1 Introduction

Global demand for energy has been steadily increasing over the last decades, imposing a substantial dependence on fossil fuels. Electrification of the mobility or industrial sector will further reinforce this trend, leading to increased energy consumption [1]. This results in a myriad of the world’s ecological problems from greenhouse gas emissions to the depletion of energy sources and global warming. As policymakers enabled legislation to counteract this development like the European Union’s (EU) 20-20-20 policy or the Paris Agreement, there has been a tremendous change in the global energy sector by moving toward a more sustainable and renewable power sector. Alongside this target setting from policymakers, this development has been accompanied by deregulation of energy markets like emissions trading schemes or power pooling [2, 3].

One possible way of addressing these issues is via microgrids and distributed energy resources (DER) that offer several advantages over the classic electrical grid [4,5,6], viz., higher overall energy efficiency and more customized power quality and reliability (PQR). In particular, the literature [7] defines a microgrid as “a cluster of electricity sources and (possibly controllable) loads in one or more locations that are connected to the traditional wider power system, or macrogrid, but which may, as circumstances or economics dictate, disconnect from it and operate as an island, at least for short periods.” The same source identifies a key feature of a microgrid as being local control, i.e., it can operate in island mode and tailor PQR to end uses. However, as building operators at the regional or local level face limited budgets and a broad array of uncertainties, the decision of how and where to invest remains complex [8]. Quantitative simulation-based methods offer a way of assessing such investment decisions. Using this approach, a building operator can simulate total annual energy cost at various levels of installed DER capacity considering uncertain energy prices and other input parameters and constraints. This is especially useful for industries in which energy consumption is high, energy security crucial, and legislative standards ask for emission reductions. The semiconductor industry fits all three descriptions, yet there have not been any academic studies on the impact of DER via a microgrid on a semiconductor fabrication plant so far, which allows this paper to address a gap in the literature.

The frontend manufacturing sites of semiconductor companies consume most of the energy since the physical conditions for production are particularly demanding. The average energy consumption per unit product (wafer) area is 1.432 kWh/cm2 for Taiwanese plants and 1.41 kWh/cm2 for U.S. plants in 2000. Although energy consumption for newer fabrication plants is likely to be lower, a major reason for the high energy usage is the conditions necessary for functioning cleanrooms that are heavily used in the semiconductor industry, especially quality-grade cleanrooms that can consume 30–50 times more energy than an average commercial building of the same size and have been increasing in energy consumption annually [9]. Most other industrial manufacturing processes do not need such a level of environmental control and cleanliness. For example, a high amount of energy is needed to establish the highly stable climatic conditions in the cleanrooms. More precisely, on average, around 57% of a plant’s energy consumption comes from the facility system, which guarantees the stable conditions in the cleanrooms needed for wafer processing [10]. Taking this into consideration, it becomes clear why cleanrooms consume a high amount of energy and resources overall, also compared to other industrial manufacturing facilities [11].

The problem this paper addresses is that there have not been any academic studies so far that investigate the introduction of DER at a semiconductor fabrication site to reduce cost and mitigate risk in a microgrid although energy expenditures are very high for semiconductor companies. The objective of this paper is to investigate how much expected cost can be saved and risk mitigated at a semiconductor fabrication plant via DER.

This remainder of this paper is structured as follows. Section II provides a model of the stochastic dynamic program (SDP), viz., the objective function and constraints as well as key assumptions like models for technologies and the energy flows will be presented. Section III explains the stochastic processes to model the energy prices. Section IV summarizes the results and discusses their meaning for expected total cost and emission minimization. Section V concludes the paper. Appendices A and B contain the nomenclature and solution approach, respectively.

2 Methodology

2.1 Application of stochastic dynamic programming

Simulation-based approaches and stochastic programming are some of the most utilized methods in energy-system optimization and investment as they allow for a straightforward way to analyze decisions under uncertainty [3, 5, 12]. In the context of this paper, a simulation-based approach, i.e., SDP, will be chosen to analyze and compare scenarios that differ in relation to various key parameters. Several simulations will be run where the capacity of installed DER will be fixed at various levels where the sample paths of prices and loads will be the same across the problem instances. These are then simulated for different realizations of the uncertain parameters, and the final operational decisions will be made by means of decision analysis. With an understanding of the cause-and-effect dynamics of a system, SDP can process dynamic and also non-linear outcomes related to the underlying uncertainty of the stochastic variables. Although SDP does not handle risk ex ante as rigorously as say mixed-integer linear programming (MILP) based on stochastic programming, it allows ex-post assessment of the level of risk via varying the level of DER investment. As the minimization of the objective function belongs to the class of sequential scheduling problems, SDP is a suitable solution framework [12]. The flexibility and adaptability of SDP in the context of microgrid simulation has been demonstrated by a multitude of different studies. It can also be adjusted to different forms of objective functions (cost, energy consumption, emission reduction, etc.), along with adoption of different DER types and constraints [13,14,15]. Additionally, this form also allows us to integrate financial risk measures like the conditional value-at-risk (CVaR) [16].

Nevertheless, possible limitations for applications of a simulation-based SDP approach to microgrid modeling should also be addressed. From a methodological point of view, issues can occur when simulation is applied to American-style options. When DER units have start-up costs or ramping constraints, the future distribution of cash flows given the current state is not going to be independent of the past. Longstaff and Schwartz have developed a least-squares Monte Carlo simulation approach to solve this issue [17]. Additionally, computational effort, increasing dimensionality, and the need for deep causal understanding mean that most applications will be strongly simplified to fit in the model, which can leave out important attributes that should be considered. In the context of this paper, simplifications could leave out the lifetime of a DER generator or the maximum fraction of electricity demand to be met by demand response.

2.2 Mathematical formulation

As the research question aims to answer how much expected cost can be saved and risk mitigated via the integration of DER at a semiconductor plant, the objective is to minimize the expected discounted cost of the energy used over a test year. To achieve this, the DER equipment has to be fixed first. There are several ways to approach this objective, e.g., [18] used a deterministic approach by solving a mixed-integer linear program that includes amortized capital costs, whereas [19] applied a real options approach to value the investment in DER. [20] used a MILP model to design a microgrid model that also allows for the integration of energy subsidies. This paper follows [13] by fixing the capacity of DER at several levels and running a simulation to minimize the expected discounted cost of meeting the energy demand. A key difference between [13] and the current work is that the former is based on California data, viz., prices are from 2006–2007 and demand data are from a nursing home with quite a different correlation coefficient between electricity and heating loads (−0.91). By contrast, the current work applies the model in a completely different context and with more recent prices. As future energy prices are stochastic, an SDP approach has to be used with simulated prices. [21], for example, used Monte Carlo simulation to simulate future volatile energy prices. [22] used a non-linear Markov regime-switching model to forecast energy prices, which may be superior when it comes to long-term forecasting. [23] argue that mean-reverting price processes are a better tool for forecasting commodities, at least oil prices. Here, the approach is to solve the optimal DER scheduling problem under uncertainty for various levels of installed capacity. It is also assumed that the microgrid is under a real-time pricing tariff, which means that the per-MWh charge varies daily based on the utility’s real-time production costs.

The objective function of the SDP is the weighted average of the annualized costs and CO2 emissions based on the parameter \(0\leq \alpha \leq 1\). Since the SDP includes both stochastic electricity and natural gas prices, the minimized value function, Vt(Ψt), consisting of the weighted expected discounted operating cost as well as CO2 emissions, starts at the beginning of day t given current electricity and natural gas prices. \(\Psi _{t}\equiv \left\{EP_{t}{,}FP_{t}\right\}\) is the set of the stochastic state variables (electricity price and natural gas price) at time t. The DER technologies’ capacities are taken as fixed and dispatched optimally. The cost of the amortized DER investment is taken as given and added to the minimized operating cost at \(t=1\). For sake of simplicity, Costt(Ξt; Ψt) is the period‑t weighted operating cost and Emissionst(Ξt; Ψt) the corresponding CO2 emissions.

$$\Xi _{t}\equiv \left\{\begin{array}{c} \mathrm{Gen}_{i{,}t}{,}\text{DGHeat}_{t}{,}\text{NGHeat}_{t}{,}\text{EPurchase}_{t}{,}\\ \text{EDResponse}_{t}{,}\text{HDResponse}_{t} \end{array}\right\}$$

is the set of all decision variables at time t. A nomenclature of the symbols used with the units of measurement can be found in Appendix A.

Therefore, the SDP (1)-(10) is based on [13] and has to be solved from any day t specified as follows:

$$V_{t}\left(\Psi _{t}\right)=\min _{\Xi _{t}}\frac{\alpha }{\textit{DNCost}}\mathrm{Cost}_{t}\left(\Xi _{t};\Psi _{t}\right)+\frac{\left(1-\alpha \right)e^{\mathrm{r}\Updelta \mathrm{t}}}{\textit{DNEmissions}}E\text{missions}_{t}\left(\Xi _{t};\Psi _{t}\right)+e^{-\mathrm{r}\Updelta \mathrm{t}}E_{{\Psi _{t}}}\left[V_{t+1}\left(\Psi _{t+1}\right)\right]$$
(1)

where

$$\mathrm{Cost}_{t}\left(\Xi _{t};\Psi _{t}\right)\equiv {\sum }_{i=1}^{I}\mathrm{Gen}_{i{,}t}\text{OMVar}_{i}+{\sum }_{i=1}^{I}\mathrm{Gen}_{i{,}t}\frac{\left(FP_{t}+\text{FTDCharge}_{t}\right)}{\mathrm{EEff}_{i}}+\text{EPurchase}_{t}\left(EP_{t}+\text{ETDCharge}_{t}\right)+\text{NGHeat}_{t}\frac{\left(FP_{t}+\text{FTDCharge}_{t}\right)}{HEff}+\textit{EDRCost}\,\text{EDResponse}_{t}+\textit{HDRCost}\,\text{HDResponse}_{t}$$
(2)

and

$$\text{Emissions}_{t}\left(\Xi _{t};\Psi _{t}\right)\equiv {\sum }_{i=1}^{I}\mathrm{Gen}_{i{,}t}\frac{\textit{NGCRate}}{\mathrm{EEff}_{i}}+\text{NGHeat}_{t}\frac{\textit{NGCRate}}{HEff}+\text{EPurchase}_{t}\textit{UCRate}$$
(3)

Note that the day-t cost in (2) consists of variable DER operating and maintenance (O&M) cost, DER fuel cost, the cost of electricity purchased from the utility, the cost of natural gas purchased from the utility to meet heat loads, and costs associated with demand response. In a similar vein, (3) comprises day-t CO2 emissions from DER operations, natural gas used to meet heat loads, and electricity purchased from the utility.

The objective function in (1) is subject to the following constraints and terminal conditions:

$$V_{T}\left(\Psi _{T}\right)=\min _{\Xi _{T}}\frac{\alpha }{\textit{DNCost}}\mathrm{Cost}_{T}\left(\Xi _{t};\Psi _{t}\right)+\frac{\left(1-\alpha \right)e^{\mathrm{r}\Updelta \mathrm{t}}}{\textit{DNEmissions}}\text{Emissions}_{T}\left(\Xi _{T};\Psi _{t}\right)$$
(4)

(4) states the minimized terminal value function.

$$\mathrm{Gen}_{i{,}t}\leq \text{DGInv}_{i}\mathrm{MaxP}_{i}\overline{h}\forall i{,}t$$
(5)

(5) states that the operating level of DER generation i during day t is less than or equal to the installed available capacity of generator i every day.

$$\text{EDResponse}_{t}+{\sum }_{i=1}^{I}Gen_{i{,}t}+\text{EPurchase}_{t}=\text{EDemand}_{t}\forall t$$
(6)

(6) states that electricity demand response during day t in addition to the operating level of DER generators during day t in addition to the electricity purchased from the central utility during day t must equal the overall demand for electricity during day t to balance the electricity system.

$$\text{DGHeat}_{t}\leq {\sum }_{i=1}^{I}HR_{i}\mathrm{Gen}_{i{,}t}\forall t$$
(7)

(7) states that the heat load met from DER generation during day t must be less than or equal to the amount of useful heat produced by DER generators during day t. Selling excessive heat to cities or the macrogrid is a possible, useful feature of a microgrid, and our model can be easily modified to incorporate such decisions.

$$\text{HDResponse}_{t}+\text{DGHeat}_{t}+\text{NGHeat}_{t}=\text{HDemand}_{t}\forall t$$
(8)

(8) states that the heat demand response during day t in addition to the heat load met from DER generation during day t in addition to the heat load met from natural gas purchases during day t must be equal to the heat demand during day t to balance the heat system.

$$\text{EDResponse}_{t}\leq \textit{MaxEDR}\,\text{EDemand}_{t}\forall t$$
(9)

(9) states that the electricity demand response during day t must be less than or equal to the maximum electricity demand to be met by demand response during any day.

$$\text{HDResponse}_{t}\leq \textit{MaxHDR}\,\text{HDemand}_{t}\forall t$$
(10)

(10) states that the heat demand response during the day t must be less than or equal to the maximum heat demand to be met by demand response during any day.

2.3 Selection and simulation of stochastic processes

The choice of stochastic price processes depends on the underlying modeling case they are applied to. In this paper, where CHP plays an important role as its employment directly influences the objective function, it is important to capture daily uncertainties as CHP technologies are able to respond to such uncertainties. One way to do this is by assuming that the logarithms of the deseasonalized electricity and natural gas prices, Xt and Yt, follow correlated mean-reverting Ornstein-Uhlenbeck (OU) processes, i.e.,

$$dX_{t}=\kappa _{X}\left(\theta _{X}-X_{t}\right)dt+\sigma _{X}dS_{t}$$
(11)
$$dY_{t}=\kappa _{Y}\left(\theta _{Y}-Y_{t}\right)dt+\rho \sigma _{Y}dS_{t}+\sqrt{1-\rho ^{2}}\sigma _{Y}dW_{t}$$
(12)

For processes above, k can refer to X or Y, θk is the long-term average of the electricity/natural gas prices, κk is the rate of mean reversion, σk is the annualized price volatility, and \(\rho =\rho _{xy}\frac{1}{2}\frac{\left(\kappa _{x}+\kappa _{y}\right)}{\sqrt{\kappa _{x}\kappa _{y}}}\), where ρxy is the instantaneous correlation coefficient between \(\left\{S_{t}{,}t\geq 0\right\}\) and \(\left\{W_{t}{,}t\geq 0\right\}\), which are independent standard Brownian motion processes. Therefore, the natural logarithms of the electricity and natural gas prices are:

$$\ln EP_{t}=X_{t}+{f}_{t}^{X}$$
(13)
$$\ln FP_{t}=Y_{t}+{f}_{t}^{Y}$$
(14)

\({f}_{t}^{k}={\sum }_{l=1}^{[s/2]}({\gamma }_{1l}^{k}\cos \lambda _{l}t+{\gamma }_{1l}^{*k}\sin \lambda _{l}t)+{\sum }_{l=1}^{[s'/2]}({\gamma }_{2l}^{k}\cos {\lambda }_{l}^{'}t+{\gamma }_{2l}^{*k}\sin {\lambda }_{l}^{'}t)\) is the seasonality function that detects weekly and annual trends for k = X, Y, t = 1, …, T, s = 7, s’ = 365, and

$$\left[a/2\right]=\begin{cases} \ \frac{a}{2}\quad \text{if } a \text{ is even}\\ \frac{a-1}{2}\quad \text{otherwise} \end{cases}$$
(15)

Following the procedure in [24], the parameters in the OU processes and the seasonality function are estimated.

The OU processes stated above can be simulated using two independent standard normal random variables εX and εY, distributed with a standard deviation of one each, \(\varepsilon _{X}\)~ N(0.1) and εY  ~ N(0.1).

$$X_{t+1}=X_{t}k_{x}\left(\theta _{x}-X_{t}\right)\Delta t+\sigma _{X}\varepsilon _{X}\sqrt{\Delta t}$$
(16)
$$Y_{t+1}=Y_{t}+\kappa _{Y}\left(\theta _{Y}-Y_{t}\right)\Delta t+\sigma _{Y}\varepsilon _{Y}\sqrt{\Delta t}+\sqrt{1-\rho ^{2}}\sigma _{Y}\varepsilon _{Y}\sqrt{\Delta t}$$
(17)

3 Experimental simulation

Decisions are made daily over a simulated year, i.e., \(T=365\) and \(\Delta T=1/365\). Additionally, the discount rate is r = 0.08. The electricity and gas prices used in this paper to estimate the seasonality and the mean-reverting process are prices paid by large manufacturing companies from 2018 to 2019. Due to confidentiality reasons, single-company electricity prices cannot be shown. This is because there is a small number of manufacturers each with several production sites in Europe, and release of data could divulge proprietary information to competitors or customers. Figs. 1 and 2 show the daily electricity and gas prices. After deseasonalizing the price data for the years 2018 to 2019 via a set of cosine and sine terms in (13) and (14), the deterministic natural logarithms of the prices without seasonality are shown in Figs. 3 and 4. Furthermore, \(X_{1}\equiv \mathrm{lnEP}_{1}-{f}_{1}^{X}=3.81\), \(Y_{1}\equiv \mathrm{lnFP}_{1}-{f}_{1}^{Y}=2.36\) (assuming natural gas prices are in €/MMBTU), and \(\rho =0.29\).

Fig. 1
figure 1

Average electricity prices from 2018 to 2019 paid by large manufacturing companies in Europe

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Fig. 2
figure 2

Average natural gas prices from 2018 to 2019 paid by large manufacturing companies in Europe

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Fig. 3
figure 3

Natural logarithms of electricity prices with and without seasonality

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Fig. 4
figure 4

Natural logarithms of natural gas prices with and without seasonality

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To estimate the unknown parameters of the stochastic model, a multivariate normal linear regression model using maximum likelihood estimation was used. The logarithms of the deseasonalized electricity and natural gas prices as well as the stochastic part are now possible to simulate. Simulated sample paths for the electricity and natural gas prices are shown in Figs. 5 and 6, whereas Table 1 shows the parameter estimates for the OU processes. For this annual study, the prices were simulated for the year 2021 with daily resolution.

Fig. 5
figure 5

Actual and simulated prices for electricity

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Fig. 6
figure 6

Actual and simulated prices for natural gas

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Table 1 Parameter estimates for OU processes (assuming natural gas prices are in €/MMBTU)
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The load data for energy and natural gas are taken from a number of different large manufacturing fabrication plants. Due to confidentiality reasons, single-company load data cannot be shown. Mean daily demands are 756 MWhe and 163 MWh for electricity and heat, respectively, while the standard deviations are 40 MWhe for electricity and 57 MWh for heat. Furthermore, the correlation coefficient between the two is −0.63 as heat demand normally peaks during winter months when the cooling demand is usually lowest. A strong negative correlation between electricity and heating demand can, thus, limit the potential for CHP applications.

It is presumed that only DER technology with notional units of 0.10 MWe distributed generation (DG) engines with CHP capability are available that can operate without downtime throughout the whole year. The cost and performance parameters of the DER equipment are: \(HR=1.74\), \(EEff=0.38\), \(\textit{OMFix}=0\), \(\textit{OMVar}=16\), \(HEff=0.8\), \(\textit{NGCRate}=0.1836\), and \(\textit{UCRate}=0.55\). The latter is based on the average emission rate of the macrogrid generation mix. The T&D adders are \(\text{ETDCharge}_{t}=80\) and \(\text{FTDCharge}_{t}=16\). The associated parameters for demand response are: \(\textit{EDRCost}=50\), \(\textit{HDRCost}=25\), \(\textit{MaxEDR}=0.10\), and\(\textit{MaxHDR}=0.20.\) Performance and demand-response parameters of DER equipment above were taken from exemplary cogeneration units already installed at frontend semiconductor fabrication sites and the academic literature as [13]. The installed unit is approximately three years old but was upgraded and is still comparable to newer units.

4 Results

In this section, the application of the mathematical formulation is investigated in order to answer the research question, which aims to investigate the cost savings and risk-mitigation effects of the integration of DER into a semiconductor microgrid. Additionally, a sensitivity analysis is conducted by varying the DER capacity while holding all other parameters constant. Additionally, a second sensitivity analysis will be done by varying the volatility of energy prices. Furthermore, the analysis is used to broaden the understanding of the relationship between input parameters and output variables.

In the following, one price scenario with stochastic prices is assumed and three cases are modeled: do nothing (DN) (which states the base case), DER without DR (ND), and DER with DR (DER). For the two cases where DER equipment is installed, three capacity levels are considered: 0.10 MWe, 0.25 MWe, and 0.50 MWe. The annualized capital cost of DG equipment is between €200,000 and €300,000 per MWe according to the span mentioned in the scientific literature, which is added to any operational costs to determine the total annual energy bill. Every stochastic scenario uses N = 1000 sample paths.

4.1 Cost minimization with DER and its effect on total cost and emissions

The model is run using the solution approach in Appendix B with the stochastic variables as stated in the price simulation. Although the mathematical formulation also allows for emission minimization aside from cost minimization by varying the level of α, only cost minimization was chosen, i.e., setting \(\alpha =1\). In Fig. 7, the results are indicated for the cost and emission metrics according to several DER installation sizes and their influence on total expected cost and CO2 emissions similar to [13]. In the DN case, the expected annual energy cost is €1017 million with 4477 tonnes of CO2 emissions. By comparison, all ND and DER cases dominate from an environmental perspective. Meanwhile, 0.1 MWe and 0.25 MWe with DR also dominate from an economic perspective. With 0.1 MWe and DR, it is possible to reduce the total annual energy cost by 6%, whereas the 0.25 MWe and DR leads to a reduction of 3%. All DER cases, with and without DR, lead to operating-cost savings, ranging from 1% in the case of 0.1 MWe without DR to 11% in the case of 0.5 MWe with DR.

Fig. 7
figure 7

Efficient frontier between cost and CO2 emissions

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From an environmental perspective, the 0.5 MWe unit with DR provides the highest reduction in CO2 emissions, namely 22% (without DR 11%). The 0.1 MWe, which provides the highest cost savings, also provides a significant reduction in CO2 emissions, more precisely, 15% with DR and 3% without DR. To sum it up, larger units result in higher CO2 emissions savings compared to the DN case. This effect gets reinforced when DR is allowed, even leading to significant reductions in CO2 emissions for the small units. When looking at the annual energy bill, DR becomes essential to enable cost reductions.

To test for sensitivity, the same simulation was run with double the instantaneous volatility of the natural logarithm of the deseasonalized electricity price process, σx. Therefore, higher electricity prices are more likely to occur, which lead to overall higher expected minimized costs. The increase in total annual cost is relatively highest for the DN case with 4.1% and becomes increasingly smaller the larger the installed DER capacity with DR is, e.g., 3.3% for 100 kWe, 2.7% for 250 kWe, and 2.2% for 500 kWe (see Fig. 8). The pattern is similar for DER with no DR, being below the DN case but above the DR case relatively. Also, the average system energy efficiency (defined as energy requirement over energy consumption) is increasing with DER unit size, from 49% in the 0.1 MWe case to 53% in the 0.5 MWe case. Additionally, the share of on-site generated energy increases from 9.8% in the 0.1 MWe case to 24.5% in the 0.5 MWe case with DR. Furthermore, the level of on-site heat production increases from 17.2% in the 0.1 MWe case to 63.9% in the 0.5 MWe case. A similar pattern for energy efficiency and on-site generation can be observed for the non-high-volatility scenario.

Fig. 8
figure 8

Efficient frontier between cost and CO2 emissions with high volatility

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Operating-cost savings in the high-volatility scenario range from 1% in the 0.1 MWe ND case to 12% in the 0.5 MWe DR case and outperform their counterparts in the non-high-volatility scenario. Besides this, the pattern observed in the base case does not change much, since CO2 emissions increase only very slightly for all cases with DER, increasing with installed capacity. This is due to the fact that with higher capacity, the microgrid is able to produce more electricity with its on-site generation on the basis of higher electricity prices without a rise in heat capture. As on-site generation is more carbon intensive than via the macrogrid, CO2 emissions, therefore, increase.

4.2 Risk-management aspect of DER

We next examine the risk implications of DER adoption under uncertainty by comparing the expected minimized cost with the 95%-level CVaR, i.e., the expected cost given that the cost falls within the upper 5% of all possible outcomes. Fig. 9 indicates the relationship between the expected minimized cost and the CVaR. While the DG units in the ND case are limited in managing risk, both the small and medium units mitigate high costs if DR is allowed. More precisely, the CVaRs of the 0.1 MWe and the 0.25 MWe DER units are smaller than the CVaR of the DN case (€0.954 million and €0.986 million vs. €1021 million, respectively). Interestingly, the CVaRs of the small and medium DG units are less than the expected cost in the DN case.

Fig. 9
figure 9

Tradeoff between cost and risk

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Also, the risk-management aspects of DER were tested with higher volatility (see Fig. 10). Again, the pattern overall is not affected significantly, but the CVaR is noticeably higher. The CVaRs of the small and medium DG units are again lower than the expected cost in the DN case, thereby mirroring the outcome from the low-volatility scenario. Although the large DER unit’s CVaR increases the least compared to its annualized cost, it is still higher than those for the other installations and the DN case. The CVaR increases most for the DN case, namely 4.3% and least for the 0.5 MWe case with DR with 2.4%. This is the case because higher electricity prices occur more frequently. Again, larger DER units are less affected relatively as they have more spare capacity to react in periods of higher electricity prices and, therefore, compare better under higher volatility. This is especially true when DR is enabled. Without DR, the CVaR increase for DER units is still lower than the DN case but relatively higher than with DR, e.g., 3.8% for 0.1 MWe without DR, 3.2% for 0.25 MWe without DR, and 2.7% for 0.5 MWe without DR. The availability of DER, therefore, provides a way to control cost and risk stemming from higher volatility prices and is most effective when DR is allowed.

Fig. 10
figure 10

Tradeoff between cost and risk with high volatility

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5 Discussion

As stated by [13], microgrids that contain DER with CHP applications can provide a more sustainable pathway to capacity expansion. On the basis of the utilization of waste heat from on-site generation, heat loads can potentially be offset, thereby reducing the need for natural gas purchases. This becomes especially interesting in the face of changing energy markets and a move toward renewable energy. To put it in a nutshell, answering the research question “How much expected cost can be saved and risk mitigated at a semiconductor fabrication plant via DER adoption?” the results of this paper show that the integration of DER into semiconductor microgrids can result in lower costs, lower CO2 emissions, and lower risk relative to the installed capacity and the DN case. More precisely, the numerical example shows that 100 kWe and 250 kWe DG DER units with DR reduce the expected total cost for a semiconductor fabrication plant, namely 6% and 3% in their respective cases under normal volatility. A similar pattern can be observed for the high-volatility scenario. Hereby, DR is essential, facilitating the true potential of DER.

From a CVaR perspective, DER with DR helps to respond to higher price volatility, showing potential risk-management capabilities with a percentagewise smaller increase in CVaR compared to the expected cost for DER installations with DR in comparison with the DN case. The CVaR of the small and medium units even outperforms the total expected cost of the DN case, therefore proving their risk-management capabilities. Similar to the studies cited in Section II, the integration of DER offers an effective way to reduce CO2 emissions, especially when CHP is involved. When looking at CO2 emissions, all DER installations outperform the DN case, thereby resulting in savings of up to 22% for the largest unit with DR, whereas even the smallest unit with DR allowed still saves up to 16%.

In terms of possible expected cost reductions, the results of this paper are also similar to the findings in the academic literature. Possible cost reductions rely heavily on a myriad of factors, e.g., characteristics of the microgrid in form of DG size, the energy load of the microgrids and the structure of electricity and gas prices. In this case, relatively higher investment costs and less volatile electricity prices lead to an advantage for the small- and medium-sized DER unit compared to the DN case. These findings are similar to [5] and [20] in that most environmentally friendly technologies like CHP can be considerably more expensive than central energy generation. One possible solution to solve this problem would be the introduction of performance-related energy subsidies that account for monetized emission reductions, i.e., a maximum CO2 reduction would then also lead to a maximum cost reduction. In summary, the influencing factors reflect different aspects of technology, business, and policy that can—depending on their configuration—result in varying degrees of expected cost savings and overall efficiency. Although the answer to the research question was that DER can lead to future minimized cost, this might not hold true for all semiconductor fabrication microgrids, depending on their configuration and the market environment. Yet, even in this paper without subsidies, the right installations of DG can lead to expected cost savings and emission reductions, making it an option worth considering for a semiconductor company to respond to increasing energy demand and tighter emission regulations.

Microgrids with DER become increasingly attractive for a semiconductor production planner due to an environment where electricity costs are high and where DER technologies improve rapidly [5]. As semiconductor companies are large multinationals with production sites worldwide, they can adapt their strategy to the local requirements (e.g., local subsidies, weather, etc.) and, therefore, optimize their microgrid deployment. Semiconductor companies strategically plan future microgrid deployment at their production sites in regions like South-East Asia with mainly PV, wind, and hydropower installations. Additionally, they plan to set up their DG resources in a way to ideally cope with the specifics of semiconductor fabrication plants, e.g., high and stable energy usage as the equipment operates continuously during the whole day and the whole week and less volatile energy prices as said companies are able to negotiate electricity prices in many cases. To sum it up, research on microgrids has shown that they have the potential to save expected costs and to reduce CO2 emissions. To be exact, this paper has quantified the total expected cost and CO2 emission savings as well as the risk-management potential under the given set of variables. Yet, this depends on the economic, technical, geographical, and political configuration of the market as well as the grid and the environment that the microgrid that will be located in [20]. This also holds true for microgrids at semiconductor plants as this paper shows.

Looking ahead, due to pressure by regulators, the future of microgrids at semiconductor companies will be based on renewable, zero-emission energy resources. This comes with certain challenges like the volatility of energy production of many renewable energy resources. As such installations have very different properties to the gas-fired turbines, this opens up a new possibility for research by introducing and studying other DER. Another interesting approach would be the study of a more complex model that also includes variables that are of major importance for operators, e.g., subsidies, carbon taxes, and start-up costs for DER. Not only does this make the respective model much more complex, but also it requires the formulation of an entirely different model, e.g., due to the difficulty for simulations to handle American-style options or the wish to obtain an optimal solution via an MILP.