A distributed quadratic generation scheduling optimization and reserve allocation approach based on the decomposition of generation characteristics D´ avid Csercsik P´ azm´ any P´ eter Catholic University Faculty of Information Technology P.O. Box 278, H-1444 Budapest Email: csercsik@itk.ppke.hu P´ eter K´ ad´ ar Kand´ o K´ alm´ an Faculty of Electrical Engineering Power System Department - Alternative Energy Technologies ´ Obuda University B´ ecsi ´ ut 96/b H-1034 Budapest Email: kadar.peter@kvk.uni-obuda.hu Abstract—The operation with the limited resources requires optimization. Also in an island mode on board energy system or in the large power system the optimal power generation distribution between the operating units is crucial for increase the success of the mission or for the protection of the environment or decrease the costs. A method for generator scheduling and simultaneous allocation of reserves is proposed in this article. Based on the decomposition and piecewise linear approximation of generation characteristics, we formulate the optimization framework in a distributed manner, making the utilization of parallel computing power possible. We define a finite number of operation modes for each generator, and analyze the feasibility and resulting cost of their possible combinations. Secondary and tertiary reserves are also allocated in the process. A simple heuristic is introduced to reduce the number of operating profiles taken into account. I. I NTRODUCTION It is well known that the market share and significance of renewable technologies in the electric power industry have been largely increased [1], and significant efforts were done to effectively integrate these resources into the existing systems [2], [3]. However, as detailed in [4], the great majority of these renewable resources are variable generators having an availability limit that changes through time and cannot be pre- dicted with perfect accuracy. This variability and uncertainty add to the existing variability and uncertainty of the current systems (eg. uncertain domestic demand), and these additional issues imply unique characteristics and may change the way that system operators maintain a reliable power system. As long as technically efficient and economically feasible methods for energy storage [5], [6] are not available in industrial scale, the only way to handle these uncertainty issues is the application of system level resources or, in other words, ancillary services [7], [8]. On the other hand, the question how the available power system resources and infrastructure can be utilized in the most economic way is analyzed since the middle of the 20th century [9]. This topic has multiple aspects. Not only in the power system but also in the aircrafts are several generators. Typically two integrated drive generators supply normally the plane and a third auxiliary generator can replace either main generator (e.g. in an aircraft A320). In the Boeing 787 the number of the generators are doubled so we count 4 pieces at engine side and 2 more auxiliary units. The optimal load distribution in normal and emergency case is crucial. Optimal power flow (OPF) methods aim to optimize the operation of electric power generation, transmission, and dis- tribution networks subject to demand values or functions and transmission and generation system constraints. The literature of OPF is enormous, for recent surveys see [10], [11], [12]. Typical examples when the optimization procedure includes integer variables as well are optimal transmission switching (OTS) and network topology optimization, [13], [14], [15]. The optimal scheduling (OS) of generators, also known as unit commitment (UC) [16] has also a significant size of literature, for surveys see [17], [18], [19]. An integer approach to the problem is described in [20]. Thermal production requirements may be also taken into account [21]. OPF, OTS and OS in general are complex nonlinear large- scale problems. In such cases, decomposition methods [22] may greatly increase the computational efficiency of solution concepts, even when the price is that only sub-optimal re- sults are obtained. There is a significant amount of results corresponding to the decomposition and decentralization of OPF [23], [24], [25], [26] and OTS in literature. These papers approach the problem by decomposing the computations cor- responding to regions. Such methods receive more and more attention nowadays, as the computing power of parallelized architectures increase [27]. In the terms of OS, the increasing importance of system level resources proposes new challenges and calls for novel solutions. Frameworks which allocate energy production and reserves simultaneously may help reserve-production capable power plants to an increased vindication of their potential: In these frameworks it is immediately taken into account that as they produce energy, they create the potential of reserve allocation as well and in the same time. In the conference article [28] a model has been introduced in which generation values of generators were optimized over a