Locational Allocation and Pricing of Responsive Contingency Reserves Jose Fernando Prada and Marija D. Ilić Carnegie Mellon University Department of Engineering and Public Policy Pittsburgh, PA, USA.
[email protected],
[email protected] Abstract—In this paper we propose a robust method to determine, allocate and price the contingency reserves required to fully comply with N-1 security criteria in real-time operations. Unlike the traditional fixed reserve requirement, the method identifies adequate reserves in terms of type, quantity and location, needed to respond to expected generation outages. The provision of energy and responsive reserves is co-optimized in a two-stage Security Constrained Unit Commitment / Network Constrained Economic Dispatch, and can be readily implemented within the framework of current scheduling and two-settlement processes carried out in RTO/ISO-managed markets. A numerical example is provided to illustrate the application of the method. Locational allocation and pricing of responsive reserves can improve security of system operations and achieve more efficient dispatch costs. Index Terms—Contingency reserves, locational reserves, reserves co-optimization, reserves pricing, responsive reserves.
I.
INTRODUCTION
A fundamental aspect of power systems reliability is the security of real-time operations, which commonly refers to the ability of the system to withstand sudden disturbances like the unplanned loss of a major system component, e.g. a generation unit or transmission line [1]. In general, operational security is preserved by complying with the N-1 reliability criterion, which establishes that the system should be able to stay within its operating limits after a single contingency event. A single contingency can be narrowly understood as losing one major element in the system, or broadly as a single event that may compromise several components [2], [3]. The common practice is to ensure N-1 compliance by providing spare generation capacity during real-time operation, to provide for a set of credible generation and transmission line outages. By keeping this contingency reserve, the system should have sufficient resources to keep supplying all the load after a single contingency. The current best approach to allocate and price contingency reserves in RTO/ISO-managed electricity markets is based on the co-optimization of energy and reserves during the resource scheduling process. Although
978-1-4673-8040-9/15/$31.00 ©2015 IEEE
there are important differences in the way the scheduling is carried out between these systems, accurate generalized descriptions are provided in [4], [5]. With some simplifications this process is similarly used by vertically integrated utilities. A general description of the process is the following: • Transmission network operating constraints (thermal and stability limits) are defined in advance, during the operations planning phase, based on security analyses. A fixed generation reserve requirement is also defined based on some heuristics, normally equal to the largest expected generation outage and/or a percentage of expected demand. • A Security Constrained Unit Commitment (SCUC) is performed day ahead to establish the optimal daily generation commitment and dispatch program. This program is feasible since it complies with the network and generation operational limits (normally under a DC power flow approximation). • In the SCUC, the N-1 security criterion is enforced for single line outages through additional network constraints, so the dispatch remains feasible after a single line contingency. For generation outages, N-1 security is covered by enforcing a fixed spinning reserve requirement (a percentage of the total reserve requirement, usually 50%). • The SCUC can be further adjusted for reliability reasons and daily as system conditions vary (generally with a simplified version). Finally a Security Constrained Economic Dispatch (SCED) is used for real-time operation. The SCED has a similar formulation of the SCUC with regard to N-1 security. The co-optimization in the allocation of energy and reserves within this scheduling process refers to their simultaneous determination in the solution of the commitment/dispatch optimization problem. The cooptimization takes into account the cost of providing both energy and reserves and the technical constraints resulting from imposing the security requirements on the optimization
problem [6]. Formulations of the deterministic SCUC problem can be found in [7] - [9]. II.
FIXED VS. RESPONSIVE CONTINGENCY RESERVES
A number of problems have been identified with the imposition of a fixed reserve requirement in the formulation of the day-ahead UC. A well-known criticism is that this allocation method does not guarantee N-1 security for generation outages, since transmission congestion may prevent the effective delivery of reserves after a contingency has occurred. This is the result of using a global reserve requirement that does not define appropriate locational generation reserves in the system. As a consequence, system operators need to resort to manually adjust the dispatch program off-line to comply with security criteria, a procedure that is most of the time economically inefficient. A partial fix that is frequently used is to previously define reserve zones, based on known transmission bottlenecks in the system, and use those zones in the SCUC in order to assign zonal reserves. While this solution improves the deliverability of reserves, it is still based on a fixed definition of reserve requirements, and does not guarantee N-1 compliance under all single generation outages. An additional problem with the current allocation of contingency reserves is that it does not provide an operation program to dispatch reserves. That is, what reserves to deploy when a generation outage actually occurs in the system, since there should be an optimal way to do it, both for cost and feasibility, different for each specific generation outage. Likewise, the division between spinning and non-spinning reserve is rather arbitrary and lacks technical basis. Under the described current approach, contingency reserves are priced based on the marginal cost of assigned reserves when bidding is allowed or on the shadow price of the fixed reserve constraint. The pricing of reserves through energy and reserves co-optimization is more efficient than the alternative of using sequential pricing. However, this cooptimization pricing method is not entirely economically efficient for different reasons: in first place, it is adequate to remunerate the fixed reserve requirement but not the actual generation reserves required in the system –in terms of type, quantity and location– to ensure N-1 compliance. A subtler source of inefficiency is the following: the solution of the SCUC simultaneously ensures feasibility of the dispatch program under single line contingencies and provision of reserves against generation outages. Therefore, it covers N-2 contingencies (1 line + the largest generator). As N-2 compliance is generally not required by NERC reliability standards, the outcome should be more expensive than strict compliance with N-1 security. Setting a global reserve requirement equal to the loss of the largest generating unit, to ensure system security against generation outages, would be adequate for a system without transmission congestion but it has serious shortcomings for real networks. Zonal reserve requirements improve congestion management, but the allocation is still based on adhoc definitions which are loosely related to the set of credible contingencies that need to be addressed under the N-1 criterion. A better approach would be based on a systematic
allocation of reserves that respond to the actual conditions of the system and to its potential contingencies. Following [10] we refer to this definition as responsive contingency reserves, in contrast to the traditional fixed reserve requirement. Responsive reserves are necessarily locational, to ensure deliverability under different possible contingencies. Previous works have focused on improving zonal reserve requirements [11], or stochastic solutions of the problem, using an expected or scenario weighted co-optimization of energy and reserves [7], [10], [12]. A SCUC is used in [15] without fixed reserve requirement to test security of transmission switching solutions. A robust approach to solve the SCUC problem is proposed in [8] considering uncertainty in net nodal injections. In this paper we propose a robust method to determine the contingency reserves –in type, location and quantity– required to fully comply with the N-1 criterion. This method can be readily implemented within the framework of the current scheduling process described in the previous section. III.
LOCATIONAL ALLOCATION OF RESERVES
There is a fundamental difference in the way line outages and generation outages are treated in the SCUC/SCED formulation. Transmission line outages are subject to preventive control, since the feasibility of the solution under different contingency cases ensures that the system will remain within its operational limits after the failure of a single transmission line, without any (immediate) operator intervention. There is no explicit allocation of reserves, but they are implicit in the “security constrained” dispatch of generation. Preventive control is effective to handle line outages but inherently introduces additional constraints and increases dispatch costs. On the other hand, contingency reserves are kept as a preventive control against generation outages, but a corrective or “emergency” control will always be required to restore the power unbalance created by an outage [13]. The control action will require ramping up generators providing the reserve to rebalance the system until a new secure economic dispatch is found. Accordingly, contingency reserves should be allocated to provide for all credible generation outages, in such a way that the spare generation can be employed to balance energy supply and demand after a generator is lost, in compliance with the N-1 criterion. Based on this approach, we propose an efficient allocation of reserves to minimize the cost of supplying energy and reserves in the system, which is robust against the occurrence of any single generation outage. The steps of the proposed allocation method are outlined below and the mathematical formulation is presented next. A. Co-optimized Scheduling of Energy and Reserves We assume a competitive market for reserves exists, so generators can send offers to provide reserves into this market. Notwithstanding, the reserve allocation mechanism described below can accommodate other market arrangements. • In first place, a day-ahead SCUC determines a secure energy commitment and dispatch, without fixed reserve requirements, for the 24 hours of the next operation day. This dispatch is N-1 secure against line contingencies. • In a second stage, for any of the k credible single generation contingencies, a network constrained economic
dispatch (NCED) is carried out for each dispatch hour. The NCED considers the transmission network constraints of the base scenario, without any line outages. • The only generation dispatchable in the NCED is fast response generation that can ramp up in less than a prespecified time (normally 10 to 15 minutes), and therefore qualified to provide reserves. The dispatch of the fastresponse generation is constrained by their ramping limits, which couples the SCUC results with the SCED. Fastresponse generators may opt-out of the reserve allocation mechanism (e.g. by not submitting offers) or limit the quantity of their reserve offers. • The NCED finds a dispatch that minimizes the cost of keeping a pre-contingency reserve and the cost of using it under the k-th contingency. The reserve to be provided by a specific generator against the k–th contingency is equal to the positive difference between its dispatch level under the k-th NCED and the original dispatch under the SCUC. This is reflective of the reserve ramping up generation to respond to the contingency. The total reserve required in the system to respond against the k-th contingency is the sum of the reserves provided by each generator under that scenario, and it is by calculation locationally distributed throughout the network to ensure deliverability. • Finally, we could identify the “worst” contingency as the one requiring the higher required reserve, in a manner somehow analog to the traditional determination of the fixed reserve requirement. However, in order to fully comply with the N-1 criterion, and have reserves adequate to cover any contingency, we determine the reserve required from a generator as the maximum across the reserves computed for each contingency. Consequently, the sum of those individual reserves represents the total locationally allocated (responsive) reserve of the system. This locational reserve allocation mechanism naturally distributes the required responsive reserve into spinning and non-spinning reserve. Generation units not dispatched in the SCUC but dispatched in any NCED will be providing nonspinning reserve. Another benefit of this mechanism is that it gives to system operators a feasible plan of how to respond in an efficient way in front of a specific generation contingency. The locational pricing of contingency reserves is a consequence of its allocation. Reserves are paid the marginal bid in each specific location, that is, the highest offer accepted in each generation node. These nodal prices signal the value or reserves in the system at each specific generation location. Otherwise, if administrative costs are used to pay for different types of reserves, they can be used in a similar manner to determine the remuneration of the reserves required in different locations of the system. B. Problem Formulation 1) Security Constrained Unit Commitment (SCUC) The deterministic SCUC without reserve requirements is appropriate for the purposes of locational reserve allocation. The compact DC formulation shown below follows [14]: Nomenclature: t : index of time periods
i : index of generating units n : index of electrical nodes p : index of nodes connected to node n l : index of line contingencies, G : set of generation units T : set of time periods N: set of electrical nodes Nn : set of generating units connected to node n Pn : set of nodes directly connected to node n xit : binary variable {0,1}, equal to 1 when unit i is started up in period t uit : binary variable {0,1}, equal to 1 when unit i is committed in period t git : power output of unit i in period t Si : startup cost of unit i Ci : operating cost of unit i Dnt : power demand at node n in period t Bnp : electrical susceptance of line between nodes n and p θnp : electrical phase angle between nodes n and p Tnp : maximum power flow between nodes n and p RDi : ramp down limit of unit i RUi : ramp up limit of unit i Minimize unit startup and operating costs: ,
,
[
(
+
,
,
) ] (1)
∈
∈
Subject to: ()
+
,
()
=
; ∀ , ∀ , ∀ (2)
∈
∈
≤ ≤ −
,
≤
,
≤ −
≤
,
()
+
; ∀ , ∀ (3)
, ,
()
; ∀ , ∀ (4)
≤
≥
, ,
; ∀ , ∀ , ∀ (5)
(6)
Where the above constraints correspond to the nodal power balance, unit generation limits, unit ramping limits, line flow limits and start up sequence. For conciseness, shutdown costs and minimum up and down times are not shown. 2) Network Constrained Economic Dispatch Nomenclature: s : index of fast-response generating units k:
index of generation contingencies,
git(0)
: power output of unit i in period t from the SCUC
git(k)
: power output of unit i in period t for contingency k
rit(k)
: reserve of unit i in period t for contingency k
Oi : cost of reserves provided by unit i For each generation contingency k and period t, minimize energy and reserve costs: ( )
( )
,
( )
[
+
( )
] ; (7)
Subject to: ( )
+
∈
≤
−
=
; ∀ , ∀ , ∀ (8)
∈
≤
( )
( ) ,
.
= ,
( )
( )
=
( )
≤
( )
−
( )
− , 0 ,
≤
.
( ) ,
( )
; ∀
(9)
; ∀ , ∀ , ∀ (10) ( )
≤
( )
≤
,
; ∀ , ∀ (11) ≥
( )
∀ (12)
; ∀ , ∀ , ∀ , ∀ (13)
Where the above constraints correspond to the nodal power balance, unit generation and ramping limits, reserve definition, and line flow limits. 3) Contingency Reserve Allocation Nomenclature: rit : reserve to be provided by unit i in period t rnt : reserve at node n in period t Rt : system reserve in period t ρnt : locational price of reserves at node n in period t =
( )
Figure 1. Eight-bus 230 kV test system for reserves allocation
; ∀ (14)
TABLE I.
GENERATION AND LOAD OF TEST SYSTEM (MW)
Node
1
2
3
4
5
Gmin
2x100
70
Gmax
2x300
250
Dmax
-
300
200
6
7
-
0
-
50 150
300
8
-
20
-
2x75
-
150
-
2x200
200
-
The system capacity margin is 300 MW, equal to the size to the largest generating unit. Apparently the system is N-1 compliant since it has enough spare capacity to cover the expected worst generation contingency. The minimum cost economic dispatch for the base case without contingencies (“all in”) is shown in Table II, resulting from lines 14 and 78 being congested. Table II also shows the network constrained economic dispatch for all different single generation outages. TABLE II. N-1 case
PRE AND POST-CONTINGENCY ECONOMIC DISPATCH Network Constrained Economic Dispatch (MW)
G1
G2
G3
G4
283.5
283.5
179.6
179.6
23.1
189.6
11.1
G1 out
0.0
300.0
200.0
200.0
150.0
250.0
50.0
G2 out
300.0
0.0
200.0
200.0
150.0
250.0
50.0
G3 out
283.2
283.2
0.0
200.0
95.3
250.0
38.3
, ∀ , ∀ (17)
G4 out
283.2
283.2
200
0.0
95.3
250.0
38.3
G5 out
281.8
281.8
177.2
177.2
0.0
218.8
13.2
In (12) and (14) rit is spinning reserve when git(0) is positive and non-spinning reserve otherwise.
G6 out
278.2
278.2
179.9
179.9
27.5
0.0
6.3
G7 out
277.0
277.0
184.1
184.1
25.0
202.8
0.0
=
; ∀ (15) ∈
=
= ∈
= max
IV.
; ∀ (16) ∈
( ) ;
NUMERICAL ILLUSTRATION
In order to illustrate the use of the proposed method we applied it to an 8-bus 230 kV test system with 7 generators and 5 loads. The system is shown in Fig.1, generation and load date are shown in Table I and additional technical data can be found in the appendix. Total installed capacity is 1450 MW and peak load is 1150 MW. To show the locational distribution of reserves resulting from network constraints rather than from differential price offers, we assumed that all available reserve is offered at the same price.
All in
G5
G6
G7
When unit G6 is out, total generation is lower than demand by 200 MW, requiring load shed. Therefore the system is not completely N-1 and more reserves would be required for full compliance. The allocation of contingency reserves by unit is shown in Table III. This numerical application makes the point that a fixed reserve requirement does not ensure N-1 compliance and shows how to allocate reserves to the units that can ramp up after a generation outage to rebalance the system at minimum cost.
TABLE III. N-1 case
G3/G4
G3
G4
G5
G6
G7
G5
500 + 2.0 P + 1.00 P2
16.5
20.4
20.4
126.9
60.4
38.9
G6
1000 + 2.0 P + 0.10 P2
20.4
20.4
126.9
60.4
38.9
G7
500 + 4.0 P + 2.0 P2
16.5
20.4 20.4
G4 out
72.2
60.4
27.2
72.2
60.4
27.2
29.2
2.1
G5 out G6 out
0.3
0.3
4.4
G7 out
4.5
4.5
1.9
13.2
20.4
20.4
126.9
60.4
16.5
16.5
V.
Network Data
38.9
Line
L12
L14
L15
L23
L26
L34
Reactance (p.u.)
0.16
0.08
0.12
0.17
0.09
0.10 300
Capacity (MW)
150
200
200
150
300
Line
L36
L45
L58
L67
L78
Reactance (p.u.)
0.09
0.16
0.05
0.13
0.09
Capacity (MW)
300
150
400
250
200
CONCLUSIONS
Better allocation of contingency reserves in power systems would bring benefits in terms of the security and efficiency of operations. In particular, the allocation of locational reserves responsive to system conditions, instead of the traditional fixed requirement, can ensure N-1 compliance and more efficient pricing and remuneration. We have presented a method to allocate and price locational reserves, which is directly related to the service provided by reserves and that is readily implementable within the current scheduling process in electricity markets. The method is robust since it considers all credible single generation outages. Additional work is required to investigate the full security and economic impacts of using responsive reserves with locational pricing. Efficiency gains are expected by lowering dispatch costs resulting from the SCUC and by the definition of reserve requirements more adjusted to the actual conditions and limitations of the system. This approach could be also extended to cover line outages within a full “corrective control” scheme with additional economic benefits, or to consider other sources of uncertainty like increased used of intermittent generation. In such case, reserves to ramp down generation can be equally valuable and integrated within the proposed scheme. In future work we will look into integrated approaches to simplify the process of allocating and clearing reserves in electricity markets, including the use of offers that internalize some of the generating unit constraints. Likewise, we will investigate the impact and benefits of adding voltage optimization in the definition and provision of operating reserves through full AC network modeling. ACKNOWLEDGMENT This work has been supported by the Power Systems Engineering Research Center (PSERC), as part of the research project M-31 “Markets for Ancillary Services in the presence of Stochastic Resources”. APPENDIX Generation Cost Data Unit
2000 + 2.0 P + 0.03 P2 2000 + 0.5 P + 0.05 P2
G2
G3 out
All
G1/G2
Reserves (MW) G1
G1 out G2 out
ALLOCATION OF PRE-CONTINGENCY RESERVES
Operating Cost ($/hr)
REFERENCES [1] [2] [3] [4]
[5] [6] [7]
[8]
[9]
[10]
[11] [12] [13] [14] [15]
NERC Reliability Concepts in Bulk Power Systems, NERC Reliabilty Criteria Subcommittee, Feb. 1985. NERC Reliability Assessment Guidebook, v.3.1. NERC Planning Committee, Aug. 2012. NERC Standard TPL-001-0, “System Performance under Normal Conditions”, Apr. 2005. U. Helman, B. F. Hobbs an R. P. O’Neill, “The Design of US Wholesale Energy and Ancillary Service Auction Markets”, in Competitive Electricity Markets: Design, Implementation, Performance, F. P. Sioshansi, Ed. Oxford: Elsevier, 2008, pp. 179-243. FERC “Security Constrained Economic Dispatch – Definitions, Practices, Issues and Recommendations”. Report to Congress, Jul. 2006. Sandia National Laboratories, “A Survey of Operating Reserve Markets in US ISO/RTO-managed Electric Energy Regions”, Project Report SAND2012-100, Sept. 2012 A. Papavasiliou and S. S. Oren, “A Comparative Study of Stochastic Unit Commitment and Security-Constrained Unit Commitment Using High Performance Computing”, in ECC European Control Conference 2013, Zurich, Jul. 2013, pp. 2507-2512. D. Bertsimas, E. Litvinov, X. A. Sun, J. Zhao, and T. Zheng, “Adaptive Robust Optimization for the Security Constrained Unit Commitment Problem,” IEEE Transactions on Power Systems, vol. 28, pp. 52-63, Feb. 2013. X. Ma, H. Song, M. Hong, J. Wan, Y. Chen and E. Zak, “The SecurityConstrained Commitment and Dispatch for Midwest ISO Day-Ahead Co-Optimized Energy and Ancillary Service Market”, in IEEE 2009 PES General Meeting, Calgary, Jul. 2009, pp 1-8. J. Chen, J. S. Thorp, R. J Thomas, T. D. Mount, “Locational Pricing and Scheduling for an Integrated Energy-Reserve Market”, in Proc. of the 36th Annual Hawaii International Conference on System Sciences, Jan. 2003. J. D. Lyon, K. W. Hedman, and M. Zhang, “Reserve Requirements to Efficiently Manage Intra-zonal Congestion,” IEEE Transactions on Power Systems, vol. 29, pp. 251-258, Jan. 2014. L. Wu, M. Shahidehpour and T. Li, “Stochastic Security-Constrained Unit Commitment”, IEEE Transactions on Power Systems, vol. 22, pp. 800-811, May 2007. L. Wehenkel, “Emergency Control and its Strategies”, in Proc. of 13th Power Systems Computation Conference, Trondheim (Norway), 1999. A. J. Conejo, E. Castillo, R. Minguez and R. Garcia-Bertrand, Decomposition Techniques in Mathematical Programming, Netherlands: Springer, 2006, p.541. K. W. Hedman, M. C. Ferris, R. P. O’Neill, E.B. Fisher and S.S. Oren, “Co-Optimization of Generation Unit Commitment and Transmission Switching with N-1 Reliability”, IEEE Transactions on Power Systems, vol. 25, pp. 1052-1063, May 2010.
