K. Max Zhang

2papers

2 Papers

7.1SYMay 1
The Potential Welfare Gains from Curtailment Trading Under Non-Firm Interconnection

Richard Mahuze, Charlotte Gressel, Ali Amadeh et al.

Rapid growth of large loads led by data centers is straining grid capacity. These loads increasingly accept curtailment risk through non-firm interconnection agreements to gain faster grid access, expanding the pool of consumers subject to mandatory disconnection during supply shortfalls. Yet, blunt rules assign curtailment without reference to the wide variation in the value consumers place on avoiding curtailment, often captured by the value of lost load (VOLL). This paper introduces the network-constrained Curtailment Credit Market (CCM), a mechanism in which agents submit bids that determine bilateral credit flows, subject to transmission network constraints. We prove that the bilateral credit flow representation can reach every curtailment allocation available to an omniscient central planner (feasible-set equivalence), so the bilateral flow structure introduces no loss of allocative capability. Under truthful bidding, the CCM achieves the planner's total value of served load, matching the planner's allocative benchmark when bids reflect true interruption costs. The CCM is formulated as a bilevel clearing problem that admits an exact single-level mixed-integer linear program (MILP), solved in 0.01 to 83 seconds. Numerical experiments on three test systems validate the mechanism at increasing scale and complexity: a 3-bus toy network that isolates the core trading logic, the IEEE 24-bus reliability test system as a standard benchmark, and a reduced New York (NY) grid that captures coordination across NY load zones. Our simulations show that the CCM increases the total value of served load by 1.24 to 1.83 times relative to pro-rata curtailment. On the three test systems examined here, no participant is worse off under incentive-compatible benchmark payments than under the administrative baseline.

OCApr 1, 2019
Convexity and monotonicity in nonlinear optimal control under uncertainty

Kevin J. Kircher, K. Max Zhang

We consider the problem of finite-horizon optimal control design under uncertainty for imperfectly observed discrete-time systems with convex costs and constraints. It is known that this problem can be cast as an infinite-dimensional convex program when the dynamics and measurements are linear, uncertainty is additive, and the risks associated with constraint violations and excessive costs are measured in expectation or in the worst case. In this paper, we extend this result to systems with convex or concave dynamics, nonlinear measurements, more general uncertainty structures and other coherent risk measures. In this setting, the optimal control problem can be cast as an infinite-dimensional convex program if (1) the costs, constraints and dynamics satisfy certain monotonicity properties, and (2) the measured outputs can be reversibly `purified' of the influence of the control inputs through Q- or Youla-parameterization. The practical value of this result is that the finite-dimensional subproblems arising in a variety of suboptimal control methods, notably including model predictive control and the Q-design procedure, are also convex for this class of nonlinear systems. Subproblems can therefore be solved to global optimality using convenient modeling software and efficient, reliable solvers. We illustrate these ideas in a numerical example.