El diagrama Cl'B

In a smart grid configuration, the coordination of the energy and power flows is performed by the Energy Management System (EMS). The EMS represents the MG (VPP) central controller and its main objective is to define and synthesises the most suitable power set-points signals for DGs, ESSs and controllable loads, based on real-time operating conditions of components and system status as well as weather forecasts and market electricity prices. Therefore, the EMS serves as a gateway between the distribution network operator (DNO) or market operator (MO) and the local controllers (LCs), associated at each DG, ESS and load unit [49]. On the basis of system set-points or price inputs sent from DNO and MO, the EMS determines the optimal operating condition of local units according to a certain objective function (e.g. minimisation of energy costs and fuel consumption or maximisation of system

1.4 Energy Management Strategies 25

energy autonomy). Finally, the power scheduling set-points are transferred to LCs, which accordingly regulate the corresponding power output, depending on physical constraints of DG and ESS unit. EMS central controllers rely on suitable algorithms, which can be based on a number of management strategies. Generally, these are formulated as optimal control problem since the EMS purpose is the minimisation of a performance index defined over an extended period of time (e.g., one day) by using a sequence of instantaneous control actions. Several methods can be used for its solution, being mainly subdivided in four categories: numerical optimisation, analytical optimal control theory, instantaneous optimisation, and heuristic control techniques. In the first two cases, the problem is considered in its entirety, i.e.

taking into account at each instant information related to past, present, and future time; in the latter two, the solution at each time is calculated based only on present information.

1.4.1 Numerical global optimization

Numerical methods for global optimization require the knowledge of the entire con-trol horizon and find the global optimal concon-trol numerically. This means that the production from RES, load demands and electricity prices should be well defined and known in advance. Due to the necessity of knowing a priori the system evo-lution and to the required computational complexity, these methods are not easily implementable for real-time applications. Linear programming, dynamic program-ming and genetic algorithms belong to this category. In particular, the method most widely used is dynamic programming [50–52], which solves the optimal control backwards in time, i.e. starting from the final instant of the control horizon and proceeding backwards, ending at the initial time.

Dynamic programming (DP) was originally used in 1940 by Richard Bellman and allows the simplification of complicated control problems by means of their recursive segmentation in simpler sub-problems. The DP approach has several advantages, being able to find the global solution of both linear and non-linear problems, also in presence of control and state constraints. However, it suffers from the so-called curse of dimensionality, which entails the computational load exponential rise with the increase of state variables dimension. This drawback amplifies the computational complexity and limit the DP range of applications.

26 1. Smart Grids, Distributed Generation and Energy Storage Systems

1.4.2 Analytical optimal control techniques

Analytical methods consider the entire control horizon as well, but use an analytical problem formulation to find the solution in closed and analytical form, consequently lowering the resolution time. However, in order to obtain a suitable description which can be completely solved by using these techniques, a significant simplification and abstraction of the problem is often required. Among these methods, the most used is the Pontryagin’s minimum principle [53].

Pontryagin’s minimum principle (PMP) was formulated in 1956 by the Russian mathematician Lev Semyonovich Pontryagin as a special case of Euler-Lagrange equation of calculus of variations. Being based on non-linear second-order differen-tial equations, the dimension of the problem increases only linearly with the number of variables, which entails a low computational complexity. However, PMP pro-vides only necessary conditions for the optimal solution, potentially leading to local optimal rather than to a global solution. Another limit of this technique is that, it generally requires a-priori knowledge of the entire optimisation horizon, which considerably limits its real-time implementation, unless combined with adaptive ap-proaches.

1.4.3 Instantaneous optimisation

Instantaneous optimisation methods modify global optimal control problems into a sequence of local (instantaneous) problems, calculating the solution as a sequence of local minima. In this case, the cost function depends only on the present state of system variables, enabling their real-time implementation. These family of control strategies include: model predictive control (MPC), neural networks and particle swarm optimisation approaches. Additionally, a further development of PMP can be effectively used for on-line applications, by reducing the global optimisation problem into local and solving the control problem in the continuous time domain, without use of information regarding the future [53, 54].

1.4.4 Heuristic control methods

Heuristic control techniques are not based on explicit optimisation, since the energy management applies a pre-defined set of rules. Rules are typically derived by heuristic or mathematical models on the basis of engineering knowledge of the system and

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practical experience. These strategies are robust and computationally efficient, and hence easily implementable in real-time EMS. However, the main drawback is that the results may not be optimal, due to the lack of a formal optimisation. Rule-based control strategies and fuzzy logic methods are the most significant approaches of these control techniques.

The rule-based control strategies (RBS) are static controllers, based on rule tables of flowcharts used to define the operating point of system components. As a conse-quence, the EMS takes decision based only on current information and instantaneous conditions, which facilitates the respect of local constraints. In fact, the rules can be theoretically developed in order to deal with any violation of system boundaries. On the other hand, the rules are defined without referring to any standard methodology and need to be again synthesised for every new system configuration.