2.1. Model Construction of Distributed Wind-Hydrogen Hybrid Energy System
A distributed wind-hydrogen hybrid energy system mainly generates electricity through small and medium-sized wind energy and is connected to the grid locally to reduce wind curtailment, thereby improving the utilization rate of battery power storage and hydrogen storage [
12]. When the wind energy is connected to the grid and the power is insufficient, the fuel cell will be used to connect the grid. When there is a surplus of wind power, the electrolyzer will be used to absorb and store hydrogen to build a wind-hydrogen integrated energy system [
13]. To better study the wind power generation system, the direct drive wind turbine is selected as the research object in this study. Compared with the doubly fed wind turbine, the direct driven wind turbine has a large power density, a wide operating range, and is less affected by the frequency range. In terms of mechanical structure, the direct drive type has a multi-stage structure and does not require a speed increase gearbox. The wind power generation system model in this section is based on the process of wind energy utilization, which includes three parts, physical kinetic energy model, transmission shaft model, and electrical system model. Hydrogen energy storage is an energy storage technology with good development prospects at present. “Hydrogen-electricity” and “electricity-hydrogen” conversion devices are used to control wind power and power supply. The system designed in this study is mainly a distributed common DC bus type. The wind-hydrogen hybrid energy structure is shown in
Figure 1.
In
Figure 1, the Permanent Magent Synchronous Generator (PMSG), Electrolyzer (EL), Fuel Cell (FC), and Battery (Bat) enter the DC bus through the converter. In the energy storage system, the reason for the unbalanced power phenomenon is mainly the dynamic response delay of hydrogen energy storage, which makes the system face the volatility of wind power. This device is used for second-level response operation, assisting EL-FC to perform electric hydrogen-electric cycle operation, so as to ensure that the DC bus can maintain a stable voltage and improve the grid-connected controllability of fans [
14]. The stability of the DC bus voltage can only be ensured by keeping the balance of the system’s current input and output in the DC capacitor. The calculation of the DC bus capacitor voltage is shown in Formula (1).
In Formula (1),
represents the DC bus capacitance (F);
is DC bus voltage (V); and
,
,
, and
are the currents (A) of PMSG, Bat, FC, and EL, respectively. The system monitors the real-time parameters of each subsystem, allocates power, and operates the control part, so as to judge the current system in real-time and obtain the control signals of each subsystem [
15]. When the converter receives the control signal, it assists the system in power distribution to ensure the controllability of the grid-connected power and effectively improve the penetration performance of wind energy.
2.2. Power Dispatching Optimization Technology of Wind-Hydrogen Integrated Energy System
In order to improve the overall accuracy of the model, this study will build the RC link model based on the original Thevenin model, adding the related discipline theory based on polarization resistance and its parallel connection. Set open circuit resistance, polarization internal resistance, and internal resistance as
,
(
), and
, respectively. The charge and discharge current of the battery, the current on the polarization resistance, and the working voltage of the battery are
,
, and
. According to the parallel theory of polarization resistance and polarization capacitance, the RC link is formed in parallel. Based on the basic circuit laws and BMS design requirements, the circuit formulas (
,
) of the RC link of the Thevenin model are obtained, as shown in Formula (2).
Assume that the on-time calculation formula of BMS is
, where
is the time constant, and the state quantity of the BMS system is
; see Formula (3).
Set the polarization resistance as
,
,
, and select the constant voltage at the battery end in the BMS system as the observation to obtain the observation equation, as shown in Formula (4).
In Formula (4),
is the sampling time,
is the rated capacity of the battery,
is the observation noise, and
is the system noise, where I in the system noise can be 1–4. The battery data is mostly completed under a different battery state of charge (State of charge, SOC) [
16]. Therefore, in order to accurately identify the parameters of different models, the Ultimate Tensile Strength (UTS) sub-capacity cabinet was used for research and analysis; the object was a 3.2 Ah 18,650 lithium battery at a room temperature of 25 °C. The third order Thevenin model is used to analyze the constant current charge and discharge parameters. The model design is shown in
Figure 2. Wherein,
Figure 2a is the third-order Thevenin model, and
Figure 2b is the sampling point diagram of the complete pulse discharge process.
The battery charging state of the BMS system is 100.00%. The UTS sub-container set on the UTS sub-capacitor is set to discharge for 6 min (360 s) and then stand for 18 min (1080 s). The discharge pulse current is 0.5 C to ensure that the SOC of the battery decreases by 0.1 each time when it is charged. The experiment was repeated a total of 7 times. Finally, find the functional relationship between open circuit voltage and BMS (SOC) fitted by 7th degree polynomial, as shown in Formula (5). The polynomial fitting functions are all carried out on the basis of Matrix Laboratory (MATLAB) theory [
17].
In
Figure 2, A to B is regarded as the corresponding process of discharge of the polynomial fitting function, and B to D is regarded as the corresponding process of its resting. The BMS at a certain time node of the intercepted 7 polynomial fitting functions is 0.5. In this model, the corresponding active range of the RC network in the zero state is mainly in the A to B area. The starting point is point A. Therefore, according to the equivalent circuit model of the battery, the calculation formula of the voltage (
) in the A–B region can be obtained:
In Formula (6), the value of RC links of different orders is
. Similarly, if the parameters of the B–D static area are fitted according to the curve fitting function under the MATLAB theory, the voltage calculation method is shown in Formula (7).
However, it should be noted that if it is needed to solve the resistance, capacitance, and internal resistance of the RC link, the calculation formulas of
and
should be combined to achieve the parameter fitting, as shown in Formula (8).
Finally,
, the parameter fitting calculation formula related to the BMS function is obtained, as shown in Formula (9).
Figure 3a shows the polarization resistance of RC link, and
Figure 3b shows the polarization capacitance of RC link. Formula (9) is used as the parameter fitting calculation formula for the function relationship between
and BMS; finally the polarization resistance and capacitance of the RC link under the third order Thevenin model of the constant current charge-discharge experiment can be obtained. From the above
Figure 3a,b, the polarization resistance and capacitance
of the RC link under the third order Thevenin model are relatively stable from 0.1 to 0.9. However, the
polarization resistance is relatively stable between 0.1 and 0.9, while the polarization capacitance has a relatively large variation in this area. The reason is that the capacitor is a series-mixed structure, which is affected by factors such as leakage and breakdown. It leads to the abnormality of the equivalent circuit and increases the capacitance loss [
18]. In addition, the resistance value of capacitor and DC is infinite, so when leakage or breakdown occur, the DC resistance will decrease.
2.3. Adaptive Kalman Filtering (AUKF) Power Allocation Method
In order to improve the power distribution effect of the model proposed in this study, an unscented Kalman filter (UKF) algorithm is firstly proposed, which is a minimum mean square error estimation algorithm based on unscented transform (UT). UKF improves the adaptive performance of traditional Kalman filtering, ensures the accuracy of sampling, and makes known variables consistent with the distribution of probability density. For real-time estimation of battery SOC, charge and discharge monitoring is required during battery operation. Due to the complex electrochemical reaction causing the estimation error of the SOC value, the error will accumulate. The UKF can be adjusted by SOC and various parameters to reduce the influence of the error, and finally calculate the accurate minimum root mean square estimation result. Therefore, a dynamic equivalent circuit model is constructed according to the UKF principle, and error terms ζ and ξ are introduced at the same time, as shown in Formula (10).
where
represents three-phase power supply current. Formula (10) is used as the state measurement formula of UKF, and the UKF gain also plays a decisive role in SOC correction. In order to improve the anti-interference of non-Gaussian nature. The errors of SOC and terminal voltage exist in the state vector. Therefore,
is set as the extended state vector and
is the covariance, so the SOC estimation method is shown in Formula (11).
In Formula (11), , and represent the covariance of the error terms ζ and ξ.
The application of UKF in SOC estimation is the capacity waveform of a fully charged battery discharged at a rate of 1 C. The whole discharge time is 4150 s, with four discharges of 1000 s successively and an interval of 50 s. The SOC estimation algorithm proposed by the model is used to estimate the experimental data. Extended Kalman filter (EKF) is widely used in battery estimation. The initial SOC is based on the UKF algorithm and the standard covariance of the actual value and the initial SOC is 0.1. At the beginning of discharge, a UKF-based algorithm can well estimate the real SOC curve but an EKF-based method cannot estimate the real value of SOC. This shows that EKF is more dependent on the initial value and UKF’s algorithm converges faster. In the middle of discharge, the estimation effect of EKF and UKF algorithm is similar. However, at the end of discharge, the EKF algorithm fluctuates greatly and cannot estimate the battery SOC value very well. The same problem does not exist in the UKF algorithm. The fast convergence rate of UKF shows that it is more suitable for nonlinear systems than EKF.
Because the filtering technology in the current project can only perform the power distribution of a specific frequency band, it has certain limitations in application. Additionally, the power input value also has a certain influence on the phase delay and is difficult to meet the grid connection requirements in the application project. Therefore, this study proposes a power allocation method based on AUKF, as shown in
Figure 4.
The output power of the fan without the intervention of the energy storage system is expressed as and the smoothed output power after filtering is expressed as . The output power of the wind turbine is obtained after the intervention of the AUKF and represented by . The difference between the output power and the smoothed power is expressed as the fluctuating power of the battery . obtains the power values of EL, FC, and Bat through system operation, which are , , and , respectively. Among them, represents the power imbalance caused by the delayed response of FC and EL in the process of hydrogen energy storage, i.e., . When the SOC value is close to the limit, the SOC estimation and the change of the DC bus voltage can indicate the filtering ability of the UKF, so that the SOC value is within the safe range to meet the grid-connected power requirements of the grid.
In practical engineering, if the grid-connected power is not properly limited, when the wind speed is too large, fluctuations in the DC bus voltage will occur, which easily lead to deep charge and discharge. Therefore, the fuzzy control is integrated into the UKF to monitor the SOC and DC bus voltage changes in real time and achieve the power distribution effect based on the AUKF. The SOC is selected as the fuzzy variable, and the input of the model control quantity is selected as the change of the bus voltage relative to the reference value, so as to ensure the stability of the DC bus and ensure the power smoothing performance of the hydrogen energy storage device. The target value calculation of the extension smooth output is shown in Formula (12).
The value of the measured covariance R in UKF affects the smoothing effect of the wind power, that is, when the value of R is small, the change of the measurement equation will have a significant impact on the filtering effect. When R is large, it can cope with wind speed and sudden change of bus voltage. When the change of DC bus is positive, the energy storage system should be in the charging state; otherwise, it should be in the discharging state. The range of battery SOC is considered through fuzzy logic control. When the battery SOC is high and in the charging state or the battery SOC is low and in the discharging state, the target output power of the battery can be changed by reducing R, the difference between the smooth value and the wind power; thus, the power borne by the battery can be reduced. When the SOC of the battery is high and in the discharge state or the SOC of the battery is low and in the charge state, increase R; thus, the power borne by the battery is increased. This can slow down the overcharge and overdischarge of the battery under extreme conditions and can effectively improve the battery life. The difference between the filtered smooth power and the grid load is borne by EL and FC.
As a whole, the distributed wind-hydrogen hybrid system decomposes and coordinates different energy forms in production, transmission, consumption, etc. At the same time, it takes time, space, multiple constraints, and utilization efficiency into account, including the overall coordination and power distribution of the system. In this paper, the grid load is used as the objective function of the system, as shown in Formula (13), to change the nonadjustable generation characteristics of renewable energy.
In Formula (13), , , , , . , respectively represent the lower limit and upper limit of the extension power Pw (W). and represent the lower limit and upper limit of DC bus voltage Udc (V), respectively. and , represent the lower limit and upper limit of the hydrogen storage tank pressure Pt (kpa). represents the fuel cell power (W). represents the power of the electrolyzer (W).
For the battery energy storage constraint, in addition to considering the SOC operating range, the constraint of charging and discharging times is added. Although the operating range of the battery SOC has been optimized, the limit value of SOC is still a constraint for the safe operation of the battery. The main constraints of the energy storage battery are shown in Formula (14).
In Formula (14), is the period long term and is the number of periods. Kdis, Kch, Ukch, and Udis respectively represent the limit value of battery charge and discharge times and the battery charge and discharge times in a certain period of time.
The system model is further divided into different modes to allow the battery to compensate for the delay characteristics of hydrogen energy. According to the grid-connected power and load requirements, let the net power be , then . If , then , it means low wind speed; if so , means high wind speed. For the allocation in the energy storage system model, the pressure of the hydrogen storage tank is used as the mode division basis, four modes can be obtained and the final output power of FC, EL, and Bat can be calculated.
When
, the electrolyzer was out of operation and the model was the lack of power. The operating state of FC and Bat was selected by the pressure of the hydrogen storage tank. Mode 1: When the battery is completely supplied with the insufficient power, the SOC is too low and in extreme conditions the battery can be decommissioned. The reference power calculation is shown in Formula (15).
Mode 2: If
is equal to the FC power, that is,
less than the maximum power of the FC, then the Bat is affected by the FC delay, which will cause the unbalanced power of the system. See Formula (16) for the reference power calculation.
When , the fuel cell was out of operation, the system model still had residual power, and the operating state of FC and Bat was selected by the pressure of the hydrogen storage tank.
Mode 3: When the EL operation is affected by the high pressure of the hydrogen storage tank, the Bat absorbs all the remaining power. When the SOC is too high, and in extreme conditions, the battery can be de-operated. The reference power calculation is shown in Formula (17).
Mode 4: If
is less than the EL power, that is,
is less than the maximum power of the EL, then the Bat is affected by the EL delay, which will cause the unbalanced power of the system. See Formula (18) for the reference power calculation.