The 8th International Supercritical CO2 Power Cycles Symposium
February 27-29th, 2024, San Antonio, TX
Paper #25
Multi-Model Predictive Control for Enhanced Load Following of a
sCO2 Recompression Brayton Cycle
Jacob Albright1,2 Eric Liese1
Chemical Engineer Mechanical Engineer
National Energy Technology Laboratory National Energy Technology Laboratory
Morgantown, WV Morgantown, WV
National Energy Technology Laboratory, 3610 Collins Ferry Road, Morgantown, WV 26507, USA
1
2
NETL Support Contractor, 3610 Collins Ferry Road, Morgantown, WV 26507, USA
Jacob Albright has worked at the National Energy Technology Laboratory (NETL)
for 7 years performing work in the areas of dynamic modelling and process
control. He has worked as a research engineer under Leidos at NETL for the
past 2 years. He received a B.S. in Chemical Engineering from West Virginia
University in 2014. He supports the development of dynamic models and control
systems for sCO2 projects at NETL in the Strategic Systems Analysis &
Engineering group.
Eric Liese is a research engineer currently doing steady state and dynamic
process simulation in the Strategic Systems Analysis & Engineering division at
the U.S. Department of Energy’s (DOE) National Energy Technology Lab (NETL).
He has been working for over 30 years in various areas of experimental and
computational research for fossil fuel energy technologies, like fuel cells, gas
turbines, combined cycles, and most recently supercritical CO2 systems. Mr.
Liese received his B.S in Aeronautical Engineering from Purdue University and
M.S. in Mechanical Engineering from West Virginia University.
ABSTRACT
Supercritical carbon dioxide recompression Brayton cycles (sCO2 RCBC) are a promising
alternative to traditional steam cycles. However, increasing renewables penetration to the grid
will require fast load ramping of any new non-baseload power systems. This will require
considerations to the controls architecture to ensure safe and efficient operation of this novel
power cycle. While traditional controls, namely PI and PID, can sufficiently operate the system,
further improvements to the cycle response while still maintaining high cycle efficiency will
require the consideration of advanced control methods. This paper presents the application of a
linear multi-model predictive controller (L-MMPC) for use as a substitute to the standard
inventory management controller (IMC). Discussions on the control scheme utilized and the
improvements to the load response time and tracking are included.
INTRODUCTION
Supercritical CO2 (sCO2) driven power cycles are becoming increasingly promising as an
alternative to traditional steam-based power generation. As the world moves towards a net-zero
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carbon future, high-efficiency power systems will become increasingly necessary for both
existing fossil fuel generation, to reduce carbon emissions, as well as for new renewable energy
to increase cost effectiveness. Several projects are currently underway, including the
Supercritical Transformational Electric Power (STEP) pilot plant. This is a U.S. Department of
Energy based project to build and test both a simple Brayton cycle as well as recompression
Brayton cycle (RCBC) for the purpose of stress testing the new technology and determine the
capabilities of the advanced cycle [1-3]. The STEP team has recently commissioned the cycle
and is planning to begin operation in early 2024 [4].
Control of this process has been examined in Liese et al. [5] and was continued in Albright et al.
[6]. In both works, sufficient control is achieved to operate across the entire operational range,
i.e. from 10 to 4MW. The load tracking response demonstrated by these works is acceptable
and follows the demand profile closely but typically has a long approach to the final setpoint
(SP). Due to operation near the critical region of CO2, caution must be taken when operating the
system aggressively. The control action of specific controllers must be limited to avoid
instabilities in the process. The result of this limitation is fast load tracking during ramps but a
somewhat long settling time towards the end of a given ramp. In order to further improve the
response of this process to fast ramps in load, an advanced control method is considered.
This work uses a linear time-invariant (LTI) multi-model predictive controller (MMPC) to improve
the load tracking response of the RCBC. By replacing the primary load controller with the
MMPC, fast tracking can still be achieved while simultaneously improving the approach to the
final SP. The MMPC implementation is provided and the preliminary results for a full turndown
and partial turn-up response are given.
PROCESS MODEL & CONTROLS
The process flow diagram for the sCO2 RCBC used for this test is given in Figs. 1A and 1B. A
more detailed explanation of the models and software used can be found in Liese et al. [5]. A
brief summary of the cycle is given below.
The sCO2 RCBC is an indirect heat, gas fired, power cycle. The heat generated from the
combustor is transferred to the cycle from the primary heater (PHX). The sCO2 is heated to
approximately 715°C and then expanded in the turbine (TRB). The turbine exhaust is sent
through the high temperature recuperator (HTR) to preheat the feed to the PHX. The sCO2 is
then sent through the low temperature recuperator (LTR) for further heat recuperation. The flow
is then split into two streams that go to the main compressor (MC) and the bypass compressor
(BC). The portion of the sCO2 flow that is sent to the MC is pre-cooled in the main cooler which
is water cooled. This system (CoolSys) is shown separately in Fig 1B. The sCO2 cycle inventory
is maintained by manipulating inlet and outlet control valves to the inventory storage tank (IST).
Previous control methods applied to this system are given in Liese et al. [4] and Albright et al.
[5]. The main control architecture used in those studies is maintained for this system. There is
no significant change noted for the performance of the turbine inlet temperature (TIT), the main
compressor inlet temperature (MCIT), or the surge controllers for the compressors. All
controllers not mentioned specifically use the standard form of the PID and have been manually
tuned to achieve an acceptable response.
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AIR-IN
FAN Red
Red streams:
streams: sCO high-pressureside
CO22 high-pressure side
COMBUSTOR
NG Blue streams: CO2
Blue sCO2low-pressure
low-pressureside
side
CV-FUEL ORIFICE
Green streams: Inventory storage lines
Black streams: Combustion system lines
PHX
COMPmix
CV-212
CV-470 LTR CV-734
F S P LIT
IST
CV-778
TRB
CV-226
F S P LIT
CV-338
HIERARCHY
CoolSys W
MW-MC M I XE R
MW-NET
MC
MW-BCTRB
HTR
COMPsplit
MW-TRB
BC
CV-288
Figure 1A Process flow diagram of the recompression closed Brayton cycle.
S2 MC IN FromLTR S1
MIX-CO2 V-CO2-BYP SPLT-CO2
sCO2 Out sCO2 In
MIX-CW P-BACK
PCHECOOL
CW-OUT
V-CW SPLT-CW V-CLR
CW-IN
V-CW-BYP
P-MAIN
Figure 1B Process flow diagram of the main cooler system
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This study focuses on the changes to the inventory management control (IMC). Figure 2 shows
the control diagram of the IMC. A main load controller (MWC) receives a load setpoint (SP) and
then sends an output signal to the pressure controller (PC) for the IST. A split range controller
manipulates the tank inlet valve (CV-734) and outlet valve (CV-338) in order to remove and
introduce sCO2 inventory from/to the cycle, respectively.
Figure 2. Inventory management control with cascaded pressure control.
The IMC primary controller, MWC, that adjusts the secondary IST pressure controller SP has
been replaced with a model predictive controller (MPC). This MPC uses a linear time-invariant
representation of the dynamic model, given in eq. (1).
𝑥𝑥(𝑘𝑘 + 1) = 𝐴𝐴𝐴𝐴(𝑘𝑘) + 𝐵𝐵𝐵𝐵(𝑘𝑘) + 𝐾𝐾𝐾𝐾(𝑘𝑘) (1)
𝑦𝑦(𝑘𝑘 + 1) = 𝐶𝐶𝐶𝐶(𝑘𝑘) + 𝐷𝐷𝐷𝐷(𝑘𝑘) + 𝑒𝑒(𝑘𝑘)
𝑥𝑥(𝑘𝑘), 𝑦𝑦(𝑘𝑘), 𝑢𝑢(𝑘𝑘), 𝑒𝑒(𝑘𝑘) ∈ 𝑅𝑅 𝑛𝑛
𝑈𝑈𝐿𝐿𝐿𝐿 ≤ 𝑢𝑢𝑛𝑛 ≤ 𝑈𝑈𝑈𝑈𝑈𝑈
In eq. (1), x, u, y and e are the state, input, output and disturbance vectors, respectively. A, B, K,
C and D are the state space matrices that are to be estimated to give a linear representation of
the full dynamic model. The use of this type of representation allows for fast generation of the
optimal input sequence which is important for this application as the system is being
aggressively ramped and a fast controller response will be necessary. The optimal sequence is
determined by the MPC by minimizing a cost function given in eqs. (2) and (3).
𝐽𝐽(𝑧𝑧𝑘𝑘 ) = 𝐽𝐽𝑦𝑦 (𝑧𝑧𝑘𝑘 ) + 𝐽𝐽𝑢𝑢 (𝑧𝑧𝑘𝑘 ) + 𝐽𝐽∆𝑢𝑢 (𝑧𝑧𝑘𝑘 ) + 𝐽𝐽𝜀𝜀 (𝑧𝑧𝑘𝑘 ) (2)
𝑝𝑝 2
𝑤𝑤1,𝑖𝑖
𝐽𝐽𝑦𝑦 (𝑧𝑧𝑘𝑘 ) = � � [𝑟𝑟 (𝑘𝑘 + 𝑖𝑖|𝑘𝑘) − 𝑦𝑦1 (𝑘𝑘 + 𝑖𝑖|𝑘𝑘)]�
𝑠𝑠1,𝑖𝑖 1
𝑖𝑖=1 4
(3)
In eq. (2), J represents the overall cost function, which is a sum of several terms that are all
based on a QP decision, zk, for the current control interval k. Eq. (3) is the expanded first term of
the cost function, which is the output reference tracking function. This measures the deviation of
the output, yi, from reference value, ri, over the current control interval. The relative impact of
each cost function is determined by the weight, w1,I, and scaling factor, s1,I, which can be
manually tuned to obtain different response characteristics from the MPC. Two other adjustable
parameters can influence the performance of the MPC, namely the prediction and control
horizon. The prediction horizon (PH) is the entire range over which the cost function is
minimized. The control horizon (CH) determines the number of variables to optimize over, which
is the number of control moves at each time instant k. Typically, PH is chosen to be much larger
than CH in order to ensure a stable response as well as to reduce the computation expense
associated with a larger optimization problem as the CH increases.
Each term in the overall cost function resembles eq. (3) but are tracking a different performance
metric. Ju penalizes the input deviation from a specified reference value while J∆u penalizes
excessive input movement over the course of the control interval. Jε is the constraint violation
term but only applies to the upper and lower bounds of the process variables for this
implementation.
This MPC design approach is then used to split the operational range of the RCBC into 3
regions:
• 10 to 8MW, MPC1
• 8 to 6MW, MPC2
• 6 to 4MW, MPC3
Separating the operating range into 3 sections was done as an initial point of testing for the
MMPC. It is possible that more or less model segments would be optimal, but that is outside the
current scope of this work. Models are generated for each section and then used to design and
test a specific MPC for that section. This is done for several reasons. During regular operation,
the IST pressure increases and decreases according to the load required. This also changes the
driving force between the tank and the high- or low-pressure side of the cycle, depending on
which valve is being operated. Additionally, the low side cycle pressure decreases during turn-
down operation, moving the conditions at the inlet of the main compressor closer to the critical
point. This changes the properties significantly and can alter the dynamic response of the cycle
due to the impact of the main compressor performance on the overall cycle.
RESULTS AND DISCUSSION
Figure 3 shows the data utilized for model generation in the MPC framework. Several sections
of randomly generated perturbations are generated across the selected operational range of the
RCBC, in this case 10 to 8MW. The MWC is not operational during this data generation period,
as it is necessary to determine the output response to various input disturbances so that a
sufficient representation of the cycle can be generated for the region being examined. The load
SP adjusted here is only used to mimic the controller settings during normal operation, as it is
used to perform gain scheduling and SP adjustment in the cooler controls and turbine exhaust
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gas control. By more closely representing the response of the system while other controllers are
active, a better representation of the system can be obtained and therefore an improved
response from the MPC in this region.
Figure 3. Example of data used for LTI model generation
The settings for the MPCs generated using this data are given below in Table 1. In Table 1, the
PH and CH are given, as well as the weights associated with each cost function. These should
not be considered optimal but were found to be sufficient for this work. The input tracking, wu,
and the constraint violation, wε, weights are not adjusted for these designs as their impact was
not found to be significant. This is due the lack of an input reference value and few constraints
imposed on the current problem. It can be seen in Table 1 that the PH is increased for each
subsequent MPC design. It was found that operating closer to the minimum load of 4MW
caused a decrease in the response time and that by increasing the PH there was an increase in
the control action in these regions. To balance this increase in control action, the input
differential weight, w∆u, is increased for MPC2 and MPC3 to prevent excessive
undershoot/overshoot at the end of a given ramp. The output tracking weight, wy, is similar for
each MPC to ensure minimal SP-PV difference over the course of the response.
Table 1. MPC Settings
PH CH wy wu w∆u wε
MPC1 200 20 0.95 0.01 0.1 0.04
MPC2 1200 200 0.9 0.01 0.3 0.04
MPC3 3000 100 0.9 0.01 0.2 0.04
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Figure 4 shows the results for the turn-down scenario of the RCBC using a 3-section MPC. As
can be seen in Figure 4, the load tracks the demand SP closely for each subsequent ramp
down in power. There is a small delay in response once each ramp is initiated, which can be
attributed to the MPC model switching. Once a new MPC comes online, there is a short delay
before the MPC responds causing a sharp increase in the initial output seen around t=60, 530,
and 1100. The MPC output is somewhat aggressive, but this may be due to the way in which the
IMC operates. Due to the split range control, the output from the PC must be changed quickly to
operate both the inlet and outlet valve in quick succession to dampen any oscillations. Typically,
only one valve is operated, inlet for turn-down and outlet for turn-up, which causes a slow first-
order approach to the final demand SP as the valve slowly closes off over the course of the
response. The MPC aggressively changes the pressure SP to the PC to cause a rapid shift in
the output and operate both valves quickly. This results in a fast approach to the final SP with
some oscillation around the final SP for each segment. Further refinement of the separate
MPCs may reduce the initial undershoot but would likely increase the load tracking error or
settling time.
Figure 4. Load following response of MMPC for turndown scenario
Figure 5 shows the load following response of the RCBC for a turn-up scenario using a similar
3-section MPC. The MPCs generated for the turn-up response did not result in a similar
reduction in load tracking and settling time. The MPC response is somewhat like the turn-down
case but does not cause as rapid of a change in the load response. The load still meets the load
SP quickly but does not settle out in a similar manner. The response from 4 to 6MW and from 6
to 8MW both have small, sustained oscillations around the final SP. It is likely that the optimizer
of the MPC response could not determine the correct IST P SP to quickly settle the load
response. This may mean that a separate set of MPCs for the turn-up response may be
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required to efficiently operate this system. Additionally, the final segment from 8 to 10MW
reached a pressure pinch point between the IST P and the low pressure side of the cycle. The
response was similar to the previous two ramps, however, so the rest of the approach would not
be expected be significantly different.
Figure 5. Load following response of MMPC to turn-up scenario
Table 2 summarizes the PV-SP average difference and settling time for each MPC for both the
turn-up and turn-down scenario. As can be seen in Table 2, the avg. PV-SP difference and
settling time for the turn-down scenarios are all improved over the previous work done in
Albright et al. [6]. However, the majority of the cases for the turn-up response are worse, with
the exception of MPC2. The settling time for MPC3 in the turn-up scenario was not recorded
since the response did not reach the final demand SP. Overall, this data shows that there is
promise to using this method within the sCO2 RCBC but that there are still improvements that
can be made, particularly to the turn-up response of this method.
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Table 2. Load tracking difference and settling time for each method
Avg. Difference (MW) Settling time, 2% of final SP
(sec)
MPC1, TD 0.19 0
MPC2, TD 0.062 0
MPC3, TD 0.12 103
MPC1, TU 0.39 255
MPC2, TU 0.29 0
MPC3, TU 0.43 n/a
MWC [6], TD 0.34 320
MWC [6], TU 0.37 196
CONCLUSION
Advanced control techniques were applied to the sCO2 RCBC in order to improve the load
following response of the system. Improvements to the turndown response were achieved in the
form of close load tracking and decreased settling time to fast ramps. The load following for the
turn up scenario was not improved but does show that a multi-model approach may be
important to improving separate sections of the controller response to this system. Additionally,
a more centralized approach to the MPC may help to improve the performance by allowing the
MPC to manipulate both the tank inlet and outlet valves independently.
This work shows that the sCO2 RCBC has promising performance for fast ramps given strict
control performance. Further enhancements to this control system can be made, including
centralized MPC and adaptive MPC implementations.
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REFERENCES
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demonstration. In: ASME Turbo Expo, Phoenix, Arizona, 2019. https://doi.org/10.1115/GT2019-
91917.
[2] Macadam S., Kutin M., Follett W.W., Subbaraman G. Supercritical CO2 power cycle projects
at GTI. In: European Supercritical CO2 Conference, Paris, France, 2019.
https://doi.org/10.17185/duepublico/48911.
[3] Marion J. Supercritical CO2 10 MW Demonstration Project Under Construction.
Turbomachinery International, Vol. 63, No. 5, pp. 30-31, September/October 2022.
[4] Lesemann, M. “STEP Demo Team Pilots Innovative High-Efficiency Power Plant”. 27 Oct
2023. https://www.gti.energy/step-demo/step-demo-team-pilots-innovative-high-efficiency-
power-plant/
[5] Liese E., Albright J., and Zitney S. “Startup, Shutdown, and Load Following Simulations of a
10 MWe Supercritical CO2 Recompression Closed Brayton Cycle”, J. of Applied Energy, Volume
277, 1 November 2020, 115628. https://doi.org/10.1016/j.apenergy.2020.115628
[6] Albright J., Liese E., Zitney S. “Control Methods for Mitigating Flow Oscillations in a
Supercritical CO2 Recompression Closed Brayton Cycle”, J. of Applied Energy, Volume 352, 15
Dec 2023, 121922. https://doi.org/10.1016/j.apenergy.2023.121922
ACKNOWLEDGEMENTS
This work was performed in support of the US Department of Energy’s Fossil Energy and
Carbon Management division. The research was executed through the NETL Research and
Innovation Center’s Turbines program.
DISCLAIMER
"This report was prepared as an account of work sponsored by an agency of the United States
Government. Neither the United States Government nor any agency thereof, nor any of their
employees, makes any warranty, express or implied, or assumes any legal liability or
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Reference herein to any specific commercial product, process, or service by trade name,
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recommendation, or favoring by the United States Government or any agency thereof. The views
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