G 2 EDPS's First Module & Its First Extension Modules

: 100% renewable worldwide power grid (Global Grid) system needs a Global Grid Electricity Demand Prediction System (G 2 EDPS) with very short, short, medium and long term forecasting consoles. This paper presents the 1 st core module and its 10 extension modules in the long term prediction console. A type 1 Mamdani like Fuzzy Inference System (FIS) with 7 triangle membership functions and 49 rules is designed for 2 input and 1 output variables for a 100 year forecasting period. The maximum absolute percentage errors (MAP), the mean absolute percentage errors (MAPE), and the Symmetric MAPE (SMAPE) of the best core module and its extension modules are respectively 0, 24; 0, 08; 0, 05 and 0, 22; 0, 07; 0, 05.


Introduction
Electricity is the center of our modern daily life. It is consumed in homes, on streets, and at factories at most of our daily activities. The electricity can be generated from either non-renewable energy sources or renewable energy sources within the current electricity generation technologies. Oil, coal, gas, and nuclear are grouped in the non-renewable energy sources. Hydropower, geothermal, wind, solar, and ocean are grouped in the renewable energy sources. Non-renewable energy sources shall run out in the future. Hence, the scientific studies on modeling and developing of 100% renewable energy sources should be more important than the studies on non-renewable energy sources in near to mid future.
The Global Grid Prediction Systems (G 2 PS) [7] are developed to serve them (specifically to Global Grid). It has two major units (Global Grid Electricity Demand Prediction System: G 2 EDPS, Global Grid Peak Power Prediction System: G 2 P 3 S) [7] (please be informed that projection, prediction, forecast are used in same meaning in this study). These systems shall work with all provinces, sub-regions, countries, large regions, multinational grids, Supergrids and Global Grid in all time horizons (e.g. immediate: less than 1 month, short-run: l−3 months, medium-term: 3 months−2 years, long-run: 2 years or more; some electricity grid related forecasting studies short-range: up to a week a head, medium-range: up to 10 years ahead, long-range: 50 years ahead) [7] (see [8,9,10,11,12].
The long run forecasting is used for the strategic planning such as preparing the expansion plans of the electrification grids and the energy management systems [8,9,10,11,12].

net/index.htm) (*not to scale, fictitious and for information purposes only so that no representation of power plants locations and transmission lines).
This study presents an interim milestone (part) of an ongoing research, development and demonstration (RD 3 ) program (project, effort) as publicized the G 2 EDPS's 1 st core module and its extension modules in the long term prediction console, which run on Scilab [13], R [14], RStudio [15], Microsoft Office Excel [16], Apache OpenOffice Calc [17] (long range period: 100 years ahead).

Literature Review
The current literature review was completed on only some of the academic publication online database and journals by only some key terms and phrases in June 2015 (from 11 th of June to 01 st of July: 20 days period). The keywords were first selected from some previous research studies and documents in the literature. Then new key terms were added by the author and connected with others. They were used in a narrowing content manner (from large to narrow scope or general to specific). The keywords were (1) "Fuzzy Logic Inference System" and "Electricity", (2) "Fuzzy Logic Inference System" and "Forecast", (3) "Fuzzy Logic Inference System" and "Demand", (4) "Fuzzy Logic Inference System" and "Electricity" and "Forecast", (5) "Fuzzy Logic Inference System" and "Electricity" and "Demand", (6) "Fuzzy Logic Inference System" and "Electricity" and "Forecast" and "Demand", (7) "Fuzzy Inference System" and "Electricity", (8) "Fuzzy Inference System" and "Forecast", (9) "Fuzzy Inference System" and "Demand", (10) "Fuzzy Inference System" and "Electricity" and "Forecast", (11) "Fuzzy Inference System" and "Electricity" and "Demand", (12) "Fuzzy Inference System" and "Electricity" and "Forecast" and "Demand", (13) "Fuzzy Control System" and "Electricity", (14) "Fuzzy Control System" and "Forecast", (15) "Fuzzy Control System" and "Demand", (16) "Fuzzy Control System" and "Electricity" and "Forecast", (17) "Fuzzy Control System" and "Electricity" and "Demand", (18) "Fuzzy Control System" and "Electricity" and "Forecast" and "Demand", (19) "Fuzzy Rule System" and "Electricity", (20) "Fuzzy Rule System" and "Forecast", (21) "Fuzzy Rule System" and "Demand", (22) "Fuzzy Rule System" and "Electricity" and "Forecast", (23) "Fuzzy Rule System" and "Electricity" and "Demand", (24) "Fuzzy Rule System" and "Electricity" and "Forecast" and "Demand". There were 15 academic publication online database in this study. The reviewed documents were only journal papers, conference papers, books and chapters of books. Bachelor dissertations, master thesis, and doctor of philosophy thesis weren't taken into consideration, likewise, reports and technical articles in magazines weren't reviewed in this study. The advanced and expert search options were used on the database websites. The search results were grouped under 5 classes (all, relevant, irrelevant, not close or far or indirect relation, close or direct relation) as in the electronic supplementary file. The studies such as electricity price forecasting were grouped under indirect relation set. The power load and electricity demand research documents were positioned in the direct relation set. Some of the search results were presented in a very short and well organized way in " Fig. 2 It was understood that these studies could be grouped according to their scope such as smart grids (e. g. [33]), classical or conventional grids (transmission and distribution) (e. g. [34]), and household applications (e. g. [37]). Moreover, the power systems forecasting horizons in the literature were diversified as the real time/very short term (minutes to a day) (e. g. [36]), the short term (a day to a week) (e. g. [37]), the medium term (a week to a year) (e. g. [38]) and the long term (more than a year often upto ten years) (e. g. [39]) (see [40]). Hence, only the long term studies were investigated in detail in this review. There were more than 40 studies. Some of these studies were compared their models with the actual historical data (model and comparison on historical data). There weren't any future projections in these studies. On the other hand, some of the studies presented the future forecast. Al-zahra et.  [44]. There were also some other important and interesting studies within the similar topics, approaches, scopes and forecasting horizons. The maximum forecasting period was 20 years in these documents (future projection studies).
The literature review was finalized in 25 days (11/06/2015 to 01/07/2015: search, review, classify; 01/07/2015 to 05/07/2015: investigate, prepare). This detailed and widened literature review exposed that some researchers were interested in the power systems forecasting subject, however there weren't any publications found on the long term forecasting of the Global Grid Concept.
This study is most probably the first research on this concept, so that it has its own very unique difficulties. The main challenge is the concept itself. Another challenge is its forecasting horizon (long term: 100 years).

G 2 EDPS, Its First Core Module & Core Module's Extensions
The G 2 EDPS consists of several consoles and modules with bottom up and side by side level approaches [7]. On the bottom up designs, the future electricity consumption (G 2 EDPS) will be predicted from one of the smallest units up to the largest units (i. e. provinces to countries, to regions, finally to the world). On the side by side (SS code) level approaches, the future electricity demand shall be predicted directly. It has simple, backwards and forwards computation considerations. It shall be a generic system (flexible, intelligent, self-enlargeable, self-expanding, self-reporting, self-learning). It will have direct connection and relation to the data and information sources. It has a globally unique data warehouse (e. g. temperature, population, time, and consumption) (common for G 2 PS), a global unique forecast accuracy metrics pool (common for G 2 PS), several different prediction core modules and their extension modules with heuristics and optimizations (different or common for G 2 EDPS and G 2 P 3 S) " Fig. 3". The G 2 EDPS 1 st core module's forecasting model (long term prediction console) is a side by side approach for the Global Grid electricity demand with a one node type 1 (fuzzy) Mamdani [45,46] like fuzzy inference system (FIS) with 7 triangle fuzzy membership functions (MF) and 2 input (world population, global annual temperature anomalies) and 1 output (Global Grid annual electricity demand) variables on the international basis for a 100 years ahead prediction period. This type of FIS is preferred in this study, because of its expert knowledge capturing capability [45,46,47]. This core module has its own data preprocessing, knowledge base (database, rule base), fuzzifier, inference system, defuzzifier, best core model defuzzifier selection, extension improvements generation, best extension model, and 100 year projection reporting units.
The world population (both sexes combined, as of 1 July in thousands) is employed as the input variable. It is employed as the first input variable in this module, because of its influencing power on the electricity consumption. Its historical and future projection data are directly gathered from the Department of Economic and Social Affairs of the Population Division at the United Nations [48]. The description of this variable is exactly presented as it is on the official website "Total Population -Both Sexes. De facto population in a country, area or region as of 1 July of the year indicated" [48].
The historical data (year, world population (both sexes combined, as of 1 July (thousands))) is gathered and presented in "Tab. 1".  The future projection data is taken from the same website. The projection data (year, population (both sexes combined, as of 1 July (thousands))) is gathered and presented in "Tab. 2". The historical and future projection data of this module will concurrently be updated with the updates of the United Nations (UN).
The global annual temperature anomalies (degrees Celsius: °C) is also used as the input variable. The global annual temperature anomalies (degrees Celsius: °C) is used as the second input variable in this module, because it is a very well known and common measure in the climate research and the absolute temperature effects on the electricity consumption are well defined in the literature. This variable is very well distinguished by the following statement in the global climate research community: "reason to work with anomalies, rather than absolute temperature is that absolute temperature varies markedly in short distances, while monthly or annual temperature anomalies are representative of a much larger region" [49] (also personal communication with Reto Ruedy via e-mail). Its historical data are taken from the Goddard Institute for Space Studies Laboratory in the Earth Sciences Division of National Aeronautics and Space Administration's (NASA) Goddard Space Flight Center [50]. The historical data (year, global annual temperature anomalies (degrees Celsius)) is gathered is gathered and presented in "Tab. 3".  Tables, Table AII.7.5. [51]. The projection data (Global Annual Temperature Anomalies Projection (degrees Celsius)) is gathered and presented in "Tab. 4". The historical and future projection data of this module will concurrently be updated with the updates of the NASA (see [50], and the IPCC (see [51]).
The annual electricity demand of Global Grid (terawatt hour: TWh) is the output variable. Its historical data are based on the official records at the International Energy Agency (IEA) [52]. The historical data (year, energy production (Mtoe), total primary energy supply (TPES) (Mtoe), electricity consumption (TWh), energy production (TWh)) is gathered is gathered and presented in "Tab. 5". There are two important assumptions and approximations in this output. First, the annual energy production (Mtoe: million tonnes of oil equivalent) data on the IEA [53] can represent the annual electricity consumption of%100 Global Grid. Second, the direct conversion of annual energy production (Mtoe) to the total global annual electricity demand (tera: T: 1012) can be made by the IEA's unit convertor [53].
As a result, two input variables and one output variable are defined and used accordingly with an international basis for this one node Mamdani [45,46,47] like FIS in this G 2 EDPS core module " Fig. 3".
The data preprocessing (cleaning, integration, transformation, reduction) unit investigates the annual data for two inputs and one output from their data files. When all input and output annual historical data is available, they are marked as available (historical) (green shading color). When at least one of the input and output data is not available, they are marked as not available (historical). The earliest and latest year in these classified data are found and all of the data (year, inputs, output) are extracted as historical data for model fitting (i.e. t earliest.historical , t latest.historical , t: year, input t , output t ϵ model fitting set) of this G 2 EDPS core module (historical data set: green shading color). The same approach is performed for the model prediction (blue shading color) of this G 2 EDPS core module (prediction data set: t earliest.prediction , t latest.prediction ) (" Fig.  3", "Tab. 1", "Tab. 2", "Tab. 3", "Tab. 4", "Tab. 5").
The fuzzification interface or fuzzifier unit of this core module works with 7 triangular MF based on the data preprocessing unit's outcomes (" Fig. 4", "Fig. 5"). The minimum and maximum values for the input and output in the historical and prediction data set are found and used for the minimum and maximum of the fuzzy membership functions' values (data minimum , data maximum for inputs and data minimum for output). The maximum value of the output is calculated and defined as a sufficiently large value found by the linear regression approximation calculation (data maximum for output: largest regression value by all or some of the data). After the data minimum , data maximum for inputs and output is defined the fuzzy membership functions are defined for similar 7 triangular functions (" Fig. 4"). When the historical and future projection data of this module will be updated by the NASA, the IPCC and the IEA, the fuzzification interface will be run and updated. 7 triangular fuzzy membership functions will be defined and presented publicly (open public websites).
The rule base of the inference system or decision making unit has predefined 49 rules (fixed, permanent) as follows "Tab. 6":  These predefined 49 rules are designed as unchangeable in the current design of this G 2 EDPS 1 st core module (long term prediction console) (fixed, permanent).
The defuzzification interface or defuzzifier unit performs concurrently by all defuzzification methods (e. g. shortest of maximum, mean of maximum, bisector of area, centroide, largest of maximum). When new defuzzification methods will be presented in the literature, they will be integrated into the defuzzifier unit of this G 2 EDPS 1 st core module.
The fuzzifier, rule base and surface graph of this G 2 EDPS 1 st core module's model is presented in " Fig. 4". "Fig. 5". and " Fig. 6".   The main Scilab script is as follows "Tab. 7": Table 7 [54,55,56,57,58]. The current version of the forecast accuracy metrics pool covers the following error metrics. Nowadays, they are calculated by Microsoft Office Excel [16] or Apache OpenOffice Calc [17]: Forecast Errors: Mean Absolute Error (MAE): Geometric Mean Absolute Error (GMAE): Mean Square Error (MSE): Absolute Percentage Errors (APE): Minimum Absolute Percentage Error (MinAP): Maximum Absolute Percentage Error (MAP): Mean Absolute Percentage Error (MAPE): Symmetric MAPE: Relative Error: Median Relative Absolute Error (MdRAE): Geometric Mean Relative Absolute Error (GMRAE): where Actual, Predicted, t, n, * represents respectively historical annual electricity demand of the Global Grid, forecasted/predicted annual electricity demand of the Global Grid, year, total number of years and benchmark model. This G 2 EDPS 1 st core module has a best core model defuzzifier selection unit. The minimum SMAPE valued defuzzification model is first selected for the predictions. The minimum MAPE and MAP valued ones are selected after the minimum SMAPE valued ones. If there are more than one minimum SMAPE, MAPE and MAP valued models, all of them will be run for the 100 year projections.
The G 2 EDPS 1 st core module has 10 extension modules. These extensions try to find some model fitting improvements by some simplistic procedures (adjustment, correction or enhancement) based on the arithmetic average, mode, median, minimum, maximum and percentage of the forecast errors and absolute forecast errors. The first procedure calculates the arithmetic average (mean) of the forecast errors (e t ) and sum the prediction values with this calculated value. The second and third procedures work with the most repeated, observed, frequent value (mode) and the mid value (median) of the forecast errors (e t ) and the summation operator. The fourth and fifth procedures find the minimum and maximum of the absolute forecast errors (|e t |) and sum the prediction values with the non-absolute values. The sixth procedure calculates the arithmetic average of the percentage values (actual t /predicted t ) and multiply by this calculated value. The seventh, eighth, ninth and tenth procedures are similar to second, third, fourth and fifth together with sixth procedures. The following procedure ("Tab. 8") is presented for only the first one as representative for each one (all of them): There is also a small best core model extensions model selection unit working with the same principles of the G 2 EDPS 1 st best core model defuzzifier selection unit (" Fig. 3").

Analysis and Results (Module Fitting & 100 Year Forecasting)
The first input variable's historical data  and future projection (2015-2100) are directly gathered from the UN (see [48]). The historical and future projection data will concurrently be updated with the UN (1950-2010→1950-2011 and so on; 2015-2100→2020-2105). The second input variable's historical data (1880-2015) is taken from the NASA (see [50]). Its future projection data (2010-2090) is gathered from the IPCC Annex II: Climate System Scenario Tables, Table AII.7.5. (see [51]). The historical and future projection data will concurrently be updated with the NASA, and the IPCC (1880-2015→1880-2016 and so on; 2010-2090→2020-2100). The output variable's historical data (1990-2013) is based on the official records at the IEA (see [52]). The Fuzzy Toolbox 0.4.6 for the Scilab 5.5.2 (sciFLT) [13] is used for the FIS computations. The model fitting or historical prediction report is gathered by sciFLT [13], Excel [16], Calc [17] ("Tab. 9".). The shortest of maximum defuzification method is selected for future forecasting/prediction based on the best core model defuzzifier selection unit ("Tab. 9"). The bisector and centroide defuzification methods presents errors, so that they are eliminated during the analysis (open electronic supplementary files).  [17]. Only 8 th extension approach gives better performance in this study. The model fitting predictions are presented in " Fig. 7".

Conclusions
This paper presents the concepts of G 2 PS, G 2 EDPS, G 2 P 3 S and the details of designed G 2 EDPS 1 st core module's forecasting model and its extensions. This RD 3 study shall continue for reaching new enhancements of this module and designing new modules and extensions.
It is believed and hoped that the concepts of G 2 PS, G 2 EDPS, G 2 P 3 S can be developed under the Open Source Initiative (OSI) (see [59]) and the Free Software Foundation (FSF) (see [60]) approaches by freewill supportive RD 3 engineers from all over the world.