Toward net-zero carbon manufacturing operations: an onsite renewables solution

Abstract

A growing number of manufacturing firms are striving to achieve eco-friendly operations through onsite wind or solar generation. This paper proposes a zero-carbon power supply model to guide the integration of onsite renewable energy into manufacturing facilities. We intend to address two fundamental questions: (1) Is it cost-effective to deploy onsite wind turbines and solar photovoltaics (PVs) systems to achieve net-zero carbon environmental performance? (2) Is the renewable generation system able to meet the electricity demand despite the power intermittency? To answer these questions, we formulate a stochastic optimization model to minimize the levelized cost of onsite renewable energy. The goal is achieved by optimizing the sizing of wind and solar generating units. The proposed energy solution is tested in ten cities around the world under diverse climatic conditions. While PV is still expensive, we conclude that manufacturers could realize zero-carbon emissions at affordable cost provided the local wind speed is above 5 m/s.

Appendices

Appendix A

Modeling wind power generation

Let V be the random wind speed at time t, and v be its realization. The instantaneous output power of a WT, denoted as P _w(v), can be modeled by the following cubic function (Jangamshetti and Rau, 2001)

$$P_{\text{w}} (v) = \left\{ {\begin{array}{ll} 0 & {0 < v < v_{\text{c}} ,\;{\text{or}}\;v > v_{\text{s}}}, \\ {P_{m} \left( {\frac{v}{{v_{\text{r}} }}} \right)^{3} } & {v_{\text{c}} \le v < v_{\text{r}} }, \\ {P_{m} } & {v_{\text{r}} \le v \le v_{\text{s}} }, \\ \end{array} } \right.$$

(A.1)

where P _m is the WT capacity. Note that v _c is the cut-in speed, v _r is the rated speed, and v _s is the cut-off speed. It has been shown that wind speed in a particular area can be fit by either Weibull or normal distributions (Justus et al, 1978; Karki et al, 2006). The two-parameter Weibull distribution function is given as

$$F_{\text{w}} (v) = 1 - \exp \left( { - \left( {\frac{v}{{c_{\text{w}} }}} \right)^{{d_{\text{w}} }} } \right),$$

(A.2)

where c _w and d _w are the scale and the shape parameters, respectively. Equation (A.2) allows us to simulate the hourly wind speed. The relations between c _w and d _w and the mean and the variance of wind speed are governed by the following equations (Justus et al, 1978),

$$\mu_{\text{w}} = c_{\text{w}} \varGamma \left( {1 + \frac{1}{{d_{\text{w}} }}} \right),$$

(A.3)

$$\sigma_{\text{w}}^{2} = c_{\text{w}}^{2} \varGamma \left( {1 + \frac{2}{{d_{\text{w}} }}} \right) - \mu_{\text{w}}^{2} ,$$

(A.4)

where Γ(·) is the gamma function, and μ _w and $\sigma_{\text{w}}^{2}$ are the mean and the variance of wind speed. Once the yearly wind speed data are obtained, both μ _w and $\sigma_{\text{w}}^{2}$ can be estimated. Through Equations (A.3) and (A.4), the values of c _w and d _w are also known.

Appendix B

Modeling solar PV generation

Below we review the clear-sky PV generation model. Factors that have a major influence on the PV generation is summarized in Table A1. Note that the unit of the angles is rad.

Table A1 Key parameters in solar PV energy production

We present a three-step procedure to calculate the hourly PV generation based on the studies in Cai et al (2010) and Taboada et al (2012). These steps are summarized as follows.

• Step 1: Compute the sunrise and sunset time for day d ∈ {1, 2,…,365}

  $$\cos \left( { - \omega_{\text{rise}} } \right) = \cos \left( {\omega_{\text{set}} } \right) = \tan (\phi - \beta )\tan \delta ,$$

  (B.1)

  with

  $$\delta = 0.40928\sin \left( {\frac{2\pi (d + 284)}{365}} \right),$$

  (B.2)

  where δ is the solar declination angle, ω _rise and ω _set are the sunrise and the sunset angles in day d perceived from the PV panel. There is no PV output when ω < ω _rise or ω > ω _set, i.e., before sunrise or after subset.

• Step 2: Calculate the total amount of solar irradiance incident on the PV surface in a particular hour of a day

  $$I_{t} = 1370\left( {0.7^{{(\cos \varphi )^{ - 0.678} }} } \right)\left( {1 + 0.034\cos \left( {\frac{2\pi (d - 4)}{365}} \right)} \right) \times \left( {\cos \theta + 0.1\left( {1 - \frac{\beta }{\pi }} \right)} \right).$$

  (B.3)

  With

  $$\cos \varphi = \cos \delta \cos \phi \cos \omega + \sin \delta \sin \phi ,$$

  (B.4)
  $$\begin{aligned} \cos \theta & = \sin \delta \sin \phi \cos \beta - \sin \delta \cos \phi \sin \beta \cos \alpha + \cos \delta \cos \phi \cos \beta \cos \omega \\ & \quad + \cos \delta \sin \phi \sin \beta \cos \alpha \cos \omega + \cos \delta \sin \alpha \sin \omega \sin \beta , \\ \end{aligned}$$

  (B.5)

  where, I _t is the solar irradiance (W/m²) received by the PV at time t on day d. Here φ is the solar zenith angle which is given by Equation (B.4), and ω is the solar hour angle determined by the local hour t. For instance ω = −π/2 at 6 AM in the morning, and it increases 15° every hour until reaching ω = π/2 at 6 PM in the evening.

• Step 3: By incorporating the weather uncertainty, the actual output power of a PV system in hour t on day d, denoted as P _t in watts (W), can be estimated as

  $$P{}_{t} = W_{t} \eta AI_{t} \left( {1 - 0.005\left( {T_{\text{o}} - 25} \right)} \right),$$

  (B.6)

  where W _t is a random variable representing the stochastic weather condition at time t of day d. Typical values for W _t are 0.9, 0.7, and 0.3, representing a clear, a partly cloudy, and an overcast day, respectively (Lave and Kleissl, 2011).