Pekka Immonen, ABB Utility Automation Systems, USA
Multi-variable model predictive control (MPC) is an established technology with superior performance over traditional single-input/single-output (SISO) control strategies. Originally developed for petroleum refineries, MPC has become common in process industries over that past 30 years. It is only recently, however, that MPC has found its way into power plant control and optimization.
This slower progress in the power sector can be partially explained by higher performance requirements. The dynamic behaviour of power plant components is usually much faster than that found in petrochemical processes, and it requires computing power that until recently was either not available or not cost-effective. In times of low primary energy cost and less strict requirements on environmental issues, the economic advantage was also not as substantial.
What is MPC?
MPC is a common name for a control technology using dynamic process models representing the relationship between independent variables (model inputs) and dependent variables (model outputs). The inputs include manipulated variables and disturbance feed-forward variables. The model outputs are called controlled variables (CV). The models predict future outputs based on past values of manipulated variables, calculated future values of manipulated variables and past values of the feed-forward variables.
A multi-variable MPC algorithm uses inherent knowledge of the process dynamic behavior. All the interactions between the process quantities are considered in the simultaneous solution of many equations. This is different from traditional control, such as PID (proportional integral derivative), where each controller has one input and one output. With the many constraints and complex interactions involved in power plant control, multi-variable MPC is well suited to provide advanced control and optimization in the power industry.
Applicability in large-scale power plants
Recent increases in computing power have now made it possible to apply MPC to demanding large power plant applications. Initial projects focused on smaller sized industrial power plants, with MPC solutions implemented for coordinated control and optimization of multiple boilers, fuels, turbines, steam headers and power flows to and from the grid. These projects established the range of potential benefits, such as improved plant stability, higher availability and lower overall energy costs, and paved the way for a wider application in large power plants.
Currently, the most common application of MPC for large utility power plants is combustion optimization, dealing with optimum distribution of fuel and air in the boiler to reduce emissions, particularly nitrogen oxides (NOx), while improving combustion efficiency.
More recently, MPC-based solutions have been deployed in other areas of the plant, such as main and reheat temperature control and boiler-turbine coordination.
The primary objective of advanced process control is to reduce process variations. For power plants, this means improved process stability and reliability, and reduced thermal cycle stress on the high-pressure parts.
With reduced variance, the power generation process can also be operated closer to the given plant’s optimum. In many cases, this optimum is defined by constraints. By minimizing variations, the process can be pushed closer to its limit without violating the constraint (Figure 1).
Figure 1: Reduced variance of steam temperatures allows an operation closer to the limit
In a utility power plant, a large number of possible process constraints exist, and include maximum live steam temperature, pressure, steam flow and reheat temperature, minimum flue gas O2 content, maximum opacity of flue gas, NOx emissions and generator power, minimum condenser vacuum, maximum fan capacities (amps or dampers) and mindbox pressure differential dampers. The benefits from operating closer to the limits include improved heat rate, higher generation capacity and lower emissions.
Multi-variable MPC also facilitates faster ramp rates, while keeping the plant within the acceptable operating envelope in the ramp-up. This can be extremely beneficial for units in cycling operation, and in boiler runback situations.
New generation MPC packages
Some commercially available MPC packages, which have often been used to implement advanced control solutions in process industries, exhibit a number of deficiencies.
- Limitations in the choice of control models. The commonly available impulse and step response models can only be applied for inherently stable processes, and they handle integrating processes poorly;
- The controllers work poorly in the presence of significant measurement noise or unmeasured disturbances;
- Model identification relies on open loop step testing, and only SISO models can be identified.
In the absence of a suitable commercial software solution, ABB has developed its own fully-fledged MPC-based solutions the ABB Optimax portfolio that contain a variety of technologies used according to the type of optimization task required.
Boiler startup optimization, for example, is handled with first-principle models (based on physical equations). Boiler combustion optimization, however, is best handled by using state space models. The ABB Predict & Control (P&C) tool is ideally suited to solve the latter problems. It is based on new technology that replaces the typical collection of SISO step response models with a true multiple-input/multiple-output (MIMO) state space model (a state space model describes a physical system with a number of differential equations).
The new algorithm identifies accurate state space models from plant test data. The ability to identify MIMO models from a single set of closed-loop tests reduces the required testing time and greatly simplifies the modeling task.
The state space modeling approach permits the use of a Kalman filter for state estimation as part of the feedback control algorithm. The Kalman filter is a mathematical technique originally developed for trajectory estimation of space crafts. It utilizes all available information to develop the best estimate of the process state and the disturbances affecting it. In addition to the controlled variables, additional process measurements can be included in the model, providing the Kalman filter with more information and further improving state and disturbance estimation.
In a power plant, a large number of inputs (manipulated variables that can be set, and feed-forward variables generated by disturbances) and outputs (controlled, constraint and additional state-estimation process variables) exist that can be used for the control model. The selection of the model scope with the required inputs and outputs depends on the project objectives, plant configuration and the specific local economic factors.
Figure 2 illustrates the MPC inputs and outputs for a typical combustion optimization task and indicates the manipulated (MV), feed-forward (FF), and constraint (CV) variables for a divided furnace boiler.
Figure 2: Combustion optimization variables
The relationships between these parameters are shown in Table 1. The different rows of the matrix represent model inputs, while the columns define outputs. The matrix elements with a checkmark indicate physical relationships that are included in the overall model.
This approach represents traditional combustion optimization systems, where the attemperator spray flows are included as process constraints the attemperator is a device that adjusts the temperature of the spray flow to the required value. The purpose is to keep the base controls for main and reheat temperatures within a favourable control range, and to minimize reheat spray flow.
Once the model scope has been defined, the engineering tools within P&C can be used to create and modify the structure of the multi-variable controller. A user-friendly application browser is available to define the manipulated, controlled (or constraint) and the feed-forward variables. Properties associated with these variables are also defined using the configuration tool.
ABB’s MPC solutions are typically implemented at the supervisory level to manipulate set points of multiple base control loops implemented in the digital control system (DCS). Examples of such set points include fuel flow, attemperator flow and oxygen set points. For best results, it is important to have the base loops including sensors, actuators and other field instrumentation properly tuned and in good working order.
The engineering tool has a powerful data processing capability for importing, trending and filtering the collected process data, including automatic outlier identification and removal. The computational core of the modeling tools is the parametric identification tool that is used to build state space models.
The state-of-the-art algorithm combines ease-of-use with the ability to utilize both open-loop and closed-loop test data in the model identification. Trend displays are provided to illustrate the fit of the identified models to the actual measurement. A boiler main steam temperature control example is shown in Figure 3, comparing the actual temperatures (red) to the values predicted from the attemperator spray moves (blue).
Figure 3: Comparison of model predicted and measured temperatures in a power plant
The final step in MPC design is the tuning of the controller to the specific plant. With the help of weight parameters for the various feedback loops, the MPC is tuned to produce the desired plant dynamic response. The tuning includes setting weights on control errors and drifts of the different variables. A large weight is set when a small control error or drift is allowed, and vice versa. Priorities are also assigned to the various constraints. In case of conflicting constraints, the one with higher priority is satisfied first. If adequate degrees of freedom and control capacity exist, additional constraints are resolved in rank order.
Whole plant at a glance
Power plant operators need a fast and complete overview of the plant status with all details available on request. A typical optimization overview is shown in Figure 4. It can be used to monitor the status of the advanced control and optimization, and to enable or disable optimization for any given component.
Figure 4: Single-window overview of the status of a boiler-turbine optimization
Advanced MPC systems have established a track record for improving plant operations. Some of the improvements include:
- Typical NOx reductions of 8 per cent at baseload, and up to 40 per cent at swing load
- Heat rate improvements of 0.251.5 per cent at baseload
- Reduction of unburned carbon ash
- Reduced CO2 generation per MWh generated
- Maintenance of CO at desired levels
- Improved availability
- Accelerated ramp rates
A significant improvement in boiler performance is achieved by operation at the highest possible main steam temperature. Figure 5 shows how temperature variations can be reduced by means of multi-variable MPC, ensuring the precondition for a safe operation at the maximum temperature.
Figure 5: Improving heat rate through better main steam temperature control
In this case, the improved control of a pulverized coal boiler reduced the standard deviation of the main steam temperature by 80 per cent, allowing a set point increase of 10 °C. While this may sound small, the resulting heat rate improvement was 1.2 per cent, which adds up to approximately 10 000 MWh per year of additional power generated from the same fuel input.
Heat rate improvements can also be achieved by adjusting reheat spray flows as constraint variables. Because of the reduced variations in the flow rate through MPC control, they can be reduced and operated closer to the limit. By cutting the spray flow rates to one-half of the original, the corresponding heat rate improvement in another application was 0.36 per cent, providing approximately 25 000 MWh of additional power per year with the same fuel consumption. At the same time, NOx emissions fell by ten per cent.
MPC-based control systems can have a significant impact on power plant operations, energy efficiency and emissions. It is a powerful instrument to meet a fast growing need in the power business simultaneously achieving both economic and environmental benefits.
The author would like to thank Ted Matsko of ABB Process Automation, USA and Marc Antoine of ABB Power Systems, Switzerland for their invaluable contribution to the article.
On-site power plant benefits from MPC
Alcoa World Alumina LLC’s Point Comfort refinery in Texas, USA, has a production capability of 2.3 million tonnes of alumina a year. The Bayer refining process consumes a large amount of energy, delivered in the form of electrical energy and steam, which represents some 20 per cent of the overall manufacturing cost. This means the on-site power plant is an important element in the refinery’s economic performance.
The Point Comfort powerhouse is a large facility with multiple boilers, turbines and steam headers. Operating the plant is a major challenge because of fluctuating energy prices, plant complexity and high reliability requirements for steam and power supplies. To improve operational stability and flexibility while reducing energy costs, a new application was installed for coordinated control and optimization including an advanced control layer using ABB’s MPC to provide coordinated, decoupled control of header pressures and MWs.
Using a dynamic model, updating at intervals of less than 10 seconds, the controller predicts the effects of moving multiple base control set points on the system pressures. MPC is moving high-pressure and low-pressure boiler fuel set points, all three extraction valves on all four turbines, all PRVs (pressure reducing valves) and all vent valves a total of 28 manipulated base control set points.
The most immediate benefit from the MPC is greatly improved process stability an 80 per cent reduction in the pressure standard deviation was achieved. Similar improvement was observed in all other headers. Improved pressure control is important, since the optimization requires the powerhouse equipment to make more frequent transitions between maximum power generation and minimum fuel operating modes. The better control of the steam headers has also eliminated situations where a single boiler trip causes others to trip, reducing plant outages and production losses.
Verified savings of one per cent in the powerhouse overall energy costs have been realized, providing a payback time of six months for the advanced control and optimization system.
Due to the improved stability of operations and better response to upset conditions, the operators have a high level of confidence in the new system and advanced control and optimization has become the preferred mode of operation. The utilization rate of the new system is more than 99 per cent for most equipment, in spite of the numerous maintenance and retrofit projects on the boilers and turbines during this time.
One reason for the high degree of operator confidence comes from the belief that cascading plant trips have been eliminated although this has not yet been proven. The MPC controller is able to spread header pressure error over four headers instead of concentrating the error into one header. The control moves are smooth and coordinated. There are fewer phone calls to the process operators requesting manual steam flow reduction, which can cause further disturbances to the power plant. The feelings are that the economic benefit of reduced trips is even greater than the significant energy savings.