Any cogeneration system can be normally viewed as comprised of two distinct subsystems: (a) the power generation subsystem and (b) the heat recovery subsystem which continuously interact with each other in order to produce usable heat and power through a single fuel source (Figures 4.2).
The power generation subsystem of a typical residential CHP system consists of the throttle valve, the inlet and exhaust manifolds and the internal combustion engine which is coupled to an electrical generator through a crankshaft. The heat recovery subsystem
(a) Application level: Single fuel source, multiple
energy products (b) Process level: The interaction of a power gen-eration and a heat recovery subsystem Figure 4.2: Conceptual interactions of a typical cogeneration unit
involves of two levels that facilitate the exchange of heat from the combustion between (a) the engine coolant and (b) the hot exhaust gases with an external cold water stream.
The full model that was described in detail in Chapter 3 is implemented in PSE’s gPROMS •[282] and consists of a total of 379 equations. The complex Differential Al-R
gebraic Equation (DAE) system has two dynamic degrees of freedom:
(i) Throttle valve: The open area of the throttle valve determines the amount of air and
fuel that enters the system. Through the position of the throttle valve, the open area is affected, consequently the produced electrical power is manipulated. The opening of the throttle valve also determines the amount of heat that is produced through combustion. The former is one of the main products of the process while the latter is a by-product that cannot be directly measured, but only correlated with the produced power level. The throttle valve position is the sole degree of freedom of the power generation subsystem.
(ii) Inlet water flow rate: The inlet water mass flow rate is the amount of water that runs
through the heat recovery subsystem at any given time throughout the operation of the process. It affects (a) the amount of hot water produced and (b) the temperature of the produced water. More specifically, as the electrical power production of the system changes in time the flow of the water through the heat recovery subsystem determines the amount of by-product heat that is recovered through the heat exchangers, therefore, both the temperature of the water and its flow rate are affected.
Domestic cogeneration systems can be considered as multi-product processes. More specifically, the process cannot produce at the same time (a) electrical power at a desired level and (b) hot water of certain temperature and flow rate. The reason behind this is that the operation of the system is restricted by the electrical and heat efficiency of the prime mover, in this case the internal combustion engine. Figure 3.11 represents the ratio between
the electrical power and the usable heat throughout the system’s operation. In other words, consider the following example assuming that:
• The system operates at 4000rpm,
• At this level a 0.5kW electrical power demand is satisfied, • Water needs to be heated to 70oC.
Due to the restrictive power to heat ratio (in this case 20% ≠ 80%), 2kW of the fuel’s power is transformed into usable heat. The desired temperature difference can only be satisfied for a maximum of about 9g/s of water flow rate, assuming standard liquid water heat capacity of 4.18J/gK and inlet water temperature of 15oC.
Equivalently, a desired flow rate of hot water of a certain temperature dictates the oper- ating level of the CHP system, therefore the power production level cannot be determined independently. In most domestic applications, the temperature of hot water produced via the use of electrical or thermal boilers is fixed to temperatures close to 70oC. Based on the
capacity of the boilers, the flow rate of the water that can be heat up to such temperatures is determined. We have followed a similar approach where we have identified the two products of the CHP system as well as the two modes of operation of the system (also presented graphically in Figure 4.3):
Operation mode 1: The power production driven operation denotes the operation during
which a certain electrical output is guaranteed but the flow rate of the water is such that the produced hot water is of a certain temperature. In this mode of operation the main product is the electrical power.
Operation mode 2: The heat recovery driven operation corresponds to the mode of oper-
ation during which a certain flow rate of hot water of a certain temperature is guar- anteed. During this mode of operation the power production level is not guaranteed. The main product in this case is the hot water.
It is clear from the above that a control policy that takes into account only one of the aforementioned operating modes is unable to capture the full production potential of the residential CHP plant. Furthermore, a CHP plant that ignores the ability to produce one of two products at a time, at a given set-point, restricts the economic advantages that the process could have, i.e. at times of high electrical power demand, the operation of the domestic CHP plant could be such that electrical power production would partially cover the demand. The by-product hot water would be, in this case, stored in sufficiently large insulated tanks in order to cover the heating demands at a later time. This leads to reduced
Figure 4.3: The two modes of operation of the residential scale CHP. Mode 1 corresponds to the electricity production driven operation where the electricity output and hot water temperature is of interest. Mode 2 corresponds to the heat recovery driven operation where the water mass flowrate and temperature is of interest.
electricity costs from the electricity grid at times of high demand, as well as reduced costs of water heating in the near future when hot water is required. On the contrary, during times of high heating demand the operation of the plant can be switched to mode 2, where hot water production is the driving force. The by-product electrical power can be immediately traded to the electrical grid, thus providing a small profit from the CHP usage. At this point, it should be noted that the problem of switching from one mode of operation to another for a single domestic CHP plant (or for a series of them) can be considered as a supply scheduling problem with economic evaluation criteria. More specifically, optimality in terms of operation of the plant during each operating mode is the objective of the control scheme presented in this work, while the economically optimal mode of the operation which inherently addresses the question of “which operating mode should be used and when” is among the objectives of a scheduling policy. The issue of the interactions between the control of the system and its scheduling will be visited at a later stage based on the principles presented in [19].
It has become clear from the development of the process model that any CHP system can be considered as the coupling of two subsystems. Furthermore, the system can be viewed as a two-product process, according to the mode of two modes of operation (dual-operation) being used at every point in time. Based on those inherent characteristics of the system we derive a decentralized dual control approach, performed in an explicit manner through multi-parametric programming which is discussed in the next section.