Elsevier

Energy and Buildings

Volume 33, Issue 4, April 2001, Pages 309-317
Energy and Buildings

Efficient solution strategies for building energy system simulation

https://doi.org/10.1016/S0378-7788(00)00113-4Get rights and content

Abstract

The efficiencies of methods employed in solution of building simulation models are considered and compared by means of benchmark testing. Direct comparisons between the Simulation Problem Analysis and Research Kernel (SPARK) and the HVACSIM+ programs are presented, as are results for SPARK versus conventional and sparse matrix methods. An indirect comparison between SPARK and the IDA program is carried out by solving one of the benchmark test suite problems using the sparse methods employed in that program. The test suite consisted of two problems chosen to span the range of expected performance advantage. SPARK execution times versus problem size are compared to those obtained with conventional and sparse matrix implementations of these problems. Then, to see if the results of these limiting cases extend to actual problems in building simulation, a detailed control system for a heating, ventilating and air conditioning (HVAC) system is simulated with and without the use of SPARK cut set reduction. Execution times for the reduced and non-reduced SPARK models are compared with those for an HVACSIM+ model of the same system. Results show that the graph-theoretic techniques employed in SPARK offer significant speed advantages over the other methods for significantly reducible problems and that by using sparse methods in combination with graph-theoretic methods even problem portions with little reduction potential can be solved efficiently.

Section snippets

Background

Detailed simulation of building energy systems involves the solution of large sets of non-linear algebraic and differential equations. These equations emerge from component-based simulators such as TRNSYS [1] or HVACSIM+ [2], or equation-based tools such as SPARK [3] or IDA [4]. Since each of these tools employs a different solution strategy, the question arises as to which strategy is most appropriate for the kinds of equations encountered in the building simulation domain.

TRNSYS and HVACSIM+

Non-linear equation example

The first benchmark problem derives from a problem in the SPARK User’s Manual consisting of four highly non-linear equations:x1+x3+x22+x2=c1,x2=x1ex1,x1x4+x3x4+x43=c2,x4=x3e−x3SPARK finds a solution to these equations by the calculation sequence:x3=0.1,x4=x3e−x3,x1=c2−x3x4−x43x4,x2=x1ex1,x3=c2−x1−x22x2,iterateonx3Using the default SPARK solution process, Newton–Raphson iteration is performed until the difference between two successive values of x3 is less than a specified tolerance. Thus, it

Laplace’s equation example

The second benchmark problem, purposely chosen to be not well suited to the SPARK methodology, is Laplace’s equation in two dimensions. This equation models many physical phenomena, including heat transfer in a thin, square plate with uniformly distributed heat source and uniform boundary temperature. The problem is discretized by dividing the square into a uniform grid of specified size. Each cell in the grid is represented by a nodal temperature Ti,j and is governed by a heat balance equation:

HVAC benchmarks

Going beyond simple benchmark examples, the numerical methods used in SPARK were also evaluated by modeling an airflow system employing discrete-time controllers. The example used was a typical HVAC airflow network and its associated control loops, a problem involving significant computational burden [16].

A number of steady state component models were implemented as SPARK objects, including variable speed centrifugal fans, flow diverters, flow mixers and control dampers. In modeling air flow, a

Discussion

The above results confirm that the SPARK methodology offers significant reduction in solution times relative to both conventional and sparse matrix methods in the solution of certain kinds of non-linear equation systems. This is borne out most dramatically by the contrived non-linear benchmark problem, but is also quite clear from the HVAC control application. However, in the case of the example involving Laplace’s equation, we observe that without some user intervention, SPARK has difficulty

Conclusions

The principle conclusion that can be drawn from this work is that SPARK outperforms conventional and sparse matrix methods for solution of problems that can be decomposed and/or reduced with graph-theoretical techniques. Roughly speaking, execution time savings will be O(mr3) where r is the ratio of the largest cut set size to the number of equations in the problem, and m is the number of strongly connected components into which the problem partitions. Typical HVAC air flow systems simulation

Acknowledgements

Portions of this work were sponsored by the Japan Ministry of Education, the United Kingdom Royal Academy of Engineering Foresight Award Scheme and the Office of Building Technologies, Building Systems Division, US Department of Energy.

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