The multilevel control system is more practical, efficient, and stable. The artificial upwelling system can also use a multilevel control. The system studied here consists of two layers: the supervisor controller and the local controller. The supervisor controller monitors and controls the electric energy output to power consumption centers, including the sensor system and the air injection system. At the same time, it checks the system for anomalies and errors. The local controller processes ocean environment parameters to control the air injection system to optimize air injection and improve efficiency. The local controller is limited to the supervisor controller. The control system aims to fulfill the following three goals:
2.2.2. Local Controller
The local control system controls air injection according to the ocean environment. The parameters used to reflect the ocean environment include the flow velocity, illumination, and temperature. The flow velocity influences the height of upwelling plume and illumination and temperature influence the growth of kelp. The following sections will explain how the control system controls the air injection system according to the environmental parameters.
(1) Air injection rate calculation by flow velocity
The height of the upwelling plume is directly determined by the air injection rate and flow velocity. If the plume height cannot reach the kelp culture area, the upwelling is invalid. There has been some research on the behavior of plume in air-injection artificial upwelling [
21,
31,
32]. Of the three variables, target height of plume, flow velocity, and air injection rate, any two variables are known and another variable can be obtained. In this controller, flow velocity, air injection rate and target height of upwelling are input, controlled quantity and output, respectively. However, the air injection rate is limited by the maximum output power, so it has a maximum value. In practice, to ensure that the upwelling reaches the target height, the air injection rate can be variational by flow velocity or a fixed value but cannot be higher than the maximum.
(2) Growth rate calculation by temperature and illumination
Temperature and illumination directly affect the photosynthesis and respiration of kelp, thus influencing the growth rate and nutrient uptake. When the growth rate is small and less nutrients are required, the lifted nutrients cannot be completely absorbed and will be waste. Temperature and illumination will be used to calculate the growth rate of kelp.
The net growth rate of kelp is determined by the difference between its total growth rate and respiration as [
33]
where
is net growth rate,
is total growth rate and
is respiratory rate of kelp, which is influenced by temperature and can be determined by [
34]
where
is measured temperature whose unit is °
C. The total growth rate is influenced by temperature, illumination, and nutrient as [
35]
where
is dimensionless.
is calculated by photoinhibition mode as [
36]
where
is surface illumination, the unit is
and
is the optimum illumination for kelp and
. Compared with measured illumination, the underwater illumination has a certain attenuation. The optical attenuation coefficient of water can be expressed as [
37]
where
is suspended matter concentration and measured in local water, and the underwater illumination can be calculated by [
38]
where
is the depth from surface whose unit is m;
is the illumination at depth of
;
is the illumination at surface, which is measured by sensor, whose unit is Lux. And
.
is calculated as [
36]
in which
is the optimum temperature for kelp growth,
°
C and
is temperature ecological amplitude. If
,
, or else
.
and
are lower limit and upper limit of temperature ecological amplitude and
°
C,
°
C. The temperature, illumination, and flow velocity are obtained by corresponding sensors.
is affected by ratio of nitrogen to phosphorus in kelp and its value is in (0,1]. When N:P of seawater is in [
12,
16],
. When nitrogen or phosphorus is limited,
can be obtained by a complex calculation which can refer to the research done by Wu [
33].
(3) Air injection control with kelp growth model
The larger the growth rate of kelp, the larger the nutrient demand. The growth of kelp Z can be expressed as follows:
During this period, from
to
, the energy consumption of the air injection system W can be expressed as:
where
is consumption power of electric energy whose unit is watt and is determined by air injection rate as follows:
in which
is air injection rate whose unit is L/min.
The solar system produces a certain amount of electrical energy every day. Most of the electrical energy will be used in the air injection system on that day, and the rest will be used to ensure the normal operation of other systems. Therefore, when kelp growth rate is large, using up the energy generated each day to produce upwelling is effective. Under this condition, making Z max with fixed W, the working time of the air injection system can be calculated, which is in formula (9) (10). This calculation is carried by MATLAB and only considers the continuous working once a day of the air injection system.
(4) Lifted nutrients calculation
The amount of lifted nutrients is an important measure to the efficiency of upwelling. In order to calculate the amount of lifted nutrients, the volume flux of upwelling needs to be known. This volume flux is also determined by air injection rate [
31]. The expression is:
where
is the height from the bottom;
is the air injection rate determined by the opening of air pumps and its unit is m
3/s;
is the initial volume flux at
;
is head of the atmospheric pressure and is approximately equal to 10.4 m;
is offset of the nozzle origin, which can be determined as [
31]
in which
is nominal half-width of the plume near the nozzle;
is entrainment coefficient and
here. The total amount of nutrients
to be lifted can be expressed as
where
is the concentration of nutrients at depth of z.
(5) Solar power generation calculation
According to design specifications of photovoltaic power station, a formula for calculating generating capacity can be expressed as [
39]
where Ep is the electric energy generation of a system whose unit is
, HA is the daily total horizontal solar radiation and the unit is
, PAZ is the system-installed capacity and the unit is kW, K is the correction factor, which depends on line loss, surface pollution, and angle of solar panels. K is determined by the theoretical and actual energy generation.
where GH is averaged solar radiation, which can be obtained by the website of the local weather bureau and the unit is
.