Distributed demand side management via smart appliances contributing to frequency control

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1 Journal of Chongqing University (English Edition) [ISSN ] Vol. 14 No. 3 September 015 doi: /j.issn o cite this article: ZHANG Wei-chen. via smart appliances contributing to frequency control [J]. J Chongqing Univ: Eng Ed [ISSN ], 015, 14(3): via smart appliances contributing to frequency control ZHANG Wei-chen Department of Engineering, University of Cambridge, Cambridge CB3 0DS, U.K. Received 4 June 015; received in revised form 9 July 015 Abstract: Nowadays renewable energy has become a trend for energy production but its variable nature has made balancing of demand and supply of the power grid difficult. Dynamic demand management using smart appliances is proposed to serve as a way that part of the regulation burden of balancing demand and supply is shifted to the demand side. However, if all appliances respond to the same frequency deviation, they may start to synchronize, causing large power overshoots and instability of the power grid. herefore, the idea of implementing randomness into the frequency control of the appliances is proposed and this is what we call a stochastic approach. Simulators are built from scratch to model both scenarios. he effect of synchronization is analyzed and the parameters that can affect the synchronization are investigated. It has been found that the larger the contribution from the smart appliances to the power grid, the easier and faster the synchronization takes place. he stochastic approach solves the problem of synchronization and averages out the large power overshoot. However, the overall performance of stochastic operations is unacceptable due to the randomness in the operation though the mean and variance are as expected. More advanced feedback policies and schemes may be igned to achieve a better performance. Keywords: renewable energy; demand side; smart grid; smart appliance; frequency control; randomness CLC number: F407 Document code: A 1 Introduction a 1.1 Variable nature of renewables Nowadays, the power system is facing fundamental changes due to the variety of means of producing electricity. his variable nature of renewables imposes a big problem on the balancing of demand and supply in the power grid. We need vital control services in realizing the balancing and the current trend in renewables has further highlighted the importance of these services. Sometimes these services can even be critical in deciding whether a renewable project should be implemented in the first place. Supply and demand needs to be balanced to ensure optimum efficiency of operation. Unbalancing leads to poor efficiency and unreliability of the power grid [1]. ZHANG Wei-chen ( 张玮琛 ): zhangweichensy@16.com. 101

2 1. Demand side management he principle idea of demand side management is to shift part of the regulation burden of matching demand and supply to the consumer side []. It can be achieved by dynamic pricing which deals with a slower time scale or by employing the use of intelligent domestic appliances and deals with a faster time scale by deferring their energy consumption in response to the frequency of the grid. In this way, the number of spinning reserves can be reduced hence it is much cheaper to match supply and demand [3-4]. Its flexibility enables variable renewable output, which is a boost for the integration of renewable energy sources [5]. model used in the project for the purpose of analyzing the closed loop behavior of the interconnected system, where P f is the power correction contributed by the appliances, P L is the sudden change of power from the generators (in this case a sudden power loss in the power plant), and ω is the frequency deviation in radians from the grid, which is πf(t) [1,10]. 1.3 Research direction If all appliances respond to the frequency deviation in the grid by turning themselves on or off, they tend to synchronize with each other which causes unacceptable levels of overshoot in the energy demand and also leads to unstable oscillations in the system. he idea is that we can implement some randomness in the response of our appliances, hence, by the stochastic approach [6]. Design of simulation tools here are some frequency control packages on the market to simulate the dynamic behavior of a power system but they are not built in the randomness in the stochastic approach. herefore, simulators need to be built from scratch using Matlab..1 Power grid model A schematic simplified model of the power grid is shown in Fig. 1, where f(t) is the frequency deviation of the grid. A more complicated power grid model with more details is presented in Fig.. It is the power grid Fig. 1 Schematic simplified model of the power grid where f(t) is the frequency deviation of the grid Fig. Schematic model of the power grid where P f is the power correction contributed by the appliances, P L is the sudden change of power from the generators (in this case a sudden power loss in the power plant), ω is the frequency deviation in radians from the grid, and other variables in the diagram are self-correcting parameters associated with the power grid model which are carefully chosen to accommodate the simulation of this project We can model the power grid shown in Fig. in state space representation. We choose the state vector x and t t Pv( t), Pm( t), ( t) x. 10 J. Chongqing Univ. Eng. Ed. [ISSN ], 015, 14(3):

3 he power grid is then represented in the state space form as x Ax Bx. (1) t t t We then manage to obtain a complete set of equations including the expression for A, B and u for the space form representation, in which P tot signifies the total power in the power grid. u P P L f t, () Ptot g ( Rg) A 0, and B 0. t t 1 1 D 0 M M M he significance of state space form representation is that if we implement the ordinary differential equation in Matlab, it would suit all power grids. he equation xt Ax t But is unmodified and only parameters A, B, x(t) and u(t) change according to the complexity of the grid model.. Stochastic process algorithm In the stochastic case, appliances are modeled as Markov-jump linear systems or to be precise, jumpaffine systems [7-8]. hey are switched affine systems whose driving signal is the stochastic process associated with a finite Markov chain. Fig. 3 shows the Markov chain illustration. Fig. 3 Markov chain illustration he implementation of an inhomogeneous Markov chain for multiple interconnected appliances is realized using the following algorithm. 1) Detere the time for the next change of state. Reset t and generate r 1 as a random number r RND where RND denotes a random number 1, uniformly distributed in the interval [0,1]. Check the current status of each appliance and then start incrementing It () by adding either () t or () t 1 to I depending on the current status of the appliance. Note that () t and 1 () t for each non-identical appliance are different. An event of change of state happens at which I ln( r). 1 ) Detere which appliance to change state stochastically. Generate r as a random number r RND. he I is added up by probability transition rates of each appliance according to their status. herefore, by dividing each transition rates by the value of I, we can obtain the expression in the form of. 1 3 n I I I I herefore, each of the expression is in the interval [0,1] and represents a certain length on the axis between 0 and 1. he random number generated uniformly distributed in the interval can represent a device whose interval the random number is dropped upon. Change the current operating state of the random refrigerator decided by the previous algorithm and change the temperature for each appliance hence detering the overall consumption of the system and then feed it to the power grid input parameter u. 3) Repeat the algorithm above. Another set of transition rates are obtained for each refrigerator and another time interval for the next event is detered. hen the appliance is chosen. n I J. Chongqing Univ. Eng. Ed. [ISSN ], 015, 14(3):

4 Note that this algorithm is computationally simple because it only involves a random number generator and a standard quadrature routine [9]. and c v ( ) ON OFF ( ON OFF ) v. (6).3 Design of feedback policy.3.1 Deteristic operation he power grid model is simulated using state space representation. Standard refrigerator controllers operate on a hysteretic basis in which two temperature levels and trigger the motor on and off. he deteristic feedback control for the dynamic demand type refrigerators is initial control and bear problems involving synchronization and unstable systems. hreshold levels and are adjusted to change the temperature achieved by the operation of the refrigerator according to the frequency deviation. herefore a linear dependence on mains frequency deviation f is imposed on these thresholds. K is a constant of proportionality [1]. ( t) K f ( t), (3) and ( t) K f ( t). (4).3. Stochastic operation A more advanced control scheme can also be igned so that we can fix a ired value for the variance of operating temperatures as v, and we then detered the probability transition rates 1 and with a ired average temperature, or a ired average duty cycle. he control variables can then be expressed using these ired parameters as v ( ) ON OFF 1 1 ( ON OFF ) v c, (5) o realize the frequency control, we then made the ired temperature or ired operating duty cycle a linear relationship with frequency deviation. herefore, and can be made as linear functions of the frequency deviation f as below, where K and K are proportionality constants [1]. nom K f, (7) and nom K f. (8) 3 Result and discussion 3.1 Synchronization effect hree non-identical refrigerators with different parameters were simulated with the same frequency control proportional feedback to their operation threshold and, respectively. he power grid parameters are chosen as g 0.; 50; R 10; M 6.7; D 1; 1.3; Ptot 5. he refrigerator initial parameters are ; ON 38.3; OFF 0; ; ; initial 0. denotes the ambient temperature reached OFF by a refrigerator which is always OFF and P L ON denotes the steady state temperature reached by a refrigerator which is always ON. is the thermal dispersion coefficient. he power grid has a total power of 10 GW. he temperature of each refrigerator together with their operating threshold is shown in Fig. 4. he power consumption as the grid model input u is shown in Fig. 5. As we can observe, the three refrigerators are 104 J. Chongqing Univ. Eng. Ed. [ISSN ], 015, 14(3):

5 synchronized pite these non-identical parameters. hese effects cause large overshoot in power consumption and lead to a unstable system. Although the number of appliance is limited, it represents the overall effect if we implement frequency control on millions of refrigerators. In addition, the total power of the power grid, hence the proportion contributed by the smart appliance influences the effect of the synchronization. he power grids of 5 GW and 50 GW are both simulated with exactly the same refrigerator parameters, initial conditions and feedback policies. Figs. 6 and 7 show the comparison of synchronization, respectively. It can be seen from Fig. 6 that the synchronization happens easier and faster than the case shown in Fig. 7. Fig. 4 demonstrates an even faster synchronization than the 5 GW case. herefore, the larger the contribution from the frequency controlled smart appliances to the power grid, the easier and faster synchronization takes place. Fig. 4 Refrigerator temperatures and temperature boundaries of closed loop multiple refrigerators in the deteristic operation and the synchronization effect where the total power in the power grid is 10 GW Fig. 5 Power grid input parameter u of closed loop multiple refrigerators in the deteristic operation J. Chongqing Univ. Eng. Ed. [ISSN ], 015, 14(3):

6 Fig. 6 emperature boundaries and appliance temperatures of closed loop multiple refrigerators in the deteristic operation and the synchronization effect where the total power in the power grid is 5 GW Fig. 7 emperature boundaries and appliance temperatures of closed loop multiple refrigerators in the deteristic operation and the synchronization effect where the total power in the power grid is 50 GW 3. Stochastic approach hree interconnected refrigerators with different initial probability transition rates were simulated. All parameters of the refrigerators and the power grid parameters are kept the same as the section above. Fig. 8 shows the temperature of the three refrigerators. Fig. 8 shows that the synchronization effect is eliated by the randomness inserted to the refrigerator frequency control. he overall trend may look synchronized from the start, however, as the operation continues and the randomness effect takes into action, the temperature starts to drift from synchronization. his is the simulation for only three refrigerators and the result is already promising. If millions of refrigerators are interconnected in a stochastic way, it would not synchronize and the randomness averages out the large power overshoot together with the synchronization effects. 106 J. Chongqing Univ. Eng. Ed. [ISSN ], 015, 14(3):

7 Fig. 8 emperature of three closed loop refrigerators in the stochastic operation he stochastic operation with feedback is igned to achieve an expected mean and variance. However, the operation is unacceptable. Despite the fact that the mean and variance are as expected, the overall performance of the smart appliance is below the expectation of customers because the randomness in the operation leads to more frequent switching of the appliance. 4 Conclusions 4.1 Main findings he deteristic frequency control of the smart appliances has its drawbacks such as synchronization effect, which leads to large power overshoot and instability in the power grid. We found out that the larger the contribution to the power grid from the smart appliances, the easier and faster the synchronization happens. Although the stochastic approach solves the problem of synchronization, the overall performance of the smart appliance is below the expectation of customers due to the randomness in the operation 4. Future work More advanced feedback policies can be igned to achieve a better performance. More complex power grid models can also be used to simulate a more realistic situation. In addition, hybrid schemes can be employed to give a more acceptable behavior. here is still a long way to go before all the appropriate appliances in a city of even a country are replaced by new models. Of course, government subsidies and encouragement policies are also essential for this to happen. It is a project with great potential and once implemented, will have great influence on the further integration of renewable energy sources. References [1] Angeli D, Kountouriotis PA. A stochastic approach to dynamic-demand refrigerator control [J]. IEEE ransactions on Control Systems echnology, 01, 0(5): [] Aunedi M, Calderon JEO, Silva V, et. al. Economic and environmental impact of dynamic demand [J]. IEEE ransactions on Smart Grid, 013, 4(4): [3] Wang JX, Wang XF, Wu Y. Operating reserve model in the power market [J]. IEEE ransactions on Power Systems, 005, 0(1): 3-9. [4] Boyle EG. Renewable electricity and the grid-the challenge of variability [M]. London: Pub Earthscan, 009: J. Chongqing Univ. Eng. Ed. [ISSN ], 015, 14(3):

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