A NEW ENERGY MODEL FOR LONG BELT CONVEYORS

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RESEARCH CONTRIBUTIONS AND OUTLINE OF THE THESIS

The rest of the text is divided into 6 chapters. Chapter 2 gives a concise summary of the background literature relevant to the content of this thesis. This summary is divided into three themes, namely; energy consumption of BCS, electricity pricing and optimal scheduling. Each of the subsequent Chapters, apart from Chapters 7, advances a given set of objectives. These Chapters, 3-6, are formatted as manuscripts that can be read independently. The bulk of the content in Chapters 3, 5 and 6 has been published, while the content of Chapter 4 is currently in the printing process. The focus of Chapters 3 and 4 is on energy-efficiency while Chapters 5 and 6 are inclined more towards energy-cost minimisation and DSM. Chapter 3 develops a new model for long belt conveyors where energy efficiency can be archived by matching the input feed-rate and belts speed. Chapter 4 considers the energy efficiency that can be archived by capturing the energy generated by downhill conveyors as opposed to wasting this energy on a braking resistor. Chapters 5 and 6 generally consider the impact of uncertainty in practical implementations of energy-cost optimal schedules. Chapter 5 focuses on uncertainties in bulk material demand due to down-stream processes, while Chapter 6 focuses on the uncertainty in electricity pricing. Chapter 7 summarises the results of the thesis. A detailed account of this work’s contributions is as follows: In Chapter 3, a new conveyor energy model for long conveyors is proposed. The energy model is described by two equations; the first equation captures the flow of bulk material on the belt, while the second two-parameter equation quantifies the power requirements of the belt conveyor. The key contributions related to the new model in Chapter 3 are: • The new model is able to account for varying amounts of mass per unit length throughout the length of the belt to give more accurate power calculations compared to previously proposed models A recursive parameter estimating algorithm and identification set-up is proposed. Simulations are used to show case this set-up’s ability to identify parameters from noisy measurement data • A sensitivity analysis of the power equation is used to justify the different parameter convergence rates. Chapter 4 considers the energy efficiency improvements resulting from harnessing the energy generated by DHCs and an economic analysis of various belt conveyor drive configurations. The key contributions of Chapter 4 are: • A novel optimisation model that can optimally schedule BCSs with DHC under a TOU tariff that allows for selling power to the grid. The proposed optimisation model is generic and its application is demonstrated for different conveyor drive configurations • A cost analysis of energy efficient conveyor drive technologies retrofits and their sensitivity to financial variables and storage size. The analysis quantifies the amount of cost saving and/or profit that can be made under three different scenarios to help the BCS operator evaluate the economic viability of investing in regenerative drive technology. Chapter 5 considers the benefit of changing from a TOU to a CPP tariff while using a model predictive control (MPC) approach to scheduling. The key contributions of Chapter 5 are: • An MPC based optimal scheduling model for BCS under the CPP tariff. An analysis considering different amounts of storage capacities and MPC prediction horizons is also given • The introduction of a stochastic MPC scheduling algorithm based on chance-constraints in order to cater for the uncertainty in the demand of material from the BCS • A formula that gives the minimum size of storage required for the BCS to reliably deliver required bulk material is proposed. This formula is shown to be related to the prediction horizon of the stochastic MPC and the standard deviation of the material uncertainty. Chapter 6 presents an economic assessment of real-time electricity price forecast accuracy on day-ahead scheduling of two types of BCS. The two types considered are those running VSDs and fixed-speed motors.The key contributions of Chapter 6 are: • The analysis shows that the economic benefit of price forecasts is proportional to the amount of price volatility • A case study and artificial forecast data is used to illustrate and explain the inappropriateness of maximum absolute percentage error (MAPE) and root-mean square error (RMSE) as indicators of economic benefit • The introduction of Kendall’s rank correlation (RC) between the predicted and actual prices as an indicator of the economic value of a forecast method. Case study data is used to show that RC is much better than MAPE and RMSE.

DEMAND-SIDE MANAGEMENT AND ELECTRICITY PRICING

Plants with BCS usually run on electricity from the grid. The rapidly increasing cost of electricity prices make it necessary to find more energy efficient ways of operating energy intensive industrial plants such as BCS. Electricity is supplied through the grid from sources (power stations) with varying costs of generation. The grid normally has no storage for electricity. Thus, the cheapest power stations are dispatched first. The total real-time power usage of the grid (in watts), normally fluctuates cyclically within a day, week and year. The total system load (in watts) follows a nearly predictable pattern of relatively short peak usages on top of an almost flat and persistent base load [12]. As a result, it is cheaper to supply the base load than the peak loads. For this reason, demand-side management (DSM) programmes are being introduced in order to reduce and flatten the total system load. DSM programmes can either be incentive based or time based. An incentive based programme (IBP) encourages the electricity consumer to reduce their consumption during peak usage times by offering monetary rewards proportional to their power reduction. Alternatively, a time based programme (TBP) discourages the electricity consumption during peak times by imposing high electricity prices at these times [13, 14]. TBPs are being applied more widely than IBPs because they are easier to implement. This thesis therefore focuses on TBP. Time-of-use (TOU), Critical peak pricing (CPP) and real-time pricing (RTP) are some of the commonly used tariff structures, within the TBP [14, 15, 16]. Under TOU, prices of electricity are fixed for each period of the day during the whole year or season. On the contrary, in RTP, the price of electricity changes frequently, usually every hour. Under CPP, the discounted TOU prices are normally applied and relatively higher prices are used during critical days, at the utility’s discretion [14, 17]. Eskom, the South African state-owned power utility, is also moving towards more dynamic pricing schemes [18]. One of Eskom’s recent initiatives is the implementation of a critical peak pricing (CPP) pilot project currently under way1 .
Chapters 4 and 5 use a TOU tariff. Chapter 5 also focuses on CPP, while Chapter 6 deals with RTP. DSM programmes are useful to a power utility since it improves the reliability of the power system [13]. On the other-hand, dynamic prices expose electricity consumers to the risk associated with frequently changing prices [14] . This is particularly true for RTP. The best way of risk mitigation is electricity price forecasting. There is significant interest in the accurate prediction of electricity prices [19, 20, 21, 22, 23]. The techniques used for prediction include game theory, simulation models, statistical analysis and data mining models [19]. The main focus of research in the price forecasting front is to improve the forecast accuracy in terms of the commonly used performance metrics. However, the practical benefit of a price forecasting scheme and the ability to foretell its economic benefit when it is applied remains a challenge. A number of research reports indicate that the most accurate price forecast method does not necessarily provided the best economic benefit to the energy consumer or producer [24, 23, 25, 26]. It is, therefore, necessary to assess the economic benefit of price forecasting on BCS plants operating under the RTP tariff. This is the theme of Chapter 6. A logical extension to the DSM programmes is to also allow consumers that are able to generate electricity to feed it into the grid to earn income. The key enabling technology is a smart meter that tracks the bi-directional flow of energy and facilitates communication between the consumer and utility. From a financial point of view, this bi-directional flow of energy can be implemented using one of the following three trading methods, namely; feed-in tariff (FiT), power purchase agreement (PPA) and net metering [27]. Under the FiT method, the utility is mandated to buy all the electricity generated by the IPP at a fixed price. This method is usually meant to encourage the production of energy from sustainable sources such as solar-PV and wind [28]. The PPA method covers a wide range of contractual agreements, such as wheeling agreements. Wheeling allows for the generating customer to use the grid, for a fee, to supply another customer with their excess electricity.
A power purchase agreement between the generating and buying customer, and a wheeling agreement with the utility are usually required in this case [29]. On the contrary, net metering is such that the generating customer sells excess electricity to the grid whenever it is available and buys electricity whenever it is needed. Thus, the electricity meter effectively runs in reverse when the customer is generating excess. These options are being considered and implemented by utilities around the world. As an example, Eskom is also working on a newly proposed tariff called “Genflex” in order to facilitate wheeling [30, 31]. The introduction of net metering in Germany allows for house-hold electricity consumers to sell excess electricity from their roof-top solar panels to the utility, effectively using the grid as a form of electricity storage [28]. Apart from the usual renewable sources, many of the industrial and commercial consumers already produce excess heat that can be captured to generate electricity that is fed back to the grid. For example, heat from the electric arc furnace in steel making plants. These developments raise the need for a thorough understanding of how DSM programmes such as these can be exploited for the benefit of conveyor belt operators. The analysis in Chapter 4 focuses on the issue of capturing energy from downhill conveyors under the « Genflex » tariff.

A NEW ENERGY MODEL FOR LONG BELT CONVEYORS

The need for energy efficiency and energy cost savings requires a better understanding of BCS energy models. This chapter proposes an energy model for long troughed belt conveyors. The new model is necessary because of the conveyor technological advances that are currently leading to increasingly long belt conveyors being commissioned. The model is based on resistances and it captures the flow of the conveyor’s load using a partial differential equation. Unlike, the previously proposed models, the proposed model accounts for the different amounts of material mass per unit length throughout the whole of the conveyor’s length and so it is able to give a more accurate estimate of the belt’s energy consumption. The proposed model is verified by comparing it to a model proposed by Zhang and Xia in [6]. Verification results show that the power consumption calculations of the newly proposed simpler model are consistent with those of a known non-linear model with an error of less than 4%. An identification procedure for estimating the two model parameters is given. Simulations indicate that the parameters can be identified successfully from data with up to 15% measurement noise.
The proposed model gives better predictions of the power consumed and material delivered by a long belt conveyor than the steady-state models in the current literature. and cost effective running of belt conveyors, like any other application, requires accurate plant models to be used by optimising algorithms such as that demonstrated in [43]. This chapter proposes a new energy model for belt conveyors (BCs) with long, troughed belts. This model is suitable for conveyors longer than 1 km. The ultimate goal is to use the proposed model for accurate assessment of the energy consumption and cost of operating long BCs. Troughed conveyor belts are a widely used method of bulk material transportation. They are used in power plants, mining and mineral processing, food and chemical industry as well as in ports [44, 45]. The bulk material transportation industry generally regards conveyance distances over 1 km as long and thus this definition is adopted in this chapter. The current technological trend sees increasingly longer belts being deployed, with lengths up to 20 km on a single flight [46, 10]. A conveying system can also be further elongated in applications that connect several belts in series, so as to navigate a rough terrain [10]. However, long belts are more technically challenging to control at high speeds and so many are relatively slow with a typical speed of less than 8 m/s [47]. Energy efficiency in belt conveyors is achieved by matching belt speed to the input material feed-rate in order to maximise the mass of material conveyed per unit length and consequently, per unit of energy [6]. The mismatch between speed and the feed-rate exists because in practice conveyors tend to operate at slightly below full capacity.
BCs are usually oversized during design to cater for anticipated capacity expansions and sometimes to standardise component sizes in an effort to lower maintenance costs [7]. In mining applications, conveyors maybe loaded by an excavator resulting in an uneven loading of the belt so that the overall material flow rate is 50-70% of full capacity [8]. The majority of the current literature in belt conveyor modelling focuses on dynamic modelling of the belt tension, elastic properties of the belt material and modelling individual types of resistances [47, 45, 48]. However, there is also a need for the energy model to capture the quantities of material transferred by conveyors for the purposes of energy cost optimisation, as demonstrated in [43]. The current models assume a steady-state condition with a uniform material density through-out the whole belt [33, 32]. On very long belts, the effect of variable mass per unit length can be significant, because it takes a significant amount of time for material to move from a loading point (at the tail) to a discharge point(at the head).
The model proposed in this chapter is able to accurately capture the amounts of material loaded on each section of the conveyor belt and, hence, to calculate an accurate value of power required by the conveyor. The ISO 5048, DIN 22101 and CEMA modelling standards provide a concise analytical model based on resistances, in particular the primary resistance [1, 4, 5, 6]. The CEMA model requires knowledge of three friction coefficients accounting for, namely; ambient temperature correction, belt-idler friction and belt-load flexure [1]. Unlike CEMA, ISO 5048 and DIN 22101 require only one primary friction coefficient and a more generic means of calculating other resistances [4, 6, 7]. As a result, they form the basis of the model proposed in this chapter. However, all modelling standards are based on typical values of friction coefficients that require rules of thumb and an experienced engineer to estimate. A parametric model that can be estimated using field measurements, therefore, becomes a more useful and practical option for accurate predictions of energy consumption.
The proposed energy model uses a first-order partial differential equation (PDE) to capture the state of material on the belt and a two-parameter equation derived from established industry standards to quantify the conveyor’s power requirements. Unlike the previously proposed models, our model accounts for the different amounts of mass per length throughout the whole of the conveyor’s length, and it is therefore able to give a more accurate estimate of the belt’s energy consumption. The proposed model is verified by comparing its steady-state calculations to a model proposed by Zhang and Xia in [6]. The model in [6] is used for comparison, because it is also derived from ISO 5048. The results show that the proposed energy model gives power values close to those obtained from [6], under maximum loading conditions. A novel system identification set-up using a recursive algorithm to estimate the model parameter is proposed. The variables required for measurement on the proposed set-up are identified.
A sensitivity analysis of the power equation is used to justify the different parameter convergence rates, and their practical implications are discussed. The proposed model is useful in applications when the conveyor speed is controlled, as shown in the case-study application. The case-study simulation of the proposed model is shown to perform better than the steady-state approach in scheduling of a BCS under a time-of-use tariff. The remainder of the chapter is organised as follows: Section 3.2 presents the derivations of the proposed model. Section 3.3 verifies the proposed model by comparing its BC power consumption calculations to those of an existing model. Section 3.4 investigates the accuracy of the proposed model’s calculations and presents a parameter identification procedure. Section 3.5 presents a simulation example illustrating the use of the proposed model on the day-ahead scheduling of a BCS. Section 3.6 presents the conclusions.

TABLE OF CONTENTS :

• CHAPTER 1 INTRODUCTION
  • 1.1 MOTIVATION
  • 1.2 PURPOSE OF THE RESEARCH
  • 1.3 RESEARCH CONTRIBUTIONS AND OUTLINE OF THE THESIS
• CHAPTER 2 BACKGROUND
  • 2.1 ENERGY CONSUMPTION OF BELT CONVEYOR SYSTEMS
  • 2.2 DEMAND-SIDE MANAGEMENT AND ELECTRICITY PRICING
  • 2.3 OPTIMAL SCHEDULING
• CHAPTER 3 A NEW ENERGY MODEL FOR LONG BELT CONVEYORS
  • 3.1 INTRODUCTION
  • 3.2 CONVEYOR MODEL
    • 3.2.1 Conveyor resistances
    • 3.2.2 Modelling energy consumption
    • 3.2.3 Modelling bulk material flow
  • 3.3 MODEL VERIFICATION
    • 3.3.1 Steady-state power calculations
    • 3.3.2 Variable loading calculations
  • 3.4 PARAMETER IDENTIFICATION
  • 3.4.1 Parameter estimation
  • 3.5 APPLICATION CASE-STUDY
  • 3.6 CONCLUSION
• CHAPTER 4 ENERGY MANAGEMENT IN SYSTEMS WITH DOWNHILL CON-VEYORS
  • 4.1 INTRODUCTION
  • 4.2 BACKGROUND
  • 4.2.1 Conveyor drive technology
  • 4.2.2 Energy model
  • 4.3 ENERGY AND COST OPTIMISATION
    • 4.3.1 Case-study plant
    • 4.3.2 Electricity pricing
    • 4.3.3 Drive configuration options
    • 4.3.4 Optimal scheduling
  • 4.4 COST ANALYSIS
  • 4.4.1 Sensitivity analysis
  • 4.5 CONCLUSION
• CHAPTER 5 OPTIMAL SCHEDULING WITH UNCERTANITY IN MATERIAL
  • DEMAND
  • 5.1 INTRODUCTION
  • 5.1.1 Critical peak pricing
  • 5.1.2 Model predictive control
  • 5.2 CASE-STUDY MODEL
  • 5.3 OPTIMAL MPC SCHEDULES
  • 5.3.1 Simulation results and discussions
  • 5.4 CHANCE-CONSTRAINED MPC
    • 5.4.1 Chance-constraints
    • 5.4.2 Storage sizing based on confidence level
    • 5.4.3 Simulation results and discussions
  • 5.5 CONCLUSION
• CHAPTER 6 THE BENEFIT OF PRICE FORECASTS IN CONVEYOR
  • SCHEDULING
  • 6.1 INTRODUCTION
  • 6.2 PRICE DATA, CASE STUDY AND BENEFIT INDEX
    • 6.2.1 Variable speed control
    • 6.2.2 On-off control
    • 6.2.3 Typical plant schedules
    • 6.2.4 Forecast economic benefit index
  • 6.3 METHODOLOGY
  • 6.3.1 Rank correlation as an indicator of economic benefit
  • 6.4 ELECTRICITY PRICE FORECASTING
  • 6.5 SIMULATION RESULTS AND DISCUSSIONS
    • 6.5.1 Effect of price volatility on economic benefit
    • 6.5.2 Indicators of economic benefit
    • 6.5.3 Using an artificial forecast
    • 6.5.4 Sensitivity analysis
  • 6.6 CONCLUSIONS
• CHAPTER 7 SUMMARY
  • REFERENCES

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