Coordinated voltage control of renewable energy power plants in weak sending-end power grid

1 Introduction

China has gradually increased the development and investment in the field of renewable energy to address the concerns of energy shortage and environmental pollution.Various renewable energy generation technologies have been developed rapidly in the past few years, particularly wind power and photovoltaic (PV) power.Currently, there are numerous large-scale wind and PV power plants, which are mainly distributed in the “Three North” region of China.Weak sending-end power grids (WSPGs) are typically used for the large-scale development and centralized transmission of renewable energy in the Three North region [1].

A WSPG generally consists of only a few conventional power plants in addition to renewable energy power plants.In a WSPG, the network structure is weak, the short-circuit capacity is insufficient [2], and the active and reactive power support capacity is low.The spatial and temporal distribution of wind power and solar power has strong volatility and intermittency [3], [4].The voltage of a WSPG fluctuates frequently owing to the active power output fluctuations of the wind farms and PV power stations connected to the WSPG.This leads to severe challenges in ensuring the stability of power grid voltage.Thus, stringent requirements have been specified for renewable energy power plants, including voltage control performance and the reactive power regulation capability [5].

Owing to the weak reactive power support capacity of WSPGs, it is necessary to fully utilize the reactive power capacity of wind farms and PV power stations to maintain the balance of reactive power.Therefore, it is extremely important to study the reactive power and voltage control strategy of large-scale renewable energy power stations connected to a WSPG.Various devices have been installed in renewable energy power stations to achieve better voltage control performance, e.g., static synchronous compensators(STATCOMs) and static Var compensators [6].Moreover,with the development of power electronics technologies,renewable energy generation units, including wind turbine generators (WTGs) and PV arrays (PVAs), can be used for voltage control [7].However, the coordination of reactive power compensation devices with different time constants has become a difficult problem in the voltage control of renewable energy power stations.

Voltage control methods have been proposed for renewable energy power stations.In [8-12], the reactive power reference of a renewable energy power station is obtained according to the voltage deviation at the point of connection (POC) and allocated to generation units based on a proportional distribution.Control strategies based on mathematical programming algorithms are proposed in[13-19].These strategies describe a voltage control problem as a mathematical optimization problem with constraints,which can be solved using various optimization algorithms.In [13]and [14], a voltage control method based on a dynamic programming algorithm is developed for wind farms.The method can effectively suppress the voltage oscillation of wind farms after large disturbances.In [15],a central controller algorithm that is based on a dynamic programming is presented to realize voltage control for wind farms with the minimum number of capacitor steps operations.In [16-19], voltage control methods based on optimal power flow are studied.These control methods consider not only voltage control performance but also the reduction in active power loss.

The voltage control methods described above are openloop control methods with a single time section, which does not consider the dynamic regulation process of reactive power compensation devices with different time constants.Unlike the above control methods, model predictive control(MPC) is a rolling optimization control method, which can better deal with the influence of system uncertainty and shows robust voltage control performance.In [20], a voltage control method based on MPC is proposed to coordinate the reactive power of WTGs and static Var generators (SVGs).The control target is to minimize the voltage deviation at the POC and maximize the dynamic reactive power reserve of an SVG.In [21], a hierarchical and coordinated voltage control strategy for wind farms is proposed.In this strategy,the prediction information of different time scales in each layer can be fully utilized, and the control between each layer can be effectively coordinated.

Based on the above analysis, MPC can be used to coordinate a renewable energy generation unit and a reactive power compensation device to control voltage because of the following advantages:

(1) MPC does not require a precise predictive model;this can reduce the difficulty of modeling;

(2) It shows good dynamic performance because it uses a rolling optimization strategy;

(3) It can coordinate various Var devices and renewable energy generation units with different time constants [22].

The main contribution of this paper is proposing an MPC-based coordinated voltage control strategy for renewable energy power plants in WSPG, which optimally coordinates WTGs, PVAs, and a STATCOM to balance reactive power and control voltage.The reactive power capability of doubly fed induction generators (DFIGs) and PV inverters is examined.Compared to existing research,the proposed control strategy can realize power control of different generation units and reactive compensation devices with different time constants by using MPC.And an analytical method is used for calculating sensitivity coefficients which improves computation efficiency.Besides, the impacts of the active power output of WTGs and PVAs on voltage variation are considered for achieving better voltage control performance.

The rest of this paper is organized as follows:The topology of the renewable energy power plant and the structure of the voltage control strategy are provided in Section 2.The calculation of sensitivity coefficients is described in Section 3.The predictive model of the entire system is presented in Section 4.Section 5 presents the formulation of the MPC problem.Case studies are discussed in Section 6.Finally, the conclusions are presented in Section 7.

2 Renewable energy power plant and voltage control strategy

2.1 Layout of the renewable energy power plant

Fig.1 illustrates the configuration of a 360 MW renewable energy power plant consisting of a 320 MW wind farm and a 40 MW PV power station.The wind farm is comprised of four parts connected to four AC collector substations.The four substations are located at distances of 5 km, 10 km, 15 km, and 20 km from the POC.There are twenty 4 MW double-fed WTGs in each part.The WTGs are placed at a distance of 0.5 km with each other.The PV power station comprises twenty 2 MW PVAs.It is connected to an AC collector substation and placed at a distance of 25 km from the POC.The PVAs are placed at a distance of 0.3 km with each other.A ±180 MVar STATCOM located at the POC is selected as the reactive compensation device.

Fig.1 Configuration of the renewable energy power plant

2.2 Control process

Fig.2 shows the structure of the voltage control strategy.The measurements of node voltage, the active and reactive power output of each WTG and PVA, and the reactive power output of the STATCOM are transmitted to an MPC controller.Sensitivity coefficients are calculated based on an admittance matrix and the node voltage measurement.The weight coefficients of subobjective functions are calculated using the analytic hierarchy process (AHP) to achieve better voltage control performance.The MPC problem is formulated based on the active power references determined by a system operator, the calculated sensitivity coefficients and weight, and the abovementioned measurements.The details of the MPC problem formulation are presented in Section 5.After solving the MPC problem, the control commands for the WTGsPVAsand STATCOMare delivered to their local controllers.

Fig.2 Structure of the control strategy

3 Sensitivity coefficient calculation

In this section, the calculation of voltage sensitivity coefficients with respect to a power injection is presented.

The conventional method of calculating voltage sensitivity coefficients uses a Jacobian matrix, which must be rebuilt and inversed as operating conditions change.This inevitably decreases computation speed.To improve computation efficiency, an analytical calculation method that was initially applied to a radial distribution grid [23]is adopted in this study.

A power grid with N buses is considered.Γ represents the set of the buses, Γ={1,2,…,N}.Node voltage is defined asand the apparent power injection is defined asfor i ∈Γ.The apparent power injection can be obtained as follows:

where and represent the conjugates of and,respectively. is an element of admittance matrix.

Then, the partial derivatives of with respect to active power Pl and reactive power Ql at bus l ∈Γ must be obtained in advance for the derivation of the voltage sensitivity coefficients with respect to the active and reactive power injections,

Equation (2) is a linear combination ofandand (3) is a linear combination ofandAccording to the theorem in [23], (2) and (3) can be solved using a unique method.

After obtaining the value ofandthe voltage sensitivity coefficients can be calculated as

At every control step, the sensitivity coefficients are updated with new measured voltages.Additionally,the sensitivity coefficients remain unchanged at every predictive step.

4 Establishment of predictive model

In this section, the predictive models of the WTGs,PVAs, and STATCOM are established for the formulation of the MPC problem.

4.1 Predictive model of WTG

(1) State space of WTG

The control of the active and reactive power of a double-fed WTG can be decoupled through vector control.To facilitate the transformation of the formulated MPC problem into a standard quadratic programming (QP)problem, state vectors, output vectors, and control vectors are expressed as the deviations from the corresponding current measurements.The active and reactive power references of the WTG are and respectively.The current measurements of active and reactive powers are PWT(t 0) and QWT(t 0), respectively, where t0 represents the current time.Then, the control vectors can be expressed asandIn steady state, the power control behavior of the WTG can be described as a first-order lag function owing to the time delay of the communication system and control system of the WTG [24],

where and are time constants, which are in a range of 1-10 s [25].

Based on the above analysis, the state space of the WTG can be derived as

where and

(2) Reactive power capability of DFIG

As the reactive power output of a double-fed WTG is optimized for voltage control, the reactive power capacity of a DFIG must be analyzed.

The stator power output of a DFIG can be obtained as

where PS and QS are the stator active and reactive powers,respectively,δ is the load angle,US is the stator voltage,IR is the rotor current, and XS and XM are the stator reactance and mutual reactance of the DFIG, respectively.

The power output capability is limited by the maximum allowable currents of the stator and rotor and the steady state stability limit of the DFIG [26].This can be represented as

where ISmax and IRmax are the maximum allowable currents of the stator and rotor, respectively.

Fig.3 shows the three limits in the PQ plane.According to (12), the stator current limit is indicated by the red dotted semicircle centered at the origin with a radius of 3U S I Smax.The rotor current limit (13) is represented by the blue dotted semicircle centered atwith a radius ofAccording to (10), when the load angle varies from 0° to 90° at constant rotor current and stator voltage, active power increases with the load angle.This results in stable operation points.Thus, the steady state stability limit is denoted by the purple dotted vertical line at.Finally, the power output capability limit can be obtained by adding the rotor active power and stator active power, and it is indicated by the black solid curve in Fig.3.As ISmax,IRmax,XS, and XM are constants, the reactive power capacity of the DFIG is influenced by active power and terminal voltage.

Fig.3 Power output capability of DFIG

4.2 Predictive model of PVA

(1) State space of PVA

In steady state, the power control behavior of a PVA can be expressed as a first-order function,

and are time constants, which are within 100 ms[27].

Then, the state space of the PVA can be derived as

where and

(2) Reactive power capability of PV inverters

According to the theorem in [28], the power capability of PV inverters is determined by the maximum operating temperature of all semiconductor devices of PV inverters.Based on the operating temperature limitation and the relationship between active power P, reactive power Q, and apparent power S, the constraint model of the inverter power output can be formulated as

where k is the factor for the reactive power constraint.k depends on the topology, the modulation of PV inverters and the semiconductors.

Based on (18), the power output capability of PV inverters is indicated by the half-elliptical curve shown in Fig.4.The maximum value of active power,Pmax, is equal to S.Fig.4 shows that the reactive power capability of PV inverters is influenced by parameter k and the active power output.For example, when active power is P1, the maximum reactive power is Q1.

Fig.4 Power output capability of PV inverters

4.3 Predictive model of STATCOM

The reactive power control behavior of a STATCOM can also be expressed as a first-order function,

where τST is the time constant, and it is within 10 ms.

The state space model of a STATCOM can be derived as

whereand

4.4 Predictive model of the entire system

The predictive model of the entire system, which consists of NWT WTGs,NPV PVAs, and one STATCOM, can be formulated in the following form:

where

with

Suppose the sampling period is ΔTS, the continuous model can be transformed into the discrete state space model,

where G and H can be obtained by discretizing A and B,respectively,

5 Formulation of MPC problem

In this section, the MPC problem is formulated for the voltage control of the renewable energy power plant.The basic principle, cost functions, and constraints of the MPC problem are described in detail.

5.1 Basic principle of the MPC problem

MPC is also known as receding horizon control (RCH).Fig.5 shows the principle of MPC.

First, a system prediction model must be established to predict the future dynamics of the system.The red dotted line in the figure represents the predicted state variables obtained according to the system prediction model and current measurements.The predicted state variables are used to formulate the MPC problem.In the process of solving the MPC problem, an optimization problem is solved in the prediction period,ΔTP, based on the current measurements at each control point.The green dotted line in the figure represents the obtained control sequence.Only the first element of the control sequence is applied to the controller,and control actions are maintained within the control period,ΔTC [29].The above process is repeated at the next control point based on new measurements.

Thus, the MPC method considers the future dynamics of the system and uses new measurements for each optimization calculation.This improves voltage control performance.However, the time constants of different reactive power compensation devices can vary considerably.Thus, each control period is divided into several sampling periods to accurately capture the fast dynamics of Var devices with small time constants.

Fig.5 Principle of the MPC

5.2 Cost function

The control objective of the proposed control strategy is to maintain the voltages of the POC, WTGs, and PVAs within a feasible range and reduce voltage fluctuations.

(1) Objective 1:The active power output fluctuations of wind farms and PV power stations can result in a voltage limit violation at the POC.Thus, the predicted voltage deviation at the POC, ,with respect to the reference value at the POC,,is minimized.This can be expressed as

whereis the number of prediction steps.

(2) Objective 2:According to the theorem in [30], the voltages of the five medium voltage (MV) buses shown in Fig.1 can reflect the voltage conditions of the corresponding subzone.Then, the deviation between the predicted voltages of the MV buses and their reference values are minimized,

where

(3) Objective 3:Finally, the voltages of the WTGs and PVAs are optimized as follows:

The deviation between the predicted voltage and the corresponding reference value can be calculated by

where ΔVpre(k)can be replaced byandV(t0)is the voltage measured at the current time.

According to (25)-(27), the cost function can be expressed as

where ,, and are the weighting factors calculated using the AHP.

5.3 Constraints

(1) Constraints of STATCOM, WTGs, and PVAs

The power outputs of the WTGs, PVAs, and STATCOM are constrained as follows:

where and are the available active power outputs of the WTGs and PVAs respectively,and are the minimum and maximum reactive power capacities of the WTGs respectively, and and are the minimum and maximum reactive power capacities of the PVAs,respectively.Based on the analysis described in Section 4,and can be obtained considering actual operating conditions.

(2) System constraints

The active power output references of the wind farm and PV station, and specified by a system operator must be tracked.These power output references can be expressed as follows:

The formulated MPC problem can be transformed to a standard QP problem, which can be solved by commercial QP solvers in milliseconds [31].

6 Case studies

A power plant with 80 WTGs, 20 PVAs, and a ±180 MVar STATCOM connected to a WSPG is used to verify the proposed coordinated voltage control strategy.To reflect the characteristics of the WSPG, the short-circuit capacity provided by the external power grid at the POC is set as 540 MVA.The simulation model is built in the MATLAB/Simulink environment.

The objective of the coordinated voltage control strategy is to control the voltages of the POC, WTGs, and PVAs within a reasonable range when the active power output of the renewable energy power plant fluctuates.Voltage control performance is examined using the simulation model.The total simulation time is 180 s.

Fig.6 shows the active power references of the wind farm and PV station.The wind farm operation mode is changed from the balance control mode to maximum power point tracking (MPPT) mode during the simulation.The PV station operates in the MPPT mode.

Fig.6 Active power references of wind farm and PV station

Fig.7 Voltage of POC

Fig.8 Voltage of WTG_80

Fig.7 and 8 show the voltage of the POC and WTG_80 for two control strategies (coordinated voltage control (CVC)and no control (NC)).Under NC, only the STATCOM is controlled and the WTGs and PVAs work under a unit power factor.The proposed voltage control strategy effectively reduces voltage fluctuation and maintains voltage at almost 1 p.u.The voltage of the POC and of each generation unit inside the renewable energy power station are optimized.

Fig.9 shows the reactive power outputs of the STATCOM, WTG_80, and PVA_20.As the active power output increases, the reactive power output of the STATCOM increases to maintain the balance of reactive power.The reactive power outputs of the WTGs and PVAs are also optimized to improve voltage control performance.

Fig.9 Reactive power outputs of STATCOM, WTG_80,and PVA_20

Voltage control performance is observed under different short-circuit ratios (SCRs), i.e., 1.5, 2.5, and 5.0.

Fig.10 shows the voltage control performance of the proposed strategy at different SCRs.The proposed strategy can maintain the voltage of the POC within a reasonable range at all SCRs.As the SCR increases, the voltage fluctuation at the POC decreases.The reactive power output of the STATCOM at different SCRs is shown in Fig.11.As the SCR increases, the reactive power output of the STATCOM decreases.This increases reactive power reserves.This is because as the SCR increases, the shortcircuit capacity of the external power grid and the reactive power support capacity increase.

Fig.10 Voltage of POC at different SCRs

Fig.11 Reactive power output of STATCOM at different SCRs

Two scenarios are considered to analyze the influence of the time delay on voltage control performance.In scenario 1 (S1), the time constants of the active and reactive power control loops of the WTG (and ) are set as 1 s and 5 s, respectively.In scenario 2 (S2),and are set as 2 s and 8 s, respectively.Fig.12 shows the voltage of the POC in both scenarios.Voltage fluctuation is smaller in S1.When the time delay is large, the local controllers of the WTGs require more time to track the power output reference values given by the MPC controller.In the control period, the actual power outputs may differ significantly from reference values.This leads to poor voltage control performance.Therefore, voltage control performance is better when the time delay is small.

Fig.12 Voltage of POC at different time delays

7 Conclusions

MPC-based coordinated voltage control is developed to optimize the voltage of a renewable energy power plant connected to a WSPG.Active power is controlled in addition to reactive power.The reactive power capability of WTGs and PVAs is examined.In the proposed voltage control strategy, power regulation devices with different time constants, i.e., a STATCOM, WTGs, and PVAs, are coordinated to maintain voltage within a reasonable range.Case studies show the coordinated voltage control strategy exhibits good voltage control performance, which improves the voltage quality of the entire power plant.The proposed control strategy only contains voltage control objectives.More control objectives will be considered in future work.

Acknowledgements

This work was supported by National Natural Science Foundation Joint Key Project of China (2016YFB0900900).