# The comparison method of the best choice of spacecraft power system

The power system of an orbiting spacecraft or a communication satellite includes an energy conversion device, such as a solar cell array energy storage device like a battery, and a PC component, such as a direct energy transfer subsystem. Energy conversion components account for a considerable part of the total cost and weight of spacecraft or satellites. Therefore, the reduction of their size and weight has become an important design consideration for energy conversion components or solar cell arrays. Different system design configurations must be evaluated based on the complexity, cost, performance, reliability, size and weight of the electronic circuit. The overall performance comparison of the system must emphasize the reliability of the entire power supply system to the utmost extent. Compared with other system configurations, the system pad plus redundant components offset the cost or weight savings on energy conversion components.

To simplify the comparative example, this particular method considers three different power system configurations, each consisting of a solar cell array as an energy conversion device and a nickel-cadmium battery as an energy storage device. Direct energy transfer DET systems are common for both design configurations. The overall system performance comparison is based on the length of the mission or the weight and cost of the spacecraft’s multi-year working life.

**1. Stepping power system performance**Each system must be designed as a common mission goal, regardless of reliability design requirements. If the reliability target cannot be met, the reliability of the system is improved to a specific target, which can be achieved by adding redundant components to the system. Redundant optimization techniques can be used to minimize the resulting increase in system cost and weight. Finally, according to the task duration or length, only the cost and weight of the system are compared.

The spacecraft power system is considered to be composed of a solar cell array and a battery, combined with a voltage regulator and a battery charging converter. Figure 1 shows a basic spacecraft power system block diagram. It is very important for the solar array to provide enough power in the orbital irradiation part to meet the electrical load requirements on the spacecraft and to recharge the batteries. The relationship between the solar cell array and the battery is based on the energy balance equation, which can be expressed as the battery current. The energy balance equation is

Where: IBC is the charging current of the battery; IBD is the discharging current of the battery; eB is the battery discharge coefficient, with a typical value greater than 1; t is any time in the orbit; T is the orbital period of the spacecraft or satellite, according to the orbital coordinates The axis is between 80 and 95 min. The relationship defined by formula (1) must continue to any track. The battery discharge factor is a function of battery temperature, depth of discharge (DOD) and the number of repeated charge-discharge cycles.

Assuming that the component losses in the dark and bright parts of the flight are negligible, the basic nodal current equation at any time t during the orbit is

Where: K is a dissipation regular (DSR) coefficient, equal to 1.

For a pulse width modulated series regulator, the constant is defined as

In the formula: the parameter ePR represents the efficiency of the pulse width modulation series regulator; VA is the solar cell array flying in the dark period or the unregulated voltage; VR is the regulated voltage of the load, as shown in Figure 2.

Solving equations (2) based on the load curve defined by the regulated load voltage (VR) and pulse width modulation regulator efficiency (ePR) and the conditions imposed by equation (4), the spacecraft power system must be used The current-voltage (IV) characteristics of the component. The current-voltage characteristics of the solar cell array, the battery on the motherboard and the battery charge controller (CC) are clearly shown in Figure 1. Due to the non-linear I-V characteristics, it is difficult to find a simple solution to the power system equations, because the current and voltage parameters are functions of time. In addition, the I-V characteristics of the solar array and the battery are both a function of operating temperature. Moreover, the I-V characteristic of the battery depends on the state of charge (SOC) of the battery. The change of the battery voltage with the state of charge can be clearly seen from the curve in Figure 3.

Typical battery voltage (VB) relative to the state of charge characteristic of the battery, as a function of battery discharge current and battery charging current, can be seen from Figure 3. The battery overcharge as a function of the solar cell string is shown in Figure 4. The change in battery output voltage must be kept to a minimum in order to obtain the best battery performance. The change in battery voltage as a function of the battery state of charge and the parameter IBC is shown in Figure 5.

**2. Determine the modeling requirements for I-V characteristics**It is necessary to use appropriate computer models composed of conventional circuit elements to determine the I-V characteristics of solar arrays and batteries deployed on spacecraft or satellites. Sometimes, the approximate values of model parameters or assumptions made are not related to the measured component characteristics over the entire operating temperature range. In order to model meaningfully, an energy balance computer program must be developed, which contains subroutines for storage and interrogation of one, two or three variables. This will allow the design engineer of the power system to define the characteristics of the component from the measured data and the data obtained from the theoretical model.

The battery voltage can be determined as a function of battery current, state of charge, and battery operating temperature. The determination of the state of charge of the battery is the key to the integration required by the energy balance shown in formula (2.3). Changes in voltage and current as a function of temperature affect the accuracy of modeling parameters. In addition, for a specific electrolyte density, the influence of temperature on battery capacity and current density must be considered. The data given in Table 1 shows the influence of typical temperature on battery cell capacity (%).

From the data in Table 1, it can be concluded that if the current density of the battery changes, whether it is during charging or discharging, or in both processes, the capacity of the battery is affected. Increasing the current and lowering the temperature will reduce the capacity of the battery. However, when the current level is low, the capacity of the battery is less dependent on the electrical load, so the capacity increases.

The battery designer believes that the battery is discharged at a low temperature during the formation process, and a large battery capacity can be obtained at a higher temperature. This trend shows that the maximum capacity of the battery can only be obtained when the battery is discharged at a low current. In addition, the room temperature capacity can be maintained at low temperatures only when the battery has a small electrical load when it is discharged. Simply put, the changes in battery capacity and discharge rate are strictly dependent on battery temperature and electrical load conditions.

**3. The impact of on-board charging and discharging on battery electrical parameters**Relative to airborne and discharge management, stable open circuit voltage (OCV; VOC) characteristics are considered advantageous, especially for batteries installed on satellites or spacecraft. This allows simple and accurate estimation of the remaining capacity of the battery. Table 2.3 shows the actual open circuit voltage of lithium-ion batteries according to the state of charge and the internal resistance of each battery. According to the state of charge, the value of different battery types will be different.

The state of charge range exceeds 80%~100%, and the parameter values of the two batteries remain almost constant. This means that if the best open circuit voltage and internal resistance value are required at a specified battery temperature, the battery’s state of charge must be maintained at more than 80%.