## 2 Description of the Power Converter System Solution for a Cogenerator with an Induction Machine
### Balancing Active Power in the Off-Grid Mode  
Equipping the described power supply system with a power electronic converter allows for full use of the source properties in the regulation and balancing mode. A typical solution for a biogas micro power plant is the use of a cheap induction generator that requires a source of reactive power, usually a power supply network, to excite. In the case of connecting an induction generator with a power electronic converter and a battery, a source with adjustable active and reactive power, and the ability to operate in off-grid mode is obtained.  
The basic balance of active power in the off-grid mode can be described by the equation:  
\[\sum_{i=1}^{k}P_{s,i}=\sum_{i=1}^{j}P_{l,j}+\sum_{i=1}^{m}P_{b,m}, \tag{1}\]  
where \(P_{s,i}\)--active power of the energy source; \(P_{l,j}\)--active power of the load; and \(P_{b,m}\)--active power of the battery.  
The power produced by the induction generator can be calculated as:  
\[P_{G}=(T_{ICE},\omega)\eta_{G}, \tag{2}\]  
where \(T_{G}\)--torque of the ICE; \(\omega\)--angular velocity; and \(\eta_{G}\)--efficiency of the induction generator  
In order to be able to continuously balance the active power using a cogenerator with an induction generator, the converter system is equipped with a battery. When the load power changes, additional energy is taken from the battery or transferred to the battery. To regulate the power of the power generator, the controller has two options: (1) changing the rotational speed of the generator, and (2) changing the torque by controlling the dose of fuel fed to the internal combustion engine. Figure 2 shows the characteristic operating states of the power supply system and the active power waveforms for: (1) steady state; (2) a stepwise reduction in load power; (3) a stepwise increase in the load power.  
The time taken to establish a new operating point of the generator power system in response to a change in load power depends on: (1) the available battery power (and this depends on the capacity); (2) the throttle drive response time; (3) the oversupply of drive motor torque. The change in the drive power of the ICE can be forced in two ways: (1) a  
Figure 1: Block diagram of the designed power supply system with an ICE and an induction generator. ICE—internal combustion engine; G—induction generator; PC1—AC–DC power converter for induction generator; PC2—AC–DC power converter for AC grid; PC3.1—DC–DC Chang power converter for battery; PC3.2—DC–DC power converter for DC bus voltage limiting; R—load resistor; \(n\)—rotational velocity of induction generator; \(v_{\text{dc}}\); \(i_{\text{dc}}\)—voltage and current of DC bus; \(i_{\text{G}}\)—phase current of generator; \(v_{\text{b}}\), \(i_{\text{b}}\)—voltage and current of battery; \(v_{\text{bg}}\), \(i_{\text{g}}\)—voltage and current of grid. Source: author’s development.  
change in the fuel dose; (2) a change in the rotational speed. It is possible (and desirable) to use both methods simultaneously in order to obtain the highest possible active power control dynamics.  
The battery current can be controlled by controlling the torque (fuel dose control) and by changing the rotational speed:  
\[(T_{ICE}\cdot\omega)\eta_{G}-P_{l}=(U_{b}\cdot I_{b}), \tag{3}\]