# Attenuation of DC-Link Pulsation of a Four-Wire Inverter during Phase Unbalanced Current Operation
## 1 Introduction  
There is currently an exponentially growing number of receiving devices, based on impulse power supplies in every household. From the point of view of an energy supply system it is seen as an unbalanced, non-linear load. On the other hand, increasing numbers of energy consumers become energy producers, so called prosumers, due to installation of renewable energy sources. In worst case scenario, energy users would consume a large amount of energy in one phase, and produce energy in another phase (when using single-phase PV inverter) (Figure 1). These two combined factors can lead to an unbalance in phase currents, which in turn causes power transformers to operate in non-nominal conditions, leading to more losses and increasing risk of faults in the grid. Additionally, a current asymmetry can cause a voltage asymmetry at local terminals, which will then propagate into the utility grid. The simplest method of solving the above problem is reducing the grid voltage asymmetry by reducing the available power of single-phase or three-phase PV inverters in the function of the phase voltage. This method is inherently loss characterised, so other solutions should be applied to solve the mentioned problem. There are known methods for solving the grid balancing problem, mainly based on Dual Vector Current Control methods and three-phase four wire inverters [1; 2; 3]; however, these methods can only operate with an unbalanced grid, while still generating balanced currents and they have no means to compensate the grid voltage unbalance  
Currently, researchers focus on methods utilizing prosumer converters to locally balance the power flow in the grid. One of the promising methods is using a four-wire, three-phase converter with a lithium-ion energy storage and independent power control for each phase of the system [4; 5]. This method allows for the best flexibility at the cost of increased degradation of the energy store. The current asymmetry on the output of thefour-wire power converter causes large pulsation on DC link, which affects operation of the electrochemical energy storage [6; 7]. Depending on the inverter mode, the energy storage would be charged or discharged, and power delivered to the grid can be approximated as power of the DC link. Instantaneous power in DC link can be described as sum of output powers of three phases. \[p_{3f}=\sum_{k=1}^{3}\frac{1}{2}V_{k}I_{k}(\cos(\varphi_{ck}-\varphi_{ik})-\cos (2\omega t+\ \varphi_{ck}+\varphi_{ik})) \tag{1}\]  
where: \(p_{3f}\)--power in DC link, \(V_{k}\)--phase voltage, \(I_{k}\)--phase current, \(\varphi_{ck}\)--phase voltage angle, \(\varphi_{ik}\)--phase current angle. In a balanced scenario, where the inverter generates symmetric currents, sum of time variant components \(\cos(2\omega t+\ \varphi_{ck}+\varphi_{ik})\) of three phases equals zero, and there is no pulsation present. However, when asymmetry is introduced in the sum of time variant components does not equal zero, and resulting power pulsation is transferred to DC link. Frequency of this pulsation is double the frequency of main grid voltage component. This situation is undesirable, as it adds AC component to current in DC link, which in turn transfers into AC component in current in the electrochemical energy storage. Such scenario causes the energy storage to switch from charging to discharging with frequency of 100 Hz, which causes unwanted heating of the battery cells. The lithium-ion energy storage is necessary in this system, as power delivered to the system will not always be equal to power drawn from the system across three phases, and eventually DC link would be drained or overcharged, resulting in system shutdown. Additionally, a factor not considered in this paper that can improve the system is a renewable energy source, which can keep the DC link charged when the source is operational.