Abstract
The heating, ventilation, and air-conditioning (HVAC) systems account for about half of the building energy consumption. The optimization methodology access to optimal control strategies of chiller plant has always been of great concern as it significantly contributes to the energy use of the whole HVAC system. Given that conventional centralized optimization methods relying on a central operator may suffer from dimensionality and a tremendous calculation burden, and show poorer flexibility when solving complex optimization issues, in this paper, a novel distributed optimization approach is presented for chiller plant control. In the proposed distributed control scheme, both trade-offs of coupled subsystems and optimal allocation among devices of the same subsystem are considered by developing a double-layer optimization structure. Non-cooperative game is used to mathematically formulate the interaction between controlled components as well as to divide the initial system-scale nonlinear optimization problem into local-scale ones. To solve these tasks, strategy updating mechanisms (PSO and IPM) are utilized. In this way, the approximate global optimal controlled variables of devices in the chiller plant can be obtained in a distributed and local-knowledge-enabled way without neither global information nor the central workstation. Furthermore, the existence and effectiveness of the proposed distributed scheme were verified by simulation case studies. Simulation results indicate that, by using the proposed distributed optimization scheme, a significant energy saving on a typical summer day can be obtained (1809.47 kW·h). The deviation from the central optimal solution is 3.83%.
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Abbreviations
- ADMM:
-
alternating direction multiplier method
- AGSO:
-
augmented group search optimization algorithm
- ALM:
-
augmented Lagrangian method
- BAS:
-
building automation system
- COP:
-
coefficients of performance
- DCSA:
-
differential cuckoo search algorithm
- DFO:
-
diffusion optimization problem
- DTO:
-
distributed optimization problem
- ESC:
-
extremum seeking control
- GA:
-
genetic algorithm
- HVAC:
-
heating, ventilation, and air-conditioning
- IoT:
-
Internet of things
- IPM:
-
inter point method
- IRBSO:
-
improved ripple bee swarm optimization algorithm
- LRS:
-
recursive least squares estimation technique
- MINLP:
-
mixed integer nonlinear programming
- MM:
-
manual method
- NN:
-
neural networks
- OCL:
-
optimal chiller loading
- P2P:
-
peer-to-peer
- PLR:
-
partial load rate
- PSO:
-
particle swarm optimization
- SA:
-
simulated annealing algorithm
- VAV:
-
variable air volume
- A :
-
strategy space
- D :
-
set of devices of a subsystem
- S :
-
set of all subsystems
- X :
-
state space
- Γ :
-
system disturbance
- C ch :
-
supply-side generation of chillers (kW)
- C u :
-
demand-side cooling load of users (kW)
- \({\underline{C}}\) :
-
lower limit of capacity (kW)
- \({\bar C}\) :
-
upper limit of capacity (kW)
- ChillerCapFTemp :
-
cooling capacity factor
- ChillerEIRFTemp :
-
energy input to cooling output factor (function of temperature)
- ChillerEIRPLR :
-
energy input to cooling output factor (function of part load ratio)
- fit (X i):
-
fitness function of particle i
- gBest :
-
swarm’s best known position
- H :
-
pump head (m)
- {unload}chiller,i :
-
lower limit of chiller i’s cooling capacity (kW)
- \({\overline {load} ^{{\rm{chiller}},i}}\) :
-
upper limit of chiller i’s cooling capacity (kW)
- M :
-
penalty coefficient
- n pump,i :
-
relative speed of pump i, npump, i ∈ [0,1]
- P :
-
energy consumption (kW·h)
- pBest :
-
particle’s best known position
- Q cw :
-
chilled water flow rate (m3/h)
- \({{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over Q} }_{{\rm{cw}}}}\) :
-
changes in chilled water flow rate (m3/h)
- \({{\tilde Q}_{{\rm{cw}}}}\) :
-
estimation of chilled water flow rate, m3/h
- \({\tilde {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{Q} }_{CW}}\) :
-
estimation of changes in chilled water flow rate (m3/h)
- \(\underline {{Q_{{\rm{cw}}}}} \) :
-
lower limit of chilled water flow rate (m3/h)
- \(\overline {{Q_{{\rm{cw}}}}} \) :
-
upper limit of chilled water flow rate (m3/h)
- t :
-
time step
- T cond,e :
-
entering cooling water temperature (°C)
- T cw :
-
chilled water temperature (°C)
- T cw,l :
-
leaving chilled water temperature (°C)
- T cw,r :
-
entering chilled water temperature (°C)
- \({{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over T} }_{{\rm{cw}}}}\) :
-
changes in chilled water temperature (°C)
- \({{\tilde T}_{{\rm{cw}}}}\) :
-
estimation of chilled water temperature (°C)
- \({\tilde {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{T} }_{CW}}\) :
-
estimation of changes in chilled water temperature (°C)
- \(\underline {{T_{{\rm{cw}}}}} \) :
-
lower limit of chilled water temperature (°C)
- \(\overline {{T_{{\rm{cw}}}}} \) :
-
upper limit of chilled water temperature (°C)
- V control :
-
controlled variable
- V environment :
-
environment variables
- V set :
-
parameters set by end users
- α :
-
compensation factor
- η :
-
pump efficiency
- *:
-
optimal solution
- chiller:
-
parameters of chiller subsystem
- i :
-
subsystem/device series number
- −i :
-
other components except for component i
- i, j :
-
device j of subsystem i
- pump:
-
parameters of pump subsystem
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 51978481). The support provided by China Scholarship Council (No. 202006260140) during a visit to Cardiff University is acknowledged.
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Li, S., Pan, Y., Wang, Q. et al. A non-cooperative game-based distributed optimization method for chiller plant control. Build. Simul. 15, 1015–1034 (2022). https://doi.org/10.1007/s12273-021-0869-5
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DOI: https://doi.org/10.1007/s12273-021-0869-5