Segunda propuesta de algoritmo de clasificación de patrones resueltos en

The closed-loop validation of the decentralized control scheme of the domestic CHP system is performed in two modes, following the dual mode approach of the control scheme. In the first mode, the power generation driven approach is validated and presented while in the second, the heat recovery driven approach is tested. The closed loop validation happens through the interaction of MATLAB_{•and gPROMS}R _{•, as well as the software tool presented in Chapter}R

2.

Mode 1 Power production driven closed-loop validation

During this mode of operation, the controllers attempt to (i) meet a power output set-point and simultaneously (ii) produce hot water of a predefined temperature. The latter was set to 70o_C. The flow rate of hot water is not of the essence during this mode of operation,

therefore only the power generation subsystem controller and the heat recovery subsystem controller of Mode 1 are used. The results of the closed-loop simulation are presented in Figure 4.10.

Both controllers follow the set-points effectively and efficiently. The power generation subsystem controller shows an exceptional response even for large step changes while the heat generation subsystem controller in Mode 1 manages to reject the uncertainty of operation via the manipulation of the water flow rate in a good time span. Note that the undershoots on the temperature profile in the closed-loop validation results are the result of a saturated action in the water mass flow rate i.e. the system has reached its lower operating bound and there is no control scheme that could produce better results in that case).

Mode 2 Hot water production driven closed-loop validation

During this mode of operation, the controllers attempt to produce hot water of a predefined temperature (70o_C) and flow rate. The electrical power generation during this mode of

operation is not of the essence. The power production levels are dictated by the desired water flow rate and temperature. For this reason, the power generation subsystem controller, the heat recovery subsystem controller of Mode 2 as well as the flow rate controller are used. The results of the closed-loop simulation are presented in Figure 4.11.

0 20 40 60 80 100 20 40 60 80 100 Time (s) Temperature (

o C) TemperatureTemperature set point

0 20 40 60 80 100 0 0.5 1 1.5 Time (s) Flow rate (kg/s) 0 20 40 60 80 100 0 0.5 1 Time (s) Power (x10kW) 0 20 40 60 80 100 0 0.5 1 Time (s) Electrical power Electrical power set point

Figure 4.10: Closed-loop validation results for set-point tracking in power production driven operation (Mode 1). (Clockwise from top left: water temperature (output set-point tracking), water flow rate (system input), throttle valve position (system input), power generation (output tracking))

In operational Mode 2, all three controllers behave as expected. The power generation subsystem controller follows the set-point so closely that it is very difficult to notice a devi- ation after the start up. The flow rate controller manages to manipulate the outlet flow rate efficiently while the inlet flow rate disturbance is treated seamlessly by the heat generation subsystem controller.

Note that the two control structures ensure operational optimality in their respective operational mode. Overall optimal operation of the plant depends on two additional con- siderations. The first is the design of the plant. A different engine size could result into a certain mode of operation to be more favorable due to different dynamics, fuel consumption, initial capital cost and capturing the operational objectives. The second is the transition between the two modes of operation based on the demand for hot water and electrical power throughout the operation of a plant. Therefore, the integration of process design, control and scheduling is of great importance here as it combines operational optimality with process control, scheduling and the consideration of process economics [101, 270, 277].

0 20 40 60 80 100 0 50 100 Time(s) Temperature ( o C) 0 20 40 60 80 100 0 0.5 1 1.5 Time(s) Flow rate (kg/s) Outlet flowrate Inlet flowrate Flowrate set point

0 20 40 60 80 100 0 0.5 1 1.5 Time(s) Power (x10kW) Electrical power Electrical power set point

0 20 40 60 80 100 0 0.5 1 Time(s) Temperature Temperature set point

Figure 4.11: Closed-loop validation results for set-point tracking in heat recovery driven operation (Mode 2). (Clockwise from top left: water temperature (output set-point tracking), controlled water flow rate (input and output set-point tracking), throttle valve position (input), power generation (output and coordinated set-point tracking))

Control objectives and performance

The performance of the controllers in both modes of operation is regarded as successful since they are able to maintain their respective set-points. More specifically, the controller perfor- mance is determined via comparing the mean value of the deviation of the real outputs to the set-points for different controller design alternatives. The controller with the lowest devia- tion was chosen. Prior to that, any control design with more than 2% deviation between the real output and the set-point in stable operation was discarded1 _{There are several instances}

in both operating modes where the real hot water temperature deviates from the predefined temperature set-point of 70o_C. In Mode 1 this is attributed to saturated control actions as

the water flow rate graphs indicate (i.e. flat lines at the lower acceptable level of the flow). In the Mode 2 this is attributed to (i) the gradual acceleration or deceleration of the angular velocity of the internal combustion engine, (ii) the flywheel inertia and (iii) the simultaneous need of a certain amount of water which, as described in Section 4.2 is not always possible. Given the fact that in real CHP applications the hot water is typically stored in hot water tanks prior to application, a fact that normalized temperature differences, such deviations

1_{Stable operation is not achievable in Mode 2 operation for the power generation controller for which the}

were allowed. Alternatively, either the engine type needs to be reconsidered or a design that allows the release of hot exhaust gases needs to be included2_{. Note that here water boiling}

is prevented.

4.5 Concluding remarks

In this work we presented a decentralized multi-parametric model predictive control approach to efficiently operate a domestic CHP system. We took into consideration a (i) dual mode control scheme as well as (ii) the physical division of the CHP system into a power generation subsystem and a heat generation subsystem from the modeling starting point, all the way to the control design and closed-loop validation via the PAROC framework. We showed how the dual control scheme can effectively operate the system in a power generation driven mode and in a heat recovery system mode.

In the next chapters, the interactions between the two modes of operation will be dis- cussed as part of the integration of the control policies with operational scheduling driven by economic objectives. Furthermore, the design of the system will be visited as part of a unified framework for the simultaneous solution of the design, control and scheduling problem.

2_{The latter refers to Mode 2 were the engine is unable to decelerate quickly enough to prevent overheating}

Chapter 5

A simultaneous design and control

optimization approach based on

PAROC and classical control

Simultaneous design and classical control optimization via approximate models.

Portions of this chapter have been submitted for publication in:

• Diangelakis, N.A.; Pistikopoulos E.N.; A multi-scale energy systems engineering ap- proach to residential combined heat and power systems. (2016) Computer & Chemical Engineering, in print

5.1 Introduction

The design of the CHP system described in Chapter 3 is a key decision that can, in the long term, affect the environmental and financial impact of the plant. Consider a cogener- ation plant that due to its limited size is unable to cover the electrical demand in times of “expensive” electrical power or one that is unable to produce heating power at the desired levels, eventually leading to discomfort within the residencies. On the other hand, a larger plant would be able to cover the demand but it would require a considerably larger invest- ment cost thus rendering the overall acquisition and maintenance costs unsustainable. At the time scale of the system’s operation, the rate fluctuations of the grid electrical power and the grid natural gas are key to the policy that is applied in order to cover the residen- tial demand, which can be covered either from the cogeneration plant or external sources. Clearly, financial criteria prevail for these decisions, therefore the design of the system plays an important role here as well, since the financially optimal operation needs to be within the

feasible operational space of the plant which depends on its design. The short term decisions should not be neglected either. The ability of a controller scheme to bring the system to the desired operating set-points is subjected to feasibility and financially optimal operation, and also depend on the design of the plant. Process intensification is therefore necessary when considering such systems. These complex interactions between design, operations and control can be simultaneously analyzed through an integrated approach which is the subject of this chapter.

In particular, based on the PAROC framework of Chapter 2 we develop an integrated framework for the simultaneous design and control optimization featuring:

1. a dynamic ‘high fidelity’ process model of the CHP system (Chapter 3),

2. suitable approximate models that adequately capture its operation (Chapter 4), 3. a dynamic optimization formulation that simultaneously optimizes a conventional PI

control scheme and the design of the system,

4. a multi-parametric model predictive control formulation based on the optimal design of the approximate model (Chapter 4) and

5. a simultaneous design and control optimization framework by multi-parametric pro- gramming (Chapter 6)

The next section presents (i) the currently available residential scale CHP technology, (ii) the operational characteristics of a residential scale CHP system and (iii) the ‘high fidelity’ process model.

5.2 Design and control of the domestic heat and power