874

Transactions of the American Nuclear Society, Vol. 116, San Francisco, California, June 11–15, 2017

Thermal Energy Storage Systems and their Integration with NPPs

Steam Accumulator Storage Integration into a Nuclear Power Plant

Seth Bisett, Alina LaPotin, Erich Schneider

University of Texas at Austin, Department of Mechanical Engineering, Nuclear and Radiation Engineering Program, 1 University Station C2200, Austin, TX 78712

sbisett@utexas.edu, alapotin@utexas.edu, eschneider@mail.utexas.edu

INTRODUCTION

The growth of non-dispatchable renewables

benefits technologies with flexible load capabilities. Baseload technologies must accept low prices and revenues during low-demand periods that arise with increasing frequency as renewables deployment grows. For this reason, generators such as combined cycle gas turbines threaten to out-compete baseload, and nuclear power plants are facing early retirement. If utilities are to consider future nuclear power plants to be attractive investments they must excel at roles other than baseload generation.

Energy storage offers a means to avoid times of low prices and capitalize on times of high prices, as well as for nuclear to participate in ancillary markets and provide grid stability and regulation services. This paper explores the use of steam accumulators to store energy for a pressurized water reactor (PWR). The discharging steam from the accumulator provides heat to a feedwater heater, replacing steam, which bleeds off of the high-pressure turbine during normal operation. The utilization of the accumulator as a heat source for the feedwater heater increases the electrical power output of the PWR during discharge, as more electricity can be produced for a constant thermal input from the steam generator.

This study first presents the proposed layout of the steam accumulator integrated into a PWR and the base case values used. Next a brief overview of the thermodynamic model governing the charging and discharging processes of the accumulator is presented. An economic model describes the capital cost estimation and revenue potential for the system. These models are evaluated at varying values of energy, power, and pipe lengths. Results show the relationship between energy, power, and accumulator size, and their effect on net annual revenue and storage efficiency. The cases presented here provide direction for future work for optimizing the size and power output of the accumulator.

METHODOLOGY

The accumulator uses 32 inch diameter natural gas pipe for large-scale, high pressure steam storage. The steam accumulator will be incorporated into a PWR to serve as a heating source for the feedwater heater. Therefore, the plant equipment must be scaled in size to accommodate changing thermal and electrical loads during charging and

discharging. This is advantageous over the use of a separate turbine and condenser due to scaling benefits received by the capital cost of the equipment. Additionally, it ensures that the plant equipment is always being used, even during the storage period. A layout of an ideal Rankine cycle with reheat and base case properties is shown in Figure 1.

Fig. 1. Base Case thermodynamic state points. The base case power output is 1318 MWe. [1]

In the base case, the thermal power provided by the steam generator is 3500 MWt and the electrical power is 1318 MWe. The 3500 MWt power of the steam generator is maintained in order to consistently remove the heat flux from the reactor. Figure 1 shows the Rankine cycle as it functions during the storage period, or the period when no charging or discharging of the accumulator occurs.

During charging, low-pressure water from a make-up tank is used to bring the mass of the accumulator back to its fully charged state. Steam from the secondary loop of the PWR is heat exchanged with the water in the accumulator until it reaches a desired temperature and pressure. This diverted steam decreases the mass flow rate through the turbines, which reduces the electrical power output. In this paper, a minimum electrical power output of 60% of the base case is considered during charging.

During the discharge period, steam from the accumulator provides heat to the feedwater heater. The mass flow rate of the discharging accumulator is varied to provide a constant energy source to the feedwater and ensure that the inlet conditions to the steam generator remain unchanged. A maximum electrical power during discharge is set at 140% of the base case. This corresponds to a

875

Transactions of the American Nuclear Society, Vol. 116, San Francisco, California, June 11–15, 2017 Transactions of the American Nuclear Society, Vol. 116, San Francisco, California, June 11–15, 2017

Thermal Energy Storage Systems and their Integration with NPPs

maximum supplemental electrical power of 528 MWe provided by the accumulator. The results section of this paper examines the optimal power provided by the accumulator. Example values for a discharging period providing 362 MWe are shown in Figure 2.

Fig. 2. Sample discharge case values showing a total electrical power output of 1680 MWe. In this example, the total output is 127% of the base case. [1]

After the water passes through the feedwater heater, it is collected in a low pressure holding tank. This make-up water is introduced back into the cycle during the charging period to offset the mass which was removed from the accumulator during discharging.

Thermodynamic Model

In order to evaluate the processes of charging, and discharging the accumulator, a thermodynamic model is employed. Ultimately, this thermodynamic model interfaces with the economic model described later to determine the efficiency and profitability of various configurations of power, energy, and pipe length.

For the purpose of examining a complex multiple phase system such as the one proposed, a non-equilibrium thermodynamic model is required. According to Stevanovic, the quasi-equilibrium approach is unable to adequately account for interactions between the two phases of water and disregards transient phenomena that become relevant to vital data such as latent heats and pressure of the system [2]. The model used in this work is written in MATLAB and iterates over small timesteps to solve for complete state data along the operation cycle (charging and discharging).

The thermodynamic model uses a constant value for heat loss over the course of operation by taking the maximum saturation temperature for which the pipes were designed (286° C at 70 bar). This maximum pressure comes from an analysis of the hoop stress on the proposed pipes and leaves a safety factor of 2 [4]. During these tests the maximum pressure of the accumulator is set to 60 bar. Other

assumptions are that the Rankine cycle is ideal, with an isentropic turbine and pump.

Recent improvements to the thermodynamic model were made in order to better partition heat loss from the system into the correct phases and to check balances of energy, mass, and volume throughout operation. The heat loss was previously held constant and allocated to each phase based on volume fraction, but this was improved to be allocated based on mass fraction. Heat loss is still held constant throughout the process.

After a full cycle, the accumulator must return to its original mass, quality, and pressure. The energy required to bring the accumulator back to its fully charged state is the pump work required to pressurize the accumulator and the enthalpy that must be added to bring the accumulator to the required mass and quality.

A charging mass flow rate of 547 kg/s is chosen because it is the maximum mass flow rate that can be diverted during charging while maintaining the minimum power output of 60% of the base case. From the energy input and mass flow rate, the charging time can is calculated.

The efficiency ratio of the accumulator is the ratio of the electrical energy provided by discharging the accumulator, to the energy lost by charging the accumulator. The efficiency ratio is calculated according to Equation 1, where �� is the discharge time, �� is the electrical power provided solely by the accumulator during discharge, �� is the charge time, P is the base case electric power, and �� is the electric power during the charging time. Thus the efficiency ratio represents the ratio of the additional energy provided by the accumulator to the energy lost during charging.

��������� � � �� � ���� � �� � ��� �����������������������

The key outputs of the thermodynamic model are the energy data for the steam mixture at all points during charging and discharging, efficiency ratio, and the charge and discharge times.

Economic Model The economic model calculates the net annual

revenue produced by the steam accumulator system by considering four factors. These are the revenue produced when discharging steam from the accumulator (RD), the opportunity cost of selling electricity at the market price rather than storing and waiting for more favorable prices (OC), the amortized capital cost of the accumulator system (CC), and the annual fixed and variable operation and maintenance cost (O&M). All of these quantities are calculated in dollars (USD) per year. The net annual revenue of the system is then calculated according to Equation 2.

876

Transactions of the American Nuclear Society, Vol. 116, San Francisco, California, June 11–15, 2017

Thermal Energy Storage Systems and their Integration with NPPs

������������������ � �� � �� � �� � ������������������ The capital cost of the system is divided into two categories: power dependent costs in $/MW of discharging capacity and energy dependent costs in $/MWh of electrical energy discharged. The capital cost estimate has been modified from previous studies to reflect the integration of the accumulator into the feedwater heater. The energy dependent components include the steel pipe, insulation, make-up tanks, and building to house the accumulator.

The power dependent components include the turbines, condenser, and generator. The power dependent cost of the accumulator is the cost to scale the plant equipment from the loads required by the base case to the loads required by the discharge case. Minimum turbine loads preclude large accumulator discharge powers. Therefore, the turbine load in the charge case can be no less than 60% of the base case. In fact, this turbine load is found to be the best for net revenue potential because it corresponds to the highest charging mass flow rate, lowest charging time, and lowest OC. Additionally, the turbine load in the discharge case can be no greater than 140% of the base case, or 1846 MWe.

The power dependent capital cost is derived for the plant equipment cost of a 1400 MWe nuclear plant. Scaling benefits are applied to these capital costs. A linear regression of steam turbine costs finds that a scaling factor of 0.82 can be applied to the cost of the equipment, using Equation 3, to find the projected cost of the equipment at varying powers [3].

��� � �����

�������������������

Here, C is cost in dollars and K is capacity (measured in the unit appropriate to the equipment or plant being scaled). 𝐶𝐶� and 𝐾𝐾�, respectively, are the cost and capacity of the item at the scale for which data is available, while the unsubscripted values are the cost and capacity at the target scale. The effect of this scaling is to ascribe a unit cost (dollars per unit of capacity) benefit to larger-capacity systems. The costs scaled to the base case values (1318 MWe) are presented in Table 1. Table I: Scaled Capital Costs (M$) of Plant Equipment

Component 1400 MWe Base Case Turbines Generator Condenser

809 281 246

770 268 319

The capital costs shown in Table 1 are scaled to the discharge and charge electrical power outputs cases as well, and the total power dependent capital cost for each case is determined. The incremental power dependent capital cost of adding a steam accumulator to the plant is then the

difference between the base case and the discharge case. The energy dependent capital costs are not given

scaling benefits. The total overnight power and energy dependent capital costs are amortized according to a 40 year lifetime and 7% interest rate to determine the annual capital cost (CC). Following standard assumptions, the O&M cost per year is taken as 5% of CC.

A representative daily electricity price profile is also needed to quantify the revenue effects of storage. Prior work described the selection of a simple sinusoidal price curve and the effect of varying price period on net revenue. The previous work concluded that the most profitable cases occur when prices are most volatile, so a period of 6 hours is chosen for all cases analyzed in this paper. [4]

RESULTS

The thermodynamic and economic models are coupled to determine the effect of accumulator electrical power, energy, and pipe length on the net annual revenue produced by the addition of the storage system and the efficiency ratio of the storage system. In Figure 3, the net revenue as a function of non-dimensional pipe length is shown for a 530 MWh accumulator. The minimum pipe length (Lmin) is taken to be 125 km. Irreversible losses and declining thermal-to-electric efficiencies preclude shorter lengths from being feasible. In this design, the 125 km length of pipe is envisioned as being divided into 200 meter lengths, and stacked in an array which will fit into a building 65 meters wide by 10 meters tall.

Fig. 3. Net annual revenue for a 530 MWh accumulator at varying pipe lengths and accumulator electrical powers.

Figure 3 shows that the shortest possible pipe length leads to the highest net annual revenue at different accumulator electrical powers. This can be explained by the lower energy dependent capital cost of a smaller system. While smaller powers correspond to lower power dependent capital costs, higher power levels increase the amount of energy that can be sold at the highest price. Therefore, Figure 3 shows that the best case of the four power levels examined is 265 MW, rather than the lowest power. In Figure 4, one can see that this effect is even more pronounced for higher energy levels.

877

Transactions of the American Nuclear Society, Vol. 116, San Francisco, California, June 11–15, 2017 Transactions of the American Nuclear Society, Vol. 116, San Francisco, California, June 11–15, 2017

Thermal Energy Storage Systems and their Integration with NPPs

Fig. 4. Net annual revenue of a 1060 MWh accumulator.

At higher energies, the capital cost is further offset by higher power levels because the discharge time is greater and more electricity provided by the accumulator can be sold. Figure 4 also illustrates that the lowest power level creates the worst economic case because less energy is sold at the peak price. Figure 3 and 4 advise the selection of the shortest possible pipe length for the cases that follow. Once the 125 km pipe length is selected, several runs were performed to determine the optimal accumulator electrical power and energy, which maximize net annual revenue. Both data sets use the minimum pipe length for each energy.

Fig. 5. Net annual revenue and efficiency ratio plotted as a function of accumulator electrical power and energy.

While the 1060 MWh energy case led to higher net revenue, it is important to note that a 100% increase in energy produced a 15% increase in the maximum net revenue. This is because as energy increases, the average electricity price during discharge decreases. In other words, while electricity is produced for a longer period of time, it is being sold at lower prices. Additionally, higher energies lead to greater charging times and greater opportunity costs from charging. The efficiency ratio was also calculated, according to Equation 1, at varying power levels. Results for both revenue and efficiency are displayed in Figure 5.

When comparing the optimal values in Figure 5, it is evident that efficiency ratio is not directly related to net

revenue. Optimizing on efficiency ratio does not correspond to an optimal net revenue case.

CONCLUSION

Thermal energy storage integrated into the feedwater heater of a PWR can allow the plant to compete with flexible load power generation, as the addition of the storage system is shown to be economical in cases in which electricity prices are volatile. Because the goal of the system is to generate the maximum possible revenue, the optimization process must couple physical laws governing the energy storage in the accumulator with an economic model. An accumulator power and energy must be chosen with a high discharge rate to take advantage of peak electricity prices, but must be balanced by the high capital costs of a larger system. Ramp rates and mechanical stresses place a practical upper and lower limit on the maximum and minimum electrical powers provided by the accumulator.

Reducing capital costs can shift the optimal case to higher power and energy levels, which will be an important factor in the success of pairing nuclear power plants with steam accumulator storage. Figure 3 showed that the capital cost of the shortest pipe length increases the net revenue dramatically, even though the shortest pipe length is the least efficient. Figure 5 showed that despite a larger energy capacity to store more steam, the increased opportunity cost of charging a large accumulator for a longer time make the revenue gain small in comparison to a smaller accumulator. The other important conclusion from the data is that efficiency ratio is not directly related to revenue. The optima for efficiency and revenue do not coincide, therefore, optimizing solely for efficiency does not accomplish the goal of generating maximum revenue. Future optimization work should focus on maximizing net revenue rather than efficiency.

REFERENCES

1. R. E. LANE, Modeling and Integration of Steam Accumulators in Nuclear Steam Supply Systems, MS Thesis. The University of Texas, 2016. 2. V. D. STEVANOVIC, B. MASLOVARIC, and S. PRICA, “Dynamics of Steam Accumulation”, Applied Thermal Engineering, Vol. 37, pp. 73-79 (2012). 3. J. S. HEZIR and E. M. DAVIS, “Analysis of GW-Scale Overnight Capital Costs”, Energy Policy Institute of Chicago, (2011). 4. A. LAPOTIN and E. SCHNEIDER, “An Economic Model of a Steam Accumulator Storage System for Nuclear Power Plants”, ANS Winter Meeting and Nuclear Technology Expo, (2016).