we form in this study, transmission network gateways (T-Gs) and microgrid gateways (MG-Gs) that are illustrated in Fig. 1. These gateways have discrete modes that can be represented by the status of remotely controlled switches. 3.2.1. Transmission network gateways (T-G) Generators and loads that are attached to the transmission network should connect the network via T-Gs. Therefore, T-Gs can have either the discrete mode mg if the underlying connection type is generator or the discrete mode mi if it is connecting an industrial load. These two modes mg and mm are expressed in

Eq. (17) and Eq. (18), respectively.

⎧ ⎪ ⎨1,

If a generator 2, If a generator mg = −1, If a generator ⎪ ⎩ 0, If a generator

is is is is

supplying power starting shutting down off.

(17)

mi =

1, If connected to a load 0, If not connected to a load.

(18)

3.2.2. Microgrid gateway (MG-G) A MG-G is located at the point of common coupling (PCC) in the microgrid and it makes the connection between the transmission network and the microgrids. A MG-G can have either of following three modes:

mm =

1, If the microgrid exports power 0, If the microgrid is disconnected −1, If the microgrid imports power.

(19)

If the operator would like to operate the microgrid in an isolated manner, then the mode, mm , is 0. If the microgrid is supplying power to the main grid, then the mode is 1 whereas if it imports power from the transmission grid, then the mode is −1.

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3.3. Transmission network

4.1. Aggregation of microgrid elements

Both large-scale conventional generators and industrial energy customers that have higher demand are present in the transmission network. The power generated by the transmission network generator i ∈ TG at a given time t is modeled by,

4.1.1. Power generators Power generation inside a microgrid includes photovoltaic (PV) panels, wind plants, and conventional generators. The total power generated by PV panels of one microgrid is the total of all the power generated by solar panels inside it. The individual power generation of a solar panel is given by Eq. (6), which depends on the PV panel area, efficiency, and the solar irradiation. Thus, the total power generated by all PV panels (Psk (t )) in kth microgrid can be expressed as,

pig ≤ pig (t ) ≤ pg , i

(20)

where, pig and pig are the maximum and minimum power limits. Also, we assume that the generation cost function of a thermal generator takes the form of a second-degree polynomial function (Moon et al., 20 0 0) where its coefficients are determined by the least squares method (El-Hawary and Mansour, 1982) utilizing input-output curves and fuel type characteristics. Hence, the cost model of the generator i attached to the transmission grid is given by

cgi

=α

i g

2 pig

(t ) + β

i g

pig

(t ) + γ

i g,

(t ) = δ (t ), j

(22)

where, δ j (t) is a constant that is varied according to the time.



pi,k s (t ).

(25)

∀i∈PV

Likewise, the total wind power inside kth microgrid, Pwk (t ) is denoted by,

Pwk (t ) =



pi,k w (t ).

(26)

∀i∈WP

(21)

where, αgi , βgi and γgi are ith generator-related constants. We model the industrial loads that are connected to the transmission grid as time-dependent constant power loads. These industrial loads can have both active power and reactive power demands. As per assumption 2, the reactive power demand of these loads is catered. Then, the active power demand of the jth (j ∈ LI ) j industrial load, pq (t ) can be expressed as

pqj

Psk (t ) =

The total power generated by the conventional generators inside the kth microgrid, Pdk (t ) is subjected to accumulated minimum   k (P kd = ∀i∈MG pi,k ) and maximum power (P d = ∀i∈MG pi,k ) limits as d d expressed by k

P kd ≤ Pdk (t ) ≤ P d .

(27)

In addition to the power generation model, the generator also has an associated cost model. Thus, for the cost function of the aggregated generator model in a microgrid, we form the following equation:

Cdk = αdk (Pdk (t ))2 + βdk Pdk (t ) + γdk , 3.4. Network rules

where,

According to the Kirchhoff’s nodal rule that governs the power flow in the whole electricity network, we formulate Eq. (23), which states that the power entering a node should be equal to zero. If the node set in the electricity network is N and link set is A = N × N, we denote xij as the power flow of link (i, j) where i, j ∈ N. The value of bi is positive if it is a generator node, negative if it is a load node or zero if it is a transshipment node. Transshipment node is a node that only alters the status of the network while not contributing to changes in active power flows.

 j:(i, j )∈A



xi j −

x ji = bi

(23)

j:(i, j )∈A

Because of the Assumption 2, we do not consider devices that contribute to the reactive power of the grid (e.g. capacitor banks). Therefore, xij in the above equation corresponds to active power flow only. These active power flows are limited by physical characteristics of transmission lines which are expressed by

0 ≤ x i j ≤ xi j ,

(24)

where, xi j is the maximum limit of the power flow in link (i, j). We assume that for the distribution level links, xi j is infinite, whereas for the transmission level links it has a finite value. 4. Proposed framework Our proposed framework includes three parts, aggregation of microgrid elements considering both physical limits and cost models of underlying elements, participation of these aggregated models in the DSM problem to obtain optimal decisions, and distribution of these aggregated decisions to the lower level energy customers.

αdk

=



i,k ∀ i ∈ M G αd ,

βdk

=

(28)



i,k ∀i∈MG βd ,

and

γdk

=



∀i∈MG γd . i,k

4.1.2. Power consumers In the microgrid, there are two types of energy customers, commercial and residential. The aggregated power consumption model of commercial energy customers can be expressed as in Eq. (29), which is the total power consumed by all the commercial customers in the kth microgrid.

Pck (t ) =



pcj,k (t )

(29)

∀ j∈LC

As residential energy customers have three types of appliances, we aggregate the power consumption of them according to the appliance category. The aggregated model of C1 devices (base load) can be expressed as follows: k Pr1 =

 

∀ j∈LR ∀l∈C1

pl,r1j,k (t ).

(30)

As the C2 devices have power limits, the aggregated model of C2 k

devices are subjected to maximum (P r2 ) and minimum (P kr2 ) power limits. k

∀t

P kr2 ≤ Prk (t ) ≤ P r2 , where,  

P kr2 =



∀ j∈LR

(31) 

l, j,k

∀l∈C2 pr2 ,

∀t

and

k

P r2 =

∀t. Moreover, starting time of the aggregated C2 model is the earliest of starting time of all C2 devices while ending time is the latest of the ending time of all C2 devices in kth microgrid. For the purpose of aggregating energy limits of C2 devices, we first derive new minimum and maximum energy l, j,k l, j,k limits (er2 and er2 ) of an individual C2 appliance considering start and end times, and energy requirements of the device as follows. We have illustrated an example of two individual C2 ∀ j∈LR

l, j,k

∀l∈C2 pr2 ,

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Fig. 2. Example of individual energy limits of two C2 devices.

Fig. 4. Individual energy limits of two batteries.

Fig. 3. Example of aggregated energy of the C2 appliances.

Fig. 5. Aggregated energy of two batteries in the microgrid.

device’s new energy limits formed according to Eqs. (32) and (33) in Fig. 2.

k (t )) is also limited by The aggregated power of C3 devices (Pr3 the aggregated minimum and maximum limits as expressed in Eq. (36). These aggregated limits are obtained through the summation of respective power limits of all C3 devices in the kth microgrid.

el,r2j,k = max(0, el,r j,k,req − pr2 (tel,2j,k − t )) l, j,k

for l ∈ C2 l, j,k





er2 = min el,r j,k,req , pl,r2j,k t − tsl,2j,k

(32)



for l ∈ C2

k

k P kr3 ≤ Pr3 (t ) ≤ Pr3

(33)

k ) is Then the aggregated C2 appliance model’s energy (Er2 bounded as in Eq. (34), where the minimum and maximum energy

When formulating the aggregated cost model for C3 devices in microgrid, we take the average of ωl, j, k inside a microgrid as the weighing parameter. Therefore, the aggregated user utility function (Urk (t )) can be formulated as:

k

of aggregated model, (E kr2 and E r2 , respectively) are the summation of respective parameters of all C2 devices in all houses inside kth microgrid. k

k E kr2 ≤ Er2 (t ) ≤ E r2

(34)

(36)

Urk (t ) = (

1  nr3

ωl, j,k )(Pr3k (t ) −

∀ j ∀l∈C3

k = where, Pro microgrid.



∀j



k 2 Pro ) ,

(37)

∀ j ∀l∈C3



l,k, j

∀l∈C3 pro

and nr3 is the all C3 devices inside a

The energy and power relationship of aggregated C2 model is expressed in Eq. (35). Fig. 3 illustrates an example of the energy limits of the aggregated model of C2 appliances with two C2 devices.

4.1.3. Energy storage In order to form the microgrid aggregated battery model constraints, we first modify the constraints of Eqs. (2)–(4) as follows to

k k Er2 (t + 1 ) = Er2 (t ) + Pr2k × t, ∀l ∈ C2

form new minimum (eˆb ) and maximum (eˆ

(35)

m,k

m,k

) energy constraints.

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7

Fig. 6. Overall model detailing the transmission network and one microgrid.

Fig. 7. Power limits of C1 base load and the solar irradiation.

Fig. 4 shows an example of energy limits of two individual batteries that are formed according to these new energy limits. m,k

eˆb

= max(em,k , em,k (0 ) − pm,k t, b b b em,k,req − pb (t − τ )) b m,k

m,k

eˆ

= min(eb , em,k (0 ) + pb t, b m,k

(38)

m,k

em,k,req − pm,k (τ − t )) b b

(39)

Fig. 8. Comparison of power generation inside microgrid.

Then, the aggregated model’s battery power and energy are limited by minimum and maximum power and energy limits, respectively. These limits are formed through the summation of individual battery limits, particularly power limits in Eq. (1) and energy limits in Eqs. (38) and (39). Eqs. (40) and (41) denote aggregated power and energy limits while Eq. (42) shows the

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Fig. 9. Comparison of energy storage inside microgrid.

Fig. 10. Comparison of power consumption inside microgrid.

relationship between power and energy of the aggregated battery model.

P kb ≤ Pbk (t ) ≤

k Pb

(40)

k

E kb ≤ Ebk (t ) ≤ E b

(41)

Ebk (t + 1 ) = Ebk (t ) + Pbk (t ) t

(42)

Fig. 5 shows an example of aggregated energy limits that includes two batteries inside a microgrid. Aggregated battery cost model (Eq. (43)) takes the same form  of Eq. (5), but with aggregated constants (αbk = ∀m∈B αbm,k , βbk =    m,k m,k m,k k k ∀m∈B βb , γb = ∀m∈B γb , and b = ∀m∈B b ).

Cbk = αbk



Pbk (t ) − βbk

γ



Pbk (t + 1 )Pbk (t )+ (43)

t=0

tinT

k b

T −2 

(min( (t ) − δbk Ebk,max , 0 ))2 + bk Pbk

tinT

4.2. Participation in the DSM In this subsection, we formulate the DSM problem using the optimization tool. All the network elements in both transmission and distribution grids, which have active contribution to the changes in the power flow, should be incorporated to the DSM problem. While transmission elements can participate directly in the DSM, the distribution grid elements participate in DSM in the form of aggregated models, which were formulated in the previous subsection. When formulating the DSM problem, we impose a market rule such that all the PV panels and batteries installed in the individual households participate in the market separately. This rule leads to the prohibition in using the distributed power generation directly for individual household consumption. The overall system’s objective is to achieve the maximum social welfare. Therefore, under previously stated assumptions and rules, such a problem can be formulated as

Minimize



∀i∈TG

cgi (t ) +



(Cdk (t ) + Urk (t ) + Cbk (t ))

∀k

subject to (1 ) − (3 ), (21 ) − (31 ), (34 ) − (37 ), (40 ) − (43 ).

(44)

This optimization problem aims to minimize the cost of generation, cost of operating the batteries, and user dissatisfaction. The decision variables of power generation and consumption are constrained by physical and cost limits of both transmission grid elements and aggregated models. 4.3. Distribution of the aggregated decisions As the microgrid participates in DSM as one unit, it is important to establish methods to obtain individual power parameters for entities that form the aggregated microgrid model. Thus, we propose the following methodology for distribution of the aggregated decision values among microgrid energy customers: 4.3.1. Power generators Renewable energy sources are aggregated by summing up their power generation. As the network has the policy of consuming all the energy generated by the renewable energy sources, their individual values would not change. However, for allocating power to individual dispatchable generators, we solve the following optimization problem for the kth microgrid:

Minimize Subject to

 ∀i∈MG

 ∀i∈MG

cdi,k (t )

pi,k (t ) = P˙dk , (9 ), d

(45)

where, P˙dk denotes the optimal power obtained for the kth microgrid’s aggregated dispatchable generation after solving Eq. (44). 4.3.2. Power consumers As the power consumed by commercial energy customers is represented by a constant, their power consumption remains the same. This is also true for the residential customer’s C1 devices, which provide the base load. However, C2 and C3 devices need power distribution algorithms. For C2 devices, we formulate such an algorithm as follows. If some of the devices should fulfill their energy requirement in the next time slot, priority is given to them, and their energy requirements are immediately satisfied. Let us dek note Prem as the remaining amount of power from the optimal 2 k ) after satisfying those priority power allocated for C2 devices (P˙r2

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9

Fig. 11. Comparison of individual user dissatisfaction for five user types.

devices’ power requirements. Then, for all other C2 devices, we call, j,k culate a priority factor φ2 , which is expressed as

φ

l, j,k 2

=

el,r2j,k,req l, j,k

tej,k pr2 2

,

(46)

where, priority factor φ2 depicts the urgency in acquiring the required energy limit of the C2 device. Then, the power for C2 devices will be allocated according to l, j,k

pl,r2j,k (t ) = 

φ2l, j,k



∀j

l, j,k ∀l∈C2 φ2

k Prem 2.

(47)

For C3 devices too, we calculate a priority factor, φ3 given by

l, j,k

φ3l, j,k = ωl, j,k pl,roj,k .

, which is

(48)

Note that the above equation considers the user defined ωl, j, k factor. Then, we take the weighted sum and allocate the obtained k ) fairly to all C devices as aggregated power for C3 devices (P˙r3 3

pl,r3j,k (t ) = 

φ3l, j,k



∀j

∀l∈C3

φ3l, j,k

k P˙r3 .

(49)

4.3.3. Energy storage For the assignment of individual battery charging and discharging power patterns, we form an optimization model as

Minimize



∀m∈B

subject to



∀b∈B

cbm,k (t )

pm,k (t ) = P˙bk , (16 ) − (20 ), b

(50)

where, P˙bk is the optimal value obtained by the aggregated model.

5. Simulation model 5.1. Physical model As the transmission network, we have used the modified IEEE 14 bus test network (Christie, 20 0 0) that is illustrated in Fig. 6. We have extended the network by replacing the fixed loads with microgrids and replaced synchronous condensers with transshipment nodes. Each microgrid is modeled following the IEEE 13 bus distribution system (13b, 1992). We have formed 11 microgrids that connect to the transmission network. Two generators with a maximum capacity of 100 MW and 200 MW are attached to the transmission grid. However, we have excluded the industrial loads and commercial loads as our focus is on large-scale residential loads. All households in a microgrid are categorized into five user types and all users have two C2 devices and two C3 devices. Parameters for these four appliances of five user types are given in Table 2. C1 device’s power consumption is randomly obtained through maximum and minimum limits that are depicted in Fig. 7. Also, we assume that the solar irradiance follows a similar pattern throughout the area under consideration. Therefore, all the PV units of the network are subjected to solar irradiance level that is also depicted in Fig. 7. Note that all the values in Fig. 7 have scaled down to unity. Moreover, we deploy two micro-generators in a microgrid each with a capacity of 20 kW and 50 kW. We chose parameters for efficiency and the area for PV panels such that their maximum capacity was 1.5 kW, 3 kW, or 5 kW. Fifty percent of residential users have installed one of three types of PV panels. Moreover, 50% of users who already installed PV panels have also installed one of three types of batteries in their premises. Parameters for PV panels and the battery types are given in Table 3. Also, none of the microgrids has wind plants, and gateways can have either state depending on the market decision.

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B. Amarasekara et al. / Computers and Operations Research 000 (2017) 1–12 Table 2 Parameters of residential user appliances. Device

Parameters

User type 1

User type 2

User type 3

User type 4

C2 Device 1

pr2 , pl,r2j,k

1.4, 0

N/A

N/A

1.5, 0

1.4, 0

tsl,2j,k , tel,2j,k

6 pm, 6 am

7 pm, 5 am

8 pm, 6 pm

j,req el,k, r2

10

C2 Device 2

C3 Device 1

C3 Device 2

l,k, j

12

14

1.2, 0

1.0, 0

1.5, 0

2.1, 0

2.5, 0

tsl,2j,k , tel,2j,k

8 pm , 5 pm

8 pm, 6 am

9 pm, 5 am

10 pm, 4 am

8 pm, 6 am

j,req el,k, r2

3

4

3

5

4

2.2, 0

2.4, 0

N/A

N/A

2.5, 0

tsl,3j,k , tel,3j,k

10 am, 10 pm

11 am, 11 pm

ωl, k, j

8

9

pr3 , pl,r3j,k

0.4, 0

0.3, 0

l,k, j

pr2 , pl,r2j,k

l,k, j

pr3 , pl,r3j,k

l,k, j

10 am & 8 pm

10 am

7 pm

8 am

12 am & 12 pm

12 am

10 pm

11 am

ωl, k, j

8

9

10

11

12

Type 1 : eb = 3 kWh, em,k = 0.5 kWh, em,k,req = 2.4 kWh b b m,k m,k em,k ( 0 ) = 1.5 kWh, p = -1 kWh, pb = 1 kWh b b

panels is same for both CM and AM as we fully utilized the PV power in both cases. However, more power is generated by microgenerators in CM than AM except at 6 am, 7 am, and 8 pm. We can see that the major load changes in the network happen during these three intervals. For example, all EVs leave their charging stations by either 6 am or 7 am. Also, 60% of washers are starting to request power at 8pm. Therefore, in order to satisfy the need, AM allocates more power to loads during these periods.

m,k

m,k

Type 2 : eb = 7 kWh, em,k = 1 kWh, em,k,req = 5.6 kWh b b m,k m,k em,k ( 0 ) = 3.5 kWh, p = -1.5 kWh, pb = 1.5 kWh b b m,k

Type 3 : eb = 12 kWh, em,k = 2 kWh, em,k,req = 9.6 kWh b b m,k (0 )= 6 kWh, pm,k em,k = -3 kWh, pb = 3 kWh b b Capacity: 20 kW, αgi =0.05, βgi =0.4, γgi =0 Capacity: 50 kW, αgi =0.08, βgi =0.6, γgi =0 Capacity: 200 MW, αdi,k =0.2, βdi,k =0.9, γdi,k =0 Capacity: 100 MW, αdi,k =0.2, βdi,k =0.9, γdi,k =0

6.1.2. Energy storage The amount of power allocated to energy storage devices in the microgrid is shown in Fig. 9. Here, it is shown that the power allocated for the aggregated battery model in AM is different from that of CM. This happens because of the changes in the battery cost function between these two models.

5.2. Comparison model Our proposed model for solving the DSM optimization problem is a hierarchical approach with aggregators, which is not fully centralized or distributed. Hence, to compare the results given by our model, we have chosen the fully CM, such as the one that is formulated in Xing et al. (2015) as the benchmark model. In the benchmark model, upper level controller solves the following optimization problem for every component in the network: ∀i∈TG

  ∀k ∀m∈B

 

cdi (t ) +

∀k ∀i∈MG

cbm,k (t ) +

0.4, 0

12 pm & 10 pm

Batteries

cgi (t ) +

0.5, 0

8 am & 6 pm

Capacities: 1.5 kW, 3 Kw and 5 kW



10 0.5, 0

tsl,3j,k

PV panels

Minimize

12 pm, 1 am

tel,3j,k

Table 3 PV panels, batteries and generators parameters.

Generators

User type 5



ul,r j,k (t )

(51)

∀k ∀l∈C3

subject to (1 ) − (3 ), (7 ) − (22 ). 6. Results and discussion In this section, we present the behavior of our proposed aggregation model where all the results are compared with the benchmark model formulated in Section 5. 6.1. Power allocation at aggregation point level First, we analyze the power generation, consumption, and storage allocation at the aggregation points and results are only shown for microgrid 1. 6.1.1. Power generation Micro-generators and PV panels installed by residential energy customers are the two sources of power inside a microgrid. We compare the power provided by these two sources under DSM implemented with AM and CM in Fig. 8. Power generated by PV

6.1.3. Power consumption In our model, residential load is composed of three appliance classes. In Fig. 10, we compare the power allocation for these three device classes between AM and CM. As we can see from the figure, the AM can allocate more power to the underlying devices in most of the time periods. Hence, it can be shown that participating demand response schemes as an aggregated unit allows more power allocation to energy customers than participating as individuals. So far, we have analyzed the power characteristics at the aggregation point. Next, we analyze the fulfillment of power and cost requirements at the energy customer level. 6.2. Power allocation at energy customer level 6.2.1. Residential energy customer satisfaction In our formulated optimization problem, the main aim was to reduce generation and storage cost while minimizing user dissatisfaction for C3 devices. Fig. 11 shows the user dissatisfaction obtained for AM and CM for the five user types we used in this work. For user 1–4, AM provides less dissatisfaction than CM model. However, for user 5, AM has a higher dissatisfaction than CM only between 11pm and 2pm. Therefore, we can state that our proposed AM has a higher capability to satisfy the user demands most of the time. 6.2.2. Cost born by individual energy customer with PV and battery Here, we studied the cost that has occurred through power import when using AM. Under the policy used in this work, the user has to pay for the net power obtained from the grid. Hence, the cost reduces when the net import amount of the power from the grid is reducing. In Fig. 12, we have compared the revenue of a

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Fig. 12. Net power of individual user type.

11

Fig. 13. Comparison of scalability with increasing energy customers.

user without both a PV panel and a battery, a user with a PV panel but without a battery, and a user with both a PV panel and a battery. As we can see from the figure, when the user is accommodating a PV panel, the user imports less energy from the main grid compared to a user without a PV panel. If the user further installs a battery, then under the policy studied in this paper, the user benefits from less amount of energy import from 8 am to 3 pm. However, from 3 pm to midnight, charging of the battery causes an additive effect on net import. It is noteworthy that this behavior can be changed according to policies such as reward schemes. 6.3. Scalability In this section, we compare the scalability of our proposed AM approach with the benchmark model of CM. For the metric, we used the execution time of the two models. We varied the scale of the problem by two methods, by changing the number of users that are associated with a microgrid and by changing the time slot size. First, we evaluated two models with users ranging from 1100 to 110,0 0 0 within a one-day time period with one-hour time slots and the computation times for both AM and CM are shown in Fig. 13. Each simulation is repeated 10 times with different user consumption, generation, and storage settings and then the average computation time for these runs is obtained. Simulations are executed using a workstation with a processor of 3.4 GHz, 8 cores and 8 GB RAM. As both CM and AM are formed as convex optimization problems, the computational time is bound to be polynomial (Vandael et al., 2013). As shown in the figure, the CM’s execution time is several orders higher than AM due to the increasing computational space. In addition, due to the memory capacity limitation, CM could not solve for users more than 3300, while the proposed AM was able to provide optimized values for the range of users we were interested in. This was mainly because the variables of the optimization problem solved by the upper level controller did not increase in AM due to the fixed number of aggregation points. However, the time taken to form aggregated models and to distribute the optimal decisions increased with the number of residential users. Next, we increased the time slots for a one-day time period from one-hour to five-minute time intervals. The results are shown in Fig. 14, where the computation time is the average of 10 repetitive simulation runs with different PV power generation and user

Fig. 14. Comparison of scalability with increasing time slots.

consumption values. Though execution time of both methods increased with number of time slots, the proposed AM has a lower magnitude of execution time than CM. 6.4. Evaluation summary In this work, we proposed the AM as a solution for the largescale DSM problems while the results are benchmarked with CM. The proposed AM has an advantage over CM as it preserves the privacy more than CM. This is because CM requires the privacy concerned data of all network elements while in AM, aggregators require the privacy data of only their underlying network elements. Moreover, to further improve the privacy treats in AM, the data aggregation step at the aggregators can utilize privacy preserving techniques such as cluster-based private data aggregation and slice-mixed aggregation (Li et al., 2009). Simulation results analyzed at the aggregation point show that the AM is able to maintain a lower cost for generation inside the microgrid most of the time. Moreover, it promises a higher power allocation for residential loads than CM. At the individual energy

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customer level, simulation results show that AM is providing better power allocation to energy customers leading to a higher satisfaction level for C3 devices. These results establish the fact that participating demand response programs as a group or community leads to a better satisfaction level than the individual participation most of the time. Moreover, we compared the net power imported from the grid for a user when a PV panel and a battery is installed. In regards to the policy used in this paper, we see that though installing a PV panel reduces the net import, battery installation does not yield a reduction in import at all times. Finally, in terms of scalability, AM scales well with increasing number of users and time slots compared to the benchmark model. 7. Conclusion In this paper, we focused on the problem of accommodating large-scale distribution level residential users with smart grid DSM. As the main obstacle for incorporation was the large dimension of users, we proposed an AM to reduce the scale of the problem. In particular, we formed microgrids that aggregate underlying users’ physical device and cost constraints by establishing certain rules. After obtaining aggregated decisions for a model, these values should be distributed among individual energy customers. To this end, we have proposed simple power distribution methods to satisfy the individual energy and market needs of the energy customers. Our proposed approach was deployed in a test power network and compared with the fully CM. The results showed that when participating in a DSM problem as an aggregated unit, the satisfaction of the residential users increased due to higher power allocation. This result is further verified by the individual energy customer level analyses. Moreover, we showed that when using this model, the computation time significantly decreased compared to using a centralized approach. References Aliprantis, D., Penick, S., Tesfatsion, L., Zhao, H., 2010. Integrated retail and wholesale power system operation with smart-grid functionality. In: Proceedings of IEEE PES General Meeting. IEEE, pp. 1–8. Anderson, R.N., Boulanger, A., Powell, W.B., Scott, W., 2011. Adaptive stochastic control for the smart grid. Proc. IEEE 99 (6), 1098–1115. Asmus, P., 2010. Microgrids, virtual power plants and our distributed energy future. Electr. J. 23 (10), 72–82. doi:10.1016/j.tej.2010.11.001. Awais, M., Javaid, N., Shaheen, N., Iqbal, Z., Rehman, G., Muhammad, K., Ahmad, I., 2015. An efficient genetic algorithm based demand side management scheme for smart grid. In: Proceedings of the 18th International Conference on NetworkBased Information Systems, pp. 351–356. doi:10.1109/NBiS.2015.54. Brown, A., Salter, R., 2011. Can smart grid technology fix the disconnect between wholesale and retail pricing? Electr. J. 24 (1), 7–13. Chedid, R., Akiki, H., Rahman, S., 1998. A decision support technique for the design of hybrid solar-wind power systems. IEEE Trans. Energy Convers. 13 (1), 76–83. Chen, S.X., Tseng, K.J., Choi, S.S., 2009. Modeling of lithium-ion battery for energy storage system simulation. In: Proceedings of 2009 Asia-Pacific Power and Energy Engineering Conference. IEEE, pp. 1–4. Chen, X., Wei, T., Hu, S., 2013. Uncertainty-Aware household appliance scheduling considering dynamic electricity pricing in smart home. IEEE Trans. Smart Grid 4 (2), 932–941. doi:10.1109/TSG.2012.2226065. Christie, R., 20 0 0. Power Systems Test Case Archive. Electrical Engineering department, University of Washington https://www2.ee.washington.edu/research/ pstca/. Distribution, 1992. Test Feeders https://ewh.ieee.org/soc/pes/dsacom/testfeeders/. Eid, C., Codani, P., Chen, Y., Perez, Y., Hakvoort, R., 2015. Aggregation of demand side flexibility in a smart grid: a review for European market design. In: Proceedings of the 12th International Conference on the European Energy Market (EEM). IEEE, pp. 1–5. El-Hawary, M.E., Mansour, S.Y., 1982. Performance evaluation of parameter estimation algorithms for economic operation of power systems. IEEE Trans. Power Appar. Syst. PAS-101 (3), 574–582. Galus, M.D., La Fauci, R., Andersson, G., 2010. Investigating PHEV wind balancing capabilities using heuristics and model predictive control. In: Proceedings of IEEE PES General Meeting. IEEE, pp. 1–8. Gkatzikis, L., Koutsopoulos, I., Salonidis, T., 2013. The role of aggregators in smart grid demand response markets. IEEE J. Sel. Areas Commun. 31 (7), 1247–1257. Godina, R., Rodrigues, E.M.G., Pouresmaeil, E., Matias, J.C.O., Catalão, J.P.S., 2016. Model predictive control technique for energy optimization in residential sec-

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