Michael C. Wellons, Ajit V. SapreMobil Research & Development Corp.

Princeton, N.J.

Arthur I. Chang, T.L. LairdMobil Oil Corp.

Beaumont, Tex.

Mobil Research & Development Corp. has developed an on-line power plant optimization system that accurately represents commercial power plant operations over a wide range of operating conditions.

At Mobil Oil Corp.'s Beaumont, Tex., refinery the "Optimus" (optimization of utility systems) technology reduced fuel consumption in the cogeneration facility by 3%. This improvement in efficiency is saving the refinery an estimated $2 million/year.

In addition, the technology improved power plant operational reliability and accountability, of the operating staff.

### BACKGROUND

Generating the steam and power required to run a modern refinery is a substantial operating cost. In today's environment of shrinking margins and stiff competition, finding ways to improve the efficiency of power plant operations and reduce operating costs can have a great impact on the refinery's profitability.

While off-line models and optimizers often can provide directional guidance toward improved operations, frequent on-line optimization is required to improve power plant efficiency and reduce operating costs continually.

Implementation of an on-line power plant optimization system requires three key components:

- A rigorous nonlinear simulation model
- A robust and efficient optimizer
- Reliable and accurate power plant operating data.

### SIMULATION MODEL

The simulation model used for on-fine optimization must represent and predict power plant operations accurately over a wide range of process steam and power demands.

Individual unit models must represent operation over the full operating range, including process changes, process upsets, and turnarounds.

To satisfy these conditions, the power plant simulator must have nonlinear rating models, including accurate steam properties and rigorous mass and energy balances.

Historically, linear programming (LP) models have been used for both off-line and on-line optimization of power plants. Nonlinear models, with steam tables and rigorous mass and energy balances, however, provide a more accurate representation of power plant operations. 1 2

Most LP models are based on a fixed enthalpy (fixed temperature and pressure) for each steam header. But with rigorous steam properties, a nonlinear model can accurately calculate enthalpy as a function of the current steam header temperature and pressure. These values vary along the header and change with process conditions.

This nonlinear model allows for rigorous energy balances at every node of the steam-generation network. And as operating conditions vary, the energy balances improve the accuracy of the simulation, the predicted power generation from turbines, and the projected internal steam consumption (including deaeration, boiler feedwater preheating, steam turbines to drive the boiler feed-water pumps, and forced-draft and induced-draft fans).

This improved prediction is a big advantage when the model is put on-line.

Most LP power plant models also have linearized or constant-efficiency representations for boiler and turbine performance. Nonlinear representation of unit performance also leads to more accurate simulation and prediction of unit operation.

For example, an LP model typically has a linear flow/power model for turbine performance at design conditions. As actual process conditions vary, however, these linear representations do not accurately reflect the current unit performance.

With a nonlinear model, the design curves can be converted to thermodynamic efficiency (% of isentropic expansion), which is a nonlinear function of steam flow and more accurately reflects turbine performance at varied conditions.

The MESA nonlinear simulator was selected because it provides a more accurate representation of the utilities system, as compared to an CP model. And MESA was much easier to modify. (A PC interface allows the user to change the model structure and parameters easily.)

The MESA simulator was developed specifically for power plants and is widely used in both the petroleum and utilities industries.

### OPTIMIZATION

On-line optimization of power plant operations requires optimization technology that is robust, efficient, and able to solve nonlinear problems.

Typically, on-line optimization systems are automated, which means problem solving and termination of the entire optimization system must be reliable, regardless of the input data. And because the resulting targets are being used in real time to operate the power plant, speed in solving the optimization problem is important.

The Successive Quadratic Programming (SQP) algorithm is widely considered the most efficient and robust technology for solving nonlinear, continuous optimization problems.4 5 Optimus uses Mobil's proprietary SQP optimization technology, MOPT (Mobil optimizer), to optimize power plant operations.

In combination with the simulation model, MOPT can be used to optimize operation of the entire power plant, providing optimal targets for all of the boilers, turbines, and letdowns, while meeting all constraints on unit operation. MOPT has been commercially proven in a number of optimization applications at Mobil, and contains proprietary enhancement that cannot be found in commercially available SQP codes.

Some of the strengths of MOPT include a reliable line-search strategy, efficient Hessian updating, automatic scaling of variables and constraints, and an efficient quadratic programming solution algorithm.

The objective of power plant optimization is to determine operating targets for all units. This minimizes total operating costs while meeting all mechanical and operational constraints on power plant operations.

As a consequence, the power plant optimization problem can be expressed in terms of an objective function to be minimized (total operating cost), the variables the optimizer will adjust (boiler, turbine, and letdown loadings), and the constraints on the power plant operations (minimum and maximum unit loadings).

The objective-reducing operating costs-should include such things as the cost of fuel for boilers and gas turbines, the purchase or sale of electrical power, and the cost of water treatment. The "decision" variables are the operating variables that the optimizer adjusts to minimize total operating cost. The constraints represent mechanical and operational limits that the optimized targets must satisfy.

Typically, the decision variables correspond to the manipulated variables of the control system (i.e., the degrees of freedom of the process), while the constraints correspond to limitations on the controlled variables and other operational specifications.

For example, a single-stage turbine can be controlled to produce a certain amount of power by adjusting the steam flow through the turbine. Both the power produced and the steam flow must be within minimum and maximum operating conditions.

For the optimization problem, steam flow is a decision variable, while power is a constraint, with specified minimum and maximum bounds. In terms of the simulation model, the decision variables must be inputs to the model, while the constraints are conditions imposed on the model inputs and outputs.

For on-line implementation, additional optimization features, such as "maximum move size," can be employed to ensure reasonable operational changes during any optimization cycle. This feature allows the user to specify a maximum change (relative or absolute) the optimizer is allowed to make in any decision variable or constraint in a single run of the optimizer. "Maximum move size" smooths out the resulting targets and ensures modest changes in unit operations from one run of the optimizer to the next.

The MOPT algorithm used in Optimus is a sophisticated optimization strategy that simultaneously adjusts all of the decision variables while satisfying mechanical and operational constraints. During optimization, satisfaction of the constraints is not required at intermediate points; however, the final set of decision variables computed by the MOPT algorithm will be an optimal solution that satisfies all of the constraints.

The optimizer will not return an infeasible set of targets. If the constraint specifications make the entire optimization problem infeasible (no set of targets can satisfy all the constraints), the MOPT algorithm will "terminate," issuing warnings to the log file and failing to return any targets.

The MOPT algorithm optimizes the power plant operations by solving a succession of quadratic representations of the optimization problem (successive quadratic programming). For each iteration, the MOPT algorithm performs the following steps:

- Run a "base case" simulation with the current value of the decision variable.
- Linearize the constraints.
- Form a quadratic representation of the objective function.
- Solve the resulting quadratic program.
- Perform a tine search along the new search direction.
- Update the decision variables and check for optimal operation.

The solution of the quadratic program represents the "search direction"-the change in decision variables along which the next point is chosen. The line search finds the best point along the search direction that minimizes the original nonlinear objective function and improves the feasibility of the original nonlinear constraints.

The MOPT algorithm declares the new set of decision variables to be optimal if the KKT (Karash-Kuhn-Tucker) conditions are satisfied. This requires all variables and constraint bounds to be satisfied, with no possibility of additional improvement in operating cost. If these conditions are not met, the MOPT algorithm returns to Step 1 for another iteration.

### DATA TREATMENT

Even if the simulation model accurately reflects unit performance, the quality of the simulation and the applicability of the optimized targets is a direct function of the quality of the process data.

At a minimum, there must be enough reliable process measurements to accurately describe current power plant operations. In other words, there must be process measurements for all required inputs to the simulation model.

Ideally, there should be redundant measurements of key flows, temperatures, and pressures to validate or reconcile the data. Most process power plants, however, do not have this degree of instrumentation and can run only a minimum of process measurements.

To ensure the efficacy of the on-line optimization system, the raw process data must be screened for obviously bad data and checked for Consistency using mass and energy balances (for example, checking balances on the headers and around major pieces of equipment). If there is insufficient redundant data to perform a data reconciliation, a data validation procedure should be implemented to gauge the quality of the data.

If poor data are used as the basis for an optimization, the resulting targets will be inconsistent and unattainable, and the operators will quickly lose confidence in the optimization system. As a result, optimization should be attempted only if all data validation checks are satisfied.

In developing the on-line system at Beaumont, significant effort went into designing the data validation checks. There are 28 criteria that are evaluated on every run of the optimization system to ensure data accuracy and consistency.

### BEAUMONT PLANT

The Beaumont refinery's power plant system is a cogeneration facility comprising three power plants (called PP-2, PP-2A, and PP3) generating steam at four different pressures (Fig. 1).

PP-2, the oldest plant, contains eight high-pressure (HP) boilers and five turbine generators. Three of these turbine generators are three-stage condensing machines used to control the pressure of the refinery's medium and low-pressure (MP and LP) steam.

PP-2A comprises a very-high-pressure (VHP) boiler and a two-stage turbine generator, which are tied into the PP-2 HP and MP headers. PP-3 is located 1 mile away and has three VHP boilers and three turbine generators.

PP-3 is connected to the other two power plants by an MP steam transfer line. The power plant, in conjunction with process wasteheat boilers and turbines, generates all the steam required by the process units, and nearly all the electrical power.

The Beaumont refinery has a distributed control system (DCS) which, in the utilities area, is used only for data acquisition. The power plant does not have digital control capability and, as a result, there are no advanced control applications. Because of the lack of advanced control, on-line optimization of the power plant is implemented in an open-loop fashion.

Prior to the implementation of Optimus, an on-line LP system was used to optimize power plant operations. This system was very unreliable and lacked the model fidelity of the current system.

The LP model would produce reasonable targets in the middle of the operating range (near the point of linearization) but the quality and consistency of the targets degraded rapidly as the system moved away from "standard operating conditions."

Additionally, the older LP system generated targets by matching measured demand, so any error in measured steam exports would manifest itself in unattainable boiler-loading targets.

### IMPLEMENTATION

The computer system used for the on-line power plant optimizer is depicted in Fig. 2. The optimization system resides on a DEC Vax 4100 which is linked to the PI data base (Oil Systems Inc.) and to the DCS (TDC 3000) through a computer gateway.

The PI data base contains data for the on-line optimization system. Process data and other inputs are retrieved from PI; the resulting simulation and optimization results are stored in PI and then sent down to the DCS for display on the operators' consoles.

At their consoles, the operators can specify model parameters, data Validation criteria, and optimization bounds. Results from the optimization runs are viewed on the operators' guide displays, which show current operating points and recommended targets.

Because the current operating points and targets also are stored in PI, the current performance of the on-line system is available throughout the refinery.

The optimization system is implemented in an open-loop fashion; therefore, it is up to the operators to manually implement the recommended targets. An electronic log of operating compliance is maintained, This feature was useful during project implementation, and it is also used for troubleshooting system problems.

The on-line optimization system runs automatically every 30 min, but also can be executed on demand.

Fig. 3 shows schematically the procedure of the on-line system. For each run of the optimization system, the following steps are performed:

- Data screening-This procedure checks for "bad" process values (e.g., range errors) and power plant units not in service (in the event of boiler inspections, etc.). If a unit is shut down, all process flows and power associated with that unit are "zeroed out." Shutdowns then are excluded from the optimization automatically.

Because the time it takes to change loads and "line-out" boilers and turbines is relatively short, and because the power plant is always responding to changes in power and steam demands, no steady-state check is performed. If the process data are substantially out of mass balance, they will be flagged during data validation.

- Simulation-A "base case" simulation is performed to establish current power plant operation and generate all unmeasured flows needed for header balances. The simulation philosophy used in the on-line system is to bring into the model all the measured boiler, turbine, letdown, and vent flow rates and let the simulator calculate exports (or offsets) for each header (i.e., balance the headers).

For optimization, the simulated exports are held fixed to ensure that the optimal targets will meet current steam demand. Thus the system matches current steam supply instead of current steam demand.

- Model tuning-Model parameters are adjusted so that the simulation matches plant performance. This includes adjusting header offsets and shifting the turbine-generator efficiency curves to match simulated and actual power.

There are not yet sufficient process data in the DCS to calculate turbine or boiler efficiencies on-line. Individual unit performance, however, was calibrated with test runs at the beginning of the project.

- Data validation-The quality of the current plant data is verified based on the results from the base case simulation. Validation checks on header balances, turbine-generator mass balances, and simulated-vs.-actual power are analyzed. If any validation check is failed, the optimization is not performed.

A typical validation check for one of the headers is shown in Fig. 4. The allowable limits for each validation check are determined from plant experience and model sensitivity studies.

- Optimization-All boilers, turbine generators, and letdowns are optimized subject to minimum and maximum operating constraints, process steam and power demands, and header balances, with the objective of minimizing power plant operating costs while ensuring safe and reliable operation. In all, more than 30 process variables are optimized.

As noted, the simulated (not measured) exports are held constant during optimization. Because the simulated exports are consistent with current steam supply (boiler, turbine, and letdown flow rates), the resulting targets will be attainable. In contrast, if operating targets are generated to match measured exports, the resulting boiler targets will be biased by measurement error and will not be consistent with the current (observed) boiler loads.

- Target update-The operating targets are updated with the most recent optimization results, based on: criteria for improved operation (a minimum delta between base case and optimized operating cost), substantial changes in power plant conditions, and the elapsed time since the last update.

The Optimus technology was implemented jointly by the refinery engineering and operations staff and the central engineering office. The entire project, from conceptual design to plant implementation, was completed in less than 1 year.

The formation of a project team that cut across organization lines within the refinery and the central engineering office allowed: a better understanding of the refinery's needs, buying from key personnel, quick development of the prototype technology, and rapid refinement of the prototype to a commercial product.

### OFF-LINE TOOLS

A companion PC off-line planning tool was developed for use at the refinery. This system allows the refinery engineer or operations support staff to retrieve current or historical operating data and run the same model and optimizer as the on-line system.

The user can make changes in model parameters, steam and power demands, equipment limits and the service status of power plant units. This allows the user to evaluate and optimize power plant operations during process unit turnarounds (and determine the feasibility of concurrent power plant turnarounds), as well as predict power plant operations for alternative steam and power demands.

An off-line optimizer with discrete decision capability also has been developed. This tool can be used for design optimization and driver selection (motor vs. steam turbine).

This optimizer uses mixed-integer nonlinear programming technology, which combines the MOPT optimizer, for continuous nonlinear optimization, with integer programming

Integer variables are used to model discrete decisions such as the existence or service status of a unit (on/off) or the choice of drivers for process loads. Limited testing of this methodology suggests superior results, compared to heuristic decision-making tools.

### PERFORMANCE, BENEFITS

A refinery audit of the on-line power plant optimization system indicated benefits of approximately $2.1 million/year, or a 3% savings in fuel consumption. The project payback period was less than 1 year.

The benefits were calculated by comparing power plant fuel consumption, as a function of refinery steam and power demand, before and after implementation of the system. The audit compared daily average operating data over a 5-month period when the optimizer was in service with a similar period prior to implementation of the optimization system.

The simulation model was used to normalize the base data for the audit analysis (comparisons were made on an equivalent simulated export basis).

Fig. 5 shows power plant fuel consumption as a function of total net refinery steam demand, before and after the implementations of Optimus. The figure indicates a clear improvement in operations, both in terms of efficiency (reduced fuel consumption) and reliability. (The decreased standard deviation indicates more consistent operation.)

The reduction in fuel consumption was largely achieved by reducing total steam generation while meeting steam and power demands. Because the refinery power plant generates virtually all of the required steam and power, many of the general operating trends that emerged from the analysis indicated a trade off between steam and power generation as conditions varied.

These trends included:

- Minimizing condensing flows while maintaining LP header balance and reducing (eliminating) LP vent. Fuel prices dictate that it is not economical to generate steam just to produce power, so condensing flows should be minimized (subject to "no LP vent") and power should be generated on noncondensing turbines, where the exhaust steam contributes to steam exports. During periods of low LP-steam demand, however, the condensing flows should be increased until the LP vent is eliminated, subject to condensing capacity.
- Shifting power generation to the most efficient turbine generators.
- Shifting steam production to the most fuel-efficient boiler. During periods of normal power and steam demand, this means maximizing use of VHP boilers. During periods of relatively low power demand, however, steam production is shifted to the HP boilers, because the incremental cost of making VHP steam to produce power outweighs the incremental benefit.
- For relatively high power demands, keeping reducing-station use at a minimum. For relatively low power demands, run the VHP boilers at a minimum (subject to steam demand) and (sometimes) increase reducing-station use, because there is more benefit in sending steam through the reducing station to pick up the additional HP steam from spray water than in using the VHP steam to produce power.

For a complex, integrated power plant-such as that at the Beaumont refinery-effective implementation of these operating strategies requires simultaneous consideration and manipulation of a large number of operating targets. As a consequence, continually meeting all of these operating strategies through manual implementation is a difficult task.

The on-line optimization system simultaneously considers all in-service power plant units to provide real-time targets that minimize total operating cost, subject to operational and safety constraints.

The on-line optimization system has been in continuous service since January 1992 and has experienced a service factor of greater than 98%. The process data validation checks out about 70% of the time. The system averages 20 target updates per day.

The power plant model accurately represents power plant operations over a wide range of operating conditions, and has provided accurate, realistic, and attainable targets. Power plant operators have been consistently able to change power plant operations to meet the recommended targets for all optimization variables.

Fig. 6 demonstrates this point, comparing actual and optimized fuel costs over a 10-day period. The operators were able to closely track the optimized targets over a 10% swing in steam and power demand during this period.

Throughout 1992, with a swing in refinery steam and power demand as great as 30%, Optimus demonstrated a high degree of accuracy, flexibility, and robustness. Targets are checked for operator compliance and tracked per shift, day, month, and year. During 1992, overall target compliance was 94%.

The Optimus on-line power plant optimization system has gained the acceptance and approval of the power plant operators.

### REFERENCES

- Poje, J.B., and Smart, A.M., "On-Line Energy, Optimization in a Chemical Complex" CEP, May 1986, pp. 39-41.
- Clark, J.K., and Helmick, N.E., "How to Optimize the Design of Steam Systems," Chem. Engr., March 1980, pp. 116-128.
- Delk, Stephen R., "Utility System Simulation: A Nonlinear Approach," Industrial Energy Technology Conference, September 1988, Houston.
- Reklaitis, G.V., Ravidran, A., and Ragsdell, K.M., Engineering Optimization, Wiley New York, 1983.
- Edgar, T.F., and Himmelblau, D.M., Optimization of Chemical Processes, McGraw-Hill, New York, 1988.

*Copyright 1994 Oil & Gas Journal. All Rights Reserved.*