**3.4 Penalty cost for ZEB**

*Green Energy Advances*

sured as pollutant emission.

particular period.

is preferred [28].

**3.3 Optimization method**

*3.3.1 Single-objective design optimization*

*3.3.2 Multi-objective design optimization*

caused by ZEB.

• Economic value [life cycle analysis (LCA), net present cost (NPC)]: The proposed renewable energy alternative will be assessed using one of the engineering economic techniques which are net present cost (NPC), life cycle analysis

In terms of environmental factors, the reduction of building load will definitely reduce the energy required from the grid and on-site RES size, which can be mea-

• Pollutant emission: The criterion measures the equivalent emission of CO2, air emissions which are the results of applying different technologies in ZEB for a

In terms of grid interaction factors, the two-way electricity flow between building and grid poses more than technological challenges; those ZEB homeowners may make heavier use of the grid than the conventional building under one-way power flow. Grid interaction index is one of the indicators used to assess the grid stress

• Grid interaction index (GII): The criterion is defined as the standard deviation of the building-grid interaction over the specified time (e.g., 1 year). It is used to estimate the average stress of building on the grid, and a low standard deviation

It is reported that there are more than 50% of design optimization problems that are addressed as single-objective optimization problems, and they are usually focused on the most important criteria such as economic cost or environmental issues. For designing ZEB, the optimization may be conducted by focusing on the only one aspect of ZEB performance, e.g., NPC and CO2 emissions. Besides, since multi-objective design optimization problems can also be transformed into singleobjective optimization problems by using weighting factor, it is reasonable to convert all of the concerned ZEB performance indices into one combined function, as shown in (Eq. (3)). Where X represents a vector of design variables at the design stage, fave and fi (i = 1, 2…n) are the combined objective and the normalized sub-objectives, respectively; wi is the corresponding weighting factor for each sub-objective:

Min *fave* = *w*<sup>1</sup> × *f*1(*X*) + *w*<sup>2</sup> × *f*2(*X*) + …+*wn* × *fn*(*X*) (3)

*g*1(*X*) ≥ 0 (5)

The design and operation of ZEB are actually integrated with building owners, environment, energy source, and smart grid; it is, therefore, a multi-objective design optimization problem with even contradicting objectives. In general, genetic algorithm (GA) is the most popular optimization approach for single-objective and multi-objective optimizations of energy systems in numerous studies [31, 32]. Besides, particle swarm

s.t.*AX* ≤ *a* (4)

*g*2(*X*) = 0 (6)

(LCA), benefit/cost analysis, and payback period.

**46**

Although the progressive incentive policies have been recognized to widely encourage the installation of renewable energy system for buildings, the financial support scheme is forecasted to be downtrend and RES cost to be high, which are a barrier for promoting future buildings to be zero energy buildings. Therefore, a penalty cost scheme may be a good solution to build up the public's confidence and encourage them to be actively involved in ZEB application.

A comparison of the building cost under different mismatch ratios is shown in **Figure 7**. It is found that the minimum total cost is supposed to be located in O1 under mismatch ratio less than 0, possibly between −1.0 and 0.0, indicating that the selection of design option under mismatch ratio of 1.0 is not cost-effective. However, the introduction of penalty cost can move the minimum cost from O1 to O2, or the higher mismatch ratio the less cost, depending on the type of penalty cost designed by designers.

The total cost (*TC*) of the building basically consists of the initial cost (*IC*) of RES (e.g., PV, WT) and the operation cost (*OC*) during the building usage stage due to the electricity consumption from grid and oil consumption (Eq. (4)). The penalty cost can be expressed as a mathematic expression, which is assumed to follow a segmented function, as shown in Eq. (5). It should be noted that the cost results may be greatly different according to the designed penalty cost:

$$\text{TC}\_{P} = \text{IC} \star \text{OC} \star \text{PC} \tag{7}$$

 *PC* = ⎧ ⎪ ⎨ ⎪ ⎩ *TC*1.0 × (*a* − α × *SF*),*SF* < *p*<sup>1</sup> *TC*1.0 <sup>×</sup> (*<sup>b</sup>* <sup>−</sup> <sup>β</sup> <sup>×</sup> *SF*),*p*<sup>1</sup> <sup>≤</sup> *SF* < *<sup>p</sup>*2 *TC*1.0 × (*c* − δ × *SF*),*SF* ≥ *p*<sup>2</sup> . (8)
