Predictive Active Power Control of Two Interconnected Microgrids
Abstract
When dealing with interconnected power systems, any sudden load changes leads to the deviation of active power and frequency in the tie-line. The daily management of the power system is also conditioned by the control of the active power and the frequency. It is a very important task in the conduct of the any electrical network to supply sufficiently and with high reliability the active power to be transmitted to the customers. Maintaining the frequency of each area and tie-line active power flow variation within prescribed value by adjusting the generator active outputs remain one of the main tasks of the network operators. This paper presents a model predictive regulator in controlling the power flow in tie-lines and frequency deviations in the microgrid, which will lead to power balance between the total active power generated and active power demand of the system. The system being studied consists of two microgrids, each made up of a wind farm, conventional thermal and hydro plants generator, photovoltaic (PV) system, storage system and active power demand. Predictive control algorithm is applied to control the power flow between two microgrids.
Keywords
Active power control Model predictive control Tie-line Renewable energy Storage system Smart gridIntroduction
MPC based LFC solutions
MPC based LFC solutions | ||
---|---|---|
MPC model | Areas | References |
Distributed model based state variables | 4 | [1] |
Distributed model based Simulink | 2; 3; 3 and 4 | |
Decentralised model based Simulink | 3 | |
Nonlinear model based Simulink | 2 and 3 | |
sRobust nonlinear based state variables | 1 | |
Robust multivariable based Simulink | 3 | [12] |
Supervisory MPC based Simulink | 4 | [13] |
Bat Inspired Algorithm based Simulink | 2 | [10] |
Economic MPC based state variable | 1 | [11] |
Most of the control strategies are based on the conventional controllers as the proportional integral and derivative (PI and PID). Which are easier to apply but most of the time give large settling time. The research carried out nowadays were initially based on artificial intelligent systems mainly on neural networks and fuzzy logic [14, 15, 16, 17, 18]. These techniques are based on the human expertise knowledge of their behaviour only and do not require any identification or system model. This is their main advantage over the others methods. The actual tendency in control strategies is the combination of the artificial intelligence algorithms with the conventional controller to solve the frequency or active power flow control issue in microgrids [19, 20, 21, 22, 23, 24]. These algorithms have attracted attention in load frequency controller design and showed their effectiveness for the design problems, but two difficulties must be taken into account. The first one is the convergence when dealing with refined search space, and the second one is the feasible trap in local minima solution due to the weakness of the local searching space ability [25, 26].
The algorithm named Model Predictive Control (MPC) belongs to a category of artificial intelligence algorithms that compute in a sequential manner using adjustments of manipulated variables to optimise and predict the future behaviour of the system. MPC is considered as one of the advanced control technique in control area [2, 27]. Its theoretical development over years can be seen by the amount of research available in the literature. As regards to the solution of load control frequency problem in power network some researches can be cited as references. Considering the imbalance uncertainty in the power system a predictive load frequency control model was presented in [2]. The presented model was based on the simplified system model that was updated using the Kalman algorithm for estimation of state and parameter considering the tie-line flow limit. The second model incorporating tie-line power flow limit, the capacity of generation units, and their change rate was proposed in [10]. According to this research, considering certain problems of LFC the MPC is a more realistic solution to the issues that power systems are dealing with nowadays. A model predictive load frequency control was presented in [11]. The proposed simplified MPC model took into account the existing network configuration and the power flow limitation in the tie-lines. Kassem [28] has proposed a model predictive controller based on neural network of a two microgrids LFC for improving the power grid dynamic performance. The effectiveness of the presented approach was demonstrated over a LFC using a fuzzy logic controller. Table 1 summarises some predictive controllers model based LFC solutions.
Khalid and Savkin [29] have proposed LFC based MPC for an optimal control of wind battery energy storage system (BESS). A model based on the prediction of frequency using Grey theory was also designed to optimise the performance of the basic predictive controller. LFC of multi-interconnected area power system using distributed model predictive was proposed in [29]. Analyses of results from three interconnected power system network have shown some improvements robustness and computational burden was show in the performance of closed-loop. Mohamed et al. [3] have presented a decentralised MPC based LFC in an interconnected power system. The results have shown that considering the proposed predictive method the overall performance of the closed loop technique has demonstrated robustness in load disturbances condition.
An economic aspect included in MPC to solve the LFC in one control area that was presented in [5]. The authors have proposed an operation cost reduction approach considering an order of magnitude similar based on the difference ratio of two set points MPC and PI controller. Sokoler et al. [30] have proposed an application of economic MPC for LFC considering a single area power system. The optimal operation control problem directly includes all the operation costs into its objectives function. Decentralised MPC based LFC in a tough situation for deregulated power systems was proposed in [6]. The effectiveness of the proposed model has been shown using different scenarios on interconnected power system model. Ersdal et al. [7] have proposed a MPC for power grid LFC when considering the imbalance uncertainty. Based on the simulations performed on the power system with a high number of wind generation integrated, it was shown that in certain cases in which the state of the art LFC applying PI controller and normal MPC have failed by violating the constraints of the system whislt the robust MPC fulfil all these constraints.
Distributed MPC strategies including application to LFC in electrical network was proposed in [1]. The distributed approach framework realises the performance similar to centralised MPC. Power system MPC-LFC was presented in [8]. The authors have modelled the limit of governor valve using fuzzy logic method and the local model predictive controllers were included into a nonlinear control system strategy. Distributed LFC based MPC of multi-area power grid after deregulation was introduced in [31]. Considering the frequency control problem as a dynamic control problem this model was designed based on the distributed model predictive considering external disturbances and the limit of active power generation constraints. Shiroei et al. [12] have proposed a robust predictive control model based LFC taking into account the generation limit constraints. The authors took into account the uncertainty and parameter variations and the proposed model was robust. MPC based LFC design concerning wind turbines was introduced in [9, 13, 32]. The proposed model introduced the fast response of frequency of a connected area power system taking into account wind turbines generation. Zhang et al. [4] have proposed a MPC for a reliable LFC with wind turbines. The algorithm used has reduced the impact of the randomness and intermittence of wind turbines effectively.
This research proposes a mathematical model of active power control based on MPC algorithm. Two microgrids interconnected via two ac tie-lines are considered and the simulation results were compared with those obtained using the open control loop or applying the optimal control. The rest of this research paper is structured as follows: In “Microgrids Presentation” the configuration of the studied system is explained. Energy model system, overall structure of the microgrids are detailed in “Energy System Model”. “Energy System Control Model” introduces the open loop and close loop modelling. “Results and Discussions” presents the system data, simulations results and discussions. The conclusion of the research is summarised in “Conclusions”.
Microgrids Presentation
Electrically coupled together, each microgrid has an equal number of generators and constitutes a coherent group (all power sources respond directly together to any load variations). This configuration is called a control area within which the frequency is assumed to be the same regardless of the state that the network can go through (static or dynamic states). Since a tie-line transmits power within or outside a control area (microgrid), this fact must be accounted in the additional power balance equations for each control area.
Energy System Model
Overall Structure of the Microgrids
From Fig. 1, it can be seen two interconnected microgrids. The main source of microgrid 1 is conventional hydro power plant (synchronous generator 1 or SG 1, denoted by P_{1}(k)) and microgrid 2 has a conventional thermal power plant as a main source (synchronous generator 2 or SG 2 denoted by P_{8}(k)). Each microgrid is embedded with a wind farm (P_{2}(k) and P_{9}(k)), PV (P_{3}(k) and P_{10}(k)), Battery Energy Storage System 1 (BESS 1) (denoted by P_{4}(k) discharging mode and P_{5}(k) charging mode), BESS 2 (denoted by P_{11}(k) discharging mode and P_{12}(k) charging mode) and system load (P_{L1}(k) and P_{L2}(k)). Two ac ties-lines are used to interconnect the two microgrids (tie-line 1 denoted by P_{6}(k) and P_{7}(k) for tie-line 2). The active powers from wind farm, PV and the active load demand considered as inputs data are given and used under profile form.
Wind Farm and PV Array
- For the first microgrid:$$ P_{1} (k)+P_{2} (k)+P_{3} (k)+P_{4} (k)-P_{5} (k)-P_{L1} (k)\ge 0 $$(1)
- For the second microgrid:$$ P_{8} (k)+P_{9} (k)+P_{10} (k)+P_{11} (k)-P_{12} (k)-P_{L2} (k)\ge 0 $$(2)
Storage System Bank
Energy System Control Model
Open Loop Modelling
- a)Constraints given in Eqs. 12 and 13 imply that the total active power of each area is equal to the active powers from the main generator, wind system, PV arrays and the battery energy system; and this total power is found applying the Kirchhoff’s current law in the main bus of each area (Eq. 12 for area 1, Eq. 13 for area 2).$$ P_{1} (k)+P_{2} (k)+P_{3} (k)+P_{4} (k)-P_{5} (k)=P_{L1} (k) $$(12)$$ P_{8} (k)+P_{9} (k)+P_{10} (k)+P_{11} (k)-P_{12} (k)=P_{L2} (k) $$(13)
- b)
Constraints given in Eqs. 1 and 2 ensure that the active power delivered by the grid, wind, PV, and BESS for each area is equal to the local load and the load will be supplied anytime and in any conditions.
- c)Constraints formulated in expression (14) ensure that the active power delivered by the PV arrays, wind system and BESS directly to the local of each area is greater than zero.$$\begin{array}{@{}rcl@{}} P_{1} &\ge& 0;P_{2} \ge 0;P_{3} \ge 0;P_{4} \ge 0;P_{5} \ge 0;P_{8} \ge 0;\\ P_{9} &\ge& 0;P_{10} \ge 0;P_{11} \ge 0;P_{12} \ge 0 \end{array} $$(14)
- d)Constraints given in expression (15) ensure that each energy sourcei is constrained by two limits: a maximum and a minimum.$$ P_{i}^{\min } \le P_{i} (k)\le P_{i}^{\max } $$(15)
- e)Equations 16 and 17 ensure that battery energy storage system charge will not be less than the minimum value or higher than its maximum value$$\begin{array}{@{}rcl@{}} soc^{\min }&\le& soc(0)+{\Delta} t.c_{p} \sum\limits_{i = 1}^{k} P_{4} (k)\\ &&-{\Delta} t.\frac{1}{c_{t} }\sum\limits_{i = 1}^{k} {P_{5} (k)\le soc^{\max }} \end{array} $$(16)$$\begin{array}{@{}rcl@{}} soc^{\min }&\le& soc(0)+{\Delta} t.c_{p} \sum\limits_{i = 1}^{k} P_{11} (k)\\ &&-{\Delta} t.\frac{1}{c_{t} }\sum\limits_{i = 1}^{k} {P_{12} (k)\le soc^{\max }} \end{array} $$(17)
Model Predictive Control (MPC) Configuration (Close Loop)
The output is defined by P_{L1}(k) + P_{L2}(k) linked to the system frequency variation expressed by (Δω_{1},Δω_{2}) and powers from renewable energy sources as inputs introduce disturbances in the process. The system must be able to keep the power transfer between the two microgrids as minimal as possible (P_{6}(k) + P_{7}(k) ≈ 0) and to maximise the production of the renewable energy sources.
System Modelling
Constraints
Results and Discussions
Optimal values of the interconnected systems [40]
h | P_{2}(t) | P_{3}(t) | P_{4}(t) | P _{G1} | P_{L1}(t) | P_{9}(t) | P_{10}(t) | P_{11}(t) | P _{G2} | P_{L2}(t) |
---|---|---|---|---|---|---|---|---|---|---|
1 | 43.31 | 0.00 | 6.35 | 199.65 | 191.22 | 21.79 | 0.00 | 8.84 | 180.63 | 178.69 |
2 | 43.32 | 0.00 | 12.71 | 206.03 | 190.23 | 16.78 | 0.00 | 11.82 | 178.6 | 176.94 |
3 | 43.52 | 0.00 | 9.81 | 203.31 | 190.42 | 13.80 | 0.00 | 8.93 | 172.73 | 168.64 |
4 | 43.42 | 0.00 | 14.68 | 208.1 | 191.33 | 13.79 | 0.00 | 10.72 | 174.51 | 173.87 |
5 | 43.14 | 0.00 | 18.14 | 211.28 | 193.05 | 13.78 | 0.00 | 12.72 | 176.5 | 175.67 |
6 | 43.78 | 0.08 | 19.65 | 213.51 | 206.43 | 13.76 | 0.09 | 17.81 | 181.66 | 172.05 |
7 | 42.62 | 7.74 | 9.12 | 209.48 | 211.26 | 13.77 | 2.18 | 8.36 | 174.31 | 172.06 |
8 | 44.41 | 10.54 | 17.28 | 222.23 | 215.12 | 19.78 | 5.90 | 19.94 | 195.62 | 197.26 |
9 | 41.63 | 11.55 | 14.47 | 217.65 | 204.09 | 13.77 | 5.02 | 16.29 | 185.08 | 184.97 |
10 | 41.70 | 14.54 | 18.40 | 224.64 | 206.14 | 17.77 | 11.14 | 19.42 | 198.33 | 174.10 |
11 | 40.79 | 16.44 | 19.87 | 227.1 | 208.13 | 18.82 | 18.43 | 17.22 | 186.04 | 183.99 |
12 | 40.58 | 17.35 | 16.08 | 224.01 | 213.91 | 14.81 | 26.62 | 10.65 | 202.08 | 200.99 |
13 | 41.87 | 19.60 | 11.38 | 222.85 | 227.75 | 13.71 | 19.62 | 3.16 | 186.49 | 191.02 |
14 | 42.62 | 19.78 | 12.09 | 224.49 | 213.31 | 13.74 | 19.49 | 14.58 | 197.81 | 185.00 |
15 | 43.26 | 20.04 | 18.60 | 231.9 | 221.78 | 13.99 | 21.40 | 19.78 | 205.17 | 204.49 |
16 | 45.72 | 17.53 | 11.07 | 227.25 | 204.53 | 14.32 | 17.71 | 10.04 | 192.07 | 191.03 |
17 | 50.25 | 21.88 | 18.50 | 240.63 | 213.03 | 15.13 | 22.62 | 19.83 | 207.58 | 206.39 |
18 | 55.55 | 0.01 | 19.14 | 224.70 | 215.95 | 20.16 | 0.00 | 18.78 | 188.94 | 177.64 |
19 | 59.03 | 0.00 | 19.23 | 228.26 | 212.53 | 36.17 | 0.00 | 19.09 | 205.26 | 189.98 |
20 | 59.95 | 0.00 | 19.70 | 229.65 | 209.21 | 47.31 | 0.00 | 16.78 | 214.09 | 189.81 |
21 | 59.85 | 0.00 | 12.73 | 222.58 | 207.02 | 46.10 | 0.00 | 12.04 | 208.14 | 177.02 |
22 | 59.62 | 0.00 | 11.00 | 220.62 | 201.57 | 42.86 | 0.00 | 11.50 | 204.36 | 175.03 |
23 | 59.04 | 0.00 | 12.56 | 221.6 | 198.95 | 36.49 | 0.00 | 15.18 | 201.67 | 189.20 |
24 | 56.59 | 0.00 | 0.62 | 207.21 | 197.11 | 22.94 | 0.00 | 0.075 | 173.015 | 170.02 |
Dynamic information of the simulations
Tie-Line | Loop | OST (MW) | STT(s) |
---|---|---|---|
MG 1 disturbed | |||
TL 1 | OL | 7.21 | 9.2 |
CL | 3.11 | 6.3 | |
PI | 7.01 | 8.5 | |
TL 2 | OL | 7.35 | 9.6 |
CL | 3.15 | 7.1 | |
PI | 7.2 | 9.1 | |
MG 2 disturbed | |||
TL1 | OL | 7.5 | 9.1 |
CL | 4.2 | 5.4 | |
TL 2 | OL | 6.7 | 8.3 |
CL | 3.4 | 6.2 | |
PI | 6.5 | 8.7 | |
MG 1 and MG 2 disturbed | |||
TL 1 | OL | 6.7 | 12.8 |
CL | 5.1 | 10.21 | |
PI | 6.3 | 13.1 | |
TL 2 | OL | 7.3 | 12.8 |
CL | 5.4 | 9.51 | |
PI | 8.1 | 12.3 |
Table 3 gives some results concerning the dynamics information of the simulations conducted after using perturbation techniques as explained in this section.
Where MG (Microgrid), PI (Proportional Integral controller), TL (Tie-Line), OL (Open-Loop), CL (Close-Loop), OST (Over-Shoot Time) and ST (Settling Time). The comparison between the open and the close loop are presented in this paper.
Conclusions
The aim of this research was to present the simulations of open loop based on optimal control theory and the close loop based on the Model Predictive Control. The comparison of these two control models were based on the network-model of interconnection of two microgrids via two ac tie-lines. The results show the effectiveness of the method used when it comes to the problem posed and resolved in this research. Three different cases were introduced by load variations in the first microgrid, second microgrid and both simultaneously, were considered to have different simulations results. Based on the simulation results, the close loop control shows a higher accuracy and faster than an open control loop strategy scheme even for complex dynamical system. All these results have demonstrated that those obtained using the closed control loop (MPC) controller have shown robustness against large power demand changes and system parameters variations and has better performance in comparison with the open loop controller. In two words: the peak undershoot and the settling time were reduced. The results presented in this research were compared with the one obtained with PI and show that the implementation of the open and closed loop of control when considering an interconnection of the sources of renewable energies (PV, wind) depend strongly on the weather.
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