3.4 Case study
3.4.2 Numerical results
In order to be able to investigate the proposed optimization based un-balance reduction with the three phase inverter on a low voltage local grid, all the elements of this complex electrical system (including the photovoltaic source, battery, and other power electronic components) has been modeled in Matlab/Simulink environment according to [P1]. The primary aim of the sim-ulation based experiments were to serve as a proof of concept for the proposed complex control structure.
Performance analysis
The aim of performance analysis is twofold. First of all, the proposed voltage unbalance indicator has to be investigated in the control structure as the cost function of the optimization based controller, and on the other hand, the control structure itself has to be exposed against engineering expectations on a proof of concept level. The results of the rst experiment can be seen in Figure (3.6) where the geometrical norm (2.11) has been used as the voltage unbalance indicator and the cost function for the optimizer on an experimental
32
3.4. CASE STUDY network with xed unbalanced load. The dashed line represents the examined low voltage local network's voltage unbalance norm (G) without the proposed controller implemented in the inverter unit of the domestic powerplant while the solid line represents the compensated network's value. Note, tat as men-tioned in the previous chapter, the geometrical norm is a unit-less value, since it represents the ideal and the real voltage phasor's symmetric difference.
0 2 4 6 8 10 12 14 16 18 20
0 0.2 0.4 0.6 0.8
1 ·105
t [s]
G
Without control Unbalance compensation
Figure 3.6: Unbalance reduction control's system performance with half charged battery and photovoltaic power source available with an experimental network. The underlying unbalance norm is the geometrical one (G). After starting the controller at t= 1sthe unbalance measure Gof the network signicantly decrease.
Robustness analysis
The robustness of the proposed controller had to be tested via simulation when dierent types of loads (inductive, capacitive, resistive) had been varied in step changes representing the on/o switching the dierent types of house-hold appliances (motors, switching mode power supplies, electric heaters, etc.).
In the experiment depicted in Figure (3.7), a load change has been introduced to the network in every 15 seconds causing the voltage unbalance to jump to a dierent value (measured in G). As it can be seen in the gure the controller successfully compensates the unbalance after each transient.
Measurements from a real unbalanced network
In order to expose the method to more realistic circumstances, the sim-ulation model was set up in such a way, that measurement data from a real network with voltage unbalance The measurements took place at the cam-pus building's power electronics laboratory, where a common 400 V connec-tion point was investigated as the behaviour of the network. Afterwards, the measurement data has been used as the input of a micro-grid segment of the Matlab/Simulink model in order to test the controller and inverters structure's performance in quasi-realistic circumstances. Figure (3.8) shows the simula-tion results with respect to G and V U F. It can be seen, that the optimal
CHAPTER 3. VOLTAGE UNBALANCE COMPENSATION
Figure 3.7: Robustness analysis with respect to step type changes in the network load (and voltage unbalance). The unbalance reduction controller successfully com-pensates the changes in the network voltage unbalance norm (G) value.
compensation that usesG as cost function decreases V U F as well. The com-pensators performance on the simulated microgrid's network loss reduction can be observed on Figure (3.9a), and Figure (3.9b).
0 2 4 6 8 10 12 14 16 18 20
0 0.2 0.4 0.6 0.8
1 ·105
t [s]
G
Without control Unbalance compensation
(a) Unbalance reduction control system performance with half charged battery and photo-voltaic power source available on a measurement driven network. The underlying unbalance norm is the geometrical one (G) in this experiment. The controller starts att= 1s.
0 2 4 6 8 10 12 14 16 18 20
0 1 2 3
t [s]
VUF[%]
Without control Unbalance compensation
(b) V U Fs evolution during control, while the cost function is still G on a measurement driven network. Due to the control actionV U F is smoothed.
Figure 3.8: Voltage unbalance compensation with a measurement driven network.
The measurement output is connected to a modeled three phase load and 34
3.4. CASE STUDY
0 2 4 6 8 10 12 14 16 18 20
0 1,000 2,000 3,000 4,000
t [s]
Ploss[W]
Without control Unbalance compensation
(a) The active power loss (Ploss) evolution during control on a measurement driven network.
The value is actively decreasing due to the result of unbalance compensation
0 2 4 6 8 10 12 14 16 18 20
−0.5 0 0.5 1
·10−7
t [s]
Qloss[VAr]
Without control Unbalance compensation
(b) The reactive power loss (Qloss) evolution during control on a measurement driven net-work. The value, however low, can be uncontrollably aected by the unbalance compensa-tion.
Figure 3.9: Voltage unbalance compensation with a measurement driven network.
The measurement was performed at the department's power electronics laboratory.
network system, consisting of symmetrical loads and network segments be-tween them. Further articial load unbalance is not necessary since the net-work's unbalance is already present. This structure enables to show that any point the inverter is connected, could restore power quality with a certain de-gree such unbalance compensation at this case. The future plan is to set up multiple devices on dierent connection points.
Performance comparison of dierent unbalance indicators
In this section the chosen unbalance indicators, V U F, and Gshall be com-pared in performance solving the same optimization problem. The only dif-ference between the three compared simulations are the APPS algorithm cost function candidate (V U F, or G), as they are compared to the uncontrolled example. The environment consist of a notable voltage unbalance and an emphasized undervoltage, so the dierence of the two approaches would be observable. The simulation's initial stance is visible in Figure (3.10) (same argumentation as with Figure (2.3)), where the triangle in the middle stands for the measured voltage phasor.
It can be observed, that in Figure (3.11) the value of V U F does not deviate much in case of dierent cost function options. However, observing the trend of G with the same circumstances, the values are showing a dierent trend
CHAPTER 3. VOLTAGE UNBALANCE COMPENSATION
Figure 3.10: The ideal and real voltage phasors at simulation time of 0.38 second.
It can be observed, that the voltage is uniformly deviating due to the network load.
with in case of the V U F based approach, the unbalance is slightly above the uncontrolled threshold, and with Ga clear reduction is shown. This is due to the case of the initial large undervoltage, which gets compensated, but with V U F it is not recognised.
In terms of network power losses with the previous example observable in Figure (3.12). In case of the active power losses the simulation with G as cost candidate produces clear reduction, but with the V U F a slight increase.
However with all approaches the reactive power slowly diverges form zero over time, which is a clear improvement point for the future.
3.5 Summary
A direct optimization based compensation structure applicable for three-phase network is proposed in this chapter. Due to the basic assumptions re-garding the network, the optimal input current phasor can be found by any derivative-free optimization method. The cost function for the proposed volt-age unbalance optimizer can be any scalar valued VU norm, however, the previously dened geometric norm is suggested here. The geometrical unbal-ance norm proposed in the previous chapter is applied as a cost function in the asymmetry reducing optimization based control utilizing an asynchronous
36
3.5. SUMMARY
0 2 4 6 8 10 12 14 16 18 20
0 0.5 1 1.5 2
Time [s]
VUF[%]
No control G based control VUF based control
0 2 4 6 8 10 12 14 16 18 20
0 0.2 0.4 0.6 0.8
1 ·105
Time [s]
G
No control G based control VUF based control
Figure 3.11: Voltage unbalance compensation when employingV U F or Gas cost function.
parallel pattern search (APPS) algorithm also presented in the chapter. Sim-ulations, performed in Matlab/Simulink environment show that the geomet-rical based indicator can serve as a basis of further research. The suggested controller structure enables the residential users owning a grid synchronized domestic power (renewable) plant to reduce voltage unbalance measurable at the connection point. The fundamental element of the system is a modied three phase inverter that is capable of the asymmetric current injection of any current waveforms to the network, via decoupled bi-directional DC-DC con-verters. The optimization-based control algorithm injects the available energy (as current waveform) in such a way, that the voltage unbalance decreases.
This is an optimization problem which is constrained by the available renew-able energy supplied by the power plant, or energy storage unit.
The proposed optimal input design based controller has been tested on a low voltage network model in a dynamical simulation environment consisting of the models of the electrical grid, a domestic power plant, an asymmetrical inverter circuit, and dierent types of loads. Dierent simulation experiments has been run for each norm and for both the power constrained and unconstrained (zero operation case) case.
CHAPTER 3. VOLTAGE UNBALANCE COMPENSATION
No control G based control VUF based control
0 2 4 6 8 10 12 14 16 18 20
No control G based control VUF based control
Figure 3.12: The network's active (Ploss) and reactive lossesQloss in case ofV U F orG as cost function.