Optimizing investments in coupled offshore wind -electrolytic hydrogen storage systems in Denmark

Highlights

• An optimized strategy for improving wind farm investments by hydrogen is proposed.

• The coupling opportunities between wind and hydrogen were examined.

• The research presents a critical analysis of wind energy application.

Abstract

In response to electricity markets with growing levels of wind energy production and varying electricity prices, this research examines incentives for investments in integrated renewable energy power systems. A strategy for using optimization methods for a power system consisting of wind turbines, electrolyzers, and hydrogen fuel cells is explored. This research reveals the investment potential of coupling offshore wind farms with different hydrogen systems. The benefits in terms of a return on investment are demonstrated with data from the Danish electricity markets. This research also investigates the tradeoffs between selling the hydrogen directly to customers or using it as a storage medium to re-generate electricity at a time when it is more valuable. This research finds that the most beneficial configuration is to produce hydrogen at a time that complements the wind farm and sell the hydrogen directly to end users.

Introduction

Wind power is one of the fastest growing energy technologies identified by a cumulative capacity of 432,419 MW at the end of 2015, compared with 59,091 MW in 2005 [1]. Denmark is one of the leading manufacturers of wind turbines, as several major wind energy companies and innovations originated from this country [2]. As an example the first offshore wind farm was installed in Denmark in 1991. In 2015, Denmark produced 42% of its electricity demands from wind energy. This includes periods where the cumulative installed wind capacity provides more electricity than the total demand [3]. While this enables a large portion of clean energy to be provided by wind, this also presents challenges with respect to system energy balancing, provision of reserves and cycling of conventional generation. In part, this behavior is reflected by the resulting electricity market prices. To understand the potential challenges of this development, one needs to examine the electricity market in Denmark.

Denmark has several electricity markets that are used to accommodate energy imbalances on the electricity system [4], the spot market (Elspot), balancing market (Elbas), and regulating market. These markets have different timescales for bidding and delivery to ensure that supply meets demand. The unpredictability of the electricity prices, in part due to variability from wind turbines [5], and the fluctuations in the regulation market price, creates challenges for investors in Danish wind farms. There are a number of techniques to address this variability including energy storage, wider regional interconnection, and demand side management. This paper explores the use of water electrolysis to provide hydrogen fuel for transportation or industrial applications while also buffering wind production, particularly during periods of low electricity market prices, when wind farms do not receive so much revenue from selling electricity. This paper also discusses the option of including a fuel cell to create an energy storage system to further buffer wind plant operation.

Similar systems have been explored in a number of scientific contributions [6], [7], [8], [9], [10]. Those reports explored different wind-hydrogen configurations in order to secure a stable renewable energy output. They included methods and approaches on the technological potential of combining the technologies, while measuring the efficiency and predicting the potential; however, they did not include an actual evaluation of the investment potential of such systems, including the discussion of exporting hydrogen directly to the grid. This paper provides a deeper understanding of the economic implications and equipment selection tradeoffs for coupling wind farms with hydrogen electrolysis and fuel cell systems.

Denmark has a national energy strategy that includes the use of storing hydrogen from excessive electricity from renewable energy sources [5], and the combination of these technologies has the potential to alleviate the above-mentioned challenge. Combining wind and hydrogen is not a novel innovation, as the first evidence goes back to 1891, where, the Danish scientist, Poul la Cour produced hydrogen using the power from a wind turbine [11]. Since then, several academic contributions have examined the combination of the technologies, in the search for a stable energy supply based on renewables entirely [12], [13], [14], [15].

Commonly those studies are conducted in regions with excellent wind conditions, such as Norway, Ireland, and The Faroe Islands [16]. These studies have been used to advice this research, given the fact that the wind patterns of those countries are very similar to Denmark [17]. Another study found that the cost of using a wind-electrolyzer system to create hydrogen from electricity and then re-generate electricity back to the grid, while technically possible, it is costly [18]. Other articles focused on the integration of a combined wind and hydrogen system with the purpose of delivering a stable 100% renewable energy supply [19]. The result of that research also found that it was possible to use hydrogen as a storage mechanism, although costly and inefficient due to the high capital cost of the electrolyzer and fuel cells. Other papers discuss the efficiency and cost of hydrogen for hydrogen fuel cell vehicles powered by wind turbines [20]. Similarly, a 2016 study focused in the United States found that the high capital cost for fuel cells makes current hydrogen power-to-power storage systems economically preclusive; however, only using an electrolyzer to produce and sell hydrogen while also acting as a responsive load to buffer the grid presented a more favorable business case [21]. Other studies have examined the possibilities of integrating hydrogen systems directly into the grid and participating in electricity markets [19], or simply using the hydrogen as storage capacity for excessive wind energy. This research aims at co-locating a hydrogen system at a wind farm to increase the competitiveness of both technologies. The industrial usage of hydrogen spans from fertilizer production [22], [23], powering of vehicles [23], refineries [22], to extracting certain types of metals. Hydrogen is produced applying several methods, ranging from anaerobic digestion using biomass, to water electrolysis to usage of fossil fuels through thermocatalytic cracking and gasification [24], which only emphasizes the possibilities of using hydrogen. More importantly, hydrogen, and the before mentioned industrial usages has been addressed as an important factor in the Danish energy roadmap for 2050 [25], [26].

Hydrogen in the (power to hydrogen) PtH system can be used for storage of low-value electricity while also providing additional services to the grid. Currently the most inexpensive way to produce hydrogen in large volumes is by converting natural gas using a steam methane reformer [27]. However, this process uses a fossil fuel which emits carbon during the production of hydrogen. A potential solution to such challenges is to use electrolysis of wind power to mitigate the carbon footprint. The case studies discussed in this section have been used to construct the specifications of the PtH. The authors in Ref. [11] suggested that regions dominated by wind power and excessive electricity can make use of the combination of wind and hydrogen at a large scale. However, as stated in Ref. [15] the environmental benefits come with potentially a higher price for energy. This research aims at exploring the opportunity of co-locating hydrogen equipment at a wind farm to take advantage of the integrated system for renewable power and flexibility. Hence, the main objective is to examine whether there is an incentive for wind farms investors to invest in electrolyzers or fuel cell systems in Denmark.

A variety of research has been conducted on optimization techniques of similar renewable energy systems. As an example, the optimal size and location of wind turbines was found through a nonlinear programming method in Ref. [28]. In Ref. [29], the operating cost of a hybrid bus with fuel cell was minimized using dynamic programming. Sequential quadratic programming (SQP) was adopted to optimize the hybrid fuel cell vehicle controller design in an inner loop while DIRECT and NOMADm algorithms were used for component selection in an outer loop [30]. On account of complexity and nonlinearity associated with component sizing and selection, heuristic optimization algorithms were used in Ref. [31]. In Ref. [32], a biomass based network was optimized with the use of genetic algorithm (GA). An independent renewable energy system with hydrogen storage was optimized by applying the GA in Ref. [33]. GA was also used to optimize an off-grid hybrid PV–Wind–Diesel system with different battery technologies in Ref. [34]. As an alternative, particle swarm optimization (PSO) method was applied to optimize the analogue renewable energy system [35], [36]. As mentioned in Ref. [29], the classic optimization method, SQP, has good performance solving non-linear programming problems while the comparison study between PSO and GA in Ref. [37] demonstrated that PSO is a slightly better choice. In addition, an improved PSO, such as adaptive PSO (APSO), is demonstrated to outperform other types of PSO in finding a better result for the objective function [45]. On account of the above reasons, in the present research, SQP was applied for equipment operations optimization while APSO was used to determine the optimal type and capacity of the electrolyzer, fuel cell and storage tank that is most beneficial to wind farm investors.

The power generated from a wind farm is typically exported to the electricity market. Since the electricity price fluctuates, there is a chance for the wind farm owner to get more benefits by optimizing their selling strategy. If the energy can be stored during a period with lower electricity prices and sold when the price increases, known as price arbitrage, greater profits can be obtained for the wind farm. This is particularly interesting because it can be the wind farm itself that depresses the prices in that area. The electrical equipment sizing and selection of PtH as well as the volume of hydrogen tank has a significant impact on the competitiveness of such combination of technologies. The equipment sizing and selection are interdependent, in other words, the operational strategy should be optimized according to different compositions of PtH. This co-optimization problem is specified later in this section.

The research objective is to examine and determine the potential of optimizing investment opportunities of offshore wind farms using a variety of hydrogen system configurations. The return on investment (ROI) which is defined in the following is used to evaluate the economic profitability of the PtH installation project and three scenarios are specified in this section as follows. The price look-ahead used in the optimization is a single day.

Configuration 1

Wind farm with PtH for electricity market arbitrage

The hydrogen system consists of a fuel cell and an electrolyzer connected to the wind farm. The system is only used to store electricity in the form of hydrogen and later used to generate electricity that can be sold in electricity market. The mathematical expressions of this problem are shown in the following equations.

Outer layer optimization: The equipment selection and sizing for the PtH system is made in this layer while each selection corresponds to an optimized operational strategy. The objective function of the outer layer is defined as the ROI in this work which is the NPV of cost divided by the yearly revenue. Using this evaluation method, the benefit of different investments can easily be determined.

Inner layer optimization: Based on the selection of equipment, which is completed in the outer layer, the optimized operation strategy is decided in the inner layer. Eq. (1) describes the amount of electricity that is required to generate x_t hydrogen from electrolysis, or the electricity that can be generated by the amount of x_t hydrogen in a fuel cell. Since the PtH can only be used to store hydrogen for a certain amount of time, the operational constraint for the first iteration should be defined separately as (3). The maximum hourly generation of hydrogen by the electrolyzer cannot exceed the size of the PtH plant as well as the available power generation from wind farm. This relation is expressed with the second equation of (4). On the other hand, the maximum allowance of hydrogen transformed into electricity is constrained by the fuel cell capacity which is constrained by the first term in first equation of (4). The accumulated hydrogen in the tank should be within the limit of the tank size which is expressed as (5), (6). The denominator of (7) represents the yearly earned profits while the numerator shows the net present value of overall cost. y₁ to y₄ represent the capacity of the electrolyzer plant, electrolyzer type, lower and upper limit of tank size as well as the range of capacity of fuel cell, respectively [38].

$$E_t^H\left(x_t\right)=\{\begin{array}{cc}\begin{array}{cc}{\mathit{\eta }}_{EL}{x}_t& x_t>0\\ P_{FC}{x}_t{\mathit{\eta }}_{FC}& x_t\le 0\end{array}& t=\left[\mathrm{1,2},\mathrm{...}T\right]\end{array}$$

Objective function for inner layer:

$$\max \left[I_r^n\left(x,y\right)\right]=\max \left\{\sum _{t=1}^{T}E{P}_t\left[E_t^W-E_t^H\left(x_t\right)\right]\right\}$$

$$\text{S}\text{.t}\text{.:}0\le x_1\le \frac{P_H}{{\mathit{\eta }}_{EL}}$$

$$\{\begin{array}{cc}\begin{array}{c}-\frac{P_{FC}}{{\mathit{\eta }}_{EL}}\frac{1}{{\mathit{\eta }}_{FC}}\le x_t\le 0\\ 0<x_t\le \min \left(\frac{P_H}{{\mathit{\eta }}_{EL}},\frac{P_{wind,t}}{{\mathit{\eta }}_{EL}}\right)\end{array}& t=\left[\mathrm{2,3...},T\right]\end{array}$$

$$\begin{array}{cc}0\le \sum _{t=1}^{N_t}{x}_t\le K_v& N_t=\left[\mathrm{2,3,4},\mathrm{...},T\right]\end{array}$$

$$\begin{array}{cc}\sum _{t=1}^T{x}_t=0& t=\left[\mathrm{1,2},\mathrm{...}T\right]\end{array}$$

Objective function for outer layer:

$$min\left(ROI\right)=min\left\{\frac{C_{FC}\left(y\right)+\frac{C_{FC}\left(y\right)}{{\left(1+r\right)}^{T_{FC}}}+C_{EL}+C_{Tk}+\sum _{n=1}^{T_{EL}}\frac{C_{OM}}{{\left(1+r\right)}^n}}{\max \left(I_r^n\left(x,y\right)\right)}\right\}$$

$$\text{S}\text{.t}\text{.}0.1\le y_1\le W_C$$

$$1\le y_2\le 3$$

$$T_L\le y_3\le T_U$$

$$0.1\le y_4\le W_{FC}$$

Configuration 2

Wind farm with PtH for generating hydrogen

In this configuration, the PtH does not sell electricity back to the grid, rather, it is used only to generate hydrogen which is sold for transportation fuel or as an industrial product and the flexible operation of the electrolyzer is used to support the wind farm. In this way the capital cost is reduced by removing the fuel cell [38]. The problem can be expressed in the following.

There are two layers in this problem. The operational optimization, defined as the inner layer, and the system sizing and the volume optimization, defined as the outer layer. In this configuration, while the electrolyzer can operate at different points, a constant amount of hydrogen is sold which relies on the storage system as a buffer. It is assumed that customers will require relatively constant supply of hydrogen. In the case of a fueling station, this could come from truck deliveries each day or for a refinery it would be a more constant pipeline delivery requirement. Eq. (12) indicates that the wind power can only be sold to the electricity market or generate hydrogen (i.e., no fuel cell). Eq. (13) shows that the profits of this system can be obtained by both selling hydrogen and electricity. The hydrogen production capability is limited by (14) which is the same as the second equation of (4). Eq. (15) means that the accumulated hydrogen in the tank should be within the limit of the tank size and (16) ensures that all the energy should be sold in the form of hydrogen at the end of each day. In this system, the objective is also in the outer layer which minimizes (17) while satisfying the constraints as the same of (8), (9), (10), (11).

$$E_t^H\left(x_t\right)=\begin{array}{cc}{\mathit{\eta }}_{EL}{x}_t& x_t>0\end{array},t=\left[\mathrm{1,2},\mathrm{...}T\right]$$

Objective function for inner layer:

$$\max \left[I_r^n\left(x,y\right)\right]=\max \left\{\sum _{t=1}^{T}E{P}_t\left[E_t^W-E_t^H\left(x_t\right)\right]+D_H{O}_e\frac{P_H}{{\mathit{\eta }}_{EL}}\left(T-1\right)S_H\right\}$$

$$\text{S}\text{.t}\text{.:}0<x_t\le \min \left(\frac{P_H}{{\mathit{\eta }}_{EL}}\frac{P_{wind,t}}{{\mathit{\eta }}_{EL}}\right),t=\left[\mathrm{1,2...},T\right]$$

$$0\le \sum _{t=1}^{N_t}{x}_t-O_e\frac{P_H}{{\mathit{\eta }}_{EL}}\left(t-1\right)\le K_v,N_t=\left[\mathrm{2,3,4..},T\right]$$

$$\sum _{t=1}^T{x}_t-O_e\frac{P_H}{{\mathit{\eta }}_{EL}}\left(T-1\right)=0$$

Objective function for outer layer:

$$min\left(ROI\right)=min\left\{\frac{C_{EL}+C_{Tk}+\sum _{n=1}^{T_{EL}}\frac{C_{OM}}{{\left(1+r\right)}^n}}{\max \left(I_r^n\left(x,y\right)\right)}\right\}$$

The consumers of hydrogen (e.g., refineries, fueling stations) will require a constant supply of hydrogen and cannot afford to turn off or not supply their customers so for the purposes of this analysis, the system operator of the wind farm will sometimes have to acquire electricity from the electricity market when the wind farm is not producing. Hence, whenever the PtH system must purchase electricity from the grid the objective function for the inner layout is modified as follows:

Objective function for inner layer:

$$\max \left[I_r^n\left(m,y\right)\right]=\max \left\{D_H{O}_e\frac{P_H}{{\mathit{\eta }}_{EL}}\left(T-1\right)S_H-\sum _{t=1}^{T}E{P}_t{P}_t\right\}$$

$$\begin{array}{cc}\text{S}\text{.t}\text{.:}0<P_t& t=\left[\mathrm{1,2...},T\right]\end{array}$$

$$\begin{array}{cc}0\le \sum _{t=1}^{N_t}\frac{P_t}{{\mathit{\eta }}_{EL}}+\sum _{t=1}^{N_t}\frac{P_{wind,t}}{{\mathit{\eta }}_{EL}}-O_e{N}_t\frac{P_H}{{\mathit{\eta }}_{EL}}\le K_v& N_t=\left[\mathrm{1,2,3},\mathrm{...},T\right]\end{array}$$

$$\sum _{t=1}^T\left(P_t+P_{wind,t}\right)-O_e{P}_H\left(T-1\right)=0$$

In (18), the last term represents the money spent on purchased energy at each hour so that the demand from (21) can be set. This mechanism will not be triggered if the wind farm can provide a sufficient amount of energy.