Dynamic Modular Modeling of Smart Loads Associated with Electric Springs and Control


Smart loads associated with electric springs (ES) have been used because fast demand-side management for smart grid. While simplified dynamic ES models have been used because power system simulation, these models do not include the dynamics of the power electronic circuits and control of the ES.This paper presents a dynamic and modular ES model that can incorporate controller design and the dynamics of the power electronic circuits. Based on experimental measurements, the order of this dynamic model has been reduced so that the model suits both circuit and system simulations.


The model is demonstrated with the radial chordal decomposition controller for both voltage and frequency regulation. The modular approach allows the circuit and controller of the ES model and the load module to be combined in the d-q frame. Experimental results based on single and multiple smart loads setup are provided to verify the results obtained from the model simulation. Then the ES model is incorporated into power system simulations including an IEEE 13 node power system and a three-phase balanced microgrid system.


  1. Electric spring
  2. Parameter estimation
  3. Radial-chordal decomposition
  4. Smart loads
  5. Microgrids




 Fig. 1 System setup in Phase III.




(a)Full results of experiment and the theoretical model.

(b)Zoom in results of experiment and the theoretical model.

(c) Full results of experiment and the estimated model.

(d) Zoom in results of experiment and the estimated model.

Fig. 2 Experimental and simulation (theoretical and estimated models) results of ES output voltage.

(a) PCC Voltage (Vg).

(b) Voltage output of ES (Ves).

(c) Current of the Smart load (Isl).

(d) P-Q power of the smart load.

Fig. 3 Experimental and simulation results on Phase II setup                                             with  a ZIP load.

(a) PCC Voltage (Vg).

(b) Voltage output of ES (Ves).

(c) Current of the Smart load (Isl).

(d) P-Q power of the smart load.

Fig. 4 Simulation results on Phase II setup with a thermostatic                                                               load.

(a) PCC voltage (Vg1/2/3).

(b)Voltage output of ES 1 (Ves1).

(c) Voltage output of ES 2 (Ves2).

(d) Voltage output of ES 3 (Ves3).

(e) P-Q power of smart load 1.

(f) P-Q power of smart load 2.

(g) P-Q power of smart load 3.

Fig. 5 Experimental and simulation results on Phase III setup.

(a) Power delivered by the renewable energy source.

(b)Phase A voltage of node 634 (Vs).

(c) Power absorbed in phase A of node 634.

(d)Sum power absorbed by smart load 1,2 and 3.

(e) Power absorbed by smart load 4.

(f) Power absorbed by smart load 5.

Fig. 6 Simulation results on Phase IV setup.

(a) Utility frequency

(b) PCC voltage (Vg)

Fig. 7 Simulation results on Phase V setup.


 In this paper, the dynamic model of an ES is firstly analyzed as a theoretical model in state space. An order-reduced model is derived by estimation based on experimental measurements. A theoretical model of the order of 6 with 4 inputs has been simplified into a 2nd-order model with 2 inputs. The RCD control is adopted as the outer-controller module in the smart load. Two models of noncritical loads, namely ZIP and thermostatic load models, are analyzed to cooperate with the ES. The estimated ES model (the inner model), outer controller and the load model can be modelled separated as modules and then combined to form the smart load model.


The modular approach offers the flexibility of the proposed model in outer-controller design and the noncritical load selection. The results obtained from the proposed model are compared with experimental measurements in different setups because model verification. The proposed model has been tested because voltage and frequency regulation. This simplified modular modeling method could pave the way because future work on modeling widely-distributed ESs in distribution networks so that various control strategies can be studied.


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