Partial decomposition approach to generate load curve forecasting scenarios

Electrical Power and Energy Systems 115 (2020) 105436

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Partial decomposition approach to generate load curve forecasting scenarios a

a

D.L. Carmo , R.C. Souza , C.R.H. Barbosa a b

T

b

Industrial Engineering Department, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil Postgraduate Program in Metrology, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil

A R T I C LE I N FO

A B S T R A C T

Keywords: Load curve forecasting Load demand Hourly data Bottom-up approach Partial decomposition approach

Detailed information about hourly load has always been considered essential when the subject is meeting the energy demand. Thus, in order to propose a support tool to the Brazilian energy market, this work presents a Scenarios Generation Framework. Such procedure uses bottom-up approach as an annual demand projection provider. The Specific Profile Generation Method is used as a way to overcome the lack of hourly data in Brazil. Not only that, Partial Decomposition Approach, a well-known methodology is used to adapt annual load demand into hourly load curves, closing all existing gaps of other methodologies. Finalizing the Scenarios Generation Framework, Monte Carlo simulation is applied over different obtained results and confidence intervals indicate the possible values of load behavior in the future, thus turning a deterministic forecasting method into a scenarios generation framework. In order to check the results, the Framework is applied and validated using the southeast Brazilian region, developing consistent scenarios which were able to keep relevant historical behavior, at the same time it inset projected behavior changes on the demand.

1. Introduction Brazil has an electricity matrix of predominantly renewable sources, with hydroelectric generation accounting for approximately 65% of the domestic supply [1]. Despite being a clean source, this strategy is vulnerable to periods of drought, and thermal plants are essential to meet the demand of the country in these cases. Thus, it is fundamental to know the hourly load demand so that an adequate dispatch of the thermal plants can be established, in addition to ensuring the incorporation of renewable energy sources and appropriate investments in the electricity generation capacity [2,3]. Load curve forecasting has always been considered fundamental for decision making related to the supply of energy demand. Load forecasting has been classified in four different classes [4]. The first one is the long-term forecast, made from one to twenty years ahead, considered fundamental to strategic planning. The second class, mostly used for maintenance scheduling and planning, includes mid-term forecasts, ranging from a month to one year. In the third class are considered the short-term load forecasts, those ranging from one hour to a few weeks, while the fourth class includes the so-called very shortterm forecasts, which vary from a few minutes to one hour ahead. Although most of load forecasting works are classified in the third class [5–7], in the first class are included some methods that stood out over the last few years for providing continuous long-term projections of entire regions. The first one is characterized by scaling the load curve

until the projection year [8,9], while the second aims at making a projection on daily, weekly, monthly and annual bases [10]. The third method focus on few specific important processes of a region [11] and the fourth method is based on scaling a synthetic load curve of considered relevant process of different sectors [12–14]. In addition to these works, it is important to emphasize that some machine learning techniques were used for long-term load projections [15–17]. Although they have been able to obtain very good results, these techniques are automated and focus on accuracy, neglecting the model interpretation and making it difficult for the common user to reason about the generated model. A method called Partial Decomposition Approach (PDA) was previously developed [18], being mainly based on the first and fourth methods mentioned in the previous paragraph [8,9,12–14]. Aiming at closing all the gaps of other proposed methods, this approach starts using as a basis annual bottom-up projections provided by a software called Forecasting Energy Consumption Analysis and Simulation Tool (FORECAST), developed by the Fraunhofer Institute [19]. It is a platform that considers the dynamics of different technologies and socioeconomic indicators of annual demand estimations for regions and countries until 2050. As an extension to FORECAST, the PDA method was developed as the core of the software Energy Load Curve Adjustment Tool (eLOAD), also designed by the Fraunhofer Institute [19], which has the objective of adapting annual load demand projection into hourly load curves.

E-mail addresses: [email protected] (D.L. Carmo), [email protected] (R.C. Souza), [email protected] (C.R.H. Barbosa). https://doi.org/10.1016/j.ijepes.2019.105436 Received 25 January 2019; Received in revised form 3 July 2019; Accepted 25 July 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.

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These advantages encouraged the development of tools like FORECAST, able to generate long-term scenarios and used to generate projections in different sectors in Europe [25–27]. It is composed by four different modules with unique characteristics in order to obtain the energy demand for each sector (Residential, Tertiary, Industry and Others). For Brazil, three of these modules were chosen (Residential, Tertiary and Industry).

Despite the extensive research database available in Brazil, in the electric sector the smart grid technology started to be officially studied only in 2010 [20]. Smart electronic energy meters are able to register the consumption in different hours of the day, being able to keep an hourly database. Because of the late adoption of this technology, until now there is no reliable hourly information of individual sectors and/or processes in the country. The most recent official data which can help in this case is the one from an Ownership and Use Habits research of 2005 [21], made by National Program of Electric Energy Conservation (PROCEL) for the residential sector, and some tertiary and industrial profiles from 2011, provided by a power utility of the southeast region [22]. In addition to being old, due to the constant changes on consumer habits, they are just overall measured profiles, making it necessary to adapt these to the present reality, as well as to different types of seasons and days. Given that, although consistent results have been obtained with the application of eLOAD, a long-term deterministic forecasting method carries a lot of inconsistencies. In the Brazilian case, forecasting hourly load curve using individual effects hourly information requires considerable synthetic data, making it necessary adaptations that smooth the results and decrease the influence of tailored data. Aiming at developing a support tool to the Brazilian energy market, which can be extended to other countries, this article presents a scheme to adapt the PDA method to generate long-term projections of load curves based on simulated scenarios. The generation of such scenarios is based on specific profiles previously obtained [23], and it is applied to the Brazilian southeast region to simulate specific load curve values until 2020. These specific profiles and load curve values are obtained considering three types of seasons (summer, winter and intermediate season) and two types of days (working and non-working days). Analysing the Brazilian southeast load curve provided by National Electrical System Operator (ONS), relevant changes on load profiles can be identified between seasons and types of day. Considering seasons, the differences happen because the temperature variations lead to changes on consumption behaviour. For example, in summer days the use of air conditioning increases a lot, while in winter days it is expected to occur an increase on the use of electrical showers and lighting. Spring and autumn have intermediate temperatures, being merged as intermediate season. Concerning the types of days, the difference happens because in working days there is a lot of tertiary and industrial sectors influence, being this same influence decreased during non-working days. Section 2 contains the description of the methods used as bases of the proposed framework. Section 3 shows the structure of the framework and how it works. Section 4 presents the data description used to illustrate the application of the proposed procedure. Section 5 analyses the results and Section 6 presents some conclusions.

2.1.1. Forecast-Residential A previous work [24] explains that refrigerators, freezers, TVs, electric showers, washing machines, air conditioning and illumination are the end-use technologies that represent 90% of the consumption of the residential sector in Brazil. Those relevant types of equipment are divided by energy-efficiency class, while other types of equipment are modelled by a category named New and Others. Thus, in the FORECAST-Residential the electricity demand depends on all the demands of end-use technologies, which are calculated by the inventory of each end-use distinguished by technological diffusion and efficiency class (Eq. (1)). Ne

Rt = rt · ∑ (Loi, t ·Spi ·Oti·Si, t ) + dothers , t

(1)

i=1

t: instant of time when the demand is estimated; Rt : Total demand of residential sector (kWh) at time t; rt : Number of residences at time t ; Ne : Number of equipment types considered; Loi, t : Level of ownership of equipment i at time t (%); Spi : Specific power of equipment i (kW); Oti : Average time (in hours) of operation or standby of equipment i at time t; Si, t : Inventory of equipment i at time t (%) ; and dothers, t : Electricity demanded by New and Others (kWh). 2.1.2. FORECAST-Tertiary The main variables in the FORECAST-Tertiary are the relevant subsectors, energy services, energy efficiency measures (EEM) and techno-economic data. For Brazil, a previous work [28] recommends using 8 subsectors and 14 energy services, selected according to the European Classification of Economic Activities [29]. Eq. (2) shows a formal description of the model and Table 1 shows the main variables.

Tt Tsub

=

ES

∑ ∑ GReg,TS,t ·DReg, TS, E, t ·PReg, TS,E × UReg,TS,E . TS = 1 E = 1 x

∏

(1 − ΔDRReg ., TS, E , EEM , t ·ΔPReg, TS, E , EEM ) ×

EEM = 1 x

2. Methods

∏

(1 − ΔDRReg, TS, E , EEM , t ·ΔUReg, TS, E , EEM )

EEM = 1

This section provides an overview of the base methods used by the proposed framework, starting with the bottom-up approach, used to produce annual demand projections. It is followed by an overview of the specific profile generation method, and it closes up showing the PDA method, used to adapt annual projections to hourly load projections.

(2)

t: instant of time when the demand is estimated; Table 1 Main variables used on tertiary.

2.1. Bottom-up approach Given that all time series to be modelled are intrinsically composed by different processes with distinct characteristics, the bottom-up approach aims at independently projecting each of these processes, aggregating them at the end. Thus, social and economic factors have significant impact, reducing the dependence on the energy consumption history [24]. 2

Tertiary Subsectors

Energy Services

Wholesale and retail Hotels, cafes and restaurants Traffic and transmission data Finance Health Education Public Offices Other services

Illumination Public illumination Ventilation and air conditioning Refrigeration Cooking Water heating Heat pumps ⋮

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SPR eq, reg, sea, td (h) = (HPR eq, reg (h) × PVr , sea, td (h)) + eeq, reg, sea, td (h)

Tt : Total demand of tertiary sector (kWh) at time t; TS : Subsectors, TSub = 8; E : Energy Services, ES = 14 ; Reg : Region; GReg, TS, t : Global variables at time t; DReg, TS, E , t : Energy service variables at time t; PReg, TS, E : Installed power by energy service (kW) at time t; UReg, TS, E : Annual use rate (h/a); ΔDRReg, TS, E , EEM , t : Diffusion rate of EEM (%); ΔPReg, TS, E , EEM : relative installed power reduction by EEM (%); and ΔUReg, TS, E , EEM : relative use rate reduction by EEM (%).

SPR eq, reg, sea, td (h) : normalized residential specific demand calculated for each equipment eq, region reg , season sea, type of day td and hour h ; HPR eq, reg (h) : normalized residential historical demand for each equipment eq, region reg and hour h ; PVr , sea, td (h) : percentage difference value between the overall average daily load curve of a year and specific average daily curve of the same year at hour h; and eeq, reg, sea, td (h) : error of each obtained demand that follows a Gaussian distribution with mean μ and variance σ 2 .

2.1.3. FORECAST-Industry In the FORECAST-Industry sector, the energy demand calculation begins with the annual production forecast and specific energy consumption (SEC). Then, the EEMs are applied to reduce the energy demand, allowing the residual to be calculated for each industrial subsector. Thus, the electricity demand will depend on cross-cutting technologies (CCT), following an approach similar to system technologies [30]. In Brazil, the industrial sector was mapped [31] and 11 subsectors and 79 industrial systems of major consumption were chosen. The electricity demand is calculated according to Eq. (3), and in Table 2 are shown the main variables used for the sector.

SPTtsub, reg, sea, td (h) = (HPTtsub, reg (h) × PVr , sea, td (h)) + etsub, reg, sea, td (h)

∑ ∑

(5)

SPTtsub, reg, sea, td (h) : normalized tertiary specific demand calculated for each subsector tsub , region reg , season sea , type of day td and hour h ; HPTtsub, reg (h) : normalized tertiary historical demand for each subsector tsub , region reg and hour h ; PVr , sea, td (h) : percentage difference value between the overall average daily load curve of a year and specific average daily curve of the same year at hour h; and etsub, reg, sea, td (h) : error of each obtained demand that follows a Gaussian distribution with mean μ and variance σ 2 . SPIisub, reg, sea, td (h) = (HPIisub, reg (h) × PVr , sea, td (h)) + eisub, reg, sea, td (h)

ISub ISysISu

It =

(4)

(6)

(SCISu, ISy, t + EstIsu, t − EEISu, t ) (3)

ISu = 1 ISy = 1

SPIisub, reg, sea, td (h) : normalized industrial specific demand calculated for each subsector isub , region reg , season sea , type of day td and hour h ; HPIisub, reg (h) : normalized industrial historical demand for each subsector isub , region reg and hour h ; PVr , sea, td (h) : percentage difference value between the overall average daily load curve of a year and specific average daily curve of the same year at hour h; and eisub, reg, sea, td (h) : error of each obtained demand that follows a Gaussian distribution of average μ and variance σ 2 (kWh).

t: instant of time when the demand is estimated ISy : Industrial systems, ISys = 1, 2, ⋯, ISysISu ; ISu : Industrial subsectors, ISub = 11. It : Total demand of tertiary sector at time t; SCIsu, ISy, t : Electricity consumption of a system ISy of a subsector ISu at time t (kWh); EstISu, t : Estimator value obtained by the added value of each subsector ISu (kWh); and EEISu, t : Energy economy obtained by EEMs applied to subsector ISu (kWh).

The errors in Eqs. (4), (5) and (6) represent expected inconsistencies that happen when generating synthetic data. As real data for the specific profiles are not available, there is no way to calculate the true values of the average μ and variance σ 2 . Thus, as explained in [20], in order to consider the existence of these errors and somehow include them on the results, uncertainty is added to the results by Monte Carlo simulation. Simulated values to residential sector (SSPR eq, reg, sea, td (h) ), and industrial sector tertiary sector (SSPTtsub, reg, sea, td (h) ) (SSPIisub, reg, sea, td (h) ) are calculated according to Eqs. (7), (8) and (9) with the objective of generating 3 different profiles (maximum, average and minimum).

2.2. Specific profile generation method In order to overcome the lack of hourly data in Brazil, a previous work from our research team [23] proposed a method to adapt the few historic hourly data available in the country to specific seasons (summer, winter and intermediate) and types of day (working day and nonworking day). For the residential (Eq. (4)), tertiary (Eq. (5)) and industrial (Eq. (6)) sectors are applied a percentage difference value (PV) obtained between the variation of an overall average daily load curve of a year and a specific average daily curve of the same year applied on the historical daily profiles obtained. Table 2 Main variables used on industry. Industrial Subsectors

Industrial Systems

Pig Iron and Steel Non-ferrous Metals Pulp and Paper Chemical Food and Drink Cement Iron Alloy Mining and Pelleting Textile Ceramic Other Industries

Sintering, … Primary aluminium, … Paper, … Oxygen, … Sugar, … Cement clinkerization, … Load reduction fusion, … Mineration, … Wiring, … Red ceramics, … Others

2 SSPR eq, reg, sea, td (h) N (SPR eq, reg, sea, td (h), σeq , dp (h ))

(7)

2 SSPTtsub, reg, sea, td (h) N (SPTtsub, reg, sea, td (h), σtsub , dp (h ))

(8)

2 SSPIisub, reg, sea, td (h) N (SPIisub, reg, sea, td (h), σisub , dp (h ))

(9)

These 3 different profiles are estimated based on a confidence interval of 95% which is applied to each value of hour (h ) considering the region, season and type of day. For each hour (h ) are generated 100 values in order to estimate the uncertainty associated and, as a consequence, adjust inconsistencies of the results. The mean, upper and lower limits of the confidence interval are used as values to compile the 3 different profiles. An example of application is shown in [23]. With 6 different profiles generated for each process (3 seasons and 2 types of days), the average in each case is the calculated specific demand for each season (sea ), type of day (td ) and hour (h ), while the variances are calculated based on the resulting 6 different profiles (dp) for each hour (h ) of a residential equipment, tertiary and industrial 3

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Fig. 1. Scenario Generation Framework Flowchart.

information (type of day, season, …) throughout the year, which are proc then scaled according to annual demand of the historical year, DHY ,p. The sum of all n relevant processes synthetic load curves created is then deducted from the total demand of historical year in order to res obtain a residual synthetic hourly load curve (LHY , h ), which represents all the processes classified as less relevant for the same year (Eq. (15)).

subsectors, as follows on Eqs. (10), (11) and (12). 30 2 σeq , dp (h ) =

∑

SPR eq, dp (h)

dp = 1 30 2 σtsub , dp (h ) =

∑ dp = 1 30

2 σisub , dp (h ) =

∑ dp = 1

(30 − 1)

(10)

SPRtsub, dp (h) (30 − 1)

(11)

n

proc sys res LHY , h = LHY , h − ∑ p = 1 LHY , p, h

∀ p ∈ Prelev , ∀ h ∈ [1, hmax , year ]

SPRisub, dp (h) (30 − 1)

(12)

hmax , year : total hours of determined year.

2.3. Partial decomposition approach (PDA)

In step three the synthetic load curves of relevant process are scaled to the projection year considering the annual projection to it generated proc by FORECAST (DPY , p ). This is made by multiplying the rate of change between projection and historical year demands by the synthetic load curve previously generated for each process for the historical year proc (LHY , p, h ) (Eq. (16)).

The Partial Decomposition Approach (PDA) is a methodology developed [18] in order to complement other approaches used for load curve projection. It is based on the possibility of de-standardizing the annual electricity demand projection of a specific year, made by FORECAST (Eq. (4), (5) and (6)), into specific demands of processes on the same year. Boßmann [18] defines as “processes” the end-use technologies of each sector. In this present paper, in residential sector it refers to types of equipment, in tertiary sector it refers to energy services and in industrial sector it refers to what are called industrial systems. The methodology basically consists of five steps. In the first step the most relevant processes are mapped using Eq. (13) and Eq. (14). A process is considered relevant (Prelev ) if the ratio of variation in the proc process specific demand, between historical (DHY , p ) and projection year proc sys (DPY , p ), and total demand in historical year (DHY ), is higher than a given critical value (crit). Otherwise, the process is considered less relevant (Plrelev ).

p ∈ Prelev if crit ≤

p ∈ Plrelev if crit >

proc LPY , p, h =

proc − DHY ,p sys DHY

proc DPY ,p proc DHY ,p

proc ·LHY , p, h

∀ p ∈ Prelev , ∀ h ∈ [1, hmax , year ]

(16)

In step four it is carried out the residual load curve scaling, referred to the less relevant processes, to the projection year. The residual synthetic load curve, previously calculated, is multiplied by the cumulative change of demand between projection and historical year (Eq. (17)). res LPY ,h =

proc sys n DPY , h − ∑ p = 1 DPY , p proc sys − ∑np = 1 DHY DHY ,p

res ·LHY ,h

∀ p ∈ Prelev , ∀ h ∈ [1, hmax , year ]

proc proc DPY , p − DHY , p sys DHY

(15)

(13)

(17)

In the last step the total synthetic scaled load curve of relevant processes is aggregated to the synthetic scaled residual load curve, sys obtaining the total load curve of a specific projection year (LPY , h ) (Eq. (18)).

proc DPY ,p

(14)

In step two a synthetic hourly load curve for each relevant process p proc is built for the historical year, LHY , p, h . It is carried out using historical specific profiles (in p.u.) allocated according to the corresponding

n

proc sys res LPY , h = LPY , h + ∑ p = 1 LPY , p, h

∀ p ∈ Prelev , ∀ h ∈ [1, hmax , year ] 4

(18)

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n

proc sys res LPY , PRO, crit , h = LPY , PRO, crit , h + ∑ p = 1 LPY , PRO, crit , p, h

3. Scenarios generation framework

∀ p ∈ Prelev , ∀ h ∈ [1, hmax , year ], ∀ PRO ∈ [pMAX , pAVE , pMIN ], ∀ crit

The scenarios generation framework works according to Fig. 1. At first the Specific Profile Generation Method described in Section 2.2 is used in historical data in order to generate three different profiles for each process ( pMAX , pAVE , pMIN ). Those three profiles are used in PDA, together with FORECAST results, with three different critical values. This strategy uses critical values of 0%, 5% and 10%, aiming to consider a first case that uses all processes (crit = 0%), without a residual load curve, a second case (crit = 5%) that considers some relevant processes and has a large residual load curve and, finally, a third case (crit = 10% ) which uses just those processes with the largest relevances to the projection, yielding a major residual load curve. It is important to emphasize that, in some cases, when the projection horizon is not large enough, the relevances of the processes do not achieve considerable values, making the cases of 5% and 10% to use just the residual load curve. This happens due to the fact that, in short horizons, large changes are not expected to happen in the load curve behaviour, so that the residual load curve, which carries most of historical behaviour, has a major influence on the projection. Thus, now the five steps of PDA, previously explained, are now adapted to the three different specific profiles described in Section 2.2 and the three different critical values (0%, 5% and 10%), thus yielding 9 different scenarios. In step one, the relevant processes are now obtained by type of profile and critical value, as shown in Eq. (19) and Eq. (20).

p ∈ Prelev, PRO if crit ≤

(24) From here, with a load curve projection for three specific profiles and three critical values, the framework aims at, primarily, projecting sys nine different scenarios (LPY , scen, h ) for each year by PDA/eLOAD. Eq. (25) shows a general equation for the framework as a whole. sysSIM sys LPY , PRO, crit , h = z (LPY , h ) + εPY , PRO, crit , h

∀ h ∈ [1, hmax , year ], ∀ PRO ∈ [pMAX , pAVE , pMIN ], ∀ crit ∈ [0%, 5%, 10%]

sysSIM sys sys ¯ PY LPY N (M ,h , scen, h , VarPY , scen, h )

∀ h ∈ [1, hmax , year ], ∀ scen ∈ [1, ⋯, 9]

(19)

9 sys ¯ PY M , scen, h = ∑scen = 1

proc proc DPY , p − DHY , p sys DHY

(20) sys VarPY , scen, h =

n

sys ∑9scen = 1 LPY , scen, h

(9 − 1)

(28)

In this section all the data used to apply the proposed framework are presented. Information about the annual demand projections, the hourly load curves used and the load profiles are described, as well as their sources. Due to limited availability of data in Brazil, the so-called processes, used for projection of the load, are restricted to equipment of the residential sector, subsectors of tertiary sector and subsectors of industrial sector. Thus, the input data used for the Scenarios Generation Framework are:

∈ [0%, 5%, 10%] (21) In step three it is made the scaling of the relevant processes synthetic load curves for each case, considering the annual projection made by FORECAST (Eq. (22)). proc ·LHY , PRO, crit , p, h

∀ p ∈ Prelev , ∀ h ∈ [1, hmax , year ], ∀ PRO ∈ [pMAX , pAVE , pMIN ], ∀ crit

▪ FORECAST annual projections; ▪ 3 different load profile scenarios for 6 specific days for each one of the 27 processes (2 916 profiles); and ▪ Hourly load curve for an entire year chosen as base year.

∈ [0%, 5%, 10%] (22) In step four, also based on the annual projection made by FORECAST, the residual synthetic load curve is scaled. As done until now, it is made for each type of profile and critical value, as shown by Eq. (23). res LPY , PRO, crit , h =

(27)

4. Database

∀ p ∈ Prelev , ∀ h ∈ [1, hmax , year ], ∀ PRO ∈ [pMAX , pAVE , pMIN ], ∀ crit

proc DPY ,p

9

∀ h ∈ [1, hmax , year ], ∀ scen ∈ [1, ⋯, 9]

proc sys res LHY , PRO, crit , h = LHY , PRO, crit , h − ∑ p = 1 LHY , PRO, crit , p, h

proc DHY ,p

sys LPY , scen, h

∀ h ∈ [1, hmax , year ], ∀ scen ∈ [1, ⋯, 9]

In step two, for each case, the synthetic load curves of all relevant processes are built and then their sum is used to calculate the residual load curve (Eq. (21)).

proc LPY , PRO, crit , p, h =

(26)

sys sys ¯ PY In equation, the mean (M , scen, h ) and the variance (VarPY , scen, h ) are calculated according to Eqs. (27) and (28), as follows.

sys DHY

∀ PRO ∈ [pMAX , pAVE , pMIN ], ∀ crit ∈ [0%, 5%, 10%]

(25)

In Eq. (25), function z represents the strategy applied to project all sys nine different scenarios using PDAs single response (LPY , h ), in order to sys ε . The error, , is the expected error from each of obtain LPY proj , h , PRO, crit , h these projections, assuming it has a Gaussian distribution with unknown mean and variance. With the error of each projection, in a next step the framework aims at simulating scenarios using Monte Carlo with Gaussian distribution, in order to reduce the existing error. Therefore, the simulated scenarios are elaborated according to Eq. (26).

proc proc DPY , p − DHY , p

∀ PRO ∈ [pMAX , pAVE , pMIN ], ∀ crit ∈ [0%, 5%, 10%] p ∈ Plrelev, PRO if crit >

∈ [0%, 5%, 10%]

4.1. Annual demand projections

proc sys n DPY , h − ∑ p = 1 DPY , p res proc · LHY , PRO, crit , h sys − ∑np = 1 DHY DHY ,p

The annual demand projections were obtained based on configurations previously described and generated by the tool FORECAST [24,28,30]. They were estimated based on an outlook in which all the processes will be more efficient in the future due to technologic innovations, the so-called autonomous diffusion scenario, besides the adoption of energy efficiency measures that have economic feasibility. The annual demand projected for Brazil by FORECAST is compared to the results presented by the Energy Research Company (EPE) [31] for 2020. Fig. 2 shows that EPE’s projections are very optimistic when

∀ p ∈ Prelev , ∀ h ∈ [1, hmax , year ], ∀ PRO ∈ [pMAX , pAVE , pMIN ], ∀ crit ∈ [0%, 5%, 10%] (23) In step five, both scaled synthetic load curves are aggregated in order to obtain the total load curve of a specific projection year for each case (Eq. (24)). 5

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Fig. 4. Estimated Southeast Region Hourly Load Curve for 2016.

4.2. Hourly load curves This article used hourly load curve data (MWh) from January 1, 2016 to December 31, 2016, for the Brazilian Southeast/Midwest subsystem, provided by the National Electrical System Operator (ONS) [32]. Data from 2016 is used because the PDA scales the base year to a future year. Thus, as this present work aims at projecting the year 2020 (leap year) as a test to the Framework, it is necessary to have also a leap year as a base (2016 was the last leap year). In case of 2017 projection to validate the results, the model automatically removes the extra day. The annual demand projections provided by EPE and shown in Section 4.1 are for the southeast region only, so it is necessary to scale the hourly load curves provided by ONS, as they aggregate the southeast and Midwest regions. According to the Brazilian Yearbook of Electrical Energy [1], developed by EPE, the Southeast region grid consumption in 2016 was 229 970 GWh, while the Midwest region grid consumption was 34 579 GWh. Thus, from a total grid consumption of 264 549 GWh for both regions, 86.93% is from the Southeast region, being this value applied to the Southeast/Midwest subsystem hourly load curve in order to obtain an estimated hourly load curve of the southeast region (Fig. 4).

Fig. 2. Brazilian Demand Projection for 2020.

compared to FORECAST projections. However, it must be considered that most of the difference between the projections is due to the diffusion scenario used on the bottom-up approach. Besides the Brazilian total demand, the FORECAST also produces projections for all processes belonging to each one of the sectors and each one of the five Brazilian regions. In Fig. 3 are presented the Brazilian Southeast demands by sector for the historical year, 2016, for a year that was projected to be used as a basis for comparison, 2017, and for the last year of projection, 2020. The Residential sector has the highest growth expectation with a growth rate of 2.41% per year from 2016 to 2020, followed by Industry and Tertiary sectors, with growth rates of 1.74% and 1.51% per year, respectively. Among Residential sector processes, the Air conditioning stood up as being responsible for most of its growth rate (6.56% per year), followed by Lighting (4.25% per year). Even considering the high expectations for these processes, the growth rate of the Residential sector was dampened by expected decreasing appliances, such as Electrical Shower (–5.62% per year) and Freezer (−1.98% per year). For Tertiary sector, the Other Services presented the expected growth rate of 2.6% per year and in the Industrial sector the Cement industry presented a growth rate of 3.45% per year. In both sectors all processes had a constant growth expectation, with no decreasing rate over the years.

4.3. Processes profiles In order to use PDA it is necessary to set specific profiles of the most relevant processes. These specific profiles are obtained using a previously explained methodology [23] based on unique process profiles of each sector extracted from real measurements databases. Regional residential unique profiles were obtained through Ownership and Habits of Use Survey (PPH) [21]. For tertiary and industrial sectors, southeast profiles were originated via average daily profiles, provided by a power utility of the southeast region from 2011 data [22]. These unique and old data had to be matched to today’s reality, as well as adapted to represent different types of seasons and days through the Specific Profiles Generation Method [23]. The synthetic profiles were thus normalized based on their maximum values because the interest for applying it to PDA is related to load behaviour, not its absolute level (the level is scaled based on annual FORECAST projections). In order to show the original data, the normalized unique processes profiles related to the residential sector, tertiary sector and industrial sector of the Southeast region were aggregated and then normalized to be presented on Figs. 5, 6 and 7, respectively. 5. Results This section presents the results for the southeast region of Brazil, previously chosen as it represents almost 50% of Brazilian energy

Fig. 3. FORECAST Southeast Demand Values by Sector. 6

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Table 3 Relevance of each process for Southeast region.

Fig. 5. Aggregated residential sector processes profiles.

PROCESSES

RELEVANCE

Air Conditioning Lighting Other Industries Electrical Shower Refrigerator Non-ferrous Metals Wholesale and Retail Hotels, Cafes and Restaurants Chemical Food and Drink Other Services Pig iron Steel Cement Traffic and Transmission Data Public Offices Pulp and Paper Mining and Pelleting Iron Alloy Textile Health Washing Machines Television Education Freezer Ceramic Finance Other Residential

1.84% 1.13% 0.99% 0.74% 0.68% 0.65% 0.56% 0.45% 0.41% 0.38% 0.35% 0.31% 0.29% 0.25% 0.21% 0.20% 0.19% 0.12% 0.10% 0.10% 0.10% 0.10% 0.08% 0.08% 0.04% 0.04% 0.01%

continuously to lose relevance in the forecasting, although it would need an enormous lead to completely lose its importance, due to residual load curve operation, when using the PDA.

Fig. 6. Aggregated tertiary sector processes profiles.

5.1. Framework validation The Framework validation was made comparing 2017 average projected scenarios with 2017 real average values. It is important to emphasize that the base year is 2016, in order to use the assumptions of previous works [24,28,30] for annual projections, and the validation is being made with predictions of one year ahead, in other words, 8760 steps ahead. Four metrics are used to measure the quality of the projection. The classic metrics, Mean Absolute Percentage Error (MAPE) and Root Mean Square Deviation (RMSE) are used to compare the average predicted scenario for 2017 with the historical load curve of the same year. Beyond these metrics were also used the Prediction Interval Coverage Probability (PICP) [33] and the Mean Prediction Interval Width (MPIW) [34] in order to verify the quality of the prediction interval. In Fig. 8 it is possible to notice the six different load profiles, for each situation. Y-axis indicates the minimum and maximum average values for the year, and the middle value on the same axis represents the average value for the specific average profile. Historical values show that Summer Working Days profiles tend to produce the highest average values, while Winter Nonworking Days have the smallest. Analysing by season, as already expected, summer has the highest values on both situations (working and nonworking days), most of it due to air conditioning use. Brazil is a tropical country rather hot, especially in the summer days’ afternoon, making the consumer behaviour change and, at the same time, also changing the peak load hours to happen between 14 h and 16 h on working days. On winter time it is possible to notice smaller values, but it is also possible to notice the peak around 19 h. This is due to the lower consumption in the afternoons and higher electrical shower usage at the early hours of the evening. It is important to study these historical characteristics because if the proposed framework is using just the residual load curve to make the

Fig. 7. Aggregated industry sector processes profiles.

consumption [1]. As previously indicated, three critical values were used to determine three perspectives with different levels of relevance for the processes. When the critical value is zero (0%), this indicates that there is no minimum impact limit for the processes, i.e., in this case all processes are used. When critical value is 0.05 (5%), all process profiles with less than 5% of relevance are not used in the projections, and finally, when it is 0.1 (10%), all profiles with less than 10% relevance do not impact. Table 3 shows the relevances calculated for each process, according to step 1 of the framework. All relevance values are low, implying that in cases of 0% critical value, synthetic specific load profiles curves are going to influence the projections, without any impact of historical load curve, while in the cases of 5% and 10% critical values the historical curve is scaled alone, implying that it is responsible for the final forecasting. As previously appointed, this was already expected to happen due to the fact that a large change on load curve is not assumed to occur for the next few years. With a larger forecasting horizon, the processes would have higher influence, making the historical load curve 7

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Table 4 2017 total metric results. 2017 Results

PICP

MIPW

RMSE

MAPE

0.65

7169.11

2902.08

7.33%

Table 5 2017 specific days’ metric results.

In Table 5 is clearly noticeable that days of summer, especially, but also intermediary seasons, were the type of days where the error metrics accused the highest errors (in scales of red). These specific days are those with the highest load values, making it clear that the prediction level is underestimating the real load level. Fig. 2 had already shown that, due to the diffusion scenario previously used on the bottom-up approach [24,28,30], the annual predicted values were pessimistic when compared to EPE. This made the predicted load level lower than the reality and can be noticed clearly on Fig. 9, as the historical load on afternoon is breaking the upper limit. It is important to emphasize that the autonomous scenario proposed for the bottom-up approach considers just the minimum application of efficiency measures, but even so the predicted values were higher than reality, indicating that not even the minor efficiency measures scenario was achieved on Brazilian Southeast region. Notwithstanding the low level of load projected, at first glance the load profile looks consistent. To confirm this, a typical load profile of 2017 was compared with a typical load profile projected by the average scenario. In Brazil, the National Electric Energy Agency (ANEEL) considers three levels of consumption in a day [35]. Thus, based on these considerations about load level, in this paper it is designated that the load between 0 h and 6 h is considered light, the load from 7 h to 17 h and 21 h to 23 h is considered medium and the load from 18 h to 20 h is heavy. Table 6 shows the participation of these levels for the historical average typical day and the predicted average scenario typical day. The results show that the framework had good results on predicting the average typical day profile. The minor difference in light and medium levels shows that the framework overestimated the light level by 0.5% taking this value from the medium level, but also was perfect on predicting the heavy load. This overestimation of light level can be possibly explained by a minor overestimation of air conditioning on residential sector annual forecasting, of which, according to the southeast load profiles [22], the consumption occurs mostly at night and dawn.

Fig. 8. Southeast historical average profiles for 2016.

projections for the 5% and 10% cases, the historical behaviour should have predominance on the projections, keeping the historical characteristics. Fig. 9 shows, in black, actual historical average values for 2017, while the red and blue dashed lines represent, respectively, upper and lower limits with a 95% confidence interval, generated by applying the framework with one hundred simulated scenarios. The grey line is the average load predicted scenario used to compare with the historical value. The Y-axis follows the same pattern as described for Fig. 8. As shown in Table 4, the MAPE and RMSE obtained for the entire year were 7.33% and 2 902.08 MWh, respectively. About the generated scenarios, although the MIPW showed a consistent prediction interval of 7 169.11 MWh in average for each hour (about 18% of the average load of each hour), the PICP of 0.65 showed that just 65% of the historical load curve values were inside this interval. To investigate the prediction on the perspective of each specific type of day, these metrics were calculated separately and are presented on Table 5. Each specific day is represented by an abbreviation that indicates summer working day (SWD), summer nonworking day (SNWD), winter working day (WWD), winter nonworking day (WNWD), intermediary working day (IWD) and intermediary nonworking day (INWD).

5.2. Long term forecasting using scenarios generation framework Based on the results obtained for 2017, proving the efficiency of the proposed approach as a long-term forecasting tool, it is now possible to extend the projections showing some results for 2020. In Fig. 10, red Table 6 Load percentage by level. Load profile

Historical Predicted

Fig. 9. Framework validation using 2017 historical values. 8

2017 Light

Medium

Heavy

25.2% 25.7%

61.0% 60.5%

13.8% 13.8%

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Table 7 Average participation of processes by load level. Process Air Conditioning Electrical Shower Process Air Conditioning Electrical Shower

2016 Light 14.3% 0.0%

Medium 1.9% 2.9%

Heavy 0.3% 8.0%

2020 Light 20.3% 0.0%

Medium 2.8% 2.1%

Heavy 1.0% 5.3%

noticed with a peak smoothing occurring between 19 h and 21 h. To reinforce this idea, in Table 7 the estimated residential air conditioning and electrical shower hourly share in the base year (2016) is compared to the hourly projections to 2020 for these appliances, made by the Framework. Between all the processes, residential air conditioning was the one with the higher participation increasing. It is expected to increase 6% just on light levels, in addition to its 0.9% increase on medium level and 0.7% increase on heavy level, with a total of 7.6% participation increasing over a typical day. Beyond the fact that increasingly people have been buying air conditioning, which explains its increase on light level, home office is being adopted by many people and can be the explanation for the residential air conditioning increase at other levels. In contrast, the electrical shower was the process with the high participation loss. With a total of 7.4% of estimated participation on a typical day on 2020, it is expected to reduce 3.5% from 2016. This drop can be explained by the fact that people are replacing electrical showers by showers fuelled by natural gas. Figs. 12 and 13 compare the load profile for an overall average typical day from the base year, 2016, and the average load profile projections made to 2017 and 2020 by the Framework for residential Air Conditioning and Electrical Shower, respectively. As already shown in Table 7, the expected growth of air conditioning on light load and the expected decreasing of electrical shower on heavy load can be observed more clearly. To give an overall view of results, Table 8 shows an analysis of average hourly projections of each sector made to 2020 in comparison with their estimated share in 2016. Table 8 shows that it is expected a decrease on average participation just for the residential heavy load. Most of it was influenced by the electrical shower decrease that has already been seen, but is important to emphasize that in the residential sector it is also expected a lower consumption of washing machines and television at this level, because of production of more efficient devices.

Fig. 10. Scenarios Generation Framework projection results to 2020.

and blue dashed lines represent upper and lower limits with a 95% confidence interval, while the black line represents the average values of one hundred generated scenarios. The grey cloud includes all simulated scenarios and Y-axis follows the same pattern as described for Fig. 8. According to the results for 2020 the specific average load curves shape is expected to be quite similar to the 2017 forecasting at a glance, although some changes can be noticed with a more careful examination. As expected on a simulated scenarios projection, the maximum range between limits in 2020 is larger than the range for 2017. This happens because the longer the lead time, the lower the precision, causing the increase of confidence interval over the years, as can be seen on the boxplot presented in Fig. 11. From 2017 to 2020 there was an increase of approximately 1 000 MWh on the projections, meaning that some peaks and valleys are expected to be accentuated over the years. It is noteworthy that, despite the increase of the range having occurred mostly at dawn and afternoon hours, due to the air conditioning intense usage, the expected decrease of electrical showers consumption over the years is clearly

6. Conclusion In this article it was presented a Scenarios Generation Framework, aiming to generate long-term load forecasting scenarios. It uses bottomup approach, a Specific Profile Generation Method and, more

Fig. 11. Boxplot of load values projected for 2017 and 2020.

Fig. 12. Overall average profiles for air conditioning. 9

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caused most of the changes, even though historical significance was not neglected, keeping a load behaviour that is capable of remembering 2016 specific historical load data, but already showing signs of minor behaviour changes caused by processes with most impact. Although the framework validation has shown good results for average load levels, it is important to point out that the hourly data of the base year are estimated, and that the estimated data was used to validate the participation level of the energy processes. In Brazil there is no official source of information of hourly values that break down energy consumption by processes and/or sectors. This forces the methodology to estimate processes’ consumption as a share of total Southeast hourly load considering normalized load profiles. The framework uses the share to forecast hourly data and there is no guarantee that it represents reality, but considering that all models/methods use some kind of estimation to make projections, this is just a characteristic to be emphasized. Anyway, the results were consistent with what is expected for the Brazilian southeast region in the years to come. Thus, the Scenarios Generation Framework proved to be an interesting support tool to be used in Brazil. In Brazil, main characteristics that could not left aside in residential sector were air conditioning and electric showers; on tertiary sector, were Hotel, Cafe and Restaurant and Wholesale and Trade; and in industrial sector were the Chemical Industry and Other Industries, because these are the processes that have the most relevant impact on load curve today. To extend the Framework application to another country/region the primary idea could be maintained, but adaptations would have to be done. As an example, in cold regions heat pumps and sanitary hot water should be analyzed in order to verify its relevance to the energy load curve, just as in regions where agriculture uses a lot of electricity, a study of its impact should be done. In general, each country/region has its own characteristics that should be studied and considered as inputs to the model if their relevance is identified. It is important to emphasize that not only today’s relevant processes should be considered, but also processes that could be relevant on the forecasting horizon. New technologies that could increase the load curve, like electric vehicles, and others that could decrease the energy load curve, like distributed generation, although are not supposed to be relevant in Brazil until 2020 and because of that were not considered on the presented projections, could be widespread on other countries/regions for the forecasting horizon. If its importance is established, a particular attention should be given to its load profile construction to be used as input to PDA. As distributed generation is used to support on energy generation and helps to reduce the load demand, its profile should be constructed with negative values in order to reduce the load projection values. At last, results showed that the proposed method, at the same time that is capable of capturing important characteristics of a region and using it as an advantage to create good scenarios, is also very sensitive to assumptions used on bottom-up approach. This shows that the annual load forecasting has to be carefully made, based on reliable data and projections.

Fig. 13. Overall average profiles for electrical shower. Table 8 Average participation of sectors by load level. 2016 Sector Light Medium Heavy

Residential 23.9% 21.9% 32.0%

Tertiary 24.4% 25.6% 29.0%

Industry 40.9% 41.9% 32.3%

2020 Sector Light Medium Heavy

Residential 31.6% 24.1% 30.0%

Tertiary 27.4% 28.5% 29.3%

Industry 46.9% 47.2% 33.3%

importantly, the Partial Decomposition Approach. At first, three different specific profiles for each process were adapted and added to PDA, when three different relevance levels (critical values) were specified. The combination between the specific profiles and the relevance levels formed nine different scenarios of load curve projections, used to simulate one hundred scenarios by Monte Carlo with Gaussian distribution. Primarily, validation was made using average specific hourly load curve projection, for 2017, using 2016 as historical base, taking PICP, MPIW, RMSE and MAPE as metrics to validate the projected average load curve. A RMSE of 2 902.08 MWh and a MAPE of 7.33% show, in general, an acceptable performance for a long-term projection with a satisfactory MPIW of 7 169.11 MWh. However, the PICP value of 0.65 shows poor performance in the aspect of generated scenarios, due to the underestimated load level projection. Given that, specific average load curve projections were calculated and compared to 2017 historical values using the same four metrics in order to show the quality of scenarios and load level predictions for specific profiles. Results indicates that, although winter days had good results, with PICP, RMSE and MAPE of 0.87, 2 142.03 MWh and 5.45%, respectively, in days with higher load values the model underestimated the real load, achieving poor results for these metrics. About MPIW, a satisfactory range of prediction interval was obtained for all the cases, representing up to 20% of maximum values. At last, as a last validation analysis, load levels were specified and used to verify the framework potential to projecting load profiles. The analysis showed that even though light load level had a minor overestimation on an average typical day load profile (the framework had an error of +0.5% in light and –0.5% in medium levels), it had a good performance on predicting the heavy level, achieving great results for load profiles one year ahead. After validation, the method was used to forecast the 2020 load curve, aiming to show expected load shape changes for the next few years. Results obtained showed that processes annual projected values, previously made by bottom-up approach, are already expected to have an effect on load curve shape four years ahead. Air conditioning, with a total of 7.6% participation increasing over a typical day, and electrical shower, with a total of 3.5% participation loss over a typical day,

Acknowledgements The authors would like to thank the National Council for Scientific and Technological Development (CNPq) and the Coordination for the Improvement of Higher Education Personnel (CAPES) for the financial support. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijepes.2019.105436. 10

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