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A Multiagent Minority-Game-Based Demand-Response Management of Smart Buildings Toward Peak Load Reduction Hantao Huang, Student Member, IEEE, Yuehua Cai, Student Member, IEEE, Hang Xu, and Hao Yu, Senior Member, IEEE
Abstract—This paper presents a cyber-physical management of smart buildings based on smart-gateway network with distributed and real-time energy data collection and analytics. We consider a building with multiple rooms supplied with one main electricity grid and one additional solar energy grid. Based on smart-gateway network, energy signatures of rooms are first extracted with consideration of uncertainty and further classified as different types of agents. Then, a multiagent minoritygame (MG)-based demand-response management is introduced to reduce peak demand on the main electricity grid and also to fairly allocate solar energy on the additional grid. Experiment results show that compared to the traditional static and centralized energy-management system (EMS), and the recent multiagent EMS using price-demand competition, the proposed uncertaintyaware MG-EMS can achieve up to 50× and 145× utilization rate improvements, respectively, regarding to the fairness of solar energy resource allocation. More importantly, the peak load from the main electricity grid is reduced by 38.50% in summer and 15.83% in winter based on benchmarked energy data of building. Lastly, an average 23% uncertainty can be reduced with an according 37% balanced energy allocation improved comparing to the MG-EMS without consideration of uncertainty. Index Terms—Demand-response management, minority game (MG), peak load reduction, smart building, solar energy.
I. I NTRODUCTION MONG various energy consumers, it is reported that over 70% electricity is consumed by more than 79 million residential buildings and 5 million commercial buildings in U.S. [1], [2]. There is an increasing need to develop cyber-physical energy management system (EMS) for modern buildings supplied from the main power grid of external electricity as well as the additional power grid of new renewable solar energy [3]. Although the traditional centralized and static EMS has been successfully utilized to provide stable
A
Manuscript received May 14, 2015; revised October 31, 2015 and February 24, 2016; accepted April 29, 2016. Date of publication May 23, 2016; date of current version March 17, 2017. This work was supported in part by NTU-ERIAN, and in part by JTC I3C. The preliminary result was published in DATE’12. This paper was recommended by Associate Editor S. Hu, S. Hu, and A. Y. Zomaya. The authors are with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCAD.2016.2571847
energy supply, new challenges emerge to develop smart grid for modern buildings as follows. The first challenge is how to deal with hybrid power grids in the EMS. There is huge peak load in the main electricity power-grid as multiple rooms may access the main power grid at the same peak time. The use of renewable energy may alleviate this issue but the access to the additional power grid of renewable energy is publicly shared. As such, one needs to develop a method that can reduce the peak load at the main power grid and also balance the access to the additional power grid of renewable energy. The second challenge is the scalability of the EMS. A modern building or complex can contain residential, offices as well as shops with hundreds of rooms [4], [5], each with unique energy usage characteristic. Moreover, due to the uncertainties of photovoltaic (PV) and dynamic changing environment with largely generated monitoring data, EMS requires to operate at the granularity of shorter period. As such, the system complexity has grown rapidly and hence requires a scalable EMS with distributed and real-time control. The third challenge is to consider the uncertainty in the EMS. The stochastic nature from both energy generation and consumption can significantly affect the prediction and decision-making process of EMS. For example, there exist uncertainties in the behavior of room users, which have varying load energy profiles (i.e., the amount of energy generated by the supplier or demanded by the customer). The energy-profile data collected from energy meters/sensors tends to deviate from real values due to stochastic measurement errors [6]–[8]. As such, the EMS relying on ideal energy profile may not work in reality. A. Related Works The traditional EMS is normally realized as one centralized and static control [9]–[11] that cannot deal with aforementioned challenges. The multiagent-based EMS in contrast can provide a distributed and real-time energy data collection and also analytics [12]–[15]. In such systems, different system components are modeled as intelligent but selfish agents with communication, negotiation and decision making capabilities based on certain financial or market theories. The centralized controller is replaced by distributed smart agents such as smart gateways [16]–[18] such that it becomes more scalable for the
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management of the smart grid. Among the multiagent systems, the game-theoretical based EMS has obtained more attention because it can be utilized for both peak load reduction as well as balanced resource allocation [19]–[22]. Furthermore, although the intermittent nature of renewable energy resources generation [23] has been addressed by various forecasting techniques such as in [24], uncertainties as measurement error from energy meter [6] are not taken into consideration in previous work. Note that energy meters and sensors can be influenced by various factors such as temperature and humidity. Moreover, the energy consumer can also introduce stochastic uncertainties, which need to be considered in the EMS. B. Contribution of This Paper In this paper, we propose an uncertainty-aware MG-based EMS (UAMG-EMS) for a smart building supplied with hybrid power grids. The major contributions of this paper are summarized as follows. First, we have developed an MG multiagent-based demandresponse management for the energy resource allocation. Due to the extreme light-weight game playing strategies, realtime and decentralized EMS could be realized on smart gateway network with little hardware overhead. By designing proper attractive functions in the MG, higher renewable energy utilization efficiency regarding the fair and balanced energy allocation is achieved for the additional power grid. More importantly, with the adaptive coarse-grained renewable energy scheduling, the peak energy demand for the main power grid is also reduced significantly. Second, scalability of the proposed UAMG-EMS is greatly improved by the classification of different energy customers of rooms into a number of types (or agents) with similar energy profiles. The number of agents participating in the game is therefore reduced with better convergence. Third, the uncertainties are taken into consideration during the game playing. Kalman-filtering is deployed for each agent to reduce error from energy meter and sensor. Supervisedlearning based energy prediction is developed for each agent to forecast the energy demand with consideration of energy profile variation. Experiment results show that the proposed UAMG-EMS can achieve up to 50× and 145× improvements in term of fair solar energy allocation when compared to the traditional static and centralized energy-management system (SC-EMS) and multiagent EMS (MA-EMS) [13]. More importantly, the proposed UAMG-EMS can also reduce the peak energy demand for the main power-grid by up to 38.50%. In addition, an average 23% uncertainty can be reduced with an according 37% balanced energy allocation improved comparing to the MG-EMS without consideration of uncertainty. The rest of this paper is structured as follows. In Section II, the system architecture and problem formulation are introduced. The MG-based EMS will be elaborated in Section III with details of fair renewable energy allocation and peak energy demand reduction. Energy profile prediction, error correction and room clustering are discussed in Section IV.
With experiment results illustrated in Section V, we conclude this paper in Section VI.
II. S YSTEM D ESCRIPTION A. Multiagent-Based Cyber-Physical EMS Fig. 1 illustrates the overall distributed and real-time cyberphysical system for the EMS of the smart building with hybridenergy power-grid suppliers [9], [25]. The EMS infrastructures are mainly based on smart gateway network [16]–[18] implemented inside rooms to collect and also analyze energy data. Such an EMS is a distributed system where decision is made independently from each agent. As such, breaking-down of one gateway at room level will not affect the overall system functionality. What is more, the EMS will schedule the room electrical appliances based on a demand-response strategy and also utilize the renewable energy. First, the components of smart buildings are listed as follows. 1) Main Power Grid: The main power-grid is the primary energy supplier for the consumers from external electricity supplier. It has higher price than the additional renewable energy from solar PV panel. Moreover, it has problem of peak load at peak time. 2) Additional Power Grid: The additional power-grid is the solar PV panel [25] constructed by connected PV cells. The energy harvested by the PV panel highly depends on the insolation intensity and the area of panel. It also includes energy storage system (ESS) [26] that is used to store the remaining solar energy generated at nonbusy hours. When the demand of the main power-grid is high, the stored energy from the additional powergrid can be utilized during this busy time for reducing the peak energy demand of main power-grid. Each ESS has a monitor to indicate the state-of-charge information of ESS [27]. Generally, the ESS can be a package of chargeable batteries. Second, the components of the cyber-physical EMS are also listed as follows. 1) Smart Power-Meter [9]: Smart power meter (or smart plug) has not only the basic functionalities such as realtime sensing and recording the data of current, power and energy profiles in history, but also the capability to realize two-way communication with the monitor. A switch to physically change the supplied energy source is also included in the smart meter. 2) Smart Gateway: Smart gateway (or room agent) records and analyzes the energy profiles. It contains computation unit to perform the proposed UAMG-based allocation algorithm, which determines either to use the solar energy from additional power grid or the electricity from the main power grid at runtime. Note that the proposed cyber-physical EMS takes advantage of a light-weighted UAMG-based engine on smart-gateway network to replace the large centralized EMS. The UAMGbased engine basically consists of a cluster detector and a game arbitrator. The cluster detectors dynamically classify the rooms
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Fig. 2. Workload profiles (summer) for (a) residential rooms and (b) commercial rooms.
Fig. 1. Distributed cyber-physical architecture of smart building with hybridenergy suppliers.
into less number of agents based on the historical energy profiles. The game arbitrator decides the winning agent of MG, and broadcasts the game result back to all agents. In addition, the supervised-learning prediction and error correction algorithms are performed for the consideration of uncertainty. The proposed UAMG-based EMS has advantages in scalability, reliability, and extensibility. For example, adding or removing a room in the building does not involve the overall system modification. Moreover, the breakdown of one room will not affect the others. At the same time, the controller allows real-time and distributed control. B. Energy Consumption Behaviors The consideration of real-time varying characteristics of energy profile is critical for the EMS management. We present the energy supply and load profiles obtained from existing field tests in [23] and [28], which are adopted to build the realistic EMS management in this paper. 1) Customer-Side Energy Load Profiles: The rooms inside the same building can have vastly different energy load profiles, resulting from the diverse electrical equipments and consumer habits. Moreover, in modern building complex, it can contain rooms of residential, offices and shops with different purposes. As such, classifying customer-side energy load profiles is a good data analytics for a better EMS scheduling. For example, Fig. 2 illustrates the energy load profiles of different types of rooms from field test in New Hampshire Electric Co-op building [28]. From Fig. 2, two key characteristics can be observed. 1) The energy demand is nonuniform with regard to time. For the energy demand, there are daily peak and valley points. From Fig. 2(a), one can observe that two peaks
Fig. 3.
(a) Solar energy profile. (b) Electricity price of main power grid.
during 7–9 A . M . and 6–9 P. M . for residential rooms, when people are more active in their homes. 2) Energy load profile characteristics of different types of rooms are different. For example, the peak period of commercial rooms is on the opposite as the valley period of residential rooms, when most people are out of their homes. In addition, commercial rooms demand almost two times more energy than residential rooms do on average. Based on the above discussion, one can conclude with following design considerations for the EMS. Since the cost of the traditional main power-grid is proportional to the peak energy demand, it is most beneficial from the demand-response point of view when solar energy is utilized to compensate the mismatched peak during the peak period [29]. 2) Supplier-Side Energy Supply Profiles: The supplierside energy profiles describe the time varying amount of energy generated by energy suppliers. Since the solar energy is adopted in our hybrid power grids, we consider the energy profile of solar PV cells by National Renewable Energy Laboratory and other agencies at selected locations in USA [23]. One can obtain the typical example of solar PV cell profiles as shown in Fig. 3(a). Fig. 3(b) shows different electricity pricing strategies based on [30], where the realtime pricing profile is generated to reflect the real-time demand from the main grid. Please note that the pricing strategies only include the charges based on electricity consumptions. Based on Figs. 2 and 3, one can observe that the electricity from the main power-grid is required to form the foundation of daily energy demand in one building; and the solar energy is utilized as auxiliary energy source that can be utilized to cut down the peak energy demand. Note that the solar energy is relatively cheaper compared to the electricity from the main
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power-grid. Therefore, rooms would always prefer to use the solar energy. However, the amount of solar energy available is limited and the access to the additional power-grid of solar energy is also limited. Therefore, one needs to fairly allocate the solar energy among different types of rooms when they access the additional power grid; but also to reduce the peak power of the main power grid. C. Problem Formulation Formally, we denote the total energy demand of room type i, 1 ≤ i ≤ N at time t as a random variable Di (t). Rooms with the same type will share the same solar energy allocation strategy. The outcome of UAMG-EMS is the solar energy allocation decision for each room type represented by variable δi (t) (0, 1], solar energy proportion in total energy use δi (t) = 0, only main electrical grid energy is selected. (1) One needs to find the set of δi (t) that minimizes the standard deviation of power consumption profile (24 h) from main grid toward peak load reduction by utilizing the solar energy N (2) arg min dev (1 − δi (t))Di (t)dt δi (t)
i=1
where (1 − δi (t))Di (t) represents the power consumption from main grid at time t and N is the number of room types. Naturally, there is a constraint must be taken into account that the allocated solar energy should not exceed the available amount at any moment. It is defined as follows: N
δi (t)Di (t) ≤ B(t)
(3)
i=1
where B(t) is the amount of solar energy stored in ESS at time t. III. M ULTIAGENT M INORITY-G AME -BASED E NERGY M ANAGEMENT S YSTEM To solve the problem formulation in Section II, the multiagent MG-playing based demand-response method is utilized [16], [31]. Since the game rules consider not only real-time demand for energy usage but also the historical resource allocation results, selfish customers cannot monopolize limited solar resources in the building. Meanwhile, by incorporating with demand-response control, the peak power is reduced for the main power-grid. A. Minority Game Overview MG [32] is one of the classical problems in multiagent systems. In its original form, the El Farol Bar problem, n players make their decisions on whether to attend a bar each night. Going to a bar is only enjoyable only if it is not too crowded, otherwise people would rather stay at home. Intuitively, players adjust their behavior based on their expectations on what other players are going to do next, and these expectations are
Fig. 4.
Working flow of the proposed MG-EMS.
generated by information of what other players have already done in the past. The problem is later more generally formalized by Challet and Zhang [33]. In this form, several players participate the MG. At each game round, each player decides his own action based on historical and preference factors. After all decisions are made, the action associated with least number of players is declared as minority side and those players get the chance to win certain payoffs. The game result is also broadcast back to all players such that they can update their information and make necessary adjustments in future expectations. As each player makes his own decision independently, the game is carried out in a decentralized manner. Recently, the MG-based method has been successfully adopted to solve various resource allocation problems in multiagent systems [34], [35]. As history resource allocation result is recorded and participates as a key factor in future resource scheduling, no single selfish agent is allowed to monopolize the limited resources. In this paper, the problem described in Section II-C is mapped to a modified MG problem for the sake of peak load reduction and fair solar energy resource allocation. We introduce the detail realization of the proposed UAMG-EMS as follows.
B. Fair Allocation in Additional Power-Grid of Solar Energy The overall working flow of the proposed MG-EMS is described in Fig. 4. At every control time t, each room will play the modified MG based on its real-time energy demand and past energy allocation results to calculate its attractiveness to use solar energy for the next t period of time. These attractiveness are then gathered to the game arbitrator which decides the winning side to be allocated with solar energy, and finishes one round of MG. After that, the game result will be broadcast back to all rooms for updating their local history information. Another round of game will be played until there is not enough solar energy available for further allocation. In our system, we set t = 1 h since the time-step of energy supply and load profiles obtained from [23] and [28] is hourly based. After all solar energy gets allocated, the system moves to the next control step (i.e., next hour).
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To formally illustrate the modified MG, two factors are introduced. The preference factor decides the tendency for each player to choose the solar energy as supply for the next period of time Ek (t) (4) Prk (t) = 24 t=1 Ek (t)
Algorithm 1 MG-Based EMS Running for One Day Input: Energy supply and load profiles Output: Solar energy allocation scheme 1: for Each hour t in day do 2: Calculate Hk (t) based on Equation (5) 3: Update Prk (t) based on Equation (4) 4: for Each room k do 5: Attrk (t) = αk × Hk (t) + (1 − αk ) × Prk (t) 6: end for 7: Allocate solar energy Eta,k = min(Etk , EAts ) to room k if: Attrk (t) = max Attrp (t), p ∈ [1, Nr] Nr k 8: Update Esoc = Esoc + Nr k=1 Esolar (t) − k=1 σk (t) · Eta,k (k) 9: end for 10: END
where Prk (t) denotes the preferences at hour t for room k, Ek (t) is the predicted energy demand at time t. When a room is about to experience a high energy demand period, it will have high willingness for solar energy to reduce the cost of using power-grid energy. The history factor is used to balance the energy allocation Sk Hk (t) = 1 − N (5) r k=1 Sk where Sk represents the cost-saving for room k in the past, and Nr is the total number of rooms. The cost-saving function Sk is defined as Sk =
t
price(τ ) × Eksolar (τ )
(6)
τ =0
where price(τ ) is the electricity price difference between main power grid and solar energy at time τ , and Eksolar (τ ) is the total amount of solar energy allocated for room k at time τ . Intuitively, the more solar energy one room has been allocated before, the less chance for it to receive solar energy in the future. The MG is played as follows. At each round, each room computes its attractiveness based on preference and history factors using Attrk (t) = αk × Hk (t) + (1 − αk ) × Prk (t)
(7)
where αk is used to adjust the weight of different factors for room k. If αk is 1, the algorithm becomes historical-based decision similar to equal-distribution algorithm. On the other hand, if αk is 0, the algorithm becomes greedy algorithm. We can adjust αk to balance the history factor and priority factor. Then, the room with highest attractiveness will get allocated with solar energy. After that, all historical data is updated by actual energy usage, and the game moves to the next control step. C. Reducing Peak Energy Demand in Main Power-Grid of Electricity To make the best utilization of solar energy and reduce the peak energy demand for main power-grid, more solar energy should be allocated during peak demand times of a day. To achieve this objective, we dynamically control the maximum amount of solar energy Ets that can be allocated at each time t to be proportional to the percentage of the energy demand at t over the total energy demand in the previous day as N 24 N r r t t t Ek / Ek Es = β ∗ Ets (8) where
24 Nr t=1
ous day, Ets =
k=1
t=1 k=1
t k=1 E k is the total energy demand in the previ 24 t t=1 Esolar is the total solar energy production
amount from previous day and β is the adaptive parameter. As shown in Figs. 2 and 3(a), the peak time of energy demand and solar energy generation does not align well. Hence, the adaptive parameter β is important to smooth the energy demand from the main grid. If β is 1, the use of solar energy is proportional to the demand of main grid. However, we adjust β such that less solar energy is used when insufficient solar energy is stored. β indicates the status of available solar energy, and together with (8) we delay the use of solar energy such that the solar energy is used during the peak period. At runtime, β dynamically updates its value based on (9) β = β + Esoc − Ets /(10 ∗ Esoc ), if Esoc > Ets where Esoc is the unallocated solar energy stored in ESS (i.e., amount of energy stored). Finally, the amount of solar energy available for allocation EAts is calculated as the minimum of Es and the physically stored amount of solar energy in ESS EAts = min(Es , Esoc ).
(10)
Through such solar energy scheduling scheme, the peak energy demand to main power-grid can be reduced without altering customer energy demand. To summarize, the pseudo-code in the proposed MG-EMS running one day is shown in Algorithm 1. Inputs are received in lines 1–3 calculates the two factors for MG from (4) and (5). The for loop lines 4–6 is the MG played independently in a distributed fashion by each room based on (7). In line 7, the winner will allocate the solar energy based on the minimum of its demand and available solar energy. Finally, Esoc is updated and EMS moves to the next control step. IV. U NCERTAINTY-AWARE E NEGY DATA A NALYTICS A. Energy Data Classification To increase the scalability and reduce the complexity, clustering is further developed based on the energy profiles of different types of rooms. For classification, we first translate the energy utilization profile into abstract data point in high dimensional space. In the proposed UAMG-EMS, the observation is made that the energy profile demonstrates
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periodical behaviors. More specifically, the profile repeats in a daily basis. As such, we can represent the energy behavior of each room as a 24-dimensional tuple, where each element stands for the average energy demand for the given hour over historical data (i.e., one month) 30 day=1 Di,k (day) (11) Cik = 30 where Cik is the kth hour in the tuple of the ith room, and Di,k is the energy demand of room i on kth hour. Starting with M centers for each cluster, the Euclidean distance of each room to every center is calculated. Then, each room is decided to the center (i.e., cluster) with minimal distance. After that, the position of each center is recalculated as the average of all points within the cluster. The classification is iterated until the position change of all centers is under certain threshold. Since the energy profile shows a daily-based periodic behavior, the clustering of rooms is also daily based. Moreover, the number of clusters is known prior from possible power consumption based on the room types. Due to the effect of initial centers and the possibility of outlier case merging to a neighboring cluster, to obtain expected outcomes, we perform the clustering several times with different randomly generated centers to find the proper initial center with minimum within-cluster sum of squares (WCSSs). B. Energy Data Prediction To further dynamically capture and react upon these variations of loads at runtime, we adopt the supervised-learning based prediction method as follows. 1) Supervised-Learning-Based Prediction: The supervisedlearning is to derive a mapping from [x, y, z] ∈ X to t ∈ T such that the average mapping error is minimized, given the training sets that consist of input and output pairs. In our case, X and T denote the input features and measured outputs, respectively. In this paper, we propose to adopt the polynomial regression [36] technique to model a nonlinear relationship between the input features and measured outputs. Equation (12) illustrates the general multivariate polynomial fitting with N order t=
N i=0
ai xi +
N i=0
bi yi +
N
ci zi
(12)
i=0
where the list of ai , bi , ci , i = 0, 1...N is the coefficient to be trained and x, y, and z are independent input features such as time, temperatures and room areas [37]. After all ai , bi , and ci are computed out, one will have the capability to predict future energy consumption based on previous energy profile data. Considering our EMS, the input feature is time in our approach, while the output is the predicted amount of energy demanded. Therefore, only 1-D polynomial function is used for energy data prediction. 2) Prediction of Energy Load: Based on clustered result, we can achieve a more scalable prediction work for each cluster instead of for each room. As in any supervised-learning
engine, the result depends largely on the selection of training set. In our method, we build the training set based on three observations. First, as the energy profile shows a daily-based periodic behavior, the training is better to be based on a daily basis as well. More specifically, the training set T contains seven elements, where each element is the energy demand profile of one whole day
(13) T = Tij 1 ≤ i ≤ 7, 1 ≤ j ≤ 24 . Second, we observe that later days in the training set shall have larger impact on the prediction result. To introduce such knowledge into the training process, we assign each day with a daily weight σi , where σi > σi−1 > · · · > σ1 . Third, we observe that there exist certain days with extremely abnormal behaviors. To avoid such undesired cases, we propose to filter out the abnormal data. Specifically, we compute the average energy utilization Q over the entire training set 7 24 i=1 j=1 Tij Q= . (14) 7 Then, we define the upper bound as (3/2)Q and lower bound as (1/2)Q to recognize the abnormal situation. If the data of any training element exceeds these bounds, a special weaken factor ρi will be applied to reduce its weight in the training set. Based on above mentioned training set pruning techniques, we formalize the prediction process as a polynomial fitting problem following (12). Then the minimization of prediction errors equals to ⎛ N 2 ⎞ 7 24 (15) an xjn − Tij Wi ⎠ arg min⎝ i=1 j=1
n=0
where Wi = σi ρi , and in our approach, xj = j ∈ [1, 24]. By taking first order partial differentiation on ak for the above function and letting it equal to zero, we get 7 i=1
Wi
24 j=1
xjn+k
N
an =
n=0
7 i=1
Wi
24
Tij xjk
(16)
j=1
where k is from 1 to N. Rewrite the problem into matrix representation Fa = b
(17)
where F is an N × N matrix while a and b are N × 1 vectors. By introducing LU factorization with pivoting technique to solve (17), the coefficients a of the polynomial are obtained and thus we can utilize the fitting curve to predict the energy consumption behavior of the next day. Note that the training set T moves along the time axis so that after one prediction, the data of the latest day will be shifted in and the data of the earliest day will be shifted out from T. Using this training window, the prediction engine adapts to more recent changes since latest knowledge is dynamically included with higher weight.
HUANG et al.: MULTIAGENT MG-BASED DEMAND-RESPONSE MANAGEMENT
Fig. 5. (a) UAMG-EMS flow diagram. (b) UAMG-EMS engine architecture and data flow diagram.
C. Energy Data Correction and Update There always exist measurement errors in the data sampled by the smart energy meters and sensors. Given this fact, it is important to handle the uncertainties of energy data. 1) Kalman Filter Overview: Kalman filter, a widely applied technique in the data fusion domain, is utilized in the proposed UAMG-EMS with the prediction data as priori knowledge and the data collected from energy meter and sensor as observation correction. Based on a series of observed measurements, the Kalman algorithm will generate the more precise data over those obtained from measurements alone. In addition, the observed measurements include the noise and other inaccuracies, which fulfill our target to consider the uncertainties and model them into our uncertainty-aware EMS. 2) Correction and Update: In detail, the energy consumption profile data is a discrete sequence that can be described as x(k) = Ax(k − 1) + Bu(k − 1) + L(k)
(18)
where x(k) is the hourly energy consumption vector of kth day, A is the transformation matrix and L(k) is the process error which is the error introduced by the priori knowledge of prediction. Note that in our approach, we do not have any input and thus u = 0 and B is not considered. In our approach, the transformation matrix could be further simplified to ratio transformation x˜ i (k) , i ∈ [1, 24] (19) Ai = xˆ i (k − 1)
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Algorithm 2 UAMG-EMS Entire Process 1: BEGIN 2: Perform clustering for N rooms into M clusters 3: while day ≤ 30 do 4: //Supervised-learning prediction 5: for Each cluster do 6: Set last 7 days Training Set: T = {Tij |1 ≤ i ≤ 7, 1 ≤ j ≤ 24} 7: Calculateregression curve: 2 (y arg min( 7i=1 24 j=1 ij − Tij ) Wi ) 8: end for// Find predicted energy Ek 9: //Play minority-game between clusters 10: for Each hour t in day do 11: for Each cluster k do 12: Attrk (t) = αk × Hk (t) + (1 − αk ) × Prk (t) 13: end for t = min(Et , EAt ) to cluster 14: Allocate solar energy Ea,k s k k if: Attrk (t) = max Attrp (t), p ∈ [1, M] 15: end for 16: day + + 17: Reading (day − 1)-th data z from meter/sensor 18: //Perform Kalman filtering for (day − 1) 19: for Each hour t in (day − 1) do 20: for Each cluster k do xˆ t (day − 1) = x˜ t (day − 1) + Kt (day − 1)(zt (day − 21: 1) − x˜ t (day − 1)) 22: end for 23: Update xˆ t (day − 1) 24: end for 25: end while 26: END where x˜ i (k) denotes the predicted value for the kth day at the ith hour, and xˆ i (k − 1) denotes the (k − 1)th day’s data at ith hour provided after last filtering iteration. The energy meter/sensor is modeled as z(k) = Hx(k) + V(k)
(20)
where z(k) is the energy consumption vector provided by meter/sensor, H is the observation system parameter matrix which is actually 1 because the meter/sensor is read out directly. In addition, V(k) here denotes the error brought by the meter/sensor, which is usually known as observation noise. As a reasonable simplification, we assume that both the process error and the meter/sensor noise meet normal probability distributions, such that the means are zero and covariance are Q and R, respectively. We further assume that Q and R do not change along with time step k. Measurement noise variance R can be estimated based on the offline training samples and daily weights σi . The process noise covariance Q is tuned offline accordingly. Without losing generality, other kinds of noise with known covariance can also be handled by Kalman filter. Note for the Kalman filter to handle vector data in our case, the corresponding scalar calculation is operated elementwisely. Given an initial estimate error covariance Pi (k − 1)
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generated randomly, the Kalman filter theory [38] applies Pi (k) = Ai Pi (k − 1) + Q
TABLE I UAMG-EMS PARAMETERS
(21)
where i denotes the ith hour’s case. The Kalman gain K is Ki (k) =
Pi (k) . Pi (k) + R
(22)
Kalman gain Ki (k) will converge quickly based on the Kalman filter theory [38] and the optimized result xˆ i (k) is calculated by xˆ i (k) = x˜ i (k) + Ki (k) zi (k) − x˜ i (k) . (23) Finally, we update the value of Pi (k − 1) with Pi (k), which finishes one filter iteration. D. UAMG-EMS Summary After the sequential discussion of all the techniques and algorithm we employ in our UAMG-EMS system, the whole management process flow is clearly shown in Fig. 5(a). At first, the K-means technique clusters the rooms into M clusters based on the previous data. Once the clustering work is done, we adopt the supervised-learning based prediction method to predict the next day’s behavior based on the database. Then the clusters will participate in the MG to determine the energy allocation. Finally, the Kalman filter is utilized to correct the error, and further update the data to the database. Please note that the output of one technique may indicate the input of the next technique. Fig. 5(b) illustrates the overall UAMG-EMS engine architecture and data flow of our proposed EMS. For clarification, the entire flow of the proposed UAMG-EMS is presented in Algorithm 2. V. E XPERIMENT R ESULT A. Experiment Settings To verify our proposed EMS, we perform simulations based on the data collected from real world testbed from [23], [28], and [30]. For comparison, we also implement the following two baselines. Baseline 1: The centralized EMS based on static energy demand (SC-EMS). In this method, the solar energy generated at each hour is allocated to each room directly in proportion to its energy demand. Baseline 2: The MA-EMS is similar to [13]. In this approach, each room competes for the solar energy based on the price-motivation function Sk , which represents the quantified motivation of each room to choose solar energy at the price difference price(τ ) between solar energy and main power gird. Intuitively, as rooms with larger energy demand can obtain more energy cost savings by using solar energy, they have larger value of motivations. At each round, those rooms with larger motivation will win the competition. To illustrate the capability of the proposed MG-EMS under various energy supply and load profiles, we first set up the smart buildings with hybrid types of rooms (i.e., six residential rooms with IDs 1–6 and six commercial rooms with IDs 7–12), and with different sizes (i.e., area) of PVs from 20 to 30m2 . We have shown the peak load reduction from the main grid
and total benefits using proposed MG-EMS compared with MA-EMS and SC-EMS. Furthermore, the standard deviation of the load profile for the main grid is compared to show the generality and significance of proposed EMS. In addition, the simulation is carried out for a whole month in both summer (i.e., August) and winter (i.e., December) to avoid result bias on a certain day or season. Furthermore, to show the scalability of proposed EMS, we consider the smart building consisted of 24 residential and commercial rooms, and each room is associated with energy load profile recorded per hour for one month (i.e., 30 days). We further increase the sweep of PV area from 20 to 40 m2 . Rooms of different types have different characteristics in load behavior, which could be observed from Fig. 6. Basically, we find that residential rooms reach their peak hour workloads in the evening while commercial rooms tend to consume more energy during daytime. Finally, we consider the load profile prediction and error correction from sensors to the proposed UAMG-EMS to show the superiority over the MG-EMS. The proposed MG-EMS and UAMG-EMS are implemented by C++ and MATLAB, and all presented results are computed on an Intel Core i5 with 2.6 GHz clock frequency and 4 GB of RAM. To account for measurement errors on smart meters/sensors, we add Gaussian white noise with 3% magnitude variance on the load profile from [28]. This is reasonable because usually the energy meter/sensor is influenced by various factors like weather, and usually the noise behaves like a normal distribution of N(0, σ 2 ). In addition, we fixed the order of polynomial used in supervised-learning as 15, which is obtained through trial and error for the prediction error to be within certain user-specified bounds. Table I summarizes all the parameter settings used in our experiments. B. Classification Result Table II shows the clustering results for each iteration, in which the number represents the abstract locations1 of each 1 Since each location vector contains 24 dimensions, here we only show the 2-norm of the vector to represent the abstract locations of rooms and centers.
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TABLE II C ENTER M OVEMENT IN K-M EANS C LUSTERING
Fig. 8. Workload profiles with accumulated one-month error filtered for (a) residential rooms and (b) commercial rooms. TABLE III S TANDARD D EVIATION OF E NERGY D EMAND (12 ROOMS ) F ROM THE M AIN G RID U NDER D IFFERENT PV A REAS IN S UMMER ( I . E ., AUGUST ) Fig. 6. Supervised-learning by polynomial regression for predication of energy load profile. (a) Residential rooms. (b) Commercial rooms.
TABLE IV S TANDARD D EVIATION OF E NERGY D EMAND (12 ROOMS ) F ROM THE M AIN G RID U NDER D IFFERENT PV A REAS IN W INTER ( I . E ., D ECEMBER )
Fig. 7. Workload for (a) residential rooms with measurement error filtered and (b) commercial rooms with measurement error filtered.
cluster center (2-norm of center vector). Obviously, the center of each cluster converges quickly after only three K-means iterations, which means the clustering process is completed and all rooms are split into two main types. Note the number of centers can be decided at runtime based on user specified error bounds as well.
C. Load Prediction Result Fig. 6 shows the typical supervised-learning based load energy prediction result for commercial and residential rooms, where the energy profile of past seven days (i.e., training set) is used to predict the energy consumption for the next day. Similarly, Fig. 7 demonstrates the prediction result when measurement error is considered for energy load profiles, from which we can conclude that the 15th order polynomial achieves a fairly good fitting. The prediction error is modeled as a normal distribution N(0, σ 2 ), where variance σ 2 is estimated in the training process. In Fig. 8, the total prediction error for one month, which is defined as the absolute difference between predicted and actual energy demand. Clearly, we observe that our prediction under stochastic noises is quite close to real value, with the same scale as the meter noise (i.g., 3% perturbation from true curve).
D. Error Correction Result To account for measurement errors in smart meters/sensors, we need to update the data for latest day by performing a Kalman filtering process such that the accurate data could be recovered. As mentioned in the experiment setting, the measurement noise is modeled as a normal distribution of N(0, σ 2 ) with maximum 3% magnitude variance on the load profile. Fig. 7 compares the prediction curve, the observation curve, the Kalman filtered curve and the curve for true values. Meanwhile, prediction error, noise and Kalman filtered data error are also demonstrated in Fig. 8. Clearly, after the Kalman filtering process, an average of 23% total noise perturbation can be reduced. As a result, it can significantly improve the EMS for more accurate energy resource allocation. E. MG-EMS Result In this section, we will discuss peak load reductions and the total saving of proposed MG-EMS. As a by-product of proposed EMS, we also make sure the fair access to the limited solar energy. Fig. 9 illustrates the average daily energy demand for main electrical power-grid under different EMS in both summer and winter. The red circle symbol curve is the original energy demand without using solar energy, or called NONEMS. The peak period covers from 9 A . M . to 9 P. M . of the day. Compared with the NON-EMS case (PV area 20 m2 ), the
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TABLE V S TANDARD D EVIATION OF E NERGY D EMAND (24 ROOMS ) F ROM THE M AIN G RID U NDER D IFFERENT PV A REAS IN S UMMER ( I . E ., AUGUST )
TABLE VI S TANDARD D EVIATION OF E NERGY D EMAND (24 ROOMS ) F ROM THE M AIN G RID U NDER D IFFERENT PV A REAS IN W INTER ( I . E ., D ECEMBER )
Fig. 9. Energy demand reduction (12 rooms) for main electrical grid in (a) winter with 20 m2 , (b) winter with 25 m2 , (c) summer with 20 m2 , and (d) summer with 25 m2 solar PV area.
proposed MG-EMS reduces the peak demand for main powergrid from 20.05 to 12.33 KW in summer and from 23.05 to 19.4 KW in winter. In other words, a 38.50% and 15.83% reduction is achieved, respectively. Compared with SC-EMS and MA-EMS, the reduction ratio is 25.70% and 12.37% in summer and 15.19% and 15.84% in winter. Furthermore, MGEMS achieves a lower standard deviation of energy load profile (i.e., more flat) than SC-EMS, which further enhances the stability to access the main electrical power-grid when using the renewable solar energy under the MG-EMS control. To have a comprehensive comparison, Tables III and IV show the comparisons of standard deviations of energy demand from the main grid under different PV areas in summer and winter. It clearly indicates our proposed EMS can achieve smaller standard deviation of energy profile from the main grid. To demonstrate the scalability of proposed algorithm, we have increased the room number from 12 to 24. Fig. 10 gives the average daily energy demand from the main grid with solar area of 25 and 30 m2 . Tables V and VI are also provided for comparisons with PV areas varying from 20 to 40 m2 . Please note that when the PV area is large, a rapid drop of energy demand from the main grid may occur, which increases the fluctuation of energy consumption from the main grid. Clearly, we observe that MG-EMS can smooth the energy load profile and perform better peak load reduction from the main grid compared with SC-EMS and MA-EMS. Tables VII and VIII show the total saving using the proposed EMS compared with SC-EMS and MA-EMS under various PV areas and pricing strategies in one month. To demonstrate the total benefits of proposed EMS, we have varied the solar area under different pricing strategies based on Fig. 3. We can see that MG-EMS can achieve much larger saving compared with SC-EMS and similar saving as MA-EMS. We can also observe that under the peak/off-peak pricing strategy, MG-EMS can achieve more saving due to the high price in the peak period. The objective of peak load reduction aligns well with total saving maximization. Please
Fig. 10. Energy demand reduction (24 rooms) for main electrical grid in (a) winter with 25 m2 , (b) winter with 30 m2 , (c) summer with 25 m2 , and (d) summer with 30 m2 solar PV area.
note that MA-EMS is a greedy algorithm based on pricemotivation function Sk . The less saving of SC-EMS is due to the mismatch of solar energy generation and the peak energy consumptions. As a by-product of proposed EMS, solar energy can be also fairly allocated to rooms. Fig. 11 compares the received energy cost savings defined in (6) under the peak/off-peak pricing strategy, where each room is using different EMS schemes with PV area of 25 m2 over summer and winter, respectively. The horizontal axis represents different rooms, where the first six are residential rooms and the last six are commercial rooms. The vertical axis is the received energy cost savings counted as U.S. dollars. We can observe that our MG-EMS leads to a fairly equal distribution of energy cost savings from solar energy utilization under any seasonal variation with different energy load profiles. On the contrary, in SC-EMS, the money each room saved is directly proportional to their total energy demand. Even worse, although
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TABLE VII T OTAL S AVING (12 ROOMS ) F ROM S OLAR E NERGY U NDER D IFFERENT PV A REAS AND P RICING S TRATEGIES
TABLE VIII T OTAL S AVING (24 ROOMS ) F ROM S OLAR E NERGY U NDER D IFFERENT PV A REAS AND P RICING S TRATEGIES
TABLE IX E NERGY C OST S AVING D EVIATION U NDER D IFFERENT EMS W ITH VARYING PV A REAS IN W INTER ( I . E ., D ECEMBER )
TABLE X E NERGY C OST S AVING D EVIATION U NDER D IFFERENT EMS W ITH VARYING PV A REAS IN S UMMER ( I . E ., AUGUST ) Fig. 11. Comparison of energy cost savings obtained in different EMSs (3 months).
the decentralized control manner is achieved, only commercial rooms can get allocated with solar energy in MA-EMS because commercial rooms have larger energy demand than residential rooms almost all the time. As the agent negotiation is in a greedy or selfish fashion, commercial rooms always have larger motivation to employ solar energy. To further demonstrate the capacity of MG-EMS under different energy supply profiles as well, we sweep the PV area from 20 to 30 m2 in both summer and winter seasons, and the result is summarized in Tables IX and X, where each column illustrates the standard deviation of energy cost savings achieved among different rooms. Apparently, in MG-EMS, the standard deviation of energy cost savings almost keeps constant as the PV area is increasing. Moreover, compared with SC-EMS and MA-EMS, our MG-EMS achieves on average 50× and 145× reductions in energy cost saving deviation in summer, and on average 16× and 48× reduction in energy cost saving deviation in winter. The smaller reduction ratio in Table IX is due to the relatively less amount of solar energy generated in winter season.
Fig. 12. Comparisons of solar energy allocation (a) with error filtered and (b) without error filtered.
F. UAMG-EMS Result Fig. 12 compares the unfairness of solar energy allocation for each cluster using MG-EMS and UAMG-EMS. The unfairness is quantitatively defined as the total amount of unbalanced solar energy allocated to different clusters. In Fig. 12, orange curves and blue curves represent solar energy allocated to residential rooms and commercial rooms, respectively. The smaller the mismatch of these two curves, the better the fair
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energy allocation is achieved. Compared with nonstochastic MG-EMS, a 37% reduction of unbalance in fair solar energy allocation is observed, which verifies the effectiveness of the proposed UAMG-EMS for handling energy profile uncertainties. VI. C ONCLUSION In this paper, we have developed the UAMG-EMS for smart buildings. The energy profile classification is applied to form agents based on unique energy profiles of rooms. Multiple agents, representing for typical energy profiles of rooms, are utilized to perform the balanced renewable energy allocation in the additional power grid and also reduction of peak load in the main power grid. Moreover, uncertainties from energy load profiles are taken into count by the agents. Experiment results show that the proposed UAMG-EMS can achieve up to 50× and 145× utilization rate improvements, respectively, regarding to the fairness of solar energy resource allocation; and the peak load is also reduced by 38.50% in summer and 15.83% in winter, respectively. Moreover, by stochastically considering the load file prediction and error correction, an average 23% uncertainty can be reduced with an according 37% of balanced allocation improved. R EFERENCES [1] L. D. Harvey, Energy and the New Reality 1: Energy Efficiency and the Demand for Energy Services. London, U.K.: Earthscan, 2010. [2] N. Lu et al., “The temperature sensitivity of the residential load and commercial building load,” in Proc. IEEE Power Energy Soc. Gen. Meeting (PES), Calgary, AB, Canada, Jul. 2009, pp. 1–7. [3] J. Kleissl and Y. Agarwal, “Cyber-physical energy systems: Focus on smart buildings,” in Proc. IEEE Design Autom. Conf. (DAC), Anaheim, CA, USA, 2010, pp. 749–754. [4] F. Zhang, H. Deng, R. Margolis, and J. Su, “Analysis of distributedgeneration photovoltaic deployment, installation time and cost, market barriers, and policies in China,” Energy Policy, vol. 81, pp. 43–55, Jun. 2015. [5] D. B. Richardson and L. D. D. Harvey, “Strategies for correlating solar PV array production with electricity demand,” Renew. Energy, vol. 76, pp. 432–440, Apr. 2015. [6] G. W. Stubbings, “The mean error of an electricity meter,” J. Inst. Elect. Eng., vol. 59, no. 299, pp. 335–338, Mar. 1921. [7] S. L. L. Hsieh, “Reduction of errors due to source and meter in the nonlinearity test,” in Proc. Int. Test Conf., Washington, DC, USA, Oct. 1998, pp. 254–257. [8] F. A. S. Gonçalves et al., “Modeling approach based on experimental results for prediction of measurement errors in energy meters,” in Proc. Power Electron. Conf., Bonito, Brazil, Oct. 2009, pp. 1255–1261. [9] S. Choi, S. Park, D.-J. Kang, S.-J. Han, and H.-M. Kim, “A microgrid energy management system for inducing optimal demand response,” in Proc. IEEE Int. Conf. Smart Grid Commun. (SmartGridComm), Brussels, Belgium, 2011, pp. 19–24. [10] A. Parisio and L. Glielmo, “A mixed integer linear formulation for microgrid economic scheduling,” in Proc. IEEE Int. Conf. Smart Grid Commun. (SmartGridComm), Brussels, Belgium, 2011, pp. 505–510. [11] R. Lau et al., “Strategy and modeling for building DR optimization,” in Proc. IEEE Int. Conf. Smart Grid Commun. (SmartGridComm), Brussels, Belgium, 2011, pp. 381–386. [12] S. D. Ramchurn, P. Vytelingum, A. Rogers, and N. R. Jennings, “Agentbased homeostatic control for green energy in the smart grid,” ACM Trans. Intell. Syst. Technol., vol. 2, no. 4, 2011, Art. no. 35. [13] K. Kok, G. Venekamp, and P. Macdougall, “Market-based control in decentralized electrical power systems,” in Proc. Int. Workshop Agent Technol. Energy Syst., Toronto, ON, Canada, 2010, pp. 61–66.
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Hang Xu received the B.Eng. degree from Wuhan University, Wuhan, China, in 2015. She is currently pursuing the M.Eng. degree with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, sponsored by ERIAN. Her current research interests include distributed machine learning and smart building system.
Hantao Huang (S’14) received the B.S. degree from Nanyang Technological University, Singapore, in 2013, where he is currently pursuing the Ph.D. degree with the School of Electrical and Electronic Engineering, sponsored by MediaTek. His current research interests include data analytics, machine-learning algorithms, and low-power system design.
Hao Yu (M’06–SM’14) received the B.S. degree from Fudan University, Shanghai, China, and the Ph.D. degree from the Electrical Engineering Department, University of California at Berkeley, Berkeley, CA, USA. He was a Senior Research Staff with Berkeley Design Automation, Santa Clara, CA, USA. Since 2009, he has been an Assistant Professor with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. His current research interests include 3-D-IC and RF-IC at nano-tera scale. He has 156 peer-reviewed IEEE/ACM publications. Prof. Yu was a recipient of the Best Paper Award from ACM Transactions on Design Automation of Electronic Systems’10, the Best Paper Award nominations in Design Automation Conference (DAC)’06, International Conference On Computer Aided Design (ICCAD)’06, and Asia and South Pacific Design Automation Conference (ASP-DAC)’12, the Best Student Paper (advisor) Finalist in Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems’13, IEEE Radio Frequency Integrated Circuits Symposium’13, and International Microwave Symposium’15, and the Inventor Award from Semiconductor Research Cooperation. He is an Associate Editor and a Technical Program Committee Member for a number of journals and conferences, such as DAC, Design Automation and Test in Europe, ICCAD, International Symposium on Low Power Electronics and Design, ASP-DAC, and IEEE Asian Solid-State Circuits Conference.
Yuehua Cai (S’14) received the B.Eng. degree from the Huazhong University of Science and Technology, Wuhan, China, in 2012. He is currently pursuing the M.Eng. degree with Nanyang Technological University, Singapore, sponsored by ERIAN and JTC. His current research interests include real-time indoor positioning and distributed machine learning.
