2021 IEEE PES/IAS PowerAfrica 978-1-6654-0311-5/21/$31.00 ©2021 IEEE Generator Reserve and Load Capacity Allocation Using Ideal Generator Contribution Index Peter M. Munyao Discipline of Electrical, Electronic and Computer Engineering University of Kwa-Zulu Natal (UKZN) Durban 4041, South Africa petermunyao37@gmail.com John T. Agee Discipline of Electrical, Electronic and Computer Engineering University of Kwa-Zulu Natal (UKZN) Durban 4041, South Africa ageej@ukzn.ac.za Remy Tiako Discipline of Electrical, Electronic and Computer Engineering University of Kwa-Zulu Natal (UKZN) Durban 4041, South Africa Tiako@ukzn.ac.za Abstract— In modern power systems, emerging load centers have led to a significant increase in electricity demand thus straining power utilities. Better economics of operation, reliability of power supply and the utilization of old power plants as power reserves during peak loads are some of the advantages of the interconnected systems. Power availability is also a key factor in industrial site location hence load capacity determination for particular buses is essential. This paper aims to use the ideal generator contribution index to determine the maximum electrical load capacity allocation for a particular bus as a function of the generator’s output capacity or rated power and to find the least required generator power reserve capacity to cater to particular anticipated load demand. Keywords— power reserve capacity, distributed generation, electrical load capacity, ideal generator contribution index, generation dispatch, inter-connected systems. I. INTRODUCTION Power systems demand and supply must be constantly matched to avoid undesired consequences leading to grid shutdown. The reserve capacity is utilized to meet the system’s demand if a generator is isolated from the grid or during supply disruption [1] [2]. Reserves also ensure that all forecasted load consumption is duly met [3]. Depending on geographical region and nature of resources e.g. wind energy profile, standards have been set to ensure market participants select among existing and emerging technologies to meet more flexible and reliable generation [4] [5]. In some regions, wind is a dispatchable resource and operators can purposely control output in order to ramp the plant up and down to match load or provide reserves [5] [6]. From the load side management, load forecasting is used to project future generation and facility requirements, outages and contingency planning [7]. The process of deciding which units to use to meet a daily or weekly system needs is very complex [1]. Many variables must be considered e.g. availability of resources, transmission losses, load rate of change, fuel costs, source ramp rate, reserve requirements etc. [1]. Studies and simulations are required to determine models and feasibility of particular suggestions respectively [4]. Conventionally, solutions to load flow are solved by iterative techniques and offer no information regarding to the system structure [8]. This behooves power system engineers to apply physical principles in order to gain a better insight of how variables interplay in a network structure, in harmony with fundamental circuit laws, thus the development of ideal generator contribution index [9] [8]. The ideal generator contribution concept was initially used in the formulation of the T-index [9] using the inherent power system characteristics [8] [10]. This index is hinged on the interconnection of buses as captured in the networks Y- admittance matrix [8]. When locating new generator buses for maximum contribution of power into the system, this index is effective in ensuring that the line overloading does not occur [11]. This necessitates planning within available transmission corridors with minimum expansion thus leading to overall system stability [12] [9]. This approach results in less active power losses when implemented [9] in inter-connected power system networks. This paper aims to derive, based on ideal generator contribution index, the equations for determining the required generator reserve and load capacity with respect to generator’s capacity or the rated output. As a result, the advantages of this index are utilized within the new mathematical formulation. The economics of generation are not factored in this study as well as cost of adding new reserve units to the system. Section II shows the derivation of the index, Section III presents generator reserve and load capacity allocation by use of ideal generator contribution index formulas. Section IV highlights the results and Section V concludes the paper. II. IDEAL GENERATOR CONTRIBUTION For structurally complex circuits such as inter-connected power systems networks, it is much easier to use the network’s admittances in order to utilize the advantage offered by the connections between adjacent buses [8, 13, 14]. The ideal generator contribution index is derived from Y-admittance matrix by source (generator bus) and sink (load bus) partitioning approach [10, 15, 16, 17]. For any given system, Using Ohm’s law, the network admittance matrix is given by     =             (1) Expanding (1)   =     +     (2)   =     +     (3) Where   ,   = complex bus currents injection of both generator and load respectively.   ,   = complex bus voltage injection vectors of both generator and load respectively. The Y- admittance matrix is a square matrix with dimension (G + L) x (G + L),   is a square matrix of dimension G x G containing the connectivity between generator buses.   is a Research Grant by South Africa’s National Research Foundation (NRF), Grant No: 123444.