The system is optimized for operation corresponding to the following production character- istics:
• The CHP system can either operate on an electricity driven operation producing 2.8kW or on a heat recovery driven operation producing 0.1kg/s.
• In cases where the production can not match the aforementioned demands in either mode of operation (production below demand), the mismatch is met by utilizing grid resources.
• It is possible that an electricity driven operation mode results in heat recovery higher than the demand and vice versa. The extra electrical power is sold to the electricity grid, while the extra hot water production is penalized.
• The optimal design, as a result of the simultaneous design and PI control optimization, is defined in the ‘high fidelity’ model. The latter is simulated using both the PI control scheme and the mp-MPC scheme.
• The operation follows the production modes resulting from the dynamic optimization. • The two control schemes are compared with each other in terms of fuel and cost savings
and with the case where the demand is met through the grid.
The PI controller design is presented in 5.1 and the response of the system under PI and mp-MPC is presented in Figures 5.1a and 5.1b.
Table 5.1: PI controller configuration for all subsystems for 1520cc engine displacement volume.
Power generation subsys-
tem Power DrivenHeat recovery subsystemHeat Driven
Kp 9987.1 36688.63 988.1965
Ki 9840.5 100000 984.1965
Table 5.2 shows the comparison between the different alternatives. The results of this approach yield an internal combustion engine volume of approx. 1520cc and a change in the operating mode based on the price fluctuation of electric power. More specifically, during daytime, when the acquisition of electrical power from the grid is more expensive, a power generation driven approach is chosen, while a heat recovery approach is preferred during night time. The total savings shows the amount of monetary units saved assuming a ten year operation of the CHP plant. The relative analysis is performed on the basis that 100% corresponds to the case where the electrical power and heating demands are covered without the use of a CHP system. In that case the investment cost is assumed equal to zero.
Table 5.2: Relative energy and cost savings comparison among the three alternatives. The third alternative (bases case) corresponds to covering the energy demand via conventional centralized methods (grid electricity and natural gas boiler) and assumes an investment cost equal to zero
CHP PI control mp-MPC control
Operating cost 12.2% 8.8%
Fuel consumption 11.95% 12.2%
Investment cost $4988.82 $4988.82 Total savings (10yr) $16495 $16897
The Total savings have been calculated based on a ten year operation of the system at hand and after considering the attenuation of the initial investment.
Throughout this work we have considered alternating operating modes of the CHP sys- tem. It is worth investigating the impact that this approach has on the operation. For this purpose we also consider operation of the system under the same demand (and for the optimal design) but in this case we operate the system in different ways, considering the following three scenarios:
Scenario 1: An alternating operating mode approach is considered where the system oper-
ates under the electrical power driven operating mode in times of high electricity rates and under heat recovery driven mode otherwise.
Scenario 2: An electrical power driven mode is applied. The system treats the heat as a
byproduct.
Scenario 3: A heat recovery driven mode is applied. The system treats the the electrical
power as a byproduct.
Table 5.3 summarizes the results. Scenario 1 corresponds to the base case for which the relative comparison that takes place. It is clear that when only one mode is considered both the fuel consumption and the operating cost of the system are higher than when an alternating approach is applied. As a direct result of this, the total savings in a ten-year period of operation are also affected.
Table 5.3: Relative energy and cost savings comparison when alternating operating modes are considered. Scenario 1 corresponds to the case where a power driven production operation is used in times of expensive electricity rates and a heat recovery driven operation is used otherwis
Scenario 2 Scenario 3
Power generation driven Heat recovery driven
Operating cost +112.61% +123.295%
Fuel consumption +7.60% +7.45%
Total savings (10yr) ≠22.8% ≠25.1%
The fluctuation of the cost of (a) discarding heat or utilizing a complementary boiler, (b) fuel and (c) electricity are factors that can affect the economical benefits presented in this paper. In order to identify which of those factors has a greater impact on the economics of the optimally designed system the following simulation based sensitivity analysis was performed:
• The optimally designed CHP system was operated for 24h.
• The full scale model was utilized for that purpose, under the mp-MPC control described in 5.2.3.
• The electricity driven operation aimed at a 2.8kW production while the heat recovery driven operation for a 0.1kg/s of water at 70oC.
• Heat recovery driven operation was assumed during night time. • The electricity pricing scheme involved reduced night cost.
• The cost of heat, fuel and electricity were fluctuated by ±25% from the nominal cost. It was shown that the electricity price fluctuation had a negligible effect on the overall production cost that did not exceed ±0.5%, regardless of the fluctuation of the two other factors. This is attributed to the ability of the power subsystem controller that is able to follow the demand accurately. The fluctuation of the fuel price was also small but managed to exceed ±1% in extreme cases. On the contrary to the two previous cases, the fluctuation of heat cost was the most deterministic as it affects the economic operation of the system the most. Figure 5.2 shows the contour of the fluctuation of heat cost and fuel cost. The dependence on the heat cost on the y axis is obvious compared to the less obvious change along the x axis, showing the fuel cost fluctuation.
5.5 Conclusion
The simultaneous approach to design and PI control optimization was followed by the design of a mp-MPC. Simulation results of the optimized system, operated by PI controllers and mp-MPC controllers, were compared against each other and against the conventional case were only conventional electrical power and heat was used. Furthermore, we considered different operational strategies for the CHP system and showed the engineering relevance of the dual-mode operation of the CHP versus a monolithic approach of either only power generation driven operation or only heat recovery driven operation.
(a) The residential CHP system under PI control. The response of the water flow-rate and temper- ature outputs is excellent (achieve set-point in less than 2s) but the response of the power output appears to have a 0.5s lattency at 6s, followed by a saturated action
(b) The residential CHP system under mp-MPC control. The response of the water flow-rate, temperature and power outputs is excellent (achieve set-point in less than 2s)
Fuel cost deviation (%)
-20 -10 0 10 20
Heat cost deviation (%)
-20 -10 0 10 20 -20 -10 0 10 20
Figure 5.2: Simulation driven operational cost sensitivity analysis for fuel and heat cost fluctuations. The fuel cost fluctuations do not affect the cost significantly (same shade along the x-axis). On the contrary, the heat cost deviation affects the overall operational cost in an almost linear manner
Chapter 6
Design and control optimization: A
simultaneous approach by
multi-parametric programming
Portions of this chapter have been submitted for publication in:
• Diangelakis, N.A.; Burnak, B.; Katz, J.; Pistikopoulos E.N.; Design and control opti- mization: A simultaneous approach by multi-parametric programming (2016) AIChE Journal, submitted
6.1 Introduction
The last three decades of Process Systems Engineering research and practice, have led both academia and industry to the realization that the performance of a process is affected most deterministically by its design and ability to achieve and maintain profitable operating con- ditions under operational uncertainty. It is also clear that the degree of interaction between those two aspects is such that one cannot be determined without the consideration of the other [277]. As a result, a number of approaches have been developed for addressing the issue of operability during the early stages of process design. Process design optimization un- der operational uncertainty and feasibility, flexibility, stability, controllability and resilience metrics during process design have been extensively discussed via a series of computational methods (e.g. [274, 291]). This formed a prelude to the simultaneous consideration of design and control via (i) the formulation and solution of large scale optimization problems (includ- ing numerous decomposition approaches, e.g. [118]), (ii) flowsheet and graphical problem
representations (e.g. [8]) and (iii) control structure selection as part of the design optimiza- tion (e.g. [324]) (see Table 6.1 for a list of publications per contribution). The control schemes employed focused mainly on PI and PID formulations while a significantly smaller portion of contributions employed Model Predictive Control (MPC). The contributing factor to that decision was primarily the solution of the optimization problem corresponding to the control problem within a design optimization formulation (e.g. [22, 240]). Nevertheless, the con- sideration of a constrained optimization control method could contribute to overcome the shortcomings associated with PI and PID control (such as possible operational constraints violation). In the area of simultaneous design optimization with MPC notable approaches include (i) the back-off control approach (e.g. [329]), (ii) robust design formulations (e.g. [130]) and (iii) multi-parametric MPC approaches (e.g. [305]) (see Table 6.1 for a list of publications per contribution). Regarding (iii), the availability of the optimal solution on- line via offline optimization enabled the incorporation of explicit control actions within a (Mixed Integer) Dynamic Optimization ((MI)DO) formulation thus (i) avoiding the burden of solving multiple optimization problems online, (ii) transforming the control problem into a simple linear look-up function1 and (iii) including every aspect of the MPC without any
simplifications on the problem structure.
Table 6.1 presents a condensed literature review in the general area of design and control. More specifically, a systematic clustering of the bibliography takes place according to the following criteria: (i) are control or control metrics employed? (ii) is there optimization taking place (what kind and for which problem) or heuristics? (iii) is there a model based control scheme application?.
Table 6.1: Design and control in the literature
References Area of contribution
[17, 20, 46, 62, 65, 77, 115–117, 125, 127, 128, 135, 138, 141, 208, 242, 247, 268, 312, 325]
Feasibility, flexibility, stability, controllability and resilience considerations in steady-steady state [w/wo (MI)NLP design optimization]
[113, 330, 331, 346] Feasibility, flexibility, controllability and resilience considerations in steady-steady state (MI)DO de- sign optimization
[22, 24, 25, 27, 136, 291, 355] Simultaneous/Decomposition (MI)DO process and P-PI-PID control design
Continued on next page 1The explicit solution of a Model Predictive Control problem with a linear (Œ ≠ norm) or quadratic
(2 ≠ norm) objective function, polytopic constraints and linear state-space discrete time model dynamics is piecewise linear in the optimal actions [34, 187].
Table 6.1 – Continued from previous page
References Area of contribution
[226, 253, 304, 305, 308, 309] Simultaneous/Decomposition (MI)DO process and MPC design [52, 66, 67, 85, 118, 119, 139, 180– 182, 182, 199, 200, 233, 240, 283, 292, 369] Simultaneous/Decomposition/Back-off via (MI)NLP [8, 137, 141, 143, 151, 160, 194, 198, 209–222, 287]
Flowsheet/Graphical design and P-PI-PID control
[134, 208, 333] Multi-objective approaches [20, 39–41, 45, 127, 167, 199, 200,
270, 274, 313]
Design under uncertainty
[11, 54, 62, 180, 223, 261, 324, 326, 334]
Control structure selection and design
[140, 290, 293, 320, 347, 366] Review articles on design and control
Although multi-parametric Model Predictive Control (mpMPC) has been employed in the past in the context of simultaneous design and control optimization [303, 305, 307, 308], its application relied on an iterative procedure, because the control problem formulation needed to be adjusted for different design alternatives based on feasibility criteria. Here, we present a methodology, via the PAROC framework and software platform [277], where the control problem formulation is design dependent, therefore, the explicit control actions are a function of the design variables. As a result, a single design dependent mpMPC formulation is able to control the process for bounded values of the design variables without the need of reformulation. The approach is showcased via four case studies on (i) a settling tank, (ii) a continuously stirred tank reactor, (iii) a binary distillation column and (iv) a domestic cogeneration of heat and power unit.