The thesis describes current and voltage conditions in distribution networks during earthfaults with various fault resistances and different treatments of the network (transformer) neutral point grounding. In addition to conditions during earthfaults in networks with unearthed (isolated) and the low-resistance grounded neutral point, special attention has been paid to conditions in resonant grounded networks, or, in other words, in networks grounded over the compensation (Petersen) coil. Special consideration has been given to resonant grounded networks due to the fact that the development of numeric protection and electronic control systems has resulted in the expanded usage of this kind of neutral point treatment, also in countries where it used to be avoided. Theoretical considerations from the literature have been compared to experimental results (measurements) of earthfualts in real distribution networks. Earthfault experiments and resonant curve recordings were performed in 110/20 kV substation Botinec and 110/10 kV substation Velika Gorica. Experiments have been carried out for earthfults over various resistances (1÷5 Ω, 1 kΩ, 4 kΩ and 10 kΩ) and under various conditions (phase line dropped on dry and on wet ground, phase line connected to a branch, transient faults provoked by changeable distance spark gap), and at several points in the network for various treatments of transformer neutral point grounding (isolated, low-resistance grounded and resonant grounded). With resonant grounding, earhfaults were carried out by various compensation coil settings with and without parallel connection of corresponding shunt resistor (for increasing of active component of earthfualt current) on the compensation coil auxiliary (secondary) winding. Experiments aimed at measuring and recording of the resonance curve are necessary for analysis of design requirements and designing of equipment for control and monitoring of the appropriate compensation coil tuning in the system. Medium voltage distribution power networks supplied from two primary substations are widely spread radially operated suburban networks with several interconnection branches. Such networks are considered to be the most suitable for application of resonant grounding systems. The reason is reflected in the fact that those networks include 8 to 12 feeders connected to MV busbar having the total sum of earthfault capacitive current between 100 A and 300 A, they supply a big number of households and small industries with an average peak load of about 21 MVA. They are also characterised with a considerable number of short and long lasting interruptions due to earthfaults on overhead lines. Experiment results have been processed and evaluated in great detail and then compared to the theory. Mathematical operations reflecting digital earthfult relay protection have been performed on current and voltage measurement records providing insight into designing problems for relay protection equipment and their algorithms. Measurement results have been used for valorisation of distribution network static phase model parametered to reflect networks on which field measurements were performed. Static model results, zero current and voltage phasors are well corresponding to those acquired by measurements. When measurement results were processed, some deformations and deviations of the values measured over different instrument transformers were found out. Deformations and deviations are especially expressed at protection current transformers under certain network conditions. Therefore the thesis supposed that instrument transformers might influence the sensitivity and selectivity of the protection functions. Protection relay dynamic performance, in the sense of the relay selectivity, sensitivity, security and reliability, depends on relay design. In addition, dynamic performance of very fast relay protection depends a great deal on signals received from the secondary side of protection voltage and current transformers. Stated signals depend on the complete behaviour of instrument transformers during fault transients of the distribution network, as well as on the type of transients. Requirements for protection instrument transformers and principles of their behaviour during fault transients within the system are detailed. Protection current transformer model has been proposed together with the model results that correspond largely with the theory, standards and measurements. The problem for earthfault protection relays connected to current transformers in resonant grounded networks lies in the fact that not only small currents are being measured, but also Petersen coil generates direct current component having a large time constant. The thesis uses the protection current transformer model to describe the manner of saturation and the manner in which relays resolve such deformed signals. The thesis also shows that protection current transformers do not make more errors compared to the measuring current transformers within the small current area. Errors are decreased further on when core balance current transformers are applied to measure zero component of earthfault current. This way the application of current transformers having a lower ratio is made possible, while the error is reduced to one, and not to all three phase current transformers. Protection relays together with instrument transformers represent a very important part of electric power system. Correctly operating relay protection system enables a fast isolation of faulty part within the system resulting in a stabile system operation and enabling uninterrupted electric power supply of the majority of users within the system. Misoperation of protection relays deteriorates the quality of supply. Research, development, study of relay protection application and construction requires interdisciplinary approach consisting of in-depth knowledge of electric power systems mathematic formulations and electronic devices. For more than four decades the majority of components making a modern electric power system were successfully modelled for the needs of electro-magnetic transient analyses. The exceptions are protection relays. A progress in protection relay modelling essential for transient analyses has started only some twenty years ago. In the thesis SimPowerSystems is used as medium voltage distribution system modelling and simulating tool within Matlab/Simulink environment. Within Simulink environment, modelling and simulation of the entire system are possible combining SimPowerSystem tools with other Simulink, first of all control tools and using various Matlab operations and programming possibilities. Such approach enables integration and optimization of protection and control part of the model with electric power system model. Usage of integrators with variable integration steps and detection of zero crossing features enables precise and relatively fast simulations. The distribution system for electro-magnetic transient analyses has been modelled based on two real networks where earth fault tests were conducted earlier. Testing records of current and voltage signals have been used for calibration of the distribution system model. Generic earthfault protection relays are modelled in the thesis enabling a general presentation of relay protection operation at the same time. Each modelled relay assembly is described and analysed theoretically and supported with features necessary for modelling of individual assemblies together with a description of their influences. Programmed relay models are prepared for closed loop simulations with electro-magnetic transient simulations enabling estimation of relay algorithm behaviour during transient or disturbed conditions in the system caused by failures or by switching operations. Relay model settings could be changed and their influences on relay protection operation and coordination can be analysed. Described application and usage of relay models make development of relay protection system much easier and enable efficient training of engineers and students. Finally, a method of software modelling of protection relays is proposed that, if further developed, enables relevant testing prior to construction of relay prototypes. It has an utmost importance in the development process, since it enables testing of not only various protection algorithms and inside relay logic, but also analyses of inside relay assemblies and detailing of necessary changes without a need to change hardware and software modules in the real device.