In this work we propose a new hybrid model, a combination of the manifold learning Principal Components (PC) technique and the traditional multiple regression (PC-regression), for short and medium-term forecasting of daily, aggregated, day-ahead, electricity system-wide load in the Greek Electricity Market for the period 2004-2014. PC-regression is shown to effectively capture the intraday, intraweek and annual patterns of load. We compare our model with a number of classical statistical

more »

... hes (Holt-Winters exponential smoothing of its generalizations Error-Trend-Seasonal, ETS models, the Seasonal Autoregressive Moving Average with exogenous variables, Seasonal Autoregressive Integrated Moving Average with eXogenous (SARIMAX) model as well as with the more sophisticated artificial intelligence models, Artificial Neural Networks (ANN) and Support Vector Machines (SVM). Using a number of criteria for measuring the quality of the generated in-and out-of-sample forecasts, we have concluded that the forecasts of our hybrid model outperforms the ones generated by the other model, with the SARMAX model being the next best performing approach, giving comparable results. Our approach contributes to studies aimed at providing more accurate and reliable load forecasting, prerequisites for an efficient management of modern power systems. Energies 2016, 9, 635 2 of 40 also the physical constraints that impose limitations (congestion) on the power transferred in transmission lines we can realize why competitive pricing is not easy to implement in real-time markets. Today energy markets' products are defined in terms of delivering a predetermined amount of power over a specified period of time. These markets are usually called spot markets where the prices (spots) are determined within one hour or half an hour time periods (e.g., Australia). Spot prices emerge either from auctions which take place in the so-called market pool, where retailers and generators' representatives make offers and bids or from trading on an exchange platform either in the day-ahead or in the real-time market [1] [2][3]. The market clearing price is therefore determined by the most expensive unit dispatched in the abovementioned mechanisms over the respective trading period. The key factors that influence spot prices are mainly the demand or load as well as the ability to respond to this demand by the available generating units. Therefore, possible errors in load forecasting could have significant cost implications for the market participants. More specifically an underestimated predicted load could lead to unavailability the required reserve margin which in turn could lead to high costs from peak units. On the other hand, load overestimations would cause the problem of excess supply management pushing spot prices downwards. Load prediction is a complex procedure because of the nature of the influencing factors-weather factors, seasonal factors and social-economic factors [4]. Weather factors include temperature, relative humidity, wind speed, dew point, etc. Seasonal factors include climate variation during a year while social-economic factors are depicted through periodicities inside the time-series of the load as well as trends through years. An electricity utility also can use forecasts in making important decisions related to purchasing and generating electric power, load switching and investing in infrastructure development. Also, energy suppliers, financial institutions and other "players" in the electric energy generation and distribution markets can benefit from reliable load forecasting. Load is a variable that is affected by a large number of factors whose influences are "imprinted" in its dynamic evolution. Its historical past values, weather data, the clustering of customers according to their consumption profiles, the number of types of electric appliances in a given region as well as consumer age, economic and demographic data and their evolution in the future, are some of the crucial factors taken into account in medium and long-term load forecasting. Also, the time of the year, the day of the week and the hour of the day are time factors that must be included in load forecasting. The consumption of electricity for example in Mondays, Fridays, or holidays etc. is different. Load is also strongly influenced by weather conditions. In a survey performed in 2001 bu Hippert et al. [5], in out of 22 research papers, 13 only considered temperature, indicating the significance of this meteorological parameter in load forecasting. In this work, we have included the average temperature in the country, as a predictor, in the seasonal Auto-Regressive Integrated Moving Average (ARIMA) model for load forecasting. Load forecasting is also a necessary tool for Transmission System Operators (TSOs) since it is used for different purposes and on different time scales. Short-term forecasts (one hour-one week) are useful for dispatchers to schedule short-term maintenance, unit commitment, fuel allocation, and cross-border trade, but also to operation engineers for network feature analysis such as optimal power flow, etc. Medium term forecasts (one week-one month) are used by TSOs for planning and operation of the power system while long-term forecasts (one month-years) are required for capacity planning and maintenance scheduling. In this sense, load forecasting is of crucial importance for the operation and management of power systems and thus has been a major field of research in energy markets. There exist many statistical methods which are implemented to predict the behavior of electricity loads, with varying success under different market conditions [6]. In this approach, the load pattern is treated as a time series signal, where various time series techniques are applied. The most common approach is the Box-Jenkins' Auto-Regressive Integrated Moving Average (ARIMA) [7] model and its generalized form Seasonal ARIMA with eXogenous parameters (SARIMAX) [8, 9] . Models utilized in electricity Energies 2016, 9, 635 3 of 40