The structure of a HESS with the waste heat utilization system is shown in Figure 1. The whole system consists of an electrolyzer, fuel cell, hydrogen storage system, and waste heat utilization system. This HESS adopts the alkaline electrolyzer as the water electrolysis device due to its mature technology and fast response speed. The electrolyzer is used to absorb the excess wind power to produce hydrogen. As for the fuel cell, the proton-exchange membrane fuel cell (PEMFC) is chosen to consume hydrogen and generate electricity considering the requirement of the operating temperature match.

The hydrogen storage system includes a hydrogen tank, an air/oxygen system, and a water supply cycle. The waste heat utilization system consists of a thermal tank, a heat storage exchanger, and a heat cycle system. The heat cycle system builds a heating/cooling cycle between the electrolyzer, PEMFC, water supply tank, and heat storage tank to stabilize the system temperature. The mathematical models of the various components of the HESS are given in the following sections.

The power output of a wind plant can be modeled with wind speed and installed power (Guo et al., 2020). By further equating the wind speed change as a power output impact factor λ W t , a simplified model of the wind plant output can be expressed as P ˜ W t = λ W t P W · (7) where P W represents the installed power of the wind plant. P ˜ W t represents the actual power output of the wind plant.

While, in an actual situation, the system operator usually uses the predicted wind plant output to determine the dispatch decisions and the dispatchable power. The predicted power output and dispatchable power can be expressed as: P ^ W t = λ ^ W t P W , (8) P W t = δ P ^ W t , (9) where λ ^ W t represents the predicted power output impact factor. P ^ W t and P W t represent the predicted output and dispatchable power of the wind plant. λ ^ W t reflects the availability of power grid dispatch with wind power forecasting. P W t represents the dispatchable power, forming the dispatching curve of the wind plant, which is the grid-connected power guaranteed by the wind plant. δ means availability factor of wind plant. Based on this, we can further define the dispatch tracking deviation index of the wind plant (Guo et al., 2020), which is: Δ W = ( ∑ t = 1 T P ˜ W t − ∑ t = 1 T P W t ) / ∑ t = 1 T P ˜ W t , (10) where Δ W represents the total power deviation in the whole period of dispatch.

Distributionally robust optimization is a data-driven analysis approach and has been widely studied and applied. This method does not require an accurate probability distribution to characterize the uncertainties. Its conservativeness lies between robust optimization and stochastic optimization. Therefore, the distributionally robust optimization approach is applied in this work. In this method, we adopt the Wasserstein divergence (Guo et al., 2020) as the ambiguous set to measure the uncertainties of wind power output. Hence, we have: M ε = { P ∈ M ( Ξ ) : d W ( P , P ^ ) ≤ ε } , (11) where P represents the probability distribution of the actual power output of the wind plant. P ^ represents the empirical distribution of the power output. M ( Ξ ) represents the set formed by all possible distributions satisfying Wasserstein divergence d w , where ε is the radius of the ambiguous set. The calculation method of the parameters mentioned above can be found in (Esfahani and Kuhn, 2018).

In the cooperative dispatch, historical wind power data is commonly used to predict the wind plant output. The model that we establish combines the dispatchable power of wind plants with the availability coefficients to optimize the output of conventional units and increase the grid-connected output of wind plants. The operation cost of conventional units and carbon emissions can also be reduced. Therefore, the goal of the W-HHS’s optimal dispatch is: F = max P ˜ W t min P g e n t , i , δ ∑ t = 1 T ∑ i = 1 N [ a i ( P g e n t , i ) 2 + b i P g e n t , i + c i ] − c e δ P ^ W t , i + c p Δ W P ( P ˜ W t ) ∈ M ( Ξ ) , t ∈ T , i ∈ N , (12) where P ( P ˜ W t ) represents the probability distribution of the actual wind plant output. c e represents the on-grid power tariff. c p represents the penalty coefficient. P g e n t , i represents the power output of the units. a i , b i , and c i represent the operation cost coefficients of the conventional unit. i represents the bus index. N represents the set of all buses.

The problem established in Eqs. 12–19 is a max-min optimization problem. The actual power output of the wind plant is modeled by the uncertain ambiguous set given in Eq. 11, which cannot be solved directly. To this end, we adopt the method proposed in (Guo et al., 2020) to transform the set into a set of linear chance constraints, which are: { ε ( 1 − Δ W ) + 1 K ∑ k = 1 K s i k − γ i α ≤ 0 s i k ≥ ( 1 − Δ W ) ∑ t = 1 T P ˜ W i k , t − ∑ t = 1 T P W k , t , i + γ i s i k ≥ 0 , (20) where K is the number of data samples. α is the confidence level. P ˜ W i k , t and P W i k , t are the actual wind plant output and dispatchable grid-connected power represented by samples. s i t and γ i are corresponding dual variables.

At this time, since we use samples to describe the uncertainties of the wind plants outputs, the power balance constraint of each line in Eq. 19 can be rewritten as: { P i k , t = ∑ l P l k , t + V i k , t ∑ j = 1 N G i j = P W k , t , i + P g e n t , i + P f u e l k , t , i − P e l e k , t , i − P l o a d t , i Q i k , t = ∑ l Q l k , t − V i k , t ∑ j = 1 N B i j = Q g e n t , i − Q l o a d t , i , (21)

The lower and upper bounds of each variable restricted by the limitations of technology and environment are all considered in modeling, which is not listed due to the space limitation. Besides, we notice that product terms of two decision variables exist in Eq. 5, making the model nonlinear. This term can be piecewise linearized by the Boolean expansion method (Pereira et al., 2005).

So far, the W-HHS proposed cooperative dispatch method is transformed into a mixed-integer linear program, which can be solved with matlab 2016b and Cplex12.6.

In this section, we test our models and method on the IEEE 30-bus testbed. The actual historical data obtained from the Qinghai Province’s 90 MW wind plant is used as samples. The parameters of the system are shown in Table 1. The W-HHS is integrated on bus #12, which is also given in Figure 2. The capacity of HESS is selected according to the local energy storage configuration policy, equal to 10% of the wind plant capacity. The specific historical data is selected as the predicted value of the wind plant output. 20% prediction error is set according to the current wind power prediction level.

The Latin hypercube method generates 100 samples (Shu et al., 2014) to construct the proposed distributionally robust optimization model. The upper and lower bounds of predicted output, available power, and uncertainties of wind plants are shown in Figure 3.

To analyze the influence of heat balance and hydrogen balance on the dispatch strategy of HPS, we study four different scenarios, which are listed as follows. The results are shown in Table 2.

Case 1: Heat and hydrogen balance constraints are not considered;

Case 2: Only heat balance constraints are considered;

Case 3: Only hydrogen balance constraints are considered;

Case 4: Both hydrogen and heat balance constraints are considered.

It can be seen from Table 2 that where the hydrogen and heat balance constraints are ignored (Case 1), the dispatchable power of the wind plant is equal to the predicted value, and the operation cost of conventional units is the lowest. However, 25.04 kg extra hydrogen is needed to support the 24-h operation of the hybrid system. As constraints are added into the model, the availability coefficient of the wind plant decreases to meet hydrogen and heat balance requirements, and the cost of conventional units increases. Compared with Case 1, the wind plant availability coefficient in Case 4 has dropped by 6.33%, and the cost of conventional units has increased by 3.4%. The results of conventional unit dispatch in the four scenarios are shown in Figure 4.

According to the results in Case 2 and 3, we can figure out that the dispatch strategy that only satisfies the hydrogen balance or the heat balance requires the extra hydrogen or thermal supplement. It can be seen that when the system has sufficient day-ahead initial hydrogen storage or thermal storage, the corresponding dispatch strategy can also be adapted to increase the grid-connected power output of wind plants. When the initial hydrogen energy storage and the thermal storage are insufficient, the wind plant availability coefficient can only be reduced, and the dispatch strategy in Case 4 is adopted to maintain this efficient and economical operation of the HESS. Figure 5 shows the operation of the HESS in the four Cases.

It can be seen from Figure 5 that the PEMFC in Case 2 consumes extra hydrogen to provide an up-reserve for the hybrid system, improving the availability coefficient of wind power and meeting the heat balance constraints. In Case 3, the availability coefficient of the wind plant decreases. We can see that the probability of wind power curtailment increases while the probability of load curtailment decreases. The W-HHS calls the electrolyzer to increase hydrogen production, and the PEMFC is controlled to consume less hydrogen, thereby satisfying the hydrogen balance constraint. The SOC changes of hydrogen balance and heat balance are shown in Figure 6.

Figure 6 shows that only the dispatch strategy adopted in Case 4 can simultaneously satisfy the heat and hydrogen balance constraints. In this case, the hydrogen tank will have the remaining hydrogen. The remaining hydrogen can be used in the subsequent optimal dispatch to increase the grid-connected output of the wind plant, reflecting the character of hydrogen energy storage’s cross-cycle energy storage. When the heat balance SOC shown in Figure 6 is less than 0, it indicates that the hydrogen energy storage system must rely on additional supplementary heat energy to maintain the regular operation. This working condition means that the hydrogen energy storage system’s thermal energy generated and stored is not enough to maintain the heat balance of intermittent work. In practice, the system’s hydrogen production and power generation efficiency will decline to generate sufficient thermal energy.

Compared with Case 3, the optimal strategy in Case 4 further reduces the wind plant’s available power and grid-connected power to satisfy the heat balance. It can be seen that the heat balance constraint reduces the profits of the hybrid system. Thus, the factors that affect the heat balance constraint should be further analyzed to reduce the impact of heat balance on the operation of HESS.

From the results in Figures 5, 6, we can easily find out that when the W-HHS is in operation, the electrolyzer and PEMFC run intermittently. The electrolyzer cannot run at full power, and the PEMFC is always in reserve mode for a long time in an operation cycle. According to the heat balance model given in Eq. 5, 15, whether the heat produced can meet the heat lost by the system mainly depends on the heat dissipation coefficient of the electrolyzer and PEMFC. Therefore, the influence of the heat dissipation coefficient on the heat balance SOC constraint should be analyzed. Thus, we take the heat dissipation coefficient in a range of [1/900, 1/1,500] to study the performance of the waste heat utilization system. The results are shown in Table 3.

Table 3 shows that as the heat dissipation coefficient decreases, the operation is less influenced by the heat balance constraints. The high availability coefficient of the wind plant results in a decreased operation probability of the electrolyzer and an increased working time of the PEMFC. Hydrogen storage drops accordingly. Also, due to the decrease of heat dissipation, the thermal energy stored in the thermal tank gradually increases.

When the heat dissipation coefficient is less than 1/1,200, Case 4 is equivalent to Case 3. The hybrid system is no longer affected by heat balance constraints. Thus, we can conclude that improving the heat insulation performance and reducing the heat dissipation power will help raise the system’s operating efficiency. Meanwhile, the available grid-connected power of the wind plant increased, and the profit of the W-HHS improved.