Características comunes en los dispositivos de conmutación

The allocation of priority to individual EWHs is typically based on MG parameters, such as reserve margin and expected demand. For MG and consumer aware priority allocation as introduced in this dissertation, the stochastic nature of consumer behaviour and consumer comfort is considered during priority allocation. The resulting priorities are then considered along with the MG reserve margin to establish a DR which strives to satisfy both MG constraints and consumer comfort levels.

The MG constraint is satised by ensuring that the total demand of the EWH MG remains within a specied limit. Moreover, to maintain consumer comfort, the goal is to ensure that the temperature of the EWH water is suciently high in order to facilitate comfortable temperatures during the next hot water usage event. These two factors are accounted for in two steps; the rst step evaluates the EWH priority within the MG based on user comfort during usage events and the second step evaluates, based on the rst step, which EWHs can have power allocated to them while remaining within the power constraint.

4.8.1.1 Parameter Selection

The conventional EWH scheduling wisdom sees users allocating power to their EWH to heat in preparation for later expected hot water usage. The amount of time required for the EWH to suciently heat the water is rarely known and is based on an estimate from previous experience, typically ranging from one to two hours.

To improve on this arbitrary time estimate, an investigation into the main drivers of EWH energy ow is considered to identify the drivers with the highest weights. These drivers will then be used to develop a method to establish the relative urgency of EWHs. From the conventional wisdom of EWH scheduling, the main goal is to have hot water available for an expected hot water usage event. The components that directly inuence the heating schedule include:

ˆ Time remaining until hot water is required. ˆ Current water temperature.

ˆ Water usage.

ˆ Heating rate (energy input rate). ˆ Inlet water temperature.

ˆ Ambient temperature.

The time parameter ties all these components together. To identify the weights of each of these components, the energy and rate of energy transfer per unit of time are investigated.

Using the above established theory, the relative contribution of each aspect is weighed against the total thermal energy contained within the water of the EWH. This will provide insight into how taxing or benecial the components are, which directly impacts the heating schedule of an EWH.

Using sample EWH parameters, as shown in Table 4.4, along with the aforementioned equations, the theoretical energy magnitude expended or gained as a result of usage, loss and heating was calculated over the period of one minute. These values are then normalised to a percentage of the total EWH energy. The resulting values are summarised in Table 4.5. The sample EWH parameters were selected based on the mean EWH parameters from the eld study.

From Table 4.5 it is evident that energy recovery through hot water usage takes place at a much higher rate than both energy input through heating and heat loss through thermal radiation. Even at a low ow rate of 5 L/min, typically associated with washing hands, a magnitude of 244 W h energy can theoretically be recovered, 3.5 % of the total thermal energy contained in the EWH. The energy recovered at a high ow rate of 20 L/min, typically associated with a shower or drawing a bath, clocks in at 977 W h, 14 % of the total thermal energy contained in the EWH. Considering the energy input due to heating, the 3 kW element manages to input 50 W h of energy into the water, only 0.72 % of the total thermal energy in the EWH. Contrasting this with the heat loss, at 0.924 W h, or 0.01 % of the total thermal energy, the main concern is clearly hot water usage.

Table 4.4: Parameters of sample EWH used for cost function design.

Parameter Symbol Value Unit

Specic heat capacity of water c 1.1628 W h/(kg◦C)

Density of water ρ 1000 kg/m3

EWH volume VEW H 150 L

EWH element power PEW H 3 kW

EWH outlet temperature Thot 60 ◦C

EWH inlet temperature Tinlet 18 ◦C

EWH ambient temperature Tamb 20 ◦C

EWH thermal resistance R 0.7 ◦C/W

Cooling constant k 2.207 1/µs

Low ow usage Vrate_low 5 L/min

Medium ow usage Vrate_med 10 L/min

Table 4.5: Parameter energy values for a 1 minute period of the sample EWH.

Parameter Vrate (L/min) E (W h) % of Total

Low ow usage 5 244.183 3.50

Medium ow usage 10 488.367 7.00

High ow usage 20 976.733 14.00

EWH heating N/A 50.000 0.72

EWH heat loss N/A 0.924 0.01

EWH total energy N/A 6976.667 100.00

As a result, the largest consideration towards creating a schedule is the expected volume of hot water to be extracted, followed by the element rating of the EWH. A balance between these two components needs to be found in terms of time trade-o. Since the energy recovery is typically at a rate in the range of 4.9 - 19.5 times that of the energy input, the energy input must be allowed up to 19.5 times longer to suciently heat the water. Due to the stochastic volumes of hot water used, the expected volume usage contributes less information than the expected time of the hot water usage event, in terms of ensuring consumer comfort.

As minimal heating in preparation of a small event may be sucient for the small event, but greatly detrimental to a larger event, the expected volume usage is deemed to contribute less information required for maintaining user comfort.

First parameter: From this, the rst parameter is obtained, the expected time of the hot water usage event.

The second largest consideration towards creating a schedule is the current level of thermal energy contained within the EWH, i.e., how hot the EWH water is. If there is sucient thermal energy available, heating the water is not a high priority as the hot water usage may occur and it will maintain consumer comfort. This is contrary to a low level of thermal energy, i.e. cold water, whereby the consumer comfort will not be maintained and may require a lengthy heating period prior to the usage event to ensure consumer comfort.

Second parameter: From this, the second parameter is obtained, the current temper- ature of the EWH water.

4.8.1.2 Cost Function

In order to establish the relative urgency of the EWH power requests, the EWH MG is evaluated based on the above selected parameters. These parameters enable the evaluation of energy required at some point in the future versus the amount of time available to deliver the required energy.

In order to assign priority scores to the EWHs, each is evaluated by the selected parameters as described above. To gain better insight into the urgency

Algorithm 1: Oracle priority allocation algorithm.

1 receive thermostat result Pthermostat = {P1, ..., PN};

2 cost = cost_function(alpha, time_delta, beta, temp_delta)

3 priority = cost.argsort()[:: −1]

4 Pcumulative= cumsum(Pthermostat[priority])

5 Pselected = Pcumulative<= Plimit

6 Premainder = Plimit− Pselected

7 Poptimise = Pnotselected<= Premainder

8 prioritised = Pselected|Poptimise 9 prioritised[priority] = prioritised