Real-Time Demand Side Management Algorithm ...

energies Article

Real-Time Demand Side Management Algorithm Using Stochastic Optimization Moses Amoasi Acquah

ID

, Daisuke Kodaira

ID

and Sekyung Han *

Department of Electrical Engineering, Kyungpook National University, 80 Daehak-ro, Sangyeok-dong, Buk-gu, Daegu 41566, Korea; [email protected] (M.A.A.); [email protected] (D.K.) * Correspondence: [email protected] or [email protected]; Tel.: +82-10-2179-0612 Received: 4 April 2018; Accepted: 2 May 2018; Published: 7 May 2018







Abstract: A demand side management technique is deployed along with battery energy-storage systems (BESS) to lower the electricity cost by mitigating the peak load of a building. Most of the existing methods rely on manual operation of the BESS, or even an elaborate building energy-management system resorting to a deterministic method that is susceptible to unforeseen growth in demand. In this study, we propose a real-time optimal operating strategy for BESS based on density demand forecast and stochastic optimization. This method takes into consideration uncertainties in demand when accounting for an optimal BESS schedule, making it robust compared to the deterministic case. The proposed method is verified and tested against existing algorithms. Data obtained from a real site in South Korea is used for verification and testing. The results show that the proposed method is effective, even for the cases where the forecasted demand deviates from the observed demand. Keywords: demand-side management; peak demand control; dynamic-interval density forecast; stochastic optimization; dimension reduction; battery energy-storage system (BESS)

1. Introduction Uneven energy consumption degrades power quality and translates into high energy cost. Therefore, grid operators put much effort toward reducing peak demand through various methods, such as financial incentives. This objective is known as demand-side management (DSM) [1]. DSM is also deployed on the consumer side, to mitigate the peak, thereby lowering the electricity cost. Building energy-management systems (BEMS) have been widely deployed for DSM using various techniques such as price and incentive-based DR programs [2–4]. In recent years, most DSM techniques resort to the use of battery energy storage systems (BESS) due to their benefits such as modularity which enables them to be implemented for different application and purposes, and fast and high power response as compared to traditional energy sources [5,6]. In most BESS use cases, the operation of the BESS is determined manually. Even for an elaborate BESS, the operation strategy is intuitively designed and mostly relies on a deterministic method. In [7], the authors suggested a typical deterministic approach. A peaking interval is foretold empirically, and the BESS is charged to its full capacity prior to this interval. The BESS is then evenly discharged during the defined period. The wider the peaking interval, the higher the probability of covering all possible peak occurrences becomes. However, the performance of the peak cut would be less effective as the interval becomes wider due to the energy limit of the BESS. A narrow peaking interval has a high probability of missing the peak, but the discharge effect of the BESS is much denser, and thus the peak can be cut more deeply as long as the actual peak falls within the foretold interval. In both cases, however, the peak cut performance is generally poor because the interval is fixed as that determined during the offline analysis. Energies 2018, 11, 1166; doi:10.3390/en11051166

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Another prevalent method used by industrial energy consumers is to monitor demand and discharge BESS at its full rate when a peak occurs. The advantage of this method is that the discharge interval can be dynamically adjusted depending on the monitored demand value. Nevertheless, this method could lead to an unintended result, as the amount of discharge energy might often be more than necessary, causing an early depletion of the BESS. To tackle this problem, it is important to know with some certainty when the peak will occur as well as its value. A demand forecast can alleviate this problem [8–12]. Research has shown that BESS can effectively restrict the power demand from exceeding the predetermined value and suppress the voltage imbalance factor within the recommended value [13–15]. The research in [16] aims to reduce the electricity cost based on time-of-use (TOU) charges and peak power demand charges as issued by grid companies. The BESS is developed to reduce the peak demand and, consequently, the electricity bill for customers. With the use of BESS, the stress of utility companies can be reduced during high peak power demands. The above works use a deterministic approach to DSM [12,16–20]. This is an inadequate representation of real-life occurrences of demand. Electric power demands recorded under practical applications are time-series data with uncertainties and are mostly correlated. A single point out of the sample forecasts the future value of demand at a specific time based on historic data. On the other hand, the density forecast gives a forecast at a certain probability value, because, in reality, it is difficult to forecast the demand with certainty at a certain time in the future. Density forecast models are useful not only in forecasting the future behaviour, but also in determining optimal operation and control policies [21,22]. Most DSM approaches do not take into consideration the stochastic nature of demand. The works in [23,24] considered uncertainties in demand; Ref [23] studies a stochastic solution for stationary and mobile BESS considering uncertainties in demand and mobility. The approach does not consider dynamic-interval forecast of demand and optimization to improve the accuracy of future forecasts. Ref [24] deals with real-time forecast and control of HVAC for cost minimization and users’ thermal comfort but it is not focused on peak demand control using BESS. This paper proposes a solution to DSM via an optimal BESS schedule that takes into consideration uncertainties in demand. This papers’ contribution hinges on real-time density forecast and stochastic peak control algorithm taking into consideration uncertainties in demand to lower the electricity cost by mitigating the peak demand of a building. The approach employs dynamic-interval density forecast (DIDF) to forecast the demand distribution profile, a day ahead, multiple times in a day horizon. Although the method and subsequent accuracy of the forecast greatly affect the performance of DSM, the specific method is beyond the scope of this study; the authors are preparing this topic for a separate work. In this paper, only the concept and format of DIDF are presented for application to the dynamic scheduling of a BESS. To this end, a dimension-reduction method, termed piecewise peak approximation (PPA), is developed to reduce the dimension of the demand probability distribution (DPD) obtained from DIDF for a faster computational time. The method captures the stochastic nature of demand by using stochastic optimization [25] to provide a robust BESS schedule while satisfying the technical constraint of maximizing BESS efficiency and life cycle. The proposed method is then applied to an actual environment in South Korea to verify the performance. The rest of this paper is organized as follows. Section 2 describes the proposed approach to DSM via stochastic optimization. Section 3 discusses the problem formulation. Section 4 elaborates on a case study and experimental evaluation of the proposed approach using data from a real site in South Korea. Section 5 gives a discussion on the proposed approach as compared to a deterministic case Finally, Section 6 provides a summary of this paper with spotlights on the main concepts, results and conclusions. 2. Proposed Approach: DSM via Stochastic Optimization This paper proposes a DSM solution made up of three modules: I. Dynamic-interval density forecast module, II. Dimensionality Reduction module, III. Stochastic optimization module.

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2.1. 2.1. Dynamic-Interval Dynamic-Interval Density Density Forecast Forecast

A A density density forecast forecast is is generated generated aa day day in in advance advance based based on on empirical empirical data data as as aa probability probability 2.1. Dynamic-Interval Density Forecast a day horizon. It is important to capture the uncertainties in distribution distribution at at each each time time instance instance in in a day horizon. It is important to capture the uncertainties in demand. Most algorithms aa single for in demand. Most day-ahead day-ahead forecast algorithms forecast single value for each each time time instance in aa day day A density forecast isforecast generated a day inforecast advance basedvalue on empirical data instance as a probability horizon, Figure 1a. with is in applications, horizon, as as shown shown intime Figure 1a. The The problem with this this approach is that, that, in practical practical applications, distribution at eachin instance in problem a day horizon. It approach is important to capture the uncertainties electric demand uncertainties that need accounted for, as in 1b. electric demand has uncertainties that need to to be be accounted for, value as shown shown in Figure Figure 1b. When When in demand. Mosthas day-ahead forecast algorithms forecast a single for each time instance in aa deterministic forecast for DSM, itit is that the will be deterministic forecast is used for DSM, is expected expected thatapproach the forecasted forecasted demand willapplications, be equal equal to to day horizon, as shownis inused Figure 1a. The problem with this is that,demand in practical observed demand. When this case, the resulting BESS after optimization observed demand. When this is is the thethat case, the to resulting BESS scheduled scheduled after design design optimization is electric demand has uncertainties need be accounted for, as shown in Figure 1b. When is a able to resolve the peak, as shown in Figure 2a. On the other hand, when the observed demand able to resolve the peak, as shown in Figure 2a. On the hand, when the observed demand deterministic forecast is used for DSM, it is expected thatother the forecasted demand will be equal to deviates from the demand, BESS is to the deviates significantly significantly from the forecasted demand, the BESS is unable unable to resolve resolve the peak, peak, as as shown shown observed demand. When this is forecasted the case, the resultingthe BESS scheduled after design optimization is able in demand random depends on weather, special in Figure Figure 2b. 2b. Electric demand is random variable that depends on many many factors like like weather, special to resolve theElectric peak, as shownis inaaFigure 2a.variable On thethat other hand, when the factors observed demand deviates events, and socioeconomic factors. The density forecast provides a good description of events, andfrom socioeconomic factors. The forecast provides good of the the significantly the forecasted demand, thedensity BESS is unable to resolve theapeak, as description shown in Figure 2b. uncertainty associated with forecast; itit provides forecast probability distribution of demand at uncertainty associated with aavariable forecast;that provides forecast of probability distribution ofevents, demand at Electric demand is a random dependsaaon manyof factors like weather, special and each time instance in the day horizon, as seen in Figure 3a. We refer to this as a demand probability each time instance in the horizon, as seen in Figure 3a. We refer to of this asuncertainty a demand probability socioeconomic factors. Theday density forecast provides a good description the associated distribution (DPD) profile. details of methods are out scope of distribution (DPD) profile.aThe The details of the the forecast forecast methodsof are out of of the the scope of this this paper paper and with a forecast; it provides forecast of probability distribution demand at each time instance inand the this in work of authors. this is is to to be be considered considered in another another work of the thethis authors. day horizon, as seen in Figure 3a. We refer to as a demand probability distribution (DPD) profile. The details of the forecast methods are out of the scope of this paper and this is to be considered in another work of the authors.

(a) (a)

(b) (b)

Figure Figure 1. 1. Comparison Comparison between between (a) (a) deterministic deterministic and and (b) (b) probabilistic probabilistic forecast forecast models. models. Figure 1. Comparison between (a) deterministic and (b) probabilistic forecast models.

(a) (a)

(b) (b)

Figure 2. systems BESS schedule analysis (a) when Figure 2. 2. Deterministic Deterministic forecast forecast and and battery battery energy-storage energy-storage systems systems BESS BESS schedule schedule analysis analysis (a) (a) when when Figure Deterministic forecast and battery energy-storage forecast coincides with observed (b) when observed deviates from the forecast. forecast coincides with observed (b) when observed deviates from the forecast. forecast coincides with observed (b) when observed deviates from the forecast.

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(a)

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(b)

Figure 3. 3. (a) (a) Demand Demand forecast forecast as as aa probability probability distribution distribution (DPD); (DPD); (b) (b) Demand Demand distribution distribution forecast forecast Figure with confidence confidence interval. interval. with

As depicted in Figure 3b, the probability distribution is generally narrow at the beginning of the As depicted in Figure 3b, the probability distribution is generally narrow at the beginning of the forecast stages and becomes wider as it gets farther from the current moment. This phenomenon calls forecast stages and becomes wider as it gets farther from the current moment. This phenomenon calls for re-forecasting to restore confidence in the forecast. In dynamic-interval forecasting, the forecast is for re-forecasting to restore confidence in the forecast. In dynamic-interval forecasting, the forecast is performed multiple times in a day horizon in order to restore confidence in the forecast. The notion performed multiple times in a day horizon in order to restore confidence in the forecast. The notion is is to forecast at wider intervals during the demand off-peak period and narrow intervals during to forecast at wider intervals during the demand off-peak period and narrow intervals during demand demand peak periods. DIDF helps track the forecasted distribution with high accuracy because the peak periods. DIDF helps track the forecasted distribution with high accuracy because the confidence confidence interval of the forecast is improved in the next forecast interval. interval of the forecast is improved in the next forecast interval. 2.2. Dimensionality Reduction Module 2.2. Dimensionality Reduction Module Because of the stochastic nature of the input data, many demand profile scenarios are possible. Because of the stochastic nature of the input data, many demand profile scenarios are possible. For example, given demand distribution samples at 15-min intervals in a day horizon, there are n = For example, given demand distribution samples at 15-min intervals in a day horizon, there are 96 sample points, where n is the number of demand distributions in a day horizon. The number of n = 96 sample points, where n is the number of demand distributions in a day horizon. The number n possible demand profile scenarios thatthat cancan arise from thisthis setup is a a isa the number of of possible demand profile scenarios arise from setup is ,anwhere , where is the number samples in in each demand distribution. If there are are a = a5 =samples in each demand distribution, the of samples each demand distribution. If there 5 samples in each demand distribution, 96 , which is not feasible for 96 the number of possible demand profile scenarios can be evaluated is not feasible for realnumber of possible demand profile scenarios can be evaluated as 5 as, 5which real-time optimization a high-performance computer. A Monte simulation can be time optimization eveneven withwith a high-performance computer. A Monte CarloCarlo simulation can be used used to select plausible scenarios to follow the original demand distribution for a representational to select plausible scenarios to follow the original demand distribution for a representational selection. number of scenarios to selecttois aselect trade-off accuracy and computational selection. However, However,thethe number of scenarios is abetween trade-off between accuracy and complexity. In real-time applications, time is of the essence; therefore, using dense or high-dimensional computational complexity. In real-time applications, time is of the essence; therefore, using dense or data will affect thedata execution time. this perspective, it is perspective, prudent to perform dimensionality high-dimensional will affect theFrom execution time. From this it is prudent to perform reduction of the data with high fidelity. dimensionality reduction of the data with high fidelity. 2.2.1. Time-Of-Use (TOU) Partitioning 2.2.1. Time-Of-Use (TOU) Partitioning This paper proposes a method to reduce the dimension of DPD to improve the computational This paper proposes a method to reduce the dimension of DPD to improve the computational time of the optimization algorithm. time of the optimization algorithm. To reduce the dimension of the DPD two conditions are satisfied: To reduce the dimension of the DPD two conditions are satisfied: 1. Obtain the value of dimension reduction 1. Obtain the value of dimension reduction 2. Accurate TOU optimization is to electric cost,cost, the 2. Accurate TOU Pricing: Pricing:the theobjective objectiveofofthe thestochastic stochastic optimization is minimize to minimize electric electric cost in turn depends on TOU price which varies depending on the time of day. Figure 1 the electric cost in turn depends on TOU price which varies depending on the time of day. Figure TOU policy of the electric powerpower company (KEPCO) which shows different 1represents represents TOU policy of Korean the Korean electric company (KEPCO) whichthe shows the periods (partitions) in a day horizon with different time of use prices. The price changes are different periods (partitions) in a day horizon with different time of use prices. The price changes different depending on the theofweek and season [26]. Periods markedmarked red have thehave highest are different depending onday theof day the week and season [26]. Periods red the price tag, followed by the yellow periods,periods, with thewith green havinghaving the lowest price tag. highest price tag, followed by the yellow theperiods green periods the lowest price

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Based on the first condition, DPD of n dimension is reduced to m dimension where n is the original dimension of the DPD and m is the dimension to reduce n for a faster computational Energies 2018,maintaining 11, 1166 5 of 14 time while an appreciable level of accuracy ( m  n ). The constraint in the second condition is to ensure the reduce dimension ties in with given TOU pricing interval for first an accurate electric fulfill this, minimum possible Based on the condition, DPDcost of nevaluation. dimensionTo is reduced to the m dimension where n value is the m m  w that can take in order to satisfy the TOU constraint is defined as w. If some demand original dimension of the DPD and m is the dimension to reduce n for a faster computational time values will be misclassified into wrong TOU horizons during the reduction process, thereby while maintaining an appreciable level of accuracy (m < n). attracting a wrong TOU Ascondition such, m  As shown in Figure 4, a day ties horizon is partitioned The constraint in theprice. second is w to. ensure the reduce dimension in with given TOU into different pricing periods. The number of pricing periods in a day horizon as a result TOUthat is pricing interval for an accurate electric cost evaluation. To fulfill this, the minimum possible of value

f ,order defined as in different days the in aTOU season have different pricing From Figure 4 fvalues can take m can take to satisfy constraint is defined as w.periods. If m < w some demand will be misclassified into wrong TOU horizons during the reduction process, thereby attracting a wrong on values of f  {1,3,7,8} depending on the day of the week and season. f  1 represents the TOU price. As such, m > w. As shown in Figure 4, a day horizon is partitioned into different pricing number of partitions for Sundays in all seasons, f  3 represents the number of partitions for periods. The number of pricing periods in a day horizon as a result of TOU is defined as f , different f  7pricing Saturdays in all seasons, represents the number of partitions for weekdays in spring fall, days in a season have different periods. From Figure 4 f can take on values of f = {1,or 3, 7, 8} depending the day ofthe thenumber week and season. f for = 1weekdays representsinthe number of partitions for Sundays f  8 on and represents of partitions winter or summer. Considering all in all seasons, f = 3 represents the number of partitions for Saturdays in all seasons, f = 7 represents days in every season, the maximum value that f can take on should be the minimum values that the number of partitions for weekdays in spring or fall, and f = 8 represents the number of partitions m can take to satisfy the TOU pricing constraint (i.e., w  8 ). One caveat that needs to be taken care for weekdays in winter or summer. Considering all days in every season, the maximum value that f be w 8 .minimum  wm f  take w m c pricing of is days When f values a parameter is introduced to f can takewhere on should the thatorm can to satisfy the TOU constraint (i.e., wf =to8). Oneup caveat that taken care of is(1). days where f < w = 8. When f < w = m or pad make to m . cneeds can to be be evaluated using f ≤ w < m a parameter c is introduced to pad f to make up to m. c can be evaluated using (1). ( w  f , c  w − f, c= m m − ff ,,

f wm

f d i Pl  Pl  PlPPlP Maximum peak propensity = k PP(di ), PP(di ), ...,PP(di )k∞ where P(·) is the probability function, Pl is the peak limit.

(2)(2) (3)

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Maximum peak propensity  PP ( d i ), PP ( d i ),..., PP ( d i )

P()

where 2018, 11, is the Energies 1166

probability function, P l is the peak limit.

(3)



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The most common measure of central tendency used for such approximations is the average, as used in the deterministic case in [27,28]. This idea is also applicable in a stochastic case. However, The most common measure of central tendency used for such approximations is the average, since the peaking value is of the essence, using the average of demand distributions that fall under a as used in the deterministic case in [27,28]. This idea is also applicable in a stochastic case. However, partition could compromise the peak information. To carry the peaking feature, the distributions in since the peaking value is of the essence, using the average of demand distributions that fall under a partition are approximated as the distribution with the maximum peak propensity, as illustrated in a partition could compromise the peak information. To carry the peaking feature, the distributions Figure 5a,b. The PPA produces a reduced demand probability distribution (RDPD) represented as in a partition are approximated as the distribution with the maximum peak propensity, as illustrated , where dˆk is the distribution with the maximum peak ,  dˆPPA ,...,  dˆ m a, rreduced H Figure  { dˆ5a,b. 1 , r1 The 2 , r2  m } in produces odemand probability distribution (RDPD) represented n propensity in the k-th partition, marks the thedistribution (k + 1)-th partition end of the kr ˆ ˆ ˆ as H = < d1 , r1 >, < d2 , r2 >, ..., < where dˆk isofthe with theand maximum peak k d m , r m > , beginning propensity the k-th the beginning of the (k points + 1)-thwhere partition andpricing end of changes the k-th k partition, 1,2,..., mr.k marks th partition,inwith to potential TOU rk corresponds partition, with k =these 1, 2, price-change ..., m. rk corresponds to potential points where TOU makes pricingitchanges occur. occur. Preserving points during dimensionality reduction convenient to Preserving these price-change points during dimensionality reduction makes it convenient to apply apply the right TOU price during optimization. the right TOU price during optimization.

(a)

(b)

Figure 5.5.(a) (a)Converting Converting distributions a partition distribution to adistribution single distribution using Figure distributions in a in partition distribution to a single using piecewise piecewise peak approximation (PPA) (b) Peak propensity or failure region of demand distribution. peak approximation (PPA) (b) Peak propensity or failure region of demand distribution.

Algorithm 1 describes the PPA process. Algorithm 1 describes the PPA process. Algorithm 1. PPA ( X ). begin begin 1. q  TOU _ band ( X ) Algorithm 1. PPA (X).

1. TOU_band( X ) 2. q = c  (w  f )1{w  m}  (m  f )1{m  w} 2. c = (w − f )1{w = m} + (m − f )1{m > w} 3. for i = 1 to c 3. for i = 1 to c 4. max_ sub _ divide((qq)) 4. ZZ=max_sub_divide 5. Endfor Endfor 5. 6. each partition in Z,k in Z,k 6. for for each partition 7. HkH=max_peak_propensity (kX− 7. max_ peak _ propensity(Z ((kZ),(Zk()k,Z1), ) 1), X ) k 8. rk = Z (k ) 8. r  Z (k ) 9. Endfork 9. Endfor end

end 2.3. Stochastic Optimization Stochastic programming is an approach for modelling optimization problems that involve uncertainty. Whereas deterministic optimization problems are formulated with known parameters, real-world problems almost invariably include parameters which are unknown at the time a decision should be made. When the parameters are uncertain but assumed to lie in some given set of possible

Stochastic programming is an approach for modelling optimization problems that involve uncertainty. Whereas deterministic optimization problems are formulated with known parameters, real-world problems almost invariably include parameters which are unknown at the time a decision should be made. the parameters are uncertain but assumed to lie in some given set of7possible Energies 2018, 11,When 1166 of 14 values, one might seek a solution that is feasible for all possible parameter choices and optimizes a given objective function [25]. values, one might seek a solution that is feasible for all possible parameter choices and optimizes a Stochastic optimization given objective function [25].approaches the demand side management (DSM) problem by

min E[ f ( D, x(DSM) )] , where Stochastic optimization approaches theaverage, demand side management problem x byisoptimizing optimizing (minimizing) the total cost on the decision xX

(minimizing) the total cost on average, minE[ f ( D, x )], where x is the decision variable and D is demand ∈X random xvariable.

variable and D is demand as a Stochastic optimization evaluates the best cost and as a random variable. Stochastic optimization evaluates the best cost and controls the peak demand controls the peak demand for a given objective under demand uncertainties. for a given objective under demand uncertainties. 3. Problem Formulation 3. Problem Formulation The objective of the proposed approachisis to to provide provide demand considering The objective of the proposed approach demandside sidemanagement management considering demand uncertainties. algorithm performsaaprobability probability distribution at set intervals demand uncertainties. TheThe algorithm performs distributionforecast forecast at set intervals using empirical data. The demand probability distribution (DPD) produce after the forecast is is using empirical data. The demand probability distribution (DPD) produce after the forecast dimensionally reduced for faster computation via piecewise peak approximation (PPA). The reduce dimensionally reduced for faster computation via piecewise peak approximation (PPA). The reduce demand probability distribution (RDPD) is used as input to the stochastic optimization in conjunction demand probability distribution (RDPD) is used as input to the stochastic optimization in conjunction with energy tariff and parameter constraints which seeks a robust BESS schedule with a given objective with while energy tariff and parameter constraints which seeks a robust BESS schedule with a given satisfying BESS’s technical and efficiency constraints, as shown in Figure 6. The objective objective while satisfying technical and efficiency constraints, as shown in Figure 6. The function of the stochasticBESS’s optimization is divided into two parts: objective function of the stochastic optimization is divided into two parts:

1. 2.

1.

Energy Cost (TOU), which is computed at every time interval

Energy Cost (TOU), which is computed at at every time 2. Demand (Peak) Cost, which is evaluated the end of interval every month Demand (Peak) Cost, which is evaluated at the end of every month

Figure 6. Proposed system architecture. Figure 6. Proposed system architecture.

3.1. Energy CostCost 3.1. Energy The energy costcost represents thethe amount withinaaperiod period multiplied by the The energy represents amountofofenergy energy used used within multiplied by the TOUTOU energy price. In a In distribution sense, the totalexpected expecteddemand demand multiplied by the energy price. a distribution sense, theenergy energycost cost is is the the total multiplied by the energy price, which evaluatedusing using (4). (4). TOU TOU energy price, which cancan bebe evaluated CosttTOU = Cos 

m

TOU ∑ ggkk×CCkTOU  k k =1

(4) (4)

k 1

gk = E[dˆk + ek ]

g k  E [ dˆ k  e k ]

(5)

(5)

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where dˆk is the k-th distribution in RDPD, ek is the BESS schedule provided at the k-th instance by the optimization algorithm, CkTOU is the TOU energy price at the k-th instance, gk is the expected demand of the k-th distribution in RDPD, and CostTOU is the total expected cost of energy in a day. 3.2. Demand Cost The demand cost is the maximum 15-min average power over a month multiplied by the demand price. This is evaluated using (6). The demand cost and energy cost must be unified. Normally, the demand cost is evaluated monthly, whereas the energy cost is calculated at a unit time interval. Because of this difference in units, the demand cost needs to be evaluated correctly at unit time intervals such that the accumulated demand cost over a month is equal to the monthly demand cost, as expressed by (10). The unified daily demand cost can be evaluated using (11). Cost D = Dmax × C D

(6)

Dmax =k H1max , H2max , ..., Hqmax k∞

(7)

Hlmax =k hl1 , hl2 , ..., hlm k∞  Pl × P(dˆlk + ek ), dˆ + ek ) < Pl  lk hlk =  (dˆlk + ek ) × P(dˆlk ), dˆlk + ek ) > Pl  

(8) (9)

q

Cost D =

∑ k {hlk }mk=1 × CU k∞ ≡ Dmax × C D

(10)

l =1

U Costd =k {hlk }m k =1 × C k ∞  D . C CU = m q   28, Feb    29, Feb(leap year) q=  30, Sept, Apr, Jun, Nov    31, Otherwise

(11) (12)

(13)

where C D is demand price for a month, Hlmax is the maximum demand on the l-th day,Dmax is maximum demand for a month, hlk is the peak demand distribution at instance k on the l-th day, dˆlk is the demand distribution at an instance k in RDPD on l-th day, Pl is the peak demand limit, P(.) is a probability function, CU is the unified demand price at any instance in a day, Cost D is the monthly demand cost, Costd is the unified daily demand cost, q is the number of days in a month, with l = 1, 2, ..., q. By KEPCO policy, the demand value used to evaluate demand cost is obtained using (9); thus, if the current recorded demand is greater than the Pl, the recorded demand value is used in calculating the cost. If the recorded demand is less than the Pl, the value of the Pl is used to compute the cost. This is evaluated to achieve peak demand control. 3.3. Optimization The objective function of the stochastic optimization is formulated as the ensemble of energy cost and demand cost (EC) (14). The design optimization algorithm provides BESS control schedule candidates at each iteration of the optimization process, u x = e1 , e2 , ..., em , based on conditions established as constraints to the objective function, where u x is the x-th BESS control schedule, ek is the BESS value scheduled at the kth instance in u x , x = 1, 2, ..., s, s is the number of iterations via the optimization algorithm.

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For each u x , the ensemble of energy cost and demand cost is evaluated; this is evaluated as the minimum of both parameters. This is repeated for each iteration of the BESS control sequences until the one with the least cost on average is found. The objective function for the stochastic optimization is formulated as (16). EC = f ( H, u x ) (14) m

f ( H, u x ) = min( ∑ CostTOU , Costd ) k

(15)

argmin f ( H, u x )

(16)

k =1

ux

An inequality constraint is imposed on the objective function such that the state of the charge (SOC) of the BESS at the beginning of a day should be the same as that at the end of the day (17). Furthermore, the SOC of the BESS should be in the range of socmax and socmin , thus maximum and minimum SOC, respectively, as expressed by (18). soc0 = soc f inal

(17)

socmin ≤ sock ≤ socmax γ sock = sock−1 + ek SBESS

(18)

γ = e f f ch , γ =

1 , e f f dch

(19) (20)

where sock is the SOC at instance k; soc0 and soc f inal are the initial and final SOC, respectively, γ is the efficiency of BESS, e f f ch and e f f dch are the charge and discharge efficiency, respectively, and SBESS is the BESS capacity. The constraints guarantee that the optimization returns feasible solutions. 4. Case Study In this section, the proposed approach is implemented with a case study and simulated for results. For the case study, 2016 and 2017 data from a real-site in South Korean was obtained. The data is recorded at an interval of 15 min in a day horizon, because of KEPCO’s policy of recording peak demand in 15-min intervals. The 2016 data is used for the daily interval forecast for 2017. The 2017 forecast data is used to implement the DSM algorithm, and the observed data is used for testing and for result analysis. By convenience, a density forecast of 250 elements per each distribution is used. Dynamic-interval density forecast (DIDF) is performed following TOU partitions in a day horizon to obtain demand probability distribution (DPD). DPD of n dimensional space is reduced to m dimensional space which is referred to as a reduced reduce demand probability distribution (RDPD) via PPA for stochastic optimization. During peak times, the forecast is performed after every 15-min interval, whereas at off-peak times, the forecast is made on the order of hour intervals, followed by 2 h, 3 h, etc., depending on the size of the off-peak interval. Stochastic optimization is performed using RDPD. Particle-swarm optimization (PSO) [29] with a swarm size of 500, inertia of 0.6, and desired accuracy of 1 × 10−10 is used to implement the stochastic optimization procedure using the parameters in Table 1 at intervals following DIDF. TOU pricing is based on data from KEPCO [26]. Table 1 shows the parameters used for the case study. The simulation was realized in MATLAB 2014 on an Intel i5 processor with 16 GB of RAM. On average, it takes 55 s to complete a single run of the stochastic optimization.

of 1 × 10−10 is used to implement the stochastic optimization procedure using the parameters in Table 1 at intervals following DIDF. TOU pricing is based on data from KEPCO [26]. Table 1 shows the parameters used for the case study. The simulation was realized in MATLAB 2014 on an Intel i5 processor with 16 GB of RAM. On average, it takes 55 s to complete a single run Energies 2018, 11, 1166optimization. 10 of 14 of the stochastic Table 1. Simulation parameters. Table 1. Simulation parameters.

Parameters Parameters Peak demand limit Peak demand limit BESS capacity BESS capacity BESS efficiency BESS efficiency Initial SOC Initial SOC Maximum/Minimum Maximum/Minimum SOCSOC Number of sample points Number of sample points Number of distributions in a day Number of distributions in a day Number of samples in a distribution

Number of samples in a distribution

Symbols Symbols Pl PlSBESS SBESS γ soc 0 soc0 soc / soc socmaxmax /socmin min mm n n a

a

Symbols Symbols 6610 kW 6610 kW 500 kWh 500 kWh 90% 90% 0.2 0.2

0.9/0.2 0.9/0.2 24 24 96 96 250 250

Figures thethe results of the BESS BESS schedule as applied to the expected demand. Figures 77and and8 present 8 present results of robust the robust schedule as applied to the expected The results also show a comparison of the expected demand under the BESS schedule as well as when demand. The results also show a comparison of the expected demand under the BESS schedule as the BESS is absent. Each figure presents the expected demand, SOC of BESS, as well as the cost of well as when the BESS is absent. Each figure presents the expected demand, SOC of BESS, as well as expected when the BESS applied and when itand is not. Atitthe beginning the day, the cost ofdemand expected demand whenschedule the BESSisschedule is applied when is not. At the of beginning BESS operation the minimum SOC value, andvalue, the same value is maintained at the end of thestarts day, BESS starts from operation from the minimum SOC and the same value is maintained at of the day. The optimal BESS schedule obtained after stochastic optimization is verified against the the end of the day. The optimal BESS schedule obtained after stochastic optimization is verified most probable demand of the distribution. Figure 7a presents a stochastic algorithm against the most probable demand of the distribution. Figure 7a presents a optimization stochastic optimization considering only energy arbitrage. can be observed the BESS during the algorithm considering only energy It arbitrage. It can bethat observed thatdischarges the BESS heavily discharges heavily critical TOU periods (peak times), indicated by the red band because the TOU price is high during this during the critical TOU periods (peak times), indicated by the red band because the TOU price is high period. As such, it discharges prior to charging full capacity theduring off-peak inperiod, which during this period. As such, it discharges prior totocharging to fullduring capacity theperiod, off-peak TOU priceTOU is cheaper. 7b shows where the algorithm considers onlyconsiders the peak only demand in which price isFigure cheaper. Figurethe 7bresult shows the result where the algorithm the cost. Figure 8 presents the results where the algorithm considers both the peak demand cost and peak demand cost. Figure 8 presents the results where the algorithm considers both the peak demand energy In Figures and 8,7b the BESS schedule discharges heavily during peakthe periods cost andarbitrage. energy arbitrage. In7b Figures and 8, the BESS schedule discharges heavilythe during peak from 10 a.m. to 2 p.m. to resolve the demand peak exceeding the peak limit. periods from 10 a.m. to 2 p.m. to resolve the demand peak exceeding the peak limit.

(a)

(b)

Figure 7. 7. (a) (a) Demand Demand side side management management (DSM) (DSM) algorithm algorithm results results considering considering only only energy energy arbitrage arbitrage Figure (b) DSM DSM algorithm algorithm results results considering considering only only peak peak demand demandcontrol. control. (b)

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Figure 8. DSM algorithm results considering energy arbitrage and peak demand control. Figure 8. DSM algorithm results considering energy arbitrage and peak demand control.

From Table 2, it can be observed that implementing the algorithm considering only energy Table 2, it can be considering observed that implementing algorithm considering From Table 2,From it DSM can be observed that implementing the algorithm considering only energy only energy Figure 8. algorithm energy arbitrage and the peak demand control. 2018, 11, xresults FOR 11 arbitrage cost performsEnergies poorly in terms of PEER peakREVIEW reduction, but it is the best in terms of cost reduction. performs poorly in terms of peak butin it is the best in terms of cost reduction. arbitrage costarbitrage performscost poorly in terms of peak reduction, butreduction, it is the best terms of cost reduction. 11, x cost FOR and PEERnot REVIEW 11 This is because it seeks Energies only to2018, reduce peak demand. With a previous peak value of 1763 because seeks only cost to that reduce costpeak and not peakalgorithm demand. With a previous peak value of 1763 FromThis Table 2, it only canit be observed implementing the onlyvalue energy This is because itisseeks to reduce and not demand. With a considering previous peak Energies 2018, 11, x FOR PEER REVIEW 1 kW, the algorithm causes a new peak of 2072 kW, representing an 18% increment in peak. In contrast, kW, the considering algorithm causes new peak of 2072 kW, representing increment inpeak. peak. In contrast, arbitrage cost performs poorly in terms of reduction, but it is the best in18% terms of costin reduction. 1763 kW, the algorithm causes a11,new peak of 2072 kW, representing anan 18% increment Figure 8. of DSM algorithm results energy arbitrage and peak demand control. Energies 2018, xa FOR PEER REVIEW 1 it provides the best yearly cost reduction of ₩35,296,338 in 2017. When the algorithm features only provides the besttoyearly yearly cost reduction 35,296,338 in 2017. 2017. When the features only This is because it seeks only reducecost costreduction and not peak With a previous value of 1763 In contrast, ititprovides the best of ₩demand. 35,296,338 in Whenpeak the algorithm algorithm peak control, it is able to reduce the peak from 1763 kW to 1330 kW, which is a peak reduction of 26% peak ititis able toto reduce the peak from 1763 kW to 1330 kW,kW, which is a peak reduction of 26% algorithm causes ais new peak ofthe 2072 kW, representing ankW 18% in peak. From Table 2,features it kW, can the be observed that implementing algorithm considering only energy only peakcontrol, control, able reduce the peak from 1763 toincrement 1330 which isIna contrast, peak and a yearly cost reduction of ₩2,937,306. and abest yearly cost reduction of ₩2,937,306. it poorly provides the cost reduction ₩2,937,306. 35,296,338 in 2017. When the algorithm features only rbitrage cost performs terms of peak reduction, but it of is the best in terms of cost reduction. reduction of in 26% and a yearly yearly cost An ensemble of energy arbitrage and peak control seeks to harness the benefit of the two ensemble of the energy control seeks harness itAn iscost to reduce peak from 1763 kW peak to 1330 kW, which istoa peak reduction of 26%of the two This is because it seekspeak only to reduce and not peak demand. With a and previous peak value of 1763 An control, ensemble ofable energy arbitrage andarbitrage peak control seeks to harness the benefit ofthe thebenefit two algorithms; as such, the results show a reduction of 1308 kW in peak, representing a 26% decrease as such, thea results show aincrement reduction ofpeak. 1308 in peak, representing a 26% decrease andaanew yearly cost reduction of ₩2,937,306. kW, the algorithm algorithms; causes peak ofthe 2072 kW, representing an 18% InkW contrast, asalgorithms; such, results show reduction of 1308 kW in in peak, representing a 26% decrease and and a yearly cost reduction of ₩9,636,600. and a yearly cost reduction ₩9,636,600. of arbitrage and When peak the control seeks features to harness the benefit of the two t provides the besta yearly cost reduction of energy ₩ 35,296,338 inof2017. algorithm only yearly An costensemble 9,636,600. Although implementing energy arbitrage alone provides the best energy cost, it also results in Although implementing arbitrage alone provides best energy cost, it also results in aspeak such,from the 1763 results a energy reduction ofis1308 kWbest in peak, a 26% decrease peak control, it is able algorithms; toAlthough reduce the kWshow to 1330 kW, which a peak reduction ofthe 26% implementing energy arbitrage alone provides the energyrepresenting cost, it also results in the the worst peak control. The peak control case also has a good peak demand reduction, but also the thecost worst peak The peak control case alsodemand has a good peak demand andpeak a of yearly reduction of ₩9,636,600. nd a yearly cost reduction ₩2,937,306. worst control. The peakcontrol. control case also has a good peak reduction, but also reduction, the worst but also the worst yearly cost reduction. A combination of the two presents a compromise between these two worstimplementing yearly cost reduction. Atwo combination the two a these compromise between Although energy arbitrage alone provides the presents best energy cost,two it also results An ensemble yearly of energy arbitrage and peak control seeks topresents harness the benefit ofbetween the two cost reduction. A combination of the a of compromise factors to inthese two factors to achieve a better cost and the best cost reduction. factors achieve apeak cost the best cost reduction. theresults worst peak control also has a good peak lgorithms; as such, the show ato reduction ofbetter 1308 kW and incase peak, representing a 26%demand decreasereduction, but also the achieve a better costcontrol. and theThe best cost reduction. worst of yearly cost reduction. A combination of the two presents a compromise between these two nd a yearly cost reduction ₩9,636,600. Table 2. Simulation Simulation results. results. Table 2. Table 2. Simulation results. factors to achieve a betteralone cost and the best reduction. Although implementing energy arbitrage provides thecost best energy cost, it also results in he worst peak control. The peak control case also has aParameter good peak demand reduction,Value but also the Value Parameter Parameter Value Table 2.a Simulation worst yearly cost reduction. A combination of the two presents compromise between Original Peak (Without BESS) results. 1763these kW two Original Peak (Without BESS) 1763 kW Original Peak (Without BESS) 1763 kW actors to achieve a better cost and the best cost reduction. Energy arbitrage 2072 kW Value Energy arbitrage 2072 kWand peak demand control. New Figure Peak 8.Parameter DSMEnergy algorithm results considering energy arbitrage 2072kW kW New Peak Peakarbitrage Control 1330 New Peak Original Peak (Without BESS) 1763 kW Peak Control 1330 kWand peak demand control. BESS) Peak Control 1330 kW Figure 8. DSMBESS) algorithm results considering energy arbitrage Table(With 2.(With Simulation results. (With Ensemble 1308 kW BESS) Ensemble Energy arbitrage 2072 kW 1308 From Table it can be observed that implementing the kW algorithm only en Ensemble 1308 kW Figure 2, algorithm results considering energy arbitrage and peakconsidering demand control. New Peak8. DSMEnergy arbitrage −18% Parameter Value Figure 8. DSM algorithm results considering energy arbitrage and peak demand control. Peak Control 1330 kW arbitrage cost performs poorly in terms of peak reduction, but it is the best in terms of cost reduc Energy arbitrage −18% From Table 2, it Energy can bearbitrage observed that implementing the algorithm considering only en −18% (With BESS) Peak Reduction Peak Control 25% Original PeakThis (Without BESS) 1763 kW From Table 2, it can be observed that implementing the algorithm considering only Ensemble 1308 kW is because it seeks only to reduce cost and not peak demand. With a previous peak value ofe Peak Reduction Control 25% Peak Control 25% Peak Reduction arbitrage cost performs poorly in termsPeak of peak reduction, but it is the best in terms of cost redu Ensemble 26% From Table 2, it can be observed that implementing the algorithm only e 26% arbitrage cost performs poorly in terms of peak reduction, but it is theincrement best inconsidering terms of cost Energy arbitrage 2072 kW kW, the algorithm causes aEnsemble new peak ofcost 2072 kW, representing an 18% inpeak peak. Inredu con Ensemble 26% Energy arbitrage −18% This is because it seeks only to reduce and not peak demand. With a previous value of New Peak Original Cost (Without BESS) ₩235,084,438 cost performs poorly in terms ofof peak reduction, it is18% the increment best inalgorithm terms of cost This isPeak because it(Without seeks only to reduction reduce and not peak₩235,084,438 demand. With athe previous value o Control 1330 kW itarbitrage provides the best yearly ₩ 35,296,338 inbut 2017. When features Original Cost BESS) 235,084,438 Peak Reduction Peak Control 25% Original Cost (Without BESS) the algorithm causes acost new peak ofcost 2072 kW, representing an inpeak peak. Inredu con (With BESS) kW, Energy arbitrage ₩35,296,338 This is because it seeks only to reduce cost and not peak demand. With a previous peak value o the algorithm causes a1308 new peak of 2072 kW, representing an 18% increment inreduction peak. In con Ensemble kW peak control, it is able to reduce the peak from 1763 kW to₩35,296,338 1330 kW, which is aalgorithm peak of Ensemble 26% Energy itkW, provides the best yearly cost reduction of arbitrage ₩ 35,296,338 in 2017. When the features Energy arbitrage 35,296,338 Yearly Cost Reduction Yearly Cost Reduction Yearly Cost Reduction Peak Control ₩2,937,306 kW, the algorithm causes a new peak of 2072 kW, representing an 18% increment in peak. In con it provides the best yearly cost reduction ofControl ₩ 35,296,338 in 2017. featureo and aEnergy yearly cost reduction of ₩2,937,306. 2,937,306 Control arbitrage −18% Original Cost (Without BESS) ₩235,084,438 Peak peak control, it is able toPeak reduce the peak from 1763 kW to₩2,937,306 1330 kW,When whichthe is aalgorithm peak reduction (With BESS) (With BESS) (With BESS) Ensemble ₩9,636,600 it provides the best yearly cost reduction of ₩ 35,296,338 in 2017. When the algorithm feature Ensemble 9,636,600 peak control, it is able to reduce the peak from 1763 kW to 1330 kW, which is a peak reduction An ensemble of energy arbitrage and peak control seeks to harness the benefit of theo Peak Reduction and Peak Control 25% Ensemble ₩9,636,600 arbitrage ₩35,296,338 a yearly cost reductionEnergy of ₩2,937,306. Yearly Cost Reduction Energy arbitrage 15% peak control, it is able to reduce the peak from 1763 kW to 1330 kW, which is a peak reduction o and An a yearly reduction of ₩2,937,306. Energy arbitrage 15% algorithms; ascost such, results show a reduction ofcontrol 1308 kW in peak, representing a 26% Ensemble 26% Peak Control ₩2,937,306 Energy 15% ensemble ofthe energy arbitrage andarbitrage peak seeks to harness the benefit ofdecr the (With BESS) Yearly Cost Reduction Peak Control 1% Yearly Cost Reduction and a yearly cost reduction of ₩2,937,306. Peak Control 1% ensemble ofthe energy arbitrage andControl peak seeks to harness the benefit ofdec th a An yearly cost reduction of ₩9,636,600. Original Cost and (Without BESS) ₩235,084,438 Ensemble ₩9,636,600 Yearly Cost Reduction 1% algorithms; as such, results show aPeak reduction ofcontrol 1308 kW in peak, representing a 26% Ensemble 4% control seeks to harness the benefit of th Ensemble 4% An ensemble of energy arbitrage and peak algorithms; as such, the results show a reduction of 1308 kW in peak, representing a 26% dec Although implementing energy arbitrage alone provides the best energy cost, it also resu ₩35,296,338 Ensemble 15% 4% Energy arbitrage and aEnergy yearly arbitrage cost reduction of ₩9,636,600. Yearly Cost Reduction algorithms; as such, theThe results show a reduction of 1308 kWpeak in peak, representing 26% dec and a Peak yearly cost reduction of ₩9,636,600. the worst peak control. peak control case also has a good demand reduction, butresu als Control ₩2,937,306 Yearly Cost Reduction Peak Control 1%provides Although implementing energy arbitrage alone the best energy cost, itaalso (With BESS) andworst aAlthough yearly cost reduction of ₩9,636,600. implementing energy arbitrage alone provides the energy cost, it also resu worst yearly cost reduction. AEnsemble combination ofalso the two a best compromise between these Ensemble ₩9,636,600 4% the peak control. The peak control case has apresents good peak demand reduction, but als Although implementing energy arbitrage alone provides the best energy cost, it also resu the worst peak control. peak control good peak demand reduction, al factors to achieve areduction. betterThe cost15% the best case cost reduction. Energy arbitrage worst yearly cost Aand combination ofalso the has twoapresents a compromise betweenbut these the worst peak control. control good peak demand reduction, but al worst yearly cost Aand combination ofalso thehas twoa presents a compromise between thes Yearly Cost Reduction Peak Control 1% factors to achieve areduction. betterThe costpeak the bestcase cost reduction. worst yearly cost areduction. Aand combination of reduction. the tworesults. presents a compromise between thes Table Simulation factors to achieve better cost the best2.cost Ensemble 4%

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5. Discussion Energies 2018,proposed 11, 1166 The

12 of 14 demand side management algorithm is compared with a deterministic Energies 2018, 11, x(DO) FOR PEER REVIEW 12 of 14 optimization method using a deterministic day ahead forecast which is predominantly proposed in other research. The deterministic approach forecasts a day ahead demand profile which 5. Discussion Discussion 5. is used to evaluate an optimal BESS schedule for the next day, as shown in Figure 9a. The proposed sideside management algorithm is compared with a deterministic optimization The proposeddemand demand management algorithm is compared with a deterministic (DO) method using a deterministic day ahead forecast which is predominantly proposed in other optimization (DO) method using a deterministic day ahead forecast which is predominantly research. The deterministic forecastsapproach a day ahead demand profile which is used to evaluate proposed in other research. approach The deterministic forecasts a day ahead demand profile which an optimal BESS schedule for the next day, as shown in Figure 9a. is used to evaluate an optimal BESS schedule for the next day, as shown in Figure 9a.

(a)

(b)

Figure 9. (a) Day ahead forecast and observed demand; (b) BESS schedule on forecasted demand using deterministic optimization (DO).

(a)forecasted demand and the effect of the subsequent (b) BESS schedule that was Figure 9b shows the generated from the optimization algorithm. From the figure, it can be observed that although the Figure 9. (a) (a) Day Dayahead aheadforecast forecast and observed demand; (b) BESS schedule on forecasted demand Figure 9. and observed demand; (b) BESS schedule on forecasted demand using peakusing demand is reduced, the reduction strictly follows the peak limit. The peak is reduced from 1518 deterministic optimization deterministic optimization (DO). (DO). kW to 1370 kW, representing a 9.8% reduction. Figure 9b 10ashows showsthe theforecasted results ofdemand the BESSand schedule obtained from the optimization algorithm as Figure the effect of the subsequent BESS schedule that was Figure 9b observed shows thedemand. forecasted demand and the that effect ofBESS the subsequent BESS schedule that was applied to the It can be observed the schedule generated fails to reduce generated from the optimization algorithm. From the figure, it can be observed that although the generated from thebecause optimization algorithm.inFrom the figure, it can be observed that although the peak the peak demand of reduction inaccuracies the forecast compared to the observed demand. The peak demand is reduced, the strictly follows theaspeak limit. The peak is reduced from 1518 demand is reduced, the reduction strictly follows the peak limit. The peak is reduced from 1518 kW to BESS schedule rather increases the peak from 1563 kW to 1624 kW, representing a 3.8 increase in peak kW to 1370 kW, representing a 9.8% reduction. 1370 kW, representing a 9.8% reduction. demand. Figure 10a shows the results of the BESS schedule obtained from the optimization algorithm as Figure 10a shows shows theresults resultswhen of thethe BESS schedule obtained from side the optimization algorithm Figure 10b proposed real-time demand management is applied to the observedthe demand. It can be observed that the BESS schedule generated failssolution to reduce as applied to the observed demand. It can be observed that the BESS schedule generated fails to applied to the observed demand. It can be observed that the real time algorithms perform better, the peak demand because of inaccuracies in the forecast as compared to the observed demand. The reduce thedynamic peak demand because of inaccuracies in the forecast as compared the observed demand. since schedule the density forecast reforecast the demand at set to intervals to correct the BESS ratherinterval increases the peak from 1563 kW to 1624 kW, representing a 3.8 increase in peak The BESS schedule rather increases the peak from 1563 kW to 1624 kW, representing a 3.8 increase in deviation in the forecast. This approach is able to reduce the peak demand from 1563 kW to 1236 kW demand. peak demand.a 20.9% reduction. . representing Figure 10b shows the results when the proposed real-time demand side management solution is applied to the observed demand. It can be observed that the real time algorithms perform better, since the dynamic interval density forecast reforecast the demand at set intervals to correct the deviation in the forecast. This approach is able to reduce the peak demand from 1563 kW to 1236 kW representing a 20.9% reduction. .

(a)

(b)

Figure 10. 10. (a) schedule on on observed observed demand demand using using DO DO (b) (b) BESS BESS schedule schedule on on observed observed demand demand Figure (a) BESS BESS schedule using proposed proposed approach. approach. using

(a)

(b)

Figure 10. (a) BESS schedule on observed demand using DO (b) BESS schedule on observed demand using proposed approach.

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Figure 10b shows the results when the proposed real-time demand side management solution is applied to the observed demand. It can be observed that the real time algorithms perform better, since the dynamic interval density forecast reforecast the demand at set intervals to correct the deviation in the forecast. This approach is able to reduce the peak demand from 1563 kW to 1236 kW representing a 20.9% reduction. 6. Conclusions This paper has proposed a DSM solution that incorporates a dynamic interval density forecast with a piecewise peak approximation for stochastic optimization. The DSM solution has been verified using demand data from a real industrial site in South Korea. The results show that energy arbitrage alone cannot reduce the peak demand. In the case where the algorithm implements only energy arbitrage, a peak increase of 18% was incurred. When the algorithm implements an ensemble of energy arbitrage and peak demand cost, the peak demand is reduced by 26%. Unlike the deterministic case, where the forecast is performed once in a day horizon, the proposed solution performs the forecast at set intervals in a day horizon to restore confidence in the forecast should it deviate. This ensures a much more accurate forecast and a robust BESS schedule. For verification, the proposed demand side management algorithm is compared to a deterministic algorithm; the proposed method achieves 20.9% in peak reduction while the deterministic case achieves 9.8%. This real-time algorithm is applicable to industrial or commercial settings. Author Contributions: S.H. conceived and supervised the work. M.A.A. designed and performed the experiments and wrote the paper. D.K. proof read the paper. Acknowledgments: This work was supported by Korea Electric Power Research Institute (KEPRI) belonging to Korea Electric Power Corporation (KEPCO) for the project no. R16DA01. Conflicts of Interest: The authors declare no conflict of interest.

References 1. 2. 3. 4. 5. 6. 7.

8. 9. 10.

11.

Gelazanskas, L.; Gamage, K.A.A. Demand side management in smart grid: A review and proposals for future direction. Sustain. Cities Soc. 2014, 11, 22–30. [CrossRef] Rahmani-Andebili, M. Nonlinear demand response programs for residential customers with nonlinear behavioral models. Energy Build. 2016, 119, 352–362. [CrossRef] Palensky, P.; Dietrich, D. Demand side management: Demand response, intelligent energy systems, and smart loads. IEEE Trans. Ind. Inform. 2011, 7, 381–388. [CrossRef] Logenthiran, T.; Srinivasan, D.; Shun, T.Z. Demand side management in smart grid using heuristic optimization. IEEE Trans. Smart Grid 2012, 3, 1244–1252. [CrossRef] Ipakchi, A.; Albuyeh, F. Grid of the future. IEEE Power Energy Mag. 2009, 7, 52–62. [CrossRef] Liu, W.; Niu, S.; Xu, H. Optimal planning of battery energy storage considering reliability benefit and operation strategy in active distribution system. J. Mod. Power Syst. Clean Energy 2017, 5, 177–186. [CrossRef] Akhil, A.A.; Huff, G.; Currier, A.B.; Kaun, B.C.; Rastler, D.M.; Chen, S.B.; Cotter, A.L.; Bradshaw, D.T.; Gauntlett, W.D. DOE/EPRI Electricity Storage Handbook; United States National Nuclear Security Administration: Washington, DC, USA, 2015. Tsekouras, G.J.; Kanellos, F.D.; Mastorakis, N. Computational Problems in Science and Engineering; Springer: Berlin, Germany, 2015; Volume 343, pp. 19–59. Aneiros, G.; Vilar, J.; Raña, P. Short-term forecast of daily curves of electricity demand and price. Int. J. Electr. Power Energy Syst. 2016, 80, 96–108. [CrossRef] Khan, G.M.; Khan, S.; Ullah, F. Short-term daily peak load forecasting using fast learning neural network. In Proceedings of the 2011 11th International Conference on Intelligent Systems Design and Applications, Cordoba, Spain, 22–24 November 2011; pp. 843–848. Dash, P.K.; Satpathy, H.P.; Liew, A.C. A real-time short-term peak and average load forecasting system using a self-organising fuzzy neural network. Eng. Appl. Artif. Intell. 1998, 11, 307–316. [CrossRef]

Energies 2018, 11, 1166

12. 13. 14. 15. 16.

17. 18.

19. 20. 21. 22.

23.

24. 25. 26. 27. 28. 29.

14 of 14

Feinberg, E.A.; Genethliou, D. Peak demand control in commercial buildings with target peak adjustment based on load forecasting. Appl. Math. Power Syst. 2005, 2, 269–285. Dabbagh, M.; Hamdaoui, B.; Rayes, A.; Guizani, M. Shaving Data Center Power Demand Peaks through Energy Storage and Workload Shifting Control. IEEE Trans. Cloud Comput. 2017. [CrossRef] Lin, Q.; Yin, M.; Shi, D.; Qu, H. Optimal Control of Battery Energy Storage System Integrated in PV Station Considering Peak Shaving. Chin. Autom. Congr. (CAC) 2017, 2017, 2750–2754. Lu, C.; Xu, H.; Pan, X.; Song, J. Optimal sizing and control of battery energy storage system for peak load shaving. Energies 2014, 7, 8396–8410. [CrossRef] Cho, K.; Kim, S.; Kim, J.; Kim, E.; Kim, Y.; Cho, C. Optimal ESS Scheduling considering Demand Response for Electricity Charge Minimization under Time of Use Price Key words. Renew. Energy Power Qual. J. 2016, 264–267. [CrossRef] Elizabeth, F.Q.; Nghiem, T.X.; Behl, M.; Mangharam, R.; Pappas, G.J. Scalable Scheduling of Building Control Systems for Peak Demand Reduction. Am. Control Conf. 2012, 3050–3055. [CrossRef] Nghiem, T.X.; Behl, M.; Mangharam, R.; Pappas, G.J. Green scheduling of control systems for peak demand reduction. In Proceedings of the 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), Orlando, FL, USA, 12–15 December 2011; pp. 5131–5136. Carpinelli, G.; Khormali, S.; Mottola, F.; Proto, D. Optimal operation of electrical energy storage systems for industrial applications. IEEE Power Energy Soc. Gen. Meet. 2013, 7, 1–5. Carpinelli, G.; Celli, G.; Mocci, S.; Mottola, F.; Pilo, F.; Proto, D. Optimal Integration of Distributed Energy Storage Devices in Smart Grids. IEEE Trans. Smart Grid 2013, 4, 985–995. [CrossRef] Chiodo, E.; Lauria, D. Probabilistic description and prediction of electric peak power demand. In Proceedings of the Electrical Systems for Aircraft, Railway and Ship Propulsion (ESARS), Bologna, Italy, 16–18 October 2012. Rahmani-Andebili, M.; Venayagamoorthy, G.K. Stochastic optimization for combined economic and emission dispatch with renewables. In Proceedings of the 2015 IEEE Symposium Series on Computational Intelligence, Cape Town, South Africa, 7–10 December 2015; pp. 1252–1258. Wang, Y.; Wang, B.; Zhang, T.; Nazaripouya, H.; Chu, C.C.; Gadh, R. Optimal energy management for Microgrid with stationary and mobile storages. In Proceedings of the IEEE Power Engineering Society Transmission and Distribution Conference, Dallas, TX, USA, 2–5 May 2016. Yudong, M.; Matuško, J.; Borrelli, F. Stochastic Model Predictive Control for Building HVAC Systems: Complexity and Conservatism. IEEE Trans. Control Syst. Technol. 2015, 23, 101–116. Shapiro, A.; Philpott, A. A Tutorial on Stochastic Programming. 2007, pp. 1–35. Available online: http://stoprog.org/stoprog/SPTutorial/TutorialSP.pdf (accessed on 3 April 2018). June, S.; Mar, S. Korea Electric Power Corporation Tariff. 2013. Available online: https://cyber.kepco.co.kr/ kepco/EN/F/htmlView/ENFBHP00101.do?menuCd=EN060201. (accessed on 3 April 2018). Keogh, E.; Chakrabarti, K.; Pazzani, M.; Mehrotra, S. Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases. Knowl. Inf. Syst. 2001, 3, 263–286. [CrossRef] Chakrabarti, K.; Keogh, E.; Mehrotra, S.; Pazzani, M. Locally adaptive dimensionality reduction for indexing large time series databases. ACM Trans. Database Syst. 2002, 27, 188–228. [CrossRef] Kennedy, J.; Eberhart, R. Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks, Perth, Australia, 27 November–1 December 1995; Volume 4, pp. 1942–1948. © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).