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# Power quality Improvement in Micro grids by Repetitive Cascaded Current -Voltage control with load u

**Power quality Improvement in Micro grids by Repetitive Cascaded Current -Voltage control with load using hybrid voltage source**

**Abstract:**

A cascaded current and voltage control strategy is proposed for DC-AC converters for simultaneous improvement in power quality, based on and repetitive control strategies. This control strategy includes an inner voltage loop and current loop, which leads to obtain a low Total Harmonic Distortion (THD) in both inverter load voltages and currents exchanged with grid at same time. It enables DC-AC converters to inject balance clean currents to grid even in the presence of linear and non-linear loads. The proposed control strategy is experimentally tested to validate its performance on reducing errors and THD, under different linear and non-linear loads and it enhances using DC sources i.e., A hybrid renewable resources which includes HYDRO, WIND, SOLAR and BATTERY combination for novality. By this novel work the power will generate for a long life state and this will help in reducing the utility of Thermal electricity and helps in protecting the environment resources.

*Keywords: Micro grid, RES,Total Harmonic Distortion, H-infinity control, power quality*

1)**Introduction:**

Now a day the demand for Renewal energy sources (RES) such as solar energy, wind energy and etc. has drastically increased in order to reduce the fossil energy. Most of the renewable energy technology produces a DC power output, so an inverter is needed to convert DC energy from RESs into AC electric energy. So the RESs are normally connected to the utility grid through grid connected PWM inverters which supply the active and reactive powers to the main grid [1], [2]. These inverters are either standalone [3], [4], or grid connected [5]. In case of grid connected inverters, the inverter output voltage should be same or it should be low than that of grid voltage, and the frequency should also be same as that of grid frequency.

Standards for grid connected inverters such as IEEE 1547 [6] provide guidance on the levels of current Total Harmonic Distortion. Table I shows the maximum distortion limits allowed in current [7], [8].

In [9] it says that control task of DC-AC converters in micro grids can be divided into two parts

- Input side controller –

Is to capture maximum power from the input source

- Grid side controller –

Is to control the power delivered to grid

In general loads connected to a distribution system or micro grid are non linear in nature which create harmonically distorted current. Many of loads are also single phase and so considerable zero sequence and negative sequence components are accepted. As early said, to minimize THD several feedback control strategies have been proposed for inverters such as dead back, hysteresis controllers [10], [11]. These will not alone eliminate periodic disturbances which are caused due to non linear/unbalanced loads. So that Repetitive control theory[12] which is very well known as a simple learning control method, provides an alternative to eliminate these periodic distortions in dynamic systems using internal model principle[13] .This principle is an infinite dimensional and it can be obtained by connecting a delay line into a feedback loop.

In this paper a cascaded current and voltage structure which consists of inner voltage loop and outer current loop is proposed, in which voltage controller is responsible for the power distribution and synchronization with the grid while the current controller is responsible for the power exchanged with grid. With the help of this repetitive control theory [15] - [17], the control strategy is to obtain and maintain a low THD in both local load voltage at the inverter and grid current at same instant of time. When the inverter is connected to grid both controllers are active and if these inverters are not connected to grid the current controller is working under zero current reference. For three phase inverters, the same individual controllers are used for each phase in the natural frame of reference, when the system is implemented with a neutral point controller.

The repetitive control theory [15] – [17] is adopted in this paper to design the controllers but this is not as must. Repetitive control theory [12] as early said which is used by internal model principle [13] deals with a very large number of harmonics as it has high gain at fundamental frequency. It has been applied to constant-voltage and constant-frequency PWM inverters [18]-[20], grid connected inverters [21] and active filters to obtain a low THD.

The rest of the paper is organized as follows. The overall system structure is presented in section II which was followed by controllers design in section III. In section IV, the experimental results are presented and discussed. Finally conclusions are made in section V

**2)****System structure****:**

The proposed control system is to use an individual controller for each phase in the natural frame, which is also called as ** abc** control. This system is implemented with neutral point controller proposed in [22], shown in Fig: 1& 2 which it consists of two loops: inner voltage loop to regulate inverter local load voltage and outer current loop to regulate grid current. According to the cascaded control theory if the dynamics of outer loop is designed to be slower than inner loop, then the two loops should be designed separately. For to design the outer loop controller it should be assumed that the inner voltage loop is already in steady state i.e U

_{0}=U

_{ref .}The power controller consists of phase-locked-loop (PLL), used to provide an information of the grid voltage, which is needed to generate the current reference i

_{ref}. The inverter is assumed to be powered by a hybrid voltage source; no controller is needed to regulate the DC link voltage. Here in this case the grid voltage u

_{g}is fed forward and added to the output of the current controller which is used as a synchronization mechanism, and it does not affect the design of controller. In this paper both the controllers are designed using H- infinity Control strategy because of its excellent performance in reducing THD (Total harmonic distortion).

Fig:1 Grid connected inverter with proposed control strategy

3)**Voltage controller design****: **

In this section, voltage controller is designed based on and repetitive control techniques for a DC-AC converter. In repetitive control, the amount of delay used in the internal model is equal to the period of the external signals. This technique is widely used to track periodic signals and/or to reject periodic disturbances. We will follow the ** ** control based design procedure for repetitive controllers which was proposed in [12], uses additional measurement information from the plant. The block diagram of the control system is shown in Fig:3. It consists of plant P, internal model M, and a stabilizing compensator C. The compensator C, designed by a ** ** control problem [23] assures the exponential stability of entire system which it implies that the tracking error ‘e’ will converge to a small steady state error according to theory [12].

Fig: 2 cascaded current-voltage controllers for inverters where both adopt strategy

Fig:3 General block diagram of control strategy

*3.1)**State space model of plant Pv:*

The control plant which is shown in below Fig 4 for the voltage controller consists of Inverter Bridge and the LC filter (L_{f} & C_{f}). The PWM block together with the inverter are modeled by using an average voltage approach with the limits of available dc-link voltage [21] so that average valve of u_{f} is equal to u_{v} over a sampling period, so that PWM block & inverter bridge can be ignored.

Fig 4: Control plant P_{v} circuit for voltage controller

By considering filter inductor current i_{1,} and capacitor voltage u_{c} as state variables x_{v}= and external input w_{v}= and control input is u_{v.}. The output signal from the plant P_{v} is the tracking error e_{v}= u_{ref} - u_{o}, where u_{o} = u_{c}+ R_{d}(i_{1} – i_{2}), which is inverter local load voltage .

The plant ‘P_{v}’ described by the state equation is given by

(1)

Output equation is given by (2)

Where

A_{v} =

B_{v1} = B_{v2} =

C_{v1} = D_{v1} = D_{v2} = 0

Therefore the state space matrix is given by

P_{v} = (3)

**3.2)***Standard H*^{∞}*Problem Formulation***:**

According to [12] , the system shown in Fig 3 is exponentially stable if the closed loop finite –dimensional system from Fig:6 is stable and its transfer function from a to b, denotes that T_{ba,}, satisfies â”‚T_{ba}â”‚_{∞} < 1. To make this system stable as shown in Fig:6 ,is formulated to minimize the H^{∞} norm of the transfer function T_{z1,w1} = F_{1}(P_{v ,} C_{v}) from W_{V} = to Z_{V} = , and by introducing the weighting parameters as ζ_{v} and µ_{v} . The closed loop system is represented as

= P_{V}

U_{V} = C_{V} y_{v (4)}

Where ‘P_{V}’ is the generalized plant and **C**_{V} is the voltage controller to be designed.

The plant P_{V} consists of p_{v}, with low pass filter W_{f} = , which is internal model for repetitive control. The weighting parameters ζ_{v} and µ_{v} play an important role in the maintaining stability of system as said in [15] and [17]. Then complete generalized plant P_{V} is given by

P_{V} = (5)

then by repetitive control theory the controller **C**_{V} can be found for the plant P_{V} using the ** ** control theory by using ** hinfsyn** which is present in MATLAB.

**4)****Current Controller design****: **

** **As early said , for to design the current controller we have to assume that the inner voltage loop is already in steady state i.e..U_{0} = U_{ref} . The control plant for the current loop which is shown in below Fig: 5 consists of grid interface inductor on right hand side.

Fig:5 Control plant P_{i} circuit for current controller

Here the current controller is designed by repetitive control technique as early said in voltage controller design and the formulation is also same for the compensator **C**_{i} which was shown in Fig: 5 but with difference in subscript u replaces with i

*4.1)**State space model of plant Pi:*

As we assumed that U_{0} = U_{ref} , where U_{0} = U_{G}+U_{i} or U_{i} = U_{0} - U_{G} from figures 2 & 4, where U_{G} is the grid voltage which provides local load voltage for the inverter. The same voltages appear on both sides of grid interface inductor L_{G}, which it doesn’t affect the controller design. Here the grid voltage can be ignored when designing of controller which was important feature. During design process we only need to consider is that output is U_{i}.

By choosing state variable as a grid current flowing through grid interface inductor which was shown i.e.. x_{i} = i_{2} and the external input is w_{i} = i_{ref} , and the control input is U_{i}. The output from the plant P_{i} is e_{i} = i_{ref} – i_{2}.

Then the plant P_{i} can be described by state equation by

(6)

And the output equation is given by

y_{i} = e_{i} = C_{i1}x_{i} + D_{i1}w_{i} +D_{i2}u_{i} (7)

where , ,,

C_{i1} = 0, D_{i1} = 1 ,D_{i2} = 0

Therefore the state space matrix for current controller is given by

P_{i} =

**4.2)****Standard** ** Problem Formulation:**

Similarly the formulation for current controller is alike that of an voltage controller which was explained before as shown in fig: 6 by replacing subscript ‘u’ with ‘i’.the resulting generalized plant is obtained by

P_{i} = (9)

Fig 6: Formulation of H infinity problem for voltage controller

The plant P_{i} consists of p_{i}, with low pass filter W_{fi} = , which is internal model for repetitive control. The weighting parameters ζ_{i} and µ_{i} play an important role in the maintaining stability of system as said in [15] and [17]. The controller C_{i} can be designed by H^{∞} repetitive control theory in MATLAB with the help of ** hinfsyn** in Robust control toolbox.

**5)Experimental validation** **:**

For the experimental validation the controllers will be designed in this section, which consists of an inverter board , a three phase LC filter a three-phase grid interface inductor, a board consisting of voltage and current sensors, a step - up wye-wye transformer (12 V/230 V/50 Hz). The inverter board consists of two independent three-phase inverters which has the capability to generate PWM voltages from a hybrid voltage source. In that one inverter was used to generate a stable neutral line for the three-phase inverter. The generated three-phase voltage was connected to the grid through a controlled circuit breaker and a step-up transformer. The PWM switching frequency was taken as 12 kHz. For the hardware purpose to measure THD a Yokogawa power analyzer WT1600. The inverter parameters are taken as shown in table 2

Table 2: Inverter parameters

As a stable neutral line is available three sets of identical controllers were used which was already shown in Fig:1 A phase locked loop was used to provide the phase information needed to generate the three-phase grid current references via a *dq/abc* transformation from the current references I_{d}* and I_{q}*. To improve the voltage THD a low voltage inverters are used because in general the higher the voltage, the bigger valve is fundamental component.

*i) * *Design of Repetitive voltage controller:*

For to design of voltage controller, the weighting function for f=50Hz was choosen from [15] and [17] as W_{fv} = and the weighting parameters are chosen as ζ_{v} = 100 and µ_{v} = 1.85. The controller C_{v} which minimizes the H^{∞} norm of the transfer function for the parameters of plant shown in Table: 2 is given by

C_{v}(s) = (2.997*10^{9}s + 2.289*10^{20}) / (s^2+5.43*10^{8}+ 4.589*10^{21})

Further it can be reduced to

C_{v}(s) =

*ii)* *Design of Repetitive current controller:*

For to design of voltage controller, the weighting function for f=50Hz was choosen from [15] and [17] as W_{fi} = and the weighting parameters are chosen as

ζ_{i} = 100 and µ_{i} = 1.8.

The controller C_{i} which minimizes the H^{∞} norm of the transfer function for the parameters of plant shown in Table: 2 is given by

C_{i}(s) = 6644/(s + 5.43*10^{8})

The resulting reduced transfer function is given by

C_{i}(s) = 66/(s+543)

**6)****Simulation Results:**

** ** The controller was implemented in grid connected mode with different loads i.e. for resistive, amd nonlinear loads. In grid connected mode the results are shown below:

1)With resistive load:

The inverter output voltage and grid current output along with THD analysis are presented below by taking a balanced resistive load of Ra = Rb = Rc =12ohms, for a grid connected system are shown in Fig:7. The grid current THD for this proposed controller was 0.17% where as for inverter load volatge THD is 0.22% respectively.

Fig 8 output voltages of inverter and grid current for Resistive load

The Total harmonic distortion analysis of inverter load voltages and grid current are as shown below for pure resistive load as mentioned before are as follows

Fig 9(a): THD for inverter voltage for Resistive load

Fig: 9(b) THD for grid current for Resistive load

2)With nonlinear load:

The loacal load voltage and the grid current with the controller outputs for both volatge and current are as shown in below figures

Fig 10 a) inverter voltages and b)grid current outputs for the proposed statergy

a)

b)

Fig:11 THD analysis of a)inverter voltages and b)grid current for Nonlinear load

**7) Conclusion:**

The proposed control strategy was implemented for hybrid voltage sources in Micro grids where it consists of inner voltage loop and outer current loop with its excellent performance in reducing THD of both inverter load voltage and grid current. Experimental results are presented for resistive load and nonlinear load in grid connected mode, and at the same time the grid current and inverter load voltages were controlled by using repetitive control in this paper.

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