benefits. Such a scenario will require the investigation of the impact of DG on Available Transfer Capability (ATC) for the secure and reliable system operations.
THE IMPACT OF DISTRIBUTED GENERATION ON ATC JIANWEI LIU, M. M. A SALAMA, R. R. MANSOUR Department of Electrical & Computer Engineering, University of Waterloo Waterloo, Ontario, Canada N2L 3G1
ABSTRACT With Distributed Generations (DGs), the load demands in the grids are changed with the impetus of potential market benefits. Such a scenario will require the investigation of the impact of DG on Available Transfer Capability (ATC) for the secure and reliable system operations. In this paper, a set of the contribution factors of DGs on line flows and voltage variations are introduced with closed formulas based on AC power flow analysis. Then the index of Total DG Amount (iTDA) of each loading area in the grid on the ATC improvement is classified and the validity has been discussed. The case studies with 6-bus and 30-bus testing systems demonstrate the applicability of the proposed technique.
KEYWORDS Distributed Generation (DG), Available Transfer Capability (ATC), electricity market
I.
distribution networks, but also will somewhat induce the variations of the power flow and loading conditions in the grid. Thus, both the base case and the contingencies for the ATC calculation will be changed comparing to the cases without DG in the system.
The operations of DGs are usually out of the control of market operators, e.g., the ISOs. In such a scenario, it is very interesting and desirable to investigate if the inducing power injections by DGs will affect the ATC values of the grid, as well as how to quantify such impacts. It essentially requires the determinations of the contribution factors (CFs) of these ‘uncertain’ power supplies. Traditionally, DC power flow is applied to reduce the complexity of the calculation [8][9]. Accurate CFs need AC power flow based methods. Some valuable efforts have been reported which are mainly focused on the generation rescheduling with less concern on the load variation [10][11][12][13]. The existing techniques are not suitable for the cases of DGs that are dispersed in the grid with relatively small capacities and close to the loads.
INTRODUCTION
Available Transfer Capability (ATC) was defined to quantify open access to transmission facilities [1]. Based on ATC value, future transactions can be scheduled and transmission services can be reserved. Hence, ATC is an important market signal for the secure and reliable system operations. For the ATC calculation, the loading conditions of distribution systems are usually treated as “aggregated” (or projected) loads on the transmission system buses. It is acknowledged that, in some cases, load demand control can provide more effective solutions than generation rescheduling to mitigate the congestion problem [2][3][4].
This paper introduces a simple and direct approach for the above problem using AC power flow analysis. The validity of DGs on the ATC improvement is discussed in Section II. In Section III, the closed form contribution factors of DGs on the variations of line flows and system voltages are derived and the index of the Total DG Amount (iTDA) on ATC improvement is introduced afterwards. Section IV presents the results of applying the proposed method to a 6-bus and the IEEE 30-bus test systems. Finally, the conclusions are drawn in Section V.
II. Facing the growing load demands, Distributed Generation (DG) is expected to play an increasing and attractive role in electricity markets with the impetus of potential market benefits [5][6]. Different techniques, such as micro-turbine, renewable power supplies and energy storage devices, are emerging in the industry [5][6][7]. The real and reactive power provided by the DGs will not only affect the local voltage control in
BACKGROUND
ATC values represent the remaining transfer capabilities in the transmission networks based upon the existing committed transactions in electricity markets with the well-known mathematical model [1][2][14] ATC = TTC − ETC − TRM − CBM where:
(1)
-
TTC (Total Transfer Capability) is the maximum power that can be delivered by the system within security constraints, usually including thermal limits of transmission facilities, voltage limits and stability limits of the system.
-
ETC (Existing Transmission Commitment) is essentially the base load flows in transmission networks determined by the given market conditions.
-
TRM (Transmission Reliability Margin) and CBM (Capacity Benefit Margin) are generally the reserved ‘rooms’ of transmission for the ‘global’ and ‘local’ inherent uncertainties in system operations.
Most of the theoretical and practical efforts on ATC calculation are focused on the TTC for the determinative constraints, such as voltage limits and/or stability limits [1][2][14], facing the challenge that the most restrictive constraints may vary for different system configurations, loading conditions and contingency concerns. Conceptually, there are two categories in the literature: -
To define an optimistic or determinative estimation of TTC in a given generation-load space [1][14].
-
To search a conservative value with the worst scenario analysis in the known generation-load space [15], or a more realistic estimation with transaction patterns which are determined by the market information [2]. Usually, the ETC value is considered as known data based on the bidding information and the bilateral transactions.
The emerging DG increases the complexity of the ATC analysis. DGs are mainly customer operated and/or distribution utility controlled power supplies that can be sited throughout the distribution and sub-transmission systems. It is not a new concept in power system operation, but will be more economical and less costive than before with the modularized designs, for example the micro -turbine, wind power, fuel cell, photovoltaics and energy storage, etc. It is expected that in North America DGs will cover 25% of the load increases in the coming 10 years [5]. The DGs will essentially provide the load services to particular customers or other ancillary services in the markets [7], depending on the market tariff. The ISOs might not be able to obtain individual information of the consumer owned DG devices. However the activities of DGs are predicable in the spot price market because of their ‘profit-driven’ impetus. Researchers have pointed out that the induced customer side power supply could improve both system and market operations, e.g. the congestion management [1][3][5].
The capacity of DG ranges from tens of KWs to several MWs in the market [5][6]. Modularized power electronic interfaces provide the capability of independent
real and reactive power injection [7]. Energy storage devices can provide four-quadrant operations. With DGs, the aggregated loads appearing at the transmission system loading buses will be variable comparing to the traditional static load models. So the base loading conditions of the ATC calculation, i.e. the ETC values, will somehow be changed comparing to the ‘constant’ cases. Thus, the ATC value may be affected. Furthermore, not only the line flows, but also the system voltage profile will be changed. It is possible that, in some heavy loading conditions when the voltage limits become the most critical constraints, the power supplies from DGs may improve the system voltages thus the TTC value may be increased. Hence, in such cases, the ATC will be improved as well. Because of the relative small capacity of individual DG device and the uncertain location of such dispersed power, it is not desirable in this paper to integrate the DGs into ‘accurate’ TTC determination, but to investigate the potential effects of the DGs on the variations of the ‘known’ ATC values. The impacts of DG on the system line flows and the system voltages need to be derived first. Then, the DGs can be classified into ‘desired’, ‘undesired’ or ‘less-determinative’ categories, which may be applied as the index for the future applications.
III.
CONTRIBUTION FACTORS AND iTDA
As discussed, the DGs may be modeled as variations of the ‘aggregated’ or ‘projected’ load at the system buses (PQ and PV buses). Thus, the variation of the line flows with or without DG will represent the impact on the ETC.
In power flow analysis, the line flow between node i and node j is expressed as
r r r r S ij = y ij* ⋅ (V i − V j ) * ⋅ V i
where y ij
(2) r r is the line admittance; V i , V j are the nodal
voltage vectors. For x ∈ (Pk , Q m ) , where Pk are the real power injection at the PV or PQ buses, and Qm are reactive power injection at the PQ buses, there exists
r ∂S ij
r r r ∂V * ∂V j * r r r * ∂Vi * i (3) = yij ⋅ ( − ) ⋅Vi + (Vi − V j ) ⋅ ∂x ∂x ∂x ∂x
where -
r Vi = Vi e
jθ i
r
and V i
*
= Vi e−
jθ i
;
-
-
The
r d Vi ∂Vi = ⋅ cos θ dx ∂x
dθ i dx
(4)
d Vi d θ i + j ⋅ sin θ i + V i ⋅ cos θ i ⋅ dx dx r* d Vi ∂ Vi dθ i = ⋅ cos θ i − V i ⋅ sin θ i ⋅ ∂x dx dx d Vi d θ i − j ⋅ sin θ i + V i ⋅ cos θ i ⋅ dx dx
(5)
d Vi
i
− V i ⋅ sin θ i ⋅
d θi
in Equation (4) and (5) can be dx dx obtained from the inverse matrix of the Jacobian in the Newton-Raphson power flow method shown as follows: ,
∆θ ∆ V =
J
−1
∆P ⋅ ∆Q
(6)
∂θ ∂θ ∂P ∂Q where −1 J = ∂V ∂ V ∂ P ∂ Q Equation (3) is the closed formula of the impact on the line flows of the total power injection at each PV or PQ node. Depending on its capacity, the DG device may be modeled at either PV bus or PQ bus. By assuming the consumed power at PQ buses as constant and the genration at the PV buses as scheduled as well, the Contribution Factors (CF) can be defined as
r ∂Sij PLDG = Re al ∂x
It is observed that the values of these contribution factors are diverse according to the location, the existing generation-load pattern in the market and the expected DG amount. Considering the uncertainty of the DG operations, in some cases, it may be very desirable to determine the ‘trend’ of such impacts in a loading area rather than the accurate value. The index of the Total DG Amount (iTDA) on ATC improvement for a certain constraint (line flows or voltage limit) is then defined here with a ‘screening’ procedure based on the above contribution factors (CFs, i.e. PLDG, QLDG or VDG) with a given criteria boundary (Figure 1): -
If the CF is positive and larger than the given upper criteria, the iTDA is defined as 1 for the corresponding DG.
-
If the CF is negative and lower than the given lower criteria, the iTDA is defined as –1.
-
If the CF is between the higher and lower criteria, the iTDA is then defined as 0.
(7)
which is the real part of the Equation (3), and
r ∂S ij QLDG = Im ag ∂x
(8)
Figure 1 The index of Total DG Amount
which is the imaginary part of the Equation (3). The above CFs are the accurate impact of the existing DG on the real and reactive power flows variations, furthermore, on the ETC improvement, with the given loading conditions. Similarly, the contribution factor of the existing DG on the system voltage magnitude can be defined as d | Vi | VDG = (9) dx where x ∈ P k , Q m .
(
)
The proposed contribution factors provide accurate impact information of the individual DG on specified analysis target. The trade-off is, with the increase of the system size, the data analysis becomes very complex. Therefore, a proper simplification is necessary.
Table 1 Categories of iTDA iTDA
Constraint
Constraint
-Lineflow
-voltage limit
1
Undesired
Desired
0
Less determinative
Less determinative
-1
Desired
Undesired
The iTDA simplifies the impact of DG on the ATC improvement into 3 categories, i.e., 1, 0, -1, which can be interpreted as ‘desired’, ‘less determinative’ and ‘undesired’ for different constraints, which are summarized in the Table 1. In summary, the contribution factors reveal the accurate information of the impacts of DG, while, the
iTDA provides a simple and direct overview of such contributions.
IV.
-
The impacts of DGs on the line flows, thereafter, the ETC values, are quite diverse, as shown in Figure 3,4, and 5. For some cases, the impacts of DGs in the loading buses, i.e. the contribution factors, are so significant that it may be comparable to the generators in the PV buses. It is consistent with the well-accepted concept that the load shedding may be a very effective way for the congestion problem rather than the more expensive generation rescheduling approach [1][2].
-
Figure 4 shows the reactive power of the DGs may have much less contributions on the real power line flows in this case study. When the thermal limits become the dominant criteria for the ATC determination, the reactive power flow may be concerned. In such situation, the reactive power injections from DG could ease the congestion or even make the operating limits more severe, according to the negative or positive impacts as shown in Figure 5.
-
Figure 6 and 7 strongly indicate that the variations of the loads, both active and reactive power, could considerably affect the system voltage profile. Therefore, if voltage limits are the most critical constraints, usually in heavy loading conditions, inducing DGs will be a very desirable and efficient way to support the system voltages ‘locally’. Hence, the ATC will be increased.
2.
IEEE 30-bus testing system
CASE STUDIES
In this section, the validity of the proposed CFs is illustrated with a 6-bus test system. The applicability of the iTDA is shown with the IEEE 30-bus system. 1.
6-bus testing system
Figure 2 6-bus testing system
Table 2 Line data of the 6-bus testing system Line i-j 1-2 1-4 1-5 2-3 2-4 2-5 2-6 3-5 3-6 4-5 5-6
Rij (p.u.) 0.1 0.05 0.08 0.05 0.05 0.1 0.07 0.12 0.02 0.2 0.1
Xij (p.u.) 0.2 0.2 0.3 0.25 0.1 0.3 0.2 0.26 0.1 0.4 0.3
Bi/2 (p.u.) 0.02 0.02 0.03 0.03 0.01 0.02 0.025 0.025 0.01 0.04 0.03
The 6-bus testing system, as shown in Figure 2, has 3 generation companies (Bus 1,2 and 3) and 3 loading areas (Bus 4, 5 and 6). Bus 1 is selected as the slack bus. The based loading conditions are shown in Figure 2. The line data is given in Table 2. Assuming each loading area has a certain amount of DG, the proposed contribution factors, as shown in Figure 3, 4, 5, 6, and 7 are obtained based on the above base loading conditions. It is observed that:
The IEEE 30-bus testing system is applied here to demonstrate the idea of iTDA. The system data can be obtained in [16]. With 2 generators, 4 condensers and 24 PQ buses in 5 loading areas via 41 branches, the analysis of the impact of individual DG will only be necessary when the purpose is clear and valuable. Thus, a ‘global’ investigation with the proposed index of Total DG Amount (iTDA space) is desired.
Figure 8 shows the iTDA space for the impacts of the active power injections by DGs on the real power flow on the transmission lines. The critical boundary was set as (0,0.5). The shadowed area indicates the ‘desired’ DGs’ impact on the line flow variations, i.e. with the negative contribution factors. The black zones represent the most ‘undesired’ DGs with large positive PLDG values. The blank area is associated with the safe and ‘less-determinative’ DGs. For example, if the real power flow on line 16 is close to the operating limits, then the DGs on loading buses S12 may be extensively monitored. For lines 26-35, most of the DGs in the system will even reduce the transferred power on these lines.
Contribution Factor of ReactivePower from DG (QLDG) 0.7 0.6 0.5 0.4 0.3 QLDG 0.2
1
0.1 Bus 2 Bus 3 Bus 4 10
Controbution Factors of Real Power from DG (PLDG)
0 -0.1 -0.2
7
Lines
4
Another iTDA space discussed here is the impact of reactive power injections of DGs on the PQ bus voltages as shown in Figure 9. The black zone shows the most desired distributed reactive power locations in the 30-bus system for the specific bus voltages. The shadow areas are less benefit but still desired zone. The rest blank area is the least contributive zone. Furthermore, the symmetric shape of the iTDA space reveals the fact that the local reactive power sources rather than a ‘global’ approach, i.e. from the generators can more effectively improve the system voltage profile. So the ATC improvement can be expected.
Bus Bus Bus Bus Bus 6 5 4 3 2 Nodal injection (Qi)
Figure 5 QLDG of reactive power from DG 0.6 0.5 0.4 0.3
5
3
1
0.2 0.1 PLDG 0 -0.1 -0.2 -0.3 -0.4 Bus 5 Bus 6
Bus 4
Bus 3
11
Bus 2
9
7
Lines
Bus 2 Bus 3 Bus 4 Bus 5 Bus 6
Nodes with DG
Figure 3 PLDG of real power from DG
Contribution Factors of Reactive Power from DG (PLDG)
Figure 6 VDG of real power from DG
0.5 0.4 0.3 0.2 0.1
Bus 2
0
Bus 3
-0.1
Bus 4 4
-0.2
Lines
Bus 6
10
Bus 6
Bus 4
Bus 5
Bus 2 Bus 3
7
-0.3
nodal injections (Qi)
Bus 5
1
PLDG
Figure 4 PLDG of reactive power from DG
Figure 7 VDG of reactive power from DG
Bus 5 Bus 6
REFERENCES:
Figure 8 The iTDA space of PLDG for the 30-bus system
Figure 9 The iTDA space of VDG for the 30-bus system
V.
CONCLUSIONS
The impact of DGs on ATC is conceptually discussed in this paper. In order to measure such an impact, a set of contribution factors, such as the PLDG, QLDG and VDG, are derived from AC power flow analysis with closed formulas. Thus, the proposed approach to measure the impact is fast and accurate. The introduced iTDA space provides a direct and straightforward technique to simplify the detailed information.
The proposed methods will be used for the DG location and operation strategy analysis in the future.
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