La intensidad, el diámetro y las dendritas

Beausoleil-Morrison et al. [60] broke down the operation cycles of the CHP units to four states: stand-by, warm-up, normal, and cool-down. Figure 3.4 shows the diagram of the states which the CHP unit follows for each operation cycle.

Normal state

Warm-up

state Cool-downstate

Stand-by state Start the warm-up counter Start the start-up counter Start Yes No Send activation signal Send deactivation signal Are the activation criteria met? Are the deactivation criteria met? Is the cool-down counter up? Input Is the warm-up counter up?

Figure 3.4 Simplified diagram of the operation cycle of the CHP unit [60]

The operation cycle starts and ends at the stand-by state. The CHP unit is idle at this state and it does neither consumes fuel nor cogenerates. When the activation signal is received, the CHP unit enters the warm-up state. This unit stays in the warm-up state until its internal temperature reaches an operational value [61]. Following this, the CHP unit enters the normal state where it cogenerates and consumes fuel. The final state of the CHP’s operation cycle is the cool-down state. This state is initiated when the control system receives the deactivation signal. In this case, the fuel supply and electrical output of the CHP unit stop immediately. The heat output, on the contrary, stays positive for certain duration, due to the heated engine jacket. Regardless of the operation state, the CHP’s controller unit consumes electrical energy which is a small amount when compared to its electrical output.

In broader terms, the warm-up and cool-down states are transient states and the stand- by and normal states are stationary states. The principle difference between stationary and transient states is the criteria which is required for the change of state [60]. The criteria required for a transient to stationary state change depends on whether sufficient duration has been spent in the transient state or not [60]. In other words, switching from the transient to stationary state is simply a matter of time. Figure 3.4 shows that the duration into the transient states are determined by warm-up and cool-down counters: if the duration equals to the pre-determined transient durations, change state (blue arrows); if not retain state (red arrows).

There are two cases where the stationary to transient state-change occur. The state- change from the stand-by to warm-up occurs when the activation criteria are met. On the contrary, the state-change from normal to cool-down state happens when the deactivation criteria are met. These criteria vary depending on the operating strategy of the CHP unit. The simplest version of the activation and the deactivation criteria are based on the state of charge of the TES unit. The controller unit activates the CHP unit when the TES unit is sufficiently empty. In this way, the available capacity of the TES unit guarantees certain operating periods for each start-up event of the CHP unit. This reduces the overall number of the start-up events; hence, improve the overall efficiency. The deactivation of CHP unit occurs when the TES unit is filled. In other words, the TES unit cannot accommodate the surplus cogenerated heat anymore; therefore, the CHP unit is deactivated.

Rosato and Sibilio carried out a series of experiments to evaluate the outputs of a 6 kWe

CHP unit under various operating states [49]. In this paper, they evaluated the CHP unit’s performance in transient and stationary states. During the warm-up state, they report that the CHP unit consumes 0.9 – 1 Nm3_h-1 _{of natural gas and they recorded no output.}

This interval equates to 0.17 to 0.19 kWh of natural gas4_{. Furthermore, they measured}

warm-up durations of 62 and 91 seconds for warm and cold starts, respectively. The cold start was measured for a unit which was off for a week. The warm start duration was measured for a unit which was recently operated for four hours.

Additionally, Zheng et al. conducted similar experiments over a 25 kWe internal

combustion CCHP unit [52]. They measured warm-up durations of 125 and 300 seconds for warm and cold starts, respectively. Additionally, they measured the energy required during the warm-up period. They reported an average of 1.3 and 1.6 Nm3_h-1 _{for the warm}

and cold starts, respectively. These values correspond to 0.24 and 0.29 kWh of natural gas, respectively.

In Rosato and Sibilios’ study [49] the cool-down duration is measured to be 331 seconds. Similarly, Zheng et al. [52] recorded 315 seconds as the cool-down duration. Additionally, these studies reported that the experimented CHP units had heat outputs during the cool- down state. These values are 0.455 kWh in the case of former study [49] and 1.63 kWh in the case of latter study [52]. Both studies conclude that the impact of start-up events over CHP’s outputs is non-trivial.

Besides assessing the performance of the experimented CHP unit in the transient states, Rosato and Sibilio recorded the electrical and heat outputs of the CHP units during the normal state [49]. They found that there is a certain time lag between the moment which the CHP unit enters the normal state (starts generating electricity) and the moment which its efficiencies converge to their steady-state values. The term steady-state efficiency is used to refer to those values declared by CHP manufacturers. These figures are likely to be the best performance data due to commercial reasons. This study uses the term efficiency recovery rate to refer to the ratio of CHP’s actual efficiencies over its steady- state values.

Figure 3.5 show the electrical and thermal efficiency recovery rates which are reproduced from [49]5_{. While, the horizontal axis represents the duration into the normal}

operation in seconds, the vertical axis shows the electrical and heat recovery rates for two different operations: part load and full load. Figure 3.5 shows the measured thermal and electrical efficiencies of the CHP unit, for 0.5 and maximum load factors.

5 _{In order to reproduce an image, the author of this study used a public, online tool called Web Plot Digitizer.}

This tool uses image processing to calculate the distance of manually entered datapoints to the horizontal and vertical axes. In order to access this tool, see [104].

Figure 3.5 Recovery rates of the outputs of the CHP unit right after entering the normal state [49]

Figure 3.5 shows that the CHP’s heat output stays zero for nearly 120 seconds. This is because the internal control of the CHP unit is such that it allows cogenerated heat to be collected when the water-glycol mixture’s temperature is above a certain temperature. Additionally, the figure above shows that the cogenerated heat and electricity recover with different rates towards their maximum values. The electrical recovery rate converges to its optimum value quicker than its heat counterpart. Finally, Figure 3.5 suggest no significant difference between the part-load and full load operations in terms of output recovery rates.