A comparative study of time aggregation techniques in relation to power capacity expansion modeling

Abstract

In this paper, we studied the aggregation techniques for power capacity expansion problems. Combining a growing demand for green energy with a hard constraint on demand satisfaction causes system flexibility to be a major challenge in designing a stable energy system. To determine both the need for flexibility and which technologies that could satisfy these needs at minimum cost, the system should be analyzed on an hour-by-hour scale for a long period of time. This often leads to computationally intractable problems. One way of getting more tractable models is to aggregate the time domain. Many different aggregation techniques have been developed, all with a common goal of selecting representative time slices to be used instead of the full time scale, gaining a problem size reduction in the number of variables and/or constraints. The art of aggregation is to balance the computational difficulty against the solution quality, making validation of the techniques crucial. We propose new aggregation techniques and compare these to each other and to a selection of aggregation techniques from the literature. We validate the aggregated problems against the non-aggregated problems and look into the sensitivity of the performance of the aggregation techniques to different data sets and to the selection of different element types. Our analysis shows that aggregation techniques can be used to achieve very good solutions in a short amount of time, and that simple aggregation techniques achieve good performance similar to that of techniques with higher complexity. Even though the aggregation techniques in this paper are applied to power capacity expansion models, the methodology can be used for other problems with similar time dependence, and we believe that results in agreement with the results seen here, would be achieved.

Appendices

Terminology

Nomenclature

AT:

Aggregation technique

BS:

Benchmark solution

CA:

Cluster analysis

CC:

Cluster cluster

CCGT:

Combined cycle gas turbine

CDC:

Correlation duration curve

CEMUC:

Capacity expansion model with unit commitment

DB:

Dynamic blocking

DC:

Duration curve

DX:

Dummy selection

ES:

Exhaustive search

GS:

Grouping strategies

HC:

Hierarchical clustering

HS:

Heuristic selection

IS:

Investment selection

LC:

Level-correlation cluster

LDC:

Load duration curve

MILP:

Mixed integer linear program

NGS:

Non-grouping strategies

NRMSE:

Normalized root mean square error

OA:

Optimized RLDC approximation

OCGT:

Open cycle gas turbine

OPT:

Optimization

OS:

Optimal criteria selection

PC:

Partitioning clustering

PI:

Performance index

PV:

Photovoltaics

RDC:

Ramping duration curve

RL:

RLDC selection

RLC:

Residual load curve

RLDC:

Residual load duration curve

SC:

Single cluster

SR:

Statistical representation

UC:

Unit commitment

VRE:

Variable renewable energy

Supplements to the literature review

See Tables 21, 22 and 23 in appendix.

Table 21 Articles considering aggregated time series based on heuristic selection

Table 22 Articles considering aggregated time series based on cluster analysis

Table 23 Summary of the literature articles and their validation method

Supplements to the test cases results

See Table 24 in Appendix.

Table 24 The 20 different solutions achieved for the 219 single aggregations

Aggregation performance

See Tables 25, 26 and Figs. 7, 8 in appendix.

Table 25 Amount of different ISs observed within each type of grouping

Fig. 7

Relation between average NRMSE and average PI for all strategies. Averages are over all elements and years

Fig. 8

Relation between yearly averaged NRMSE and yearly averaged PI for all strategies divided into hour, days, and week elements

Table 26 Solution times in seconds for non-aggregated problems with fixed investment choices found by solving the aggregated problems