The overall heat balance result from a THERMOFLEX model of a proposed hybrid solar-fossil power plant is shown below. It is a condensing steam turbine power plant with an air-cooled condenser (ACC), a low pressure feedwater heater, and a deaerator. Steam is directly generated in a Linear Fresnel Collector (LFC) solar field and/or by a gas-fired package boiler installed in parallel. The solar field consists of three sections, one to preheat water, one to evaporate water, and the final section to superheat steam. The evaporator is designed to produce 30% quality steam. A steam drum separates the phases; liquid recirculates to evaporator inlet, and dry steam flows to the superheater field. Nominal turbine inlet conditions are 65 bar, 450 C, 13.6 kg/s. Nominal ACC pressure is 125 mbar in a 32 C ambient. This plant design minimizes plant makeup water requirements, consistent with desert-like site conditions present at many solar sites.
This design includes a natural-gas fired backup boiler, in parallel with the solar field, to generate steam when the field is unavailable due to maintenance, weather, or time-of-day. The backup boiler facilitates firm electric dispatch, without storage. The steam cycle is small, does not include reheat and has few heaters. Therefore the base cycle efficiency is relatively low. However, this plant is also relatively simple, inexpensive, and easily capable of operation in full solar mode, full gas-fired mode, or in hybrid mode when some steam is generated in the field and the balance is provided by the fired boiler. So, it is flexible.
This model was used to simulate operation over a year using ambient and irradiance conditions typical of Daggett California, USA. The plant was run on a 24 hour schedule for 8000 hours per year. The annual average net LHV (lower heating value) efficiency was computed from the sums of net power produced and net fuel consumed; (GWhr electric export / GWhr LHV fuel consumption). Results of the yearly simulation show this relatively low efficiency steam cycle operates at 41% effective net LHV electric efficiency, thanks to the fuel-free contribution from the solar steam generator. This efficiency level is in the high range for Rankine cycles. Plant efficiency would be far higher if the plant were shut down overnight, and would be lower in locations with poorer solar characteristics.
THERMOFLEX can compute pressure drop and heat transfer for receiver tubes carrying single phase thermal oils, single phase water, two-phase water, and superheated steam. It includes a detailed physical model of thermal-hydraulic behavior of solar fields using Direct Steam Generation (DSG).
Estimates of pressure gradient and heat transfer coefficient in two-phase flow situations is more complicated than for single-phase situations. THERMOFLEX uses a one dimensional model where the flow path is discretized into a number of steps. The model estimates step-wise local values for internal heat transfer coefficient and pressure gradient based on prevailing flow conditions and physical characteristics of the flowpath including length, roughness and fittings.
This series of three graphs show distributions of computed pressure, temperature, pressure gradient, heat transfer coefficient, mass flux, and bulk velocity from economizer inlet to superheater exit for this plant model operating at design heat balance conditions. Three distinct regions correspond to the separate fields for heating water, making steam, and superheating steam.
Pressure distribution (below) is discontinuous because of pressure losses in piping systems between fields. The temperature plot is discontinuous between economizer and evaporator because subcooled economizer exit water mixes with saturated liquid recirculated back from the steam drum. The final steam temperature exceeds the turbine inlet by 10 C, requiring use of a desuperheater between the solar field and turbine.
The pressure gradient and heat transfer coefficient distributions (below) are discontinuous in value because the mass flux in each field is different, to ensure reasonable velocities in each section. The slope of pressure gradient in evaporator is discontinuous because inlet water is slightly subcooled. The sharp discontinuity in value of heat transfer coefficient between evaporator exit where steam quality is 30%, and superheater inlet illustrates how dramatically this differs between wet low quality steam and dry vapor.
The number of paths in each field section is different, although the receiver tube diameters are the same throughout (70 mm OD). Therefore, the mass flux in each section is different, and the velocities are discontinuous at field boundaries. Velocity varies inversely with density along the flow path. These effects are shown in the plot below.
Once a plant design is established, off-design simulations are used to compute expected plant performance at site and operating conditions expected during the year. Typically simulations are done at different ambients, solar conditions, load levels, etc. Results are used to map expected plant performance throughout the operating envelope, and to compute yearly totals for power production, fuel consumption, water consumption, etc. Sometimes off-design simulations identify ways to fine-tune the original design so it more effectively satisfies expected duty cycle.
THERMOFLEX models can run in design mode, in off-design mode, or in mixed mode where some components are in design and some in off-design.
With Thermoflow software, “design” mode means the user specifies (or THERMOFLEX automatically determines) equipment physical characteristics, general configuration data, and desired thermodynamic constraints. THERMOFLEX computes the heat and mass balance and also determines the equipment size needed to realize the heat balance result. In contrast, “off-design” mode means the equipment size is already established by a design calculation (subject to user edits), and the model computes how equipment of that size operates at user-specified loading, ambient, and solar conditions. In both modes the computed heat and mass balance parameters are the same, but the method of computing them is different.
E-LINK allows Thermoflow models to be run from inside Microsoft Excel. E-LINK is a feature included with any Thermoflow software license. E-LINK is a great tool for parametric studies, performing batch runs, and making automated calculations. Values for user-selected model inputs are entered in normal Excel cells, and computed results are stored in associated cells. The inputs and outputs are treated like any other Excel cell so they can be used in formulae, as source data for charts and tables, or linked to other Excel-aware applications. With E-LINK, any number of model runs can be made in a workbook. So, E-LINK is the tool to use for making annual yield calculations where some users make 8760 simulations to map out the year.
This example uses the hybrid solar-fossil plant with DSG described on the previous page. During the day the solar and ambient conditions change. Prevailing values for these key model inputs are used to predict hourly plant operation. In this model, automated plant loading is accomplished using a steam flow controller icon. This logical component is connected upstream of the steam turbine and regulates steam flow to the turbine so it stays in a specified range. When the solar field makes less than the minimum steam turbine admission flow, the controller automatically draws steam from the backup boiler to makeup the shortfall. If the solar field makes more than the maximum admission flow, the controller shuts down the auxiliary boiler and dumps excess steam to the condenser through a letdown station. The controller’s limits maintain steam turbine power between roughly 8 and 11 MW.
Hour-by-hour simulations are used to compute annualized totals and averages. In this example the plant model is the hybrid solar-fossil power plant described above. It is operated on a 24-hour schedule with power levels ranging from just over 8 MW to a maximum of 11 MW. Power limits are established by limiting steam turbine admission flow in a range of 40 to 53.4 t/h.
Here, the hourly inputs and outputs for three particular days are shown to demonstrate how the plant operates under different conditions. Estimated ambient temperature and DNI for particular summer, winter, and shoulder season days are shown in the plot above. The ambient data is from a model of the site in southwestern US, near the Kramer Junction SEGS plants. The DNI is estimated by the program using its theoretical sun model.
Summer conditions are shown in red, winter in blue, and shoulder season in green. The solid lines show ambient temperature which has a strong impact on air cooled condenser performance, and hence steam turbine power production.
DNI (dashed lines) and solar angles vary with solar hour and day of year. These parameters strongly influence steam production in the solar field. The solar angles, not shown, are computed by the program for this location based on the day and the solar hour.
Hour-by-hour simulation results for winter, spring/fall, and summer days are plotted below. Steam turbine flow from the solar field is shown with bright green bars. Flow from the backup fossil-boiler is shown with light green bars. Steam flows are plotted on the left axis in tonne/hour (t/h). Net plant power (MW) is plotted as a solid black line on the right-hand axis.
The solar field cannot make the minimum admission flow at any hour of the winter day. For six hours in the middle of the day the solar field can make about 45% of the steam needed to load the turbine at the minimum power. Throughout the winter day the plant generates a roughly constant power level associated with minimum steam flow to the turbine.
On the summer day the solar field makes more steam than the turbine can swallow for six hours, and makes all needed steam for eight hours in the middle of the day. During early morning and late afternoon the field can still generate a significant fraction of maximum steam for the turbine.
Plant net power varies throughout the day. The variation is most pronounced in the summer and shoulder season. This variation is the result of two effects. First, the admission steam flow varies throughout the day. Increased steam flow to the turbine raises its output power. Second, the air cooled condenser’s capacity varies throughout the day. During the hottest parts of the day the capacity is reduced which in turn reduces steam turbine gross power. The model accounts for these effects automatically, consistent with plant equipment capacity.
THERMOFLEX provides physical description for plant equipment in addition to text and graphical thermodynamic reports. The 3-D view below (available starting with TFLOW20) is one of the many graphic outputs that help the user analyze the computed result.