T. P. Fluri1* and T. W. von Backstrom1

1 Department of Mechanical and Mechatronic Engineering
University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa
* Corresponding Author, fluri@sun. ac. za

Abstract

Various layouts and configurations have been proposed for the power conversion unit (PCU) of solar chimney power plants. However, no method was available to make an informed decision on which layout/configuration to choose. The aim of this paper is to present such a method and apply it to several plant configurations. It is found that PCUs with a multiple horizontal axis turbine configuration using a single rotor layout with inlet guide vanes provide the lowest cost of electricity. It has further been found that while the size and performance of the different plants vary a lot, the optimal PCUs all look very similar. The optimal number of turbines varies, but their individual size, the number of blades and even the efficiency of the PCU remain close to constant. The cost of the PCU, however, varies significantly; the specific initial cost of the PCU varies between 437 and 1644€/kW.

Keywords: Solar chimney power plant (SCPP); Cost optimization; Turbine

1. Introduction

Results from pilot plant testing in Manzanares and from various mathematical models found in the literature make large-scale solar chimney power plants a promising option for sustainable power generation [1, 2, 3]. Various layouts and configurations have been proposed for the power conversion unit (PCU) of this power plant concept; layouts with counter rotating turbines or single rotor turbines, layouts with or without inlet guide vanes (IGVs), configurations with single or multiple vertical axis turbines located in the chimney as well as configurations with multiple horizontal axis turbines located on the ground around the chimney [1, 5]. In this paper a method is described, which helps to make an informed decision on which layout/configuration to choose to minimize the cost of electricity (COE). The described method is then applied to several plant configurations. It was developed as part of the PhD dissertation of one of the authors. For more detailed explanations refer to the dissertation [6].

2. Method

The cost of electricity has been chosen as the main evaluation metric. The structure of the optimization tool, which has been implemented in Matlab, is summarized in the flow chart in Figure 1. The various elements of this optimization tool are described in this section.

The plant performance data are taken from simulation results using the models and the simulation program of Pretorius [2]. The simulation program solves the thermo-flow field in the collector and the chimney of a solar chimney power plant. Conservation equations for mass, momentum and energy are solved simultaneously using finite difference methods. Meteorological data for Sishen, South Africa; (latitude: 27.67° South; longitude: 23.00° East) are used as input to the program. The

(^SCPP

Fig. 1. Flow chart summarizing the structure of the solar chimney power conversion unit optimization tool.

impact of the chimney shadow and all frictional, inlet, outlet, support and heat losses are taken into account. For the power conversion unit an efficiency of 80 % was assumed. Sandstone has been assumed as the ground material. A dry adiabatic lapse rate has been assumed for the vertical temperature profile inside and outside the chimney. Wind effects have been disregarded.

For the present study the flow conditions at the inlet and outlet of the PCU, which have been extracted from the results of this plant performance simulations, are used as input for the PCU optimization. The simple assumption of a constant PCU efficiency of 80 % is replaced by an analytical model, which evaluates the efficiency of the PCU at the different operating conditions taking the efficiencies of the various components of the PCU into account [7].

To allow for the variation in chimney geometry, a parametric chimney cost model is employed. According to Bernardes [4], the surface area specific chimney cost, b, can be approximated as a function of the chimney height, Hc, and the chimney diameter, dc. His Equation 3-4 is used and reiterated here for convenience:

b [€/m2] = 35.39+0.2315 Hc — 0.1223 dc (1)

Note, however, that this approximation for area specific chimney cost should be scrutinized in future work: as curvature and its positive effect on stability decreases with chimney diameter, it is

doubtful that the specific chimney cost decreases with an increase in chimney diameter. The initial cost of the chimney, Cc, can then be evaluated from:

Cc [€] = b хЯс X п x dc (2)

The cost of the collector is also evaluated using an approach introduced by Bernardes [4] who assumes an area specific collector cost of 9.85 €/m2. A cost model for each component of the PCU has been implemented. See the dissertation of Fluri for details [6].

To evaluate the cost of electricity a procedure described by Riggs et al. [8] is followed. The impact of insurance cost, tax incentives and carbon credits has been disregarded. An interest rate of 8%, an inflation rate of 3.5%, a depreciation period of 30 years and a construction period of 2 years have been assumed.

Using data of Schlaich [9], it can be shown that the operating and maintenance cost for the first year (in Euro) is linearly proportional to the collector area, Ac, (in m2) with the following trend:

OCi = 0.1364AC +604481 (3)

This approximation is used for the present study.