Robust provision of demand response from thermostatically controllable loads using lagrangian relaxation

Figures & data

Table 1. A summary of existing control approaches for DR.

Ref.	Type of control	Control technique	Address uncertainties?	End-user privacy preserved?	Type of TCL
Bashash and Fathy (2013)	centralised	sliding mode control	×	×	ON-OFF
Liu and Shi (2016a)	centralised	MPC	×	×	ON-OFF
Mathieu et al. (2013)	centralised	look-ahead controller	×	✓	ON-OFF
Zhang et al. (2013)	centralised	broadcast control	×	✓	ON-OFF
Mahdavi and Braslavsky (2020)	centralised	MPC	×	×	variable-speed
Larsen et al. (2013)	distributed	MPC + dual decomposition	×	partially	N/A
Papadaskalopoulos and Strbac (2013)	distributed	LR method	×	✓	N/A
Liu and Shi (2014)	distributed	distributed MPC	×	✓	ON-OFF
Tindemans et al. (2015)	distributed	stochastic control	×	✓	ON-OFF
Burger and Moura (2017)	distributed	ADMM + optimisation	×	✓	ON-OFF
Mahdavi et al. (2017)	distributed	cluster-based MPC	×	partially	ON-OFF
Oldewurtel et al. (2014)	centralised (building-level)	stochastic MPC + affine disturbance feedback	weather predictions	N/A	N/A
Maasoumy et al. (2014)	centralised (building-level)	robust MPC	model uncertainties	N/A	N/A
Vrettos et al. (2016)	centralised	robust MPC	secondary frequency signal	N/A	N/A
Erdinc et al. (2019)	centralised	stochastic optimisation	outdoor temperature	×	ON-OFF
Diekerhof et al. (2018)	distributed	ADMM + robust MPC	thermal demand	✓	N/A
proposed	distributed	LR + robust MPC	outdoor temperature + model parameters	✓	variable-speed

Note: N/A– not applicable

Figure 1. Block diagram of the proposed hierarchical DR scheme: local controllers at each household and the coordinating controller at the central utility are derived from the LR method; each local controller employs robust MPC to account for uncertainties in thermal parameters R, C and outdoor temperature v.

Figure 2. Scenario A: certainty-equivalent scenario for n = 500.

Figure 3. Scenario B: $w_0={0.10}^{\circ }\mathrm{C}$ for n = 500.

Figure 4. Scenario C: $w_0={0.15}^{\circ }\mathrm{C}$ for n = 500.

Figure 5. Scenario D: $w_0={0.20}^{\circ }\mathrm{C}$ for n = 500.

Table 2. Comparison of the total execution time under different scenarios.

		Total execution time in the presence of uncertainties (min)
Aggregation size (n)	Total execution time under the certainty-equivalent scenario (min)	$w_0={0.10}^{\circ }\mathrm{C}$	$w_0={0.15}^{\circ }\mathrm{C}$	$w_0={0.20}^{\circ }\mathrm{C}$	$w_0={0.25}^{\circ }\mathrm{C}$
100	26.85	26.02	26.74	20.71	inf.
250	60.66	61.17	57.28	59.95	inf.
500	108.0	112.2	107.1	110.5	inf.

Note: – simulations are carried out on a computing facility equipped with Intel(R) Xeon(R) CPU E5-2680 v3 2.50 GHz and 64 GB RAM memory.– the local controller algorithm (20(20a) $\begin{array}{rl}& \underset{u_i^{(\nu +1)}(k+j)}{min}\underset{w_i(k+j)}{max}\sum _{j=0}^{N-1}[{\ell }_{i,j}(u_i(k+j\mid k))\\ & +{\lambda }^{(\nu )}(k+j)\cdot u_i(k+j\mid k)]\end{array}$(20a) ) is executed in parallel.

Figure 6. The convergence of λ at different time steps under $w_0={0.10}^{\circ }\mathrm{C}$ for n = 500.

Figure 7. The convergence of s at different time steps under $w_0={0.10}^{\circ }\mathrm{C}$ for n = 500.

Bashash, S., & Fathy, H. K. (2013, July). Modeling and control of aggregate air conditioning loads for robust renewable power management. IEEE Transactions on Control Systems Technology, 21(4), 1318–1327. https://doi.org/10.1109/TCST.2012.2204261

 Web of Science ®Google Scholar

Liu, M., & Shi, Y. (2016a). Model predictive control for thermostatically controlled appliances providing balancing service. IEEE Transactions on Control Systems Technology, 24(6), 2082–2093. https://doi.org/10.1109/TCST.2016.2535400

 Web of Science ®Google Scholar

Mathieu, J. L., Koch, S., & Callaway, D. S. (2013). State estimation and control of electric loads to manage real-time energy imbalance. IEEE Transactions on Power Systems, 28(1), 430–440. https://doi.org/10.1109/TPWRS.2012.2204074

 Web of Science ®Google Scholar

Zhang, W., Lian, J., Chang, C. Y., & Kalsi, K. (2013, November). Aggregated modeling and control of air conditioning loads for demand response. IEEE Transactions on Power Systems, 28(4), 4655–4664. https://doi.org/10.1109/TPWRS.2013.2266121

 Web of Science ®Google Scholar

Mahdavi, N., & Braslavsky, J. H. (2020, September). Modelling and control of ensembles of variable-speed air conditioning loads for demand response. IEEE Transactions on Smart Grid, 11(5), 4249–4260. https://doi.org/10.1109/TSG.2020.2991835

 Web of Science ®Google Scholar

Larsen, G. K. H., van Foreest, N. D., & Scherpen, J. M. A. (2013, June). Distributed control of the power supply-demand balance. IEEE Transactions on Smart Grid, 4(2), 828–836. https://doi.org/10.1109/TSG.2013.2242907

 Web of Science ®Google Scholar

Papadaskalopoulos, D., & Strbac, G. (2013, November). Decentralized participation of flexible demand in electricity markets–Part I: Market mechanism. IEEE Transactions on Power Systems, 28(4), 3658–3666. https://doi.org/10.1109/TPWRS.2013.2245686

 Web of Science ®Google Scholar

Liu, M., & Shi, Y. (2014). Distributed model predictive control of thermostatically controlled appliances for providing balancing service. In 53rd IEEE conference on decision and control (pp. 4850–4855). IEEE.

 Google Scholar

Tindemans, S. H., Trovato, V., & Strbac, G. (2015). Decentralized control of thermostatic loads for flexible demand response. IEEE Transactions on Control Systems Technology, 23(5), 1685–1700. https://doi.org/10.1109/TCST.2014.2381163.

 Web of Science ®Google Scholar

Burger, E. M., & Moura, S. J. (2017, May). Generation following with thermostatically controlled loads via alternating direction method of multipliers sharing algorithm. Electric Power Systems Research, 146, 141–160. https://doi.org/10.1016/j.epsr.2016.12.001

 Web of Science ®Google Scholar

Mahdavi, N., Braslavsky, J. H., Seron, M. M., & West, S. R. (2017, November). Model predictive control of distributed air-conditioning loads to compensate fluctuations in solar power. IEEE Transactions on Smart Grid, 8(6), 3055–3065. https://doi.org/10.1109/TSG.2017.2717447

 Web of Science ®Google Scholar

Oldewurtel, F., C. N. Jones, Parisio, A., & Morari, M. (2014, May). Stochastic model predictive control for building climate control. IEEE Transactions on Control Systems Technology, 22(3), 1198–1205. https://doi.org/10.1109/TCST.2013.2272178

 Web of Science ®Google Scholar

Maasoumy, M., Razmara, M., Shahbakhti, M., & Vincentelli, A. S. (2014). Handling model uncertainty in model predictive control for energy efficient buildings. Energy and Buildings, 77, 377–392. https://doi.org/10.1016/j.enbuild.2014.03.057

 Web of Science ®Google Scholar

Vrettos, E., Oldewurtel, F., & Andersson, G. (2016). Robust energy-constrained frequency reserves from aggregations of commercial buildings. IEEE Transactions on Power Systems, 31(6), 4272–4285. https://doi.org/10.1109/TPWRS.2015.2511541

 Web of Science ®Google Scholar

Erdinc, O., Tascikaraoglu, A., Paterakis, N. G., & Catalao, J. P. S. (2019, February). Novel incentive mechanism for end-users enrolled in DLC-based demand response programs within stochastic planning context. IEEE Transactions on Industrial Electronics, 66(2), 1476–1487. https://doi.org/10.1109/TIE.2018.2811403

 Web of Science ®Google Scholar

Diekerhof, M., Peterssen, F., & Monti, A. (2018). Hierarchical distributed robust optimization for demand response services. IEEE Transactions on Smart Grid, 9(6), 6018–6029. https://doi.org/10.1109/TSG.2017.2701821

 Web of Science ®Google Scholar