Surface Coal Mine Production Scheduling under Time-of-Use Power Rates

Abstract

Purpose of Review

Mining operations, similar to those in other heavy-industry applications, such as steel-making, are energy intensive. To offset power requirements, renewable energy use on active and reclaimed mine lands has increased dramatically. In concert, mining companies have begun to focus on increasing efficiencies, reducing carbon emissions, and developing sustainable mining practices.

Recent Findings

We first review opportunities for renewable energy integration; then, we elucidate the challenges (including those associated with the power grid) of doing so; and, finally, we examine the possibility of considering electricity usage and demand during the production scheduling process to capitalize on these alternative energy sources and to take advantage of favorable pricing strategies.

Summary

Utilizing real data from an active coal mine with electric equipment, we show the impacts of (i) seasonal power price fluctuations on a medium-term production schedule and (ii) hourly power price fluctuations on a short-term extraction schedule. Results reveal economic potential both for (i) the integration of renewable energy sources on reclaimed and active mine lands and (ii) the corresponding synchronization of a production schedule with time-of-use energy pricing contracts.

Appendices

Appendix A: Area Mine Optimization Model Formulations

We provide here notation for the various formulations we deploy, which possess an underlying resource-constrained project scheduling problem structure found in both open pit and underground mine production schedule optimization [69]. In general, we seek to maximize net present value. We deploy the academic solver Open Mine Planner (OMP) to produce an integer-feasible solution in the case of the medium-term schedules; we solve the short-term schedule with commercial software.

A.1 Base Case Medium-Term Formulation ($\mathcal {G}$)

The objective function of the generalized formulation maximizes the net present value of the production schedule; constraints guarantee adherence to resource availability, precedence, and quality considerations.

Objective Function

$$\begin{aligned} (\mathcal {G})\;\; \text {maximize} \quad \ \sum _{a \in \mathcal {A}} \sum _{t \in \mathcal {T}} c_{a} \cdot \frac{1}{(1+\delta )^t} \cdot y_{at} \end{aligned}$$

(A.1)

Subject to:

Maximum Daily Resource Consumption

$$\begin{aligned} \underset{a \in \mathcal {A}~t'}{\sum } \underset{\in \mathcal {\tilde{T}}_{at}}{\sum }s_{ra}y_{at'}\le \bar{s}_{rt}\qquad \forall \ r \in \mathcal {R}, t \in \mathcal {T} \end{aligned}$$

(A.2)

Daily Concurrent Activities

$$\begin{aligned} \underset{a \in \mathcal {A}~t'}{\sum } \underset{\in \mathcal {\tilde{T}}_{at}}{\sum }y_{at'}\le \bar{m}_{kt} \qquad \forall \ k \in \mathcal {K}, t \in \mathcal {T} \end{aligned}$$

(A.3)

Minimum and Maximum Weekly Resource Consumption

$$\begin{aligned} \underline{s}_{rw} \le \sum _{t \in \mathcal {\hat{T}}_w} \sum _{a \in \mathcal {A}} s_{ra}y_{at} \le \overline{s}_{rw} \qquad \forall r \in \mathcal {R}, w \in \mathcal {W} \end{aligned}$$

(A.4)

Mining Activity Predecessors

$$\begin{aligned} \sum _{t' \le t} y_{a{t'}} \le \sum _{t'=1}^{t-\ell _{a'{a}}+1} y_{{a'}t'} \qquad \forall \ a \in \mathcal {A}, {a'} \in \mathcal {P}_{a}, t \in \mathcal {T} \end{aligned}$$

(A.5)

Mining Activity Single Occurrence

$$\begin{aligned} \sum _{t \in \mathcal {T}} y_{at} \le 1 \qquad \forall a \in \mathcal {A} \end{aligned}$$

(A.6)

Minimum and Maximum Weekly Quality

$$\begin{aligned}&\underline{v}_{qw} \sum _{t \in \mathcal {\hat{T}}_w} \sum _{a \in \mathcal {A}} \frac{{c}^m_{a}}{d_a}\cdot (\sum _{t' \in \mathcal {\tilde{T}}_{at}} y_{at'}) \le \nonumber \\&\sum _{t \in \mathcal {\hat{T}}_w} \sum _{a \in \mathcal {A}} {v}_{qa}\frac{{c}^m_{a}}{d_a} \cdot (\sum _{t' \in \mathcal {\tilde{T}}_{at}} y_{at'})\le \nonumber \\&\overline{v}_{qw} \sum _{t \in \mathcal {\hat{T}}_w} \sum _{a \in \mathcal {A}} \frac{{c}^m_{a}}{d_a}\cdot (\sum _{t' \in \mathcal {\tilde{T}}_{at}} y_{at'}) \qquad \forall q \in \mathcal {Q}, w \in \mathcal {W} \end{aligned}$$

(A.7)

Binary Decision Variables

$$\begin{aligned} y_{at} \qquad \text {binary} \qquad \forall a \in \mathcal {A}, t \in \mathcal {T} \end{aligned}$$

(A.8)

In this generalized formulation, the objective function (A.1) maximizes the net present value (NPV); other applicable objectives might minimize costs or maximize profit or production volume. Constraint (A.2) represents resource consumption limits, constraint (A.3) limits the number of daily concurrent activities, and constraint (A.4) restricts the weekly consumption of resources. Constraint (A.5) enforces precedence relationships while (A.6) imposes the common-sense rule that activities are completed at most once. Constraint (A.7) enforces the minimum and maximum quality value allowable weekly. Constraint (A.8) imposes integrality conditions.

A.2 Medium-Term Formulation with Time-Adjusted Price Factor ($\mathcal {D}_m$)

We integrate a new objective-function parameter, termed $f_{at}$ and representing the time-adjusted price factor, to reflect variable demand costs for electricity.

Objective Function

$$\begin{aligned} (\mathcal {D}_m) \;\; \text {maximize} \ \sum _{a \in \mathcal {A}} \sum _{t \in \mathcal {T}} c_{a} f_{at}\cdot \frac{1}{(1+\delta )^t} \cdot y_{at} \nonumber \end{aligned}$$

Subject to: Constraints (A.2)-(A.8)

A.3 Short-Term A Formulation with Time-Adjusted Price Factor ($\mathcal {D}_{s}$)

We modify the model $(\mathcal {D}_m)$ to determine the impacts of renewable energy integration on a short-term production schedule.

Objective Function

$$\begin{aligned} (\mathcal {D}_{s}) \;\; \text {maximize} \ \sum _{a \in \mathcal {A}} \sum _{t \in \mathcal {T}} c_{a} f_{at}\cdot \frac{1}{(1+\delta )^t} \cdot y_{at} \nonumber \end{aligned}$$

Subject to: Constraints (A.2)-(A.5), (A.8)

Mining Activity completion:

$$\begin{aligned} \sum _{t \in \mathcal {T}} y_{at} = 1 \qquad \forall a \in \mathcal {A} \end{aligned}$$

(A.9)

Table 3 Current renewable energy installations on active or reclaimed mines

In the short-term formulation, the objective function maximizes net present value. Constraint (A.9) requires the completion of the activities during the scheduling horizon and replaces Constraint (A.6), the latter of which enforces that the activity occurs at most once, but not that the activity is completed within the time horizon. The newly introduced constraint allows for flexibility in activity scheduling but requires that the medium-term schedule is adhered to. Because all activities must be completed per medium-term scheduling guidance, and quality constraints are met in ($\mathcal {D}_m$), the quality constraint (A.7) included in ($\mathcal {D}_m$) is removed in ($\mathcal {D}_s$).

Appendix B: Global Renewable Energy Installations Associated with Mine Lands and Selected Literature Reviewed

Table 4 List of corporate sustainability targets and websites: further information on sustainability can be found by following the links

Table 5 List of works in review papers and mine design and operations

Table 6 List of works in power supply, grids, markets, community development, and just transition