VOLTAGE SOURCE CONVERTERS

Once the cost function has been evaluated, the resultant cost vector is used to allocate power to the MG of EWHs. The pseudo code of the algorithm can be seen in Algorithm 1. This algorithm works in two phases, the rst allocates power to the majority of EWHs and the second searches for a remaining EWH that may ll the remaining surplus capacity. The goal of this phase is to ensure the MG power demand remains within the power limit while maximising the number of EWHs that have power allocated to them. The objective is shown in (4.16) and the constraint is shown in (4.17).

Pgrid = N

X

n=1

Pn (4.16)

With the constraint that:

Pgrid <= Plimit (4.17)

Procedure:

1. Sort thermostat result by EWH priority, as determined by the cost function. 2. Cumulative sum the resultant arrays, by the P power limits

3. Determine number of EWHs able to turn on while remaining within power limit, for P power limits

4. Determine surplus capacity remaining of the P power limits

5. Determine number of EWHs able to turn on within surplus capacity remaining of the power limits (optimisation step)

4.8.2.1 Phase One

Phase one of the power allocation assigns power to the majority of eligible EWHs that fall within the power limit. This is done by determining the number of EWHs with highest priority that may be allocated power.

The input to this phase is the result of an intersect (AND) between the thermostat control, which determines based on set-point control which EWHs should heat the water, and schedule control, which is a preallocated schedule that was set for each individual EWH. Therefore, it may be that some EWHs have a power request of zero, instead of

their element value. At an algorithm level, this result is achieved by the intersect of the thermostat and schedule results.

The other input to this phase is the priority assignment of each individual EWH, based on the prior developed cost function. This is used to establish which EWHs have the highest priority and should be considered for power allocation rst. At an algorithm level, this is used to sort the thermostat and schedule result by descending order of priority. Using this priority-sorted power request vector, the number of EWHs allowed to have power allocated to them is determined. At an algorithm level, this was achieved by cumulative summing the power request vector and selecting all elements that are below the index of the element that results in a cumulative sum larger than the power limit. A mathematical representation of a cumulative sum of a vector is shown in (4.18). This ensures that all the selected EWHs will remain within the specied power limit.

An important note, the Oracle must be evaluated along with the thermostat and schedule. Since the power request vector may contain zeros, the Oracle could assign a large number of EWHs, which at time of Oracle evaluation were within the power limit, but at subsequent evaluation of the thermostat and schedule control, more non-zero power requests may be present in the Oracle allocated priority list.

yi = i X j=1 xj (4.18) 4.8.2.2 Phase Two

Phase one allocated power to the majority of EWHs which allows the MG to remain within the specied power limit. However, due to variable EWH element ratings, this may not provide an optimal solution. If, during the cumulative sum, the element that causes the power request vector to overshoot the power limit is large, say 4 kW, this method will terminate the search for more EWHs as the cumulative sum will indicate that the power limit will be exceeded beyond this point. It may be the case that directly following the large 4 kW element, a smaller 2 kW element may be requesting power that would still t within the remaining power limit.

This necessitates another evaluation of the power request vector, to establish whether there may be a suitable element which could ll in the remaining power limit to maximally utilise the specied power limit. To achieve this, the elements not considered for power allocation during phase one are measured against the remaining power limit surplus. The element with the highest priority is added to the list of EWHs that are to have power allocated to them, while remaining within the power limit constraint.

Due to the typical EWH element ratings, as shown in Table 4.6, only a single EWH may be selected from the remaining EWHs in order to preserve a balance between optimally utilising the power limit and preserving the inexpensive nature of the Oracle.

4.9 Results

Using the dened metrics from section 4.7, the Oracle performance is evaluated in this section.

Table 4.6: Parameters used during Oracle simulation.

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 100, 150, 200 L

EWH element power PEW H 2, 3, 4 kW

EWH outlet temperature Thot Simulated ◦C

EWH inlet temperature Tinlet Measured ◦C

EWH ambient temperature Tamb Measured ◦C

EWH thermal resistance R 0.7 ◦C/W

Number of EWHs N 34

Oracle actuation period ∆toracle 10 minutes

Hot temperature threshold Thot 45 ◦C

Peak limit Plimit 20, 30, 40, 50 kW

Set point temperature Tlimit 50, 60, 70 ◦C

Ripple control time start 18:00

Ripple control time end 20:00

Day period start 2016-10-13

Day period end 2016-10-14

Month period start 2016-09-19

Month period end 2016-10-17

UTC +2 hours